kindergarten grade level overview - georgia standards · georgia department of education richard...

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Georgia Standards of Excellence

Grade Level

Curriculum Overview

GSE Kindergarten

Mathematics

Georgia Department of Education


July 2018 Page 2 of 47

All Rights Reserved

Grade Level Overview

TABLE OF CONTENTS

Curriculum Maphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip4

Unpacking the Standards

bull Standards for Mathematical Practicehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip5

bull Content Standardshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip8

Mindset and Mathematics helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip18

Vertical Understanding of the Mathematic Learning Trajectory helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip19

Research of Interest to Teachers helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip20

GloSS and IKAN helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip20

Fluencyhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip21

Arc of LessonMath Instructional Frameworkhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip22

Unpacking a Taskhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip23

Routines and Rituals

bull Teaching Math in Context and Through Problemshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip24

bull Use of Manipulativeshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip24

bull Use of Strategies and Effective Questioninghelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip25

bull 0-99 or 1-100 Charthelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip26

bull Number Lines helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip28

bull Math Maintenance Activities helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip29

o Number CornerCalendar Time helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip30

o Number Talks helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip32

o EstimationEstimation 180 helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip34




All Rights Reserved

bull Mathematize the World through Daily Routineshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip37

bull Workstations and Learning Centershelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip38

bull Gameshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip38

bull Journalinghelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip39

General Questions for Teacher Usehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip40

Questions for Teacher Reflectionhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip41

Depth of Knowledgehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip42

Depth and Rigor Statementhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip44

Additional Resources Available

bull K-2 Problem Solving Rubric (creation of Richmond County Schools)helliphelliphelliphelliphelliphellip45

bull Literature Resourceshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip46

bull Technology Linkshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip46

Resources Consulted helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip47




All Rights Reserved


Elementary School Mathematics

Kindergarten

NEW Click on the link in the table to view a video that shows instructional strategies for teaching the specified standard

NOTE Mathematical standards are interwoven and should be addressed throughout the year in as many different units and tasks as possible in order to stress the natural connections that exist among

mathematical topics

Grades K-2 Key CC = Counting and Cardinality G= Geometry MD=Measurement and Data NBT= Number and Operations in Base Ten OA = Operations and Algebraic Thinking

GSE Kindergarten Curriculum Map

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7

Comparing

Numbers

Counting With

Friends

Sophisticated

Shapes

Measuring and

Analyzing Data

Investigating

Addition and

Subtraction

Further

Investigation of

Addition and

Subtraction

Show What We

Know

MGSEKCC1

MGSEKCC2

MGSEKCC3

MGSEKCC4

MGSEKMD3

MGSEKNBT1

MGSEKCC3

MGSEKCC4a

MGSEKCC5

MGSEKCC6

MGSEKCC7

MGSEKMD3

MGSEKG1

MGSEKG2

MGSEKG3

MGSEKG4

MGSEKG5

MGSEKG6

MGSEKMD3

MGSEKMD1

MGSEKMD2

MGSEKMD3

MGSEKOA1

MGSEKOA2

MGSEKOA3

MGSEKOA4

MGSEKOA5

MGSEKOA1

MGSEKOA2

MGSEKOA3

MGSEKOA4

MGSEKOA5

ALL

These units were written to build upon concepts from prior units so later units contain tasks that depend upon the concepts and standards addressed in earlier units

All units include the Mathematical Practices and indicate skills to maintain




All Rights Reserved

STANDARDS FOR MATHEMATICAL PRACTICE

The Standards for Mathematical Practice describe the varieties of expertise that mathematics

educators at all levels should seek to develop in their students These practices rest on important

ldquoprocesses and proficienciesrdquo with longstanding importance in mathematics education

The first of these are the NCTM process standards of problem solving reasoning and proof

communication representation and connections

The second are the strands of mathematical proficiency specified in the National Research

Councilrsquos report Adding It Up adaptive reasoning strategic competence conceptual

understanding (comprehension of mathematical concepts operations and relations) procedural

fluency (skill in carrying out procedures flexibly accurately efficiently and appropriately) and

productive disposition (habitual inclination to see mathematics as sensible useful and

worthwhile coupled with a belief in diligence and onersquos own efficacy)

Students are expected to

1 Make sense of problems and persevere in solving them

Mathematically proficient students in Kindergarten begin to develop effective dispositions

toward problem solving In rich settings in which informal and formal possibilities for solving

problems are numerous young children develop the ability to focus attention test hypotheses

take reasonable risks remain flexible try alternatives exhibit self-regulation and persevere

(Copley 2010) Using both verbal and nonverbal means kindergarten students begin to explain

to themselves and others the meaning of a problem look for ways to solve it and determine if

their thinking makes sense or if another strategy is needed As the teacher uses thoughtful

questioning and provides opportunities for students to share thinking kindergarten students begin

to reason as they become more conscious of what they know and how they solve problems

2 Reason abstractly and quantitatively

Mathematically proficient students in Kindergarten begin to use numerals to represent a specific

amount (quantity) For example a student may write the numeral ldquo11rdquo to represent an amount of

objects counted select the correct number card ldquo17rdquo to follow ldquo16rdquo on the calendar or build a

pile of counters depending on the number drawn In addition kindergarten students begin to

draw pictures manipulate objects use diagrams or charts etc to express quantitative ideas such

as a joining situation (Mary has 3 bears Juanita gave her 1 more bear How many bears does

Mary have altogether) or a separating situation (Mary had 5 bears She gave some to Juanita

Now she has 3 bears How many bears did Mary give Juanita) Using the language developed

through numerous joining and separating scenarios kindergarten students begin to understand

how symbols (+ - =) are used to represent quantitative ideas in a written format

3 Construct viable arguments and critique the reasoning of others

In Kindergarten mathematically proficient students begin to clearly express explain organize

and consolidate their math thinking using both verbal and written representations Through

opportunities that encourage exploration discovery and discussion kindergarten students begin

to learn how to express opinions become skillful at listening to others describe their reasoning

and respond to othersrsquo thinking and reasoning They begin to develop the ability to reason and




All Rights Reserved

analyze situations as they consider questions such as ldquoAre you surehelliprdquo ldquoDo you think that

would happen all the timehelliprdquo and ldquoI wonder whyhelliprdquo

4 Model with mathematics

Mathematically proficient students in Kindergarten begin to experiment with representing real-

life problem situations in multiple ways such as with numbers words (mathematical language)

drawings objects acting out charts lists and number sentences For example when making

toothpick designs to represent the various combinations of the number ldquo5rdquo the student writes the

numerals for the various parts (such as ldquo4rdquo and ldquo1rdquo) or selects a number sentence that represents

that particular situation (such as 5 = 4 + 1)

Kindergarten students should see addition and subtraction equations and student writing of

equations in kindergarten is encouraged but it is not required However please note that it is

not until First Grade when ldquoUnderstand the meaning of the equal signrdquo is an expectation

(1OA7)

5 Use appropriate tools strategically

In Kindergarten mathematically proficient students begin to explore various tools and use them

to investigate mathematical concepts Through multiple opportunities to examine materials they

experiment and use both concrete materials (eg 3- dimensional solids connecting cubes ten

frames number balances) and technological materials (eg virtual manipulatives calculators

interactive websites) to explore mathematical concepts Based on these experiences they

become able to decide which tools may be helpful to use depending on the problem or task For

example when solving the problem ldquoThere are 4 dogs in the park 3 more dogs show up in the

park How many dogs are in the parkrdquo students may decide to act it out using counters and a

story mat draw a picture or use a handful of cubes

6 Attend to precision

Mathematically proficient students in Kindergarten begin to express their ideas and reasoning

using words As their mathematical vocabulary increases due to exposure modeling and

practice kindergarteners become more precise in their communication calculations and

measurements In all types of mathematical tasks students begin to describe their actions and

strategies more clearly understand and use grade-level appropriate vocabulary accurately and

begin to give precise explanations and reasoning regarding their process of finding solutions For

example a student may use color words (such as blue green light blue) and descriptive words

(such as small big rough smooth) to accurately describe how a collection of buttons is sorted

7 Look for and make use of structure

Mathematically proficient students in Kindergarten begin to look for patterns and structures in the

number system and other areas of mathematics For example when searching for triangles

around the room kindergarteners begin to notice that some triangles are larger than others or

come in different colors- yet they are all triangles While exploring the part-whole relationships

of a number using a number balance students begin to realize that 5 can be broken down into

sub-parts such as 4 and 1 or 3 and 2 and still remain a total of 5




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8 Look for and express regularity in repeated reasoning

In Kindergarten mathematically proficient students begin to notice repetitive actions in

geometry counting comparing etc For example a kindergartener may notice that as the number

of sides increase on a shape a new shape is created (triangle has 3 sides a rectangle has 4 sides a

pentagon has 5 sides a hexagon has 6 sides) When counting out loud to 100 kindergartners may

recognize the pattern 1-9 being repeated for each decade (eg Seventy-ONE Seventy-TWO

Seventy- THREEhellip Eighty-ONE Eighty-TWO Eighty-THREEhellip) When joining one more

cube to a pile the child may realize that the new amount is the next number in the count

sequence

Mathematical Practices 1 and 6 should be evident in EVERY lesson




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CONTENT STANDARDS

COUNTING AND CARDINALITY (CC)

CLUSTER 1 KNOW NUMBER NAMES AND THE COUNT SEQUENCE

MGSEKCC1 Count to 100 by ones and by tens

This standard calls for students to rote count by starting at one and count to 100 When

students count by tens they are only expected to master counting on the decade (0 10 20

30 40 hellip) This objective does not require recognition of numerals It is focused on the

rote number sequence

MGSEKCC2 Count forward beginning from a given number within the known sequence

(instead of having to begin at 1)

This standard includes numbers 0 to 100 This asks for students to begin a rote forward

counting sequence from a number other than 1 Thus given the number 4 the student

would count ldquo4 5 6 helliprdquo This objective does not require recognition of numerals It is

focused on the rote number sequence

MGSEKCC3 Write numbers from 0 to 20 Represent a number of objects with a written

numeral 0-20 (with 0 representing a count of no objects)

This standard addresses the writing of numbers and using the written numerals (0-20) to

describe the amount of a set of objects Due to varied development of fine motor and

visual development a reversal of numerals is anticipated for a majority of the students

While reversals should be pointed out to students the emphasis is on the use of numerals

to represent quantities rather than the correct handwriting formation of the actual numeral

itself

In addition the standard asks for students to represent a set of objects with a written

numeral The number of objects being recorded should not be greater than 20 Students

can record the quantity of a set by selecting a number card or tile (numeral recognition)

or writing the numeral Students can also create a set of objects based on the numeral

presented

CLUSTER 2 COUNT TO TELL THE NUMBER OF OBJECTS

Students use numbers including written numerals to represent quantities and to solve

quantitative problems such as counting objects in a set counting out a given number of objects

and comparing sets or numerals

MGSEKCC4 Understand the relationship between numbers and quantities connect

counting to cardinality

This standard asks students to count a set of objects and see sets and numerals in

relationship to one another rather than as isolated numbers or sets These connections

are higher-level skills that require students to analyze to reason about and to explain

relationships between numbers and sets of objects This standard should first be

addressed using numbers 1-5 with teachers building to the numbers 1-10 later in the year




All Rights Reserved

The expectation is that students are comfortable with these skills with the numbers 1-10

by the end of Kindergarten

a When counting objects say the number names in the standard order pairing

each object with one and only one number name and each number name with one

and only one object (one-to-one correspondence)

This standard reflects the ideas that students implement correct counting procedures by

pointing to one object at a time (one-to-one correspondence) using one counting word for

every object (one-to-one taggingsynchrony) while keeping track of objects that have and

have not been counted This is the foundation of counting

b Understand that the last number name said tells the number of objects counted

The number of objects is the same regardless of their arrangement or the order in

which they were counted (cardinality)

This standard calls for students to answer the question ldquoHow many are thererdquo by

counting objects in a set and understanding that the last number stated when counting a

set (hellip8 9 10) represents the total amount of objects ldquoThere are 10 bears in this pilerdquo

(cardinality) It also requires students to understand that the same set counted three

different times will end up being the same amount each time Thus a purpose of keeping

track of objects is developed Therefore a student who moves each object as it is

counted recognizes that there is a need to keep track in order to figure out the amount of

objects present While it appears that this standard calls for students to have conservation

of number (regardless of the arrangement of objects the quantity remains the same)

conservation of number is a developmental milestone of which some Kindergarten

children will not have mastered The goal of this objective is for students to be able to

count a set of objects regardless of the formation those objects are placed

c Understand that each successive number name refers to a quantity that is one

larger

This standard represents the concept of ldquoone morerdquo while counting a set of objects

Students are to make the connection that if a set of objects was increased by one more

object then the number name for that set is to be increased by one as well Students are

asked to understand this concept with and without objects For example after counting a

set of 8 objects students should be able to answer the question ldquoHow many would there

be if we added one more objectrdquo and answer a similar question when not using objects

by asking hypothetically ldquoWhat if we have 5 cubes and added one more How many

cubes would there be thenrdquo This concept should be first taught with numbers 1-5 before

building to numbers 1-10 Students are expected to be comfortable with this skill with

numbers to 10 by the end of Kindergarten

MGSEKCC5 Count to answer lsquohow manyrdquo questions

a Count to answer ldquohow manyrdquo questions about as many as 20 things arranged in

a variety of ways (a line a rectangular array or a circle) or as many as 10 things in

a scattered configuration



July 2018 0 of 47

All Rights Reserved

b Given a number from 1-20 count out that many objects

c Identify and be able to count pennies within 20 (Use pennies as manipulatives in

multiple mathematical contexts)

This standard addresses various counting strategies Based on early childhood

mathematics experts such as Kathy Richardson students go through a progression of

four general ways to count These counting strategies progress from least difficult to

most difficult First students move objects and count them as they move them The

second strategy is that students line up the objects and count them Third students have a

scattered arrangement and they touch each object as they count Lastly students have a

scattered arrangement and count them by visually scanning without touching them Since

the scattered arrangements are the most challenging for students MGSEKCC5 calls for

students to only count 10 objects in a scattered arrangement and count up to 20 objects in

a line rectangular array or circle Out of these 3 representations a line is the easiest type

of arrangement to count

MGSEKCC6 Identify whether the number of objects in one group is greater than less

than or equal to the number of objects in another group eg by using matching and

counting strategies

This standard expects mastery of up to ten objects Students can use matching strategies

(Student 1) counting strategies or equal shares (Student 3) to determine whether one

group is greater than less than or equal to the number of objects in another group

(Student 2)

Student 1

I lined up one square and one

triangle Since there is one

extra triangle there are more

triangles than squares

Student 2

I counted the squares and I got

8 Then I counted the

triangles and got 9 Since 9 is

bigger than 8 there are more


Student 3

I put them in a pile I then

took away objects Every time

I took a square I also took a

triangle When I had taken

almost all of the shapes away

there was still a triangle left

That means there are more


MGSEKCC7 Compare two numbers between 1 and 10 presented as written numerals

This standard calls for students to apply their understanding of numerals 1-10 to compare

one from another Thus looking at the numerals 8 and 10 a student must be able to

recognize that the numeral 10 represents a larger amount than the numeral 8 Students

should begin this standard by having ample experiences with sets of objects

(MGSEKKCC3 and MGSEKKCC6) before completing this standard with just

numerals Based on early childhood research students should not be expected to be

comfortable with this skill until the end of kindergarten




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OPERATIONS AND ALGEBRAIC THINKING (OA)

CLUSTER 1 UNDERSTAND ADDITION AS PUTTING TOGETHER AND ADDING

TO AND UNDERSTAND SUBTRACTION AS TAKING APART AND TAKING FROM

All standards in this cluster should only include numbers through 10 Students will model simple

joining and separating situations with sets of objects or eventually with equations such as 5 + 2

= 7 and 7 ndash 2 = 5 (Kindergarten students should see addition and subtraction equations and

student writing of equations in kindergarten is encouraged but it is not required) Students

choose combine and apply effective strategies for answering quantitative questions including

quickly recognizing the cardinalities of small sets of objects counting and producing sets of

given sizes counting the number of objects in combined sets or counting the number of objects

that remain in a set after some are taken away

MGSEKOA1 Represent addition and subtraction with objects fingers mental images

drawings sounds (eg claps) acting out situations verbal explanations expressions or

equations

This standard asks students to demonstrate the understanding of how objects can be

joined (addition) and separated (subtraction) by representing addition and subtraction

situations in various ways This objective is primarily focused on understanding the

concept of addition and subtraction rather than merely reading and solving addition and

subtraction number sentences (equations)

MGSEKOA2 Solve addition and subtraction word problems and add and subtract

within 10 eg by using objects or drawings to represent the problem

This standard asks students to solve problems presented in a story format (context) with a

specific emphasis on using objects or drawings to determine the solution This objective

builds upon their understanding of addition and subtraction from KOA1 to solve

problems Once again numbers should not exceed 10

Teachers should be cognizant of the three types of problems There are three types of

addition and subtraction problems Result Unknown Change Unknown and Start

Unknown These types of problems become increasingly difficult for students Research

has found that Result Unknown problems are easier than Change and Start Unknown

problems Kindergarten students should have experiences with all three types of

problems The level of difficulty can be decreased by using smaller numbers (up to 5) or

increased by using larger numbers (up to 10) Please see Appendix Table 1 for

additional examples

MGSEKOA3 Decompose numbers less than or equal to 10 into pairs in more than one

way eg by using objects or drawings and record each decomposition by a drawing or

equation (drawings need not include an equation)

This standard asks students to understand that a set of (5) objects can be broken into two

sets (3 and 2) and still be the same total amount (5) In addition this objective asks

students to realize that a set of objects (5) can be broken in multiple ways (3 and 2 4 and

1) Thus when breaking apart a set (decomposing) students develop the understanding

that a smaller set of objects exists within that larger set (inclusion) This should be




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developed in context before moving into how to represent decomposition with symbols

(+ - =)

Example

ldquoBobby Bear is missing 5 buttons on his jacket How many ways can you use blue and

red buttons to finish his jacket Draw a picture of all your ideas Students could draw

pictures of

bull4 blue and 1 red button bull3 blue and 2 red buttons

bull2 blue and 3 red buttons bull1 blue and 4 red buttons

After the students have had numerous experiences with decomposing sets of objects and

recording with pictures and numbers the teacher eventually makes connections between

the drawings and symbols 5=4+1 5=3+2 5=2+3 and 5=1+4

The number sentence only comes after pictures or work with manipulatives and students

should never give the number sentence without a mathematical representation

MGSEKOA4 For any number from 1 to 9 find the number that makes 10 when added to

the given number eg by using objects or drawings and record the answer with a drawing

or equation

This standard builds upon the understanding that a number can be decomposed into parts

(KOA3) Once students have had experiences breaking apart ten into various

combinations this asks students to find a missing part of 10

Example

ldquoA full case of juice boxes has 10 boxes There are only 6 boxes in this case How many

juice boxes are missing

Student 1

Using a Ten-Frame

I used 6 counters for the 6 boxes

of juice still in the case There

are 4 blank spaces so 4 boxes

have been removed This makes

sense since 6 and 4 more equals

10

Student 2

Think Addition

I counted out 10 cubes because I

knew there needed to be ten I

pushed these 6 over here because

there were in the container

These are left over So therersquos 4

missing

Student 3

Basic Fact

I know that itrsquos 4 because 6 and 4

is the same amount as 10




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MGSEKOA5 Fluently add and subtract within 5

Students are fluent when they display accuracy (correct answer) efficiency (a reasonable

amount of steps without resorting to counting) and flexibility (using strategies such as

the distributive property) Students develop fluency by understanding and internalizing

the relationships that exist between and among numbers Oftentimes when children think

of each ldquofactrdquo as an individual item that does not relate to any other ldquofactrdquo they are

attempting to memorize separate bits of information that can be easily forgotten Instead

in order to fluently add and subtract children must first be able to see sub-parts within a

number (inclusion KCC4c) Once they have reached this milestone children need

repeated experiences with many different types of concrete materials (such as cubes

chips and buttons) over an extended amount of time in order to recognize that there are

only particular sub-parts for each number Therefore children will realize that if 3 and 2

is a combination of 5 then 3 and 2 cannot be a combination of 6 For example after

making various arrangements with toothpicks students learn that only a certain number

of sub-parts exist within the number 4

Then after numerous opportunities to explore represent and discuss ldquo4rdquo a student

becomes able to fluently answer problems such as ldquoOne bird was on the tree Three more

birds came How many are on the tree nowrdquo and ldquoThere was one bird on the tree Some

more came There are now 4 birds on the tree How many birds camerdquo Traditional flash

cards or timed tests have not been proven as effective instructional strategies for

developing fluency Rather numerous experiences with breaking apart actual sets of

objects help children internalize parts of number

NUMBERS AND OPERATIONS IN BASE TEN (NBT)

CLUSTER 1 WORK WITH NUMBERS 11ndash19 TO GAIN FOUNDATIONS FOR

PLACE VALUE

MGSEKNBT1 Compose and decompose numbers from 11 to 19 into ten ones and some

further ones to understand that these numbers are composed of ten ones and one two

three four five six seven eight or nine ones eg by using objects or drawings and

record each composition or decomposition by a drawing or equation (eg 18 = 10 + 8)

This standard is the first time that students move beyond the number 10 with

representations such as objects (manipulatives) or drawings The spirit of this standard

is that students separate out a set of 11-19 objects into a group of ten objects with

leftovers This ability is a pre-cursor to later grades when they need to understand the

complex concept that a group of 10 objects is also one ten (unitizing) Ample

experiences with ten frames will help solidify this concept Research states that students




All Rights Reserved

are not ready to unitize until the end of first grade Therefore this work in Kindergarten

lays the foundation of composing tens and recognizing leftovers

MEASUREMENT AND DATA (MD)

CLUSTER 1 DESCRIBE AND COMPARE MEASURABLE ATTRIBUTES

MGSEKMD1 Describe several measurable attributes of an object such as length or

weight For example a student may describe a shoe as ldquoThis shoe is heavy It is also really

longrdquo

This standard calls for students to describe measurable attributes of objects such as

length weight and size For example a student may describe a shoe as ldquoThis shoe is

heavy Itrsquos also really longrdquo This standard focuses on using descriptive words and does

not mean that students should sort objects based on attributes Sorting appears later in the

Kindergarten standards

MGSEKMD2 Directly compare two objects with a measurable attribute in common to

see which object has ldquomore ofrdquo or ldquoless ofrdquo the attribute and describe the difference For

example directly compare the heights of two children and describe one child as

tallershorter

This standard asks for direct comparisons of objects Direct comparisons are made when

objects are put next to each other such as two children two books two pencils For

example a student may line up two blocks and say ldquoThis block is a lot longer than this

onerdquo Students are not comparing objects that cannot be moved and lined up next to each

other

Through ample experiences with comparing different objects children should recognize

that objects should be matched up at the end of objects to get accurate measurements

Since this understanding requires conservation of length a developmental milestone for

young children children need multiple experiences to move beyond the idea that hellip

ldquoSometimes this block is longer than this one and sometimes itrsquos shorter (depending on

how I lay them side by side) and thatrsquos okayrdquo ldquoThis block is always longer than this

block (with each end lined up appropriately)rdquo

Before conservation of length The striped block is longer than the plain block when they

are lined up like this But when I move the blocks around sometimes the plain block is

longer than the striped block

After conservation of length I have to line up the blocks to measure them The plain

block is always longer than the striped block




All Rights Reserved

CLUSTER 2 CLASSIFY OBJECTS AND COUNT THE NUMBER OF OBJECTS IN

EACH CATEGORY

MGSEKMD3 Classify objects into given categories count the numbers of objects in each

category and sort the categories by count (Limit category counts to be less than or equal to

10)

This standard asks students to identify similarities and differences between objects (eg

size color shape) and use the identified attributes to sort a collection of objects Once

the objects are sorted the student counts the amount in each set Once each set is

counted then the student is asked to sort (or group) each of the sets by the amount in

each set

For example when given a collection of buttons the student separates the buttons into

different piles based on color (all the blue buttons are in one pile all the orange buttons

are in a different pile etc) Then the student counts the number of buttons in each pile

blue (5) green (4) orange (3) purple (4) Finally the student organizes the groups by

the quantity in each group (Orange buttons (3) Green buttons next (4) Purple buttons

with the green buttons because purple also had (4) Blue buttons last (5)

This objective helps to build a foundation for data collection in future grades In later

grades students will transfer these skills to creating and analyzing various graphical

representations

GEOMETRY (G)

CLUSTER 1 IDENTIFY AND DESCRIBE SHAPES (SQUARES CIRCLES

TRIANGLES RECTANGLES HEXAGONS CUBES CONES CYLINDERS AND

SPHERES)

This entire cluster asks students to understand that certain attributes define what a shape is

called (number of sides number of angles etc) and other attributes do not (color size

orientation) Then using geometric attributes the student identifies and describes particular

shapes listed above Throughout the year Kindergarten students move from informal language

to describe what shapes look like (eg ldquoThat looks like an ice cream conerdquo) to more formal

mathematical language (eg ldquoThat is a triangle It has three sidesrdquo)

In Kindergarten students need ample experiences exploring various forms of the shapes (eg

size big and small types triangles equilateral isosceles scalene orientation rotated slightly

to the left ldquoupside down‟) using geometric vocabulary to describe the different shapes In

addition students need numerous experiences comparing one shape to another rather than

focusing on one shape at a time This type of experience solidifies the understanding of the

various attributes and how those attributes are different- or similar- from one shape to another

Students in Kindergarten typically recognize figures by appearance alone often by comparing




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them to a known example of a shape such as the triangle on the left For example students in

Kindergarten typically recognize that the figure on the left is a triangle but claim that the figure

on the right is not a triangle since it does not have a flat bottom The properties of a figure are

not recognized or known Students make decisions on identifying and describing shapes based

on perception not reasoning

MGSEKG1 Describe objects in the environment using names of shapes and describe the

relative positions of these objects using terms such as above below beside in front of

behind and next to

This standard expects students to use positional words (such as those italicized above) to

describe objects in the environment Kindergarten students need to focus first on location

and position of two-and-three-dimensional objects in their classroom prior to describing

location and position of two-and-three-dimensional representations on paper

MGSEKG2 Correctly name shapes regardless of their orientations or overall size

This standard addresses students ‟identification of shapes based on known examples

Students at this level do not yet recognize triangles that are turned upside down as

triangles since they donrsquot ldquolook likerdquo triangles Students need ample experiences looking

at and manipulating shapes with various typical and atypical orientations Through these

experiences students will begin to move beyond what a shape ldquolooks likerdquo to identifying

particular geometric attributes that define a shape

MGSEKG3 Identify shapes as two-dimensional (lying in a plane ldquoflatrdquo) or three

dimensional (ldquosolidrdquo)

This standard asks students to identify flat objects (2 dimensional) and solid objects (3

dimensional) This standard can be taught by having students sort flat and solid objects

or by having students describe the appearance or thickness of shapes

CLUSTER 2 ANALYZE COMPARE CREATE AND COMPOSE SHAPES

MGSEKG4 Analyze and compare two- and three-dimensional shapes in different sizes

and orientations using informal language to describe their similarities differences parts

(eg number of sides and verticesldquocornersrdquo) and other attributes (eg having sides of

equal length)

This standard asks students to note similarities and differences between and among 2-D

and 3-D shapes using informal language These experiences help young students begin to

understand how 3-dimensional shapes are composed of 2-dimensional shapes (eg the

base and the top of a cylinder is a circle a circle is formed when tracing a sphere)

MGSEKG5 Model shapes in the world by building shapes from components (eg sticks

and clay balls) and drawing shapes

This standard asks students to apply their understanding of geometric attributes of shapes

in order to create given shapes For example a student may roll a clump of play-dough




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into a sphere or use their finger to draw a triangle in the sand table recalling various

attributes in order to create that particular shape

MGSEKG6 Compose simple shapes to form larger shapes For example ldquoCan you join

these two triangles with full sides touching to make a rectanglerdquo

This standard moves beyond identifying and classifying simple shapes to manipulating

two or more shapes to create a new shape This concept begins to develop as students

first move rotate flip and arrange puzzle pieces Next students use their experiences

with puzzles to move given shapes to make a design (eg ldquoUse the 7 tangram pieces to

make a foxrdquo) Finally using these previous foundational experiences students

manipulate simple shapes to make a new shape




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MINDSET AND MATHEMATICS

Growth mindset was pioneered by Carol Dweck Lewis and Virginia Eaton Professor of

Psychology at Stanford University She and her colleagues were the first to identify a link

between growth mindset and achievement They found that students who believed that their

ability and intelligence could grow and change otherwise known as growth mindset

outperformed those who thought that their ability and intelligence were fixed Additionally

students who were taught that they could grow their intelligence actually did better over time

Dwecks research showed that an increased focus on the process of learning rather than the

outcome helped increase a students growth mindset and ability

(from WITH+MATH=I CAN)




All Rights Reserved

Jo Boaler Professor of Mathematics Education at the Stanford Graduate School of Education

and author of Mathematical Mindsets Unleashing Students Potential through Creative Math

Inspiring Messages and Innovative Teaching was one of the first to apply growth mindset to

math achievement

You can learn how to use the power of growth mindset for yourself and your students here

httpswwwamazoncomgpwithmathican

httpswwwmindsetkitorgtopicsabout-growth-mindset

httpswwwyoucubedorg

Growth and Fixed Mindset images courtesy of Katherine Lynas (katherinelynascom) Thank

you Katherine

VERTICAL UNDERSTANDING OF THE MATHEMATICS LEARNING

TRAJECTORY

Why does it matter if you know what happens in mathematics in the grades before and after the

one you teach Isnrsquot it enough just to know and understand the expectations for your grade

There are many reasons to devote a bit of your time to the progression of standards

Yoursquoll

bull Deepen your understanding of how development of algebraic thinking has proven to be a

critical element of student mathematics success as they transition from elementary to

middle school Elementary and middle school teachers must understand how algebraic

thinking develops prior to their grade in their grade and beyond their grade in order to

support student algebraic thinking

bull Know what to expect when students show up in your grade because you know what they

should understand from the years before

bull Understand how conceptual understanding develops making it easier to help students

who have missing bits and pieces

bull Be able to help students to see the connections between ideas in mathematics in your

grade and beyond helping them to connect to what they already know and what is to

come

bull Assess understanding more completely and develop better assessments

bull Know what the teachers in the grades to come expect your students to know and

understand

bull Plan more effectively with same-grade and other-grade colleagues

bull Deepen your understanding of the mathematics of your grade

We arenrsquot asking you to take a month off to study up just asking that you reference the

following resources when you want to deepen your understanding of where students are in their

mathematics learning understand why they are learning what they are learning in your grade

and understand the mathematical ideas and connections within your grade and beyond




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Resources

The Coherence Map

httpachievethecoreorgpage1118coherence-map This resource diagrams the connections

between standards provides explanations of standards provides example tasks for

many standards and links to the progressions document when further detail is required

A visual learning trajectory of

Addition and Subtraction - httpgfletchycom20160304the-progression-of-addition-and-

subtraction

Multiplication - httpgfletchycom20151218the-progression-of-multiplication

Division - httpgfletchycom20160131the-progression-of-division

Fractions - httpsgfletchycom20161208the-progression-of-fractions

(Many thanks to Graham Fletcher the genius behind these videos)

The Mathematics Progression Documents

httpmatharizonaedu~imeprogressions

Learning Trajectories in Mathematics

httpwwwcpreorgimagesstoriescpre_pdfslearning20trajectories20in20math_ccii20r

eportpdf

RESEARCH OF INTEREST TO MATHEMATICS TEACHERS

Social Emotional Learning and Math

httpcurryvirginiaeduuploadsresourceLibraryTeachers_support_for_SEL_contributes_to_im

proved_math_teaching_and_learning_et_alpdf

Why how you teach math is important httpswwwyoucubedorg

GloSS IKAN and the overall Numeracy Project

Information on the Numeracy Project which includes GloSS and IKAN can be found here

Georgia Numeracy Project Overview

The GloSS and IKAN professional learning video found here

httpswwwgeorgiastandardsorgGeorgia-StandardsPagesFOAFoundations-of-Algebra-Day-

1aspx provides an in-depth look at the GloSS and IKAN While it was created for teachers of

Foundations of Algebra the information is important for teachers of grades K- 12

The GloSS and IKAN prezi found on georgiastandardsorg here

httpswwwgeorgiastandardsorgGeorgia-StandardsPagesGlobal-Strategy-Stage-GloSS-and-

Individual-Knowledge-Assessment-of-Number-IKANaspx




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FLUENCY

Fluency Procedural fluency is defined as skill in carrying out procedures flexibly accurately

efficiently and appropriately Fluent problem solving does not necessarily mean solving

problems within a certain time limit Fluency is based on a deep understanding of quantity and

number

Deep Understanding Teachers teach more than simply ldquohow to get the answerrdquo and instead

support studentsrsquo ability to access concepts from a number of perspectives Therefore students

are able to see math as more than a set of mnemonics or discrete procedures Students

demonstrate deep conceptual understanding of foundational mathematics concepts by applying

them to new situations as well as writing and speaking about their understanding

Memorization Memorization leads to the rapid recall of arithmetic facts or mathematical

procedures without the necessity of understanding This type of learning is not the goal of

numeracy Memorization is often confused with fluency and automaticity Fluency implies a

much richer kind of mathematical knowledge and experience Automaticity is based on strategy

development and the ability to become automatic with part-whole computation strategies

developed

Number Sense Students consider the context of a problem look at the numbers in a problem

make a decision about which strategy would be most efficient in each particular problem

Number sense is not a deep understanding of a single strategy but rather the ability to think

flexibly between a variety of strategies in context

Fluent students

bull flexibly use a combination of deep understanding number sense and automaticity

bull are fluent in the necessary baseline functions in mathematics so that they are able to

spend their thinking and processing time unpacking problems and making meaning from

them

bull are able to articulate their reasoning

bull find solutions through a number of different paths

For more about fluency see

httpwwwyoucubedorgwp-contentuploads201503FluencyWithoutFear-2015pdf and

httpsbhi61nm2cr3mkdgk1dtaov18-wpenginenetdna-sslcomwp-contentuploadsnctm-timed-

testspdf




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ARC OF LESSON (OPENING WORK SESSION CLOSING)

ldquoWhen classrooms are workshops-when learners are inquiring investigating and constructing-

there is already a feeling of community In workshops learners talk to one another ask one

another questions collaborate prove and communicate their thinking to one another The heart

of math workshop is this investigations and inquiries are ongoing and teachers try to find

situations and structure contexts that will enable children to mathematize their lives- that will

move the community toward the horizon Children have the opportunity to explore to pursue

inquiries and to model and solve problems on their own creative ways Searching for patterns

raising questions and constructing onersquos own models ideas and strategies are the primary

activities of math workshop The classroom becomes a community of learners engaged in

activity discourse and reflectionrdquo Young Mathematicians at Work- Constructing Addition and

Subtraction by Catherine Twomey Fosnot and Maarten Dolk

ldquoStudents must believe that the teacher does not have a predetermined method for solving the

problem If they suspect otherwise there is no reason for them to take risks with their own ideas

and methodsrdquo Teaching Student-Centered Mathematics K-3 by John Van de Walle and Lou

Ann Lovin

Opening Set the stage

Get students mentally ready to work on the task

Clarify expectations for products or behavior

How

bull Begin with a simpler version of the task to be presented

bull Solve problem strings related to the mathematical ideas being investigated

bull Leap headlong into the task and begin by brainstorming strategies for approaching the

task

bull Estimate the size of the solution and reason about the estimate

Make sure everyone understands the task before beginning Have students restate the task in their

own words Every task should require more of the students than just the answer

Work session Let them Grapple

Students- Grapple with the mathematics through sense-making discussion concretizing their

mathematical ideas and the situation record thinking in journals

Teacher- Let go Listen Respect student thinking Encourage testing of ideas Ask questions to

clarify or provoke thinking Provide gentle hints Observe assess and repeat

Closing Best Learning Happens Here

Students- Share answers justify thinking clarify understanding explain thinking question each

other identify patterns and make generalizations make additional connections to real world

Teacher- Listen attentively to all ideas asks for explanations offer comments such as ldquoPlease

tell me how you figured that outrdquo ldquoI wonder what would happen if you triedhelliprdquo

Take away from lesson- anchor charts and journal reflections using number pictures and words

Read Van de Walle K-3 Chapter 1




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BREAKDOWN OF A TASK (UNPACKING TASKS)

How do I go about tackling a task or a unit

Read the unit in its entirety Discuss it with your grade level colleagues Which parts do you feel

comfortable with Which make you wonder Brainstorm ways to implement the tasks

Collaboratively complete the culminating task with your grade level colleagues As students

work through the tasks you will be able to facilitate their learning with this end in mind The

structure of the units and tasks is similar task to task and grade to grade This structure allows

you to converse in a vertical manner with your colleagues school-wide There is a great deal of

mathematical knowledge and teaching support within each grade level guide unit and task

1 Read the first task your students will be engaged in Discuss it with your grade level

colleagues Which parts do you feel comfortable with Which make you wonder

Brainstorm ways to implement the tasks

2 If not already established use the first few weeks of school to establish routines and

rituals and to assess student mathematical understanding You might use some of the

tasks found in the unit or in some of the following resources as beginning tasks centers

or math tubs which serve the dual purpose of allowing you to observe and assess

Additional Resources

Math Their Way httpwwwcentereduMathTheirWayshtml

NZ Maths- httpwwwnzmathsconznumeracy-development-projects-

booksparent_node=

K-5 Math Teaching Resources- httpwwwk-5mathteachingresourcescomindexhtml

(this is a for-profit site with several free resources)

Math Solutions- httpwwwmathsolutionscomindexcfmpage=wp9ampcrid=56

3 Points to remember

bull Each task begins with a list of the standards specifically addressed in that task

however that does not mean that these are the only standards addressed in the

task Remember standards build on one another and mathematical ideas are

connected

bull Tasks are made to be modified to match your learnerrsquos needs If the names need

changing change them If the specified materials are not available use what is

available If a task doesnrsquot go where the students need to go modify the task or

use a different resource

bull The units are not intended to be all encompassing Each teacher and team will

make the units their own and add to them to meet the needs of the learners




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ROUTINES AND RITUALS

Teaching Math in Context and Through Problems

ldquoBy the time they begin school most children have already developed a sophisticated informal

understanding of basic mathematical concepts and problem-solving strategies Too often

however the mathematics instruction we impose upon them in the classroom fails to connect

with this informal knowledgerdquo (Carpenter et al 1999) The 8 Standards of Mathematical

Practice (SMP) should be at the forefront of every mathematics lesson and be the driving factor

of HOW students learn

One way to help ensure that students are engaged in the 8 SMP is to construct lessons built on

context or through story problems Fosnot and Dolk (2001) point out that in story problems

children tend to focus on getting the answer probably in a way that the teacher wants ldquoContext

problems on the other hand are connected as closely as possible to childrenrsquos lives rather than

to lsquoschool mathematicsrsquo They are designed to anticipate and to develop childrenrsquos mathematical

modeling of the real worldrdquo

Traditionally mathematics instruction has been centered around a lot of problems in a single

math lesson focusing on rote procedures and algorithms which do not promote conceptual

understanding Teaching through word problems and in context is difficult however

ldquokindergarten students should be expected to solve word problemsrdquo (Van de Walle K-3)

A problem is defined as any task or activity for which the students have no prescribed or

memorized rules or methods nor is there a perception by students that there is a specific correct

solution method A problem for learning mathematics also has these features

bull The problem must begin where the students are which makes it accessible to all learners

bull The problematic or engaging aspect of the problem must be due to the mathematics that

the students are to learn

bull The problem must require justifications and explanations for answers and methods

It is important to understand that mathematics is to be taught through problem solving That is

problem-based tasks or activities are the vehicle through which the standards are taught Student

learning is an outcome of the problem-solving process and the result of teaching within context

and through the Standards for Mathematical Practice (Van de Walle and Lovin Teaching

Student-Centered Mathematics K-3 page 11)

Use of Manipulatives

ldquoIt would be difficult for you to have become a teacher and not at least heard that the use of

manipulatives or a ldquohands-on approachrdquo is the recommended way to teach mathematics There

is no doubt that these materials can and should play a significant role in your classroom Used

correctly they can be a positive factor in childrenrsquos learning But they are not a cure-all that some

educators seem to believe them to be It is important that you have a good perspective on how

manipulatives can help or fail to help children construct ideas We canrsquot just give students a ten-

frame or bars of Unifix cubes and expect them to develop the mathematical ideas that these

manipulatives can potentially represent When a new model or new use of a familiar model is




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introduced into the classroom it is generally a good idea to explain how the model is used and

perhaps conduct a simple activity that illustrates this use rdquo

(Van de Walle and Lovin Teaching Student-Centered Mathematics K-3 page 6)

Once you are comfortable that the models have been explained you should not force their use on

students Rather students should feel free to select and use models that make sense to them In

most instances not using a model at all should also be an option The choice a student makes can

provide you with valuable information about the level of sophistication of the studentrsquos

reasoning

Whereas the free choice of models should generally be the norm in the classroom you can often

ask students to model to show their thinking This will help you find out about a childrsquos

understanding of the idea and also his or her understanding of the models that have been used in

the classroom

The following are simple rules of thumb for using models

bull Introduce new models by showing how they can represent the ideas for which they are

intended

bull Allow students (in most instances) to select freely from available models to use in solving

problems

bull Encourage the use of a model when you believe it would be helpful to a student having

difficultyrdquo (Van de Walle and Lovin Teaching Student-Centered Mathematics K-3

page 8-9)

bull Modeling also includes the use of mathematical symbols to representmodel the concrete

mathematical ideathought processsituation This is a very important yet often neglected

step along the way Modeling can be concrete representational and abstract Each type

of model is important to student understanding Modeling also means to ldquomathematizerdquo a

situation or problem to take a situation which might at first glance not seem

mathematical and view it through the lens of mathematics For example students notice

that the cafeteria is always out of their favorite flavor of ice cream on ice cream days

They decide to survey their schoolmates to determine which flavors are most popular

and share their data with the cafeteria manager so that ice cream orders reflect their

findings The problem Running out of ice cream flavors The solution Use math to

change the flavor amounts ordered

Use of Strategies and Effective Questioning

Teachers ask questions all the time They serve a wide variety of purposes to keep learners

engaged during an explanation to assess their understanding to deepen their thinking or focus

their attention on something This process is often semi-automatic Unfortunately there are many

common pitfalls These include

bull asking questions with no apparent purpose

bull asking too many closed questions

bull asking several questions all at once

bull poor sequencing of questions

bull asking rhetorical questions

bull asking lsquoGuess what is in my headrsquo questions




All Rights Reserved

bull focusing on just a small number of learners

bull ignoring incorrect answers

bull not taking answers seriously

In contrast the research shows that effective questioning has the following characteristics

bull Questions are planned well ramped in difficulty

bull Open questions predominate

bull A climate is created where learners feel safe

bull A lsquono handsrsquo approach is used for example when all learners answer at once using mini-

whiteboards or when the teacher chooses who answers

bull Probing follow-up questions are prepared

bull There is a sufficient lsquowait timersquo between asking and answering a question

bull Learners are encouraged to collaborate before answering

bull Learners are encouraged to ask their own questions

0-99 Chart or 1-100 Chart

(Adapted information from About Teaching Mathematics A Kndash8 RESOURCE MARILYN BURNS

3rd edition and Van de Walle)

Both the 0-99 Chart and the 1-100 Chart are valuable tools in the understanding of mathematics

Most often these charts are used to reinforce counting skills Counting involves two separate

skills (1) ability to produce the standard list of counting words (ie one two three) and (2) the

ability to connect the number sequence in a one-to-one manner with objects (Van de Walle

2007) The counting sequence is a rote procedure The ability to attach meaning to counting is

ldquothe key conceptual idea on which all other number concepts are developedrdquo (Van de Walle p

122) Children have greater difficulty attaching meaning to counting than rote memorization of

the number sequence Although both charts can be useful the focus of the 0-99 chart should be

at the forefront of number sense development in early elementary

A 0-99 Chart should be used in place of a 1-100 Chart when possible in early elementary

mathematics for many reasons but the overarching argument for the 0-99 is that it helps to

develop a deeper understanding of place value Listed below are some of the benefits of using

the 0-99 Chart in your classroom

bull A 0-99 Chart begins with zero where as a hundredrsquos chart begins with 1 It is important

to include zero because it is a digit and just as important as 1-9

bull A 1-100 chart puts the decade numerals (10 20 30 etc) on rows without the remaining

members of the same decade For instance on a hundredrsquos chart 20 appears at the end of

the teensrsquo row This causes a separation between the number 20 and the numbers 21-29

The number 20 is the beginning of the 20rsquos family therefore it should be in the

beginning of the 20rsquos row like in a 99rsquos chart to encourage students to associate the

quantities together

bull A 0-99 chart ends with the last two-digit number 99 this allows the students to

concentrate their understanding using numbers only within the onesrsquo and tensrsquo place

values A hundredrsquos chart ends in 100 introducing a new place value which may change

the focus of the places




All Rights Reserved

bull The understanding that 9 units fit in each place value position is crucial to the

development of good number sense It is also very important that students recognize that

zero is a number not merely a placeholder This concept is poorly modeled by a typical

1-100 chart base ten manipulatives and even finger counting We have no zero finger

zero block or zero space on typical 1-100 number charts Whereas having a zero on

the chart helps to give it status and reinforces that zero holds a quantity a quantity of

none Zero is the answer to a question such as ldquoHow many elephants are in the roomrdquo

bull Including zero presents the opportunity to establish zero correctly as an even number

when discussing even and odd Children see that it fits the same pattern as all of the

other even numbers on the chart

While there are differences between the 0-99 Chart and the 1-100 Chart both number charts

are valuable resources for your students and should be readily available in several places

around the classroom Both charts can be used to recognize number patterns such as the

increase or decrease by multiples of ten Provide students the opportunity to explore the

charts and communicate the patterns they discover

The number charts should be placed in locations that are easily accessible to students and

promote conversation Having one back at your math calendar or bulletin board area

provides you the opportunity to use the chart to engage students in the following kinds of

discussions Ask students to find the numeral that represents

bull the day of the month

bull the month of the year

bull the number of students in the class

bull the number of students absent or any other amount relevant to the moment

Using the number is 21 give directions and ask questions similar to those below

bull Name a number greater than 21

bull Name a number less than 21

bull What number is 3 more than or less than 21



bull Is 21 even or odd

bull What numbers live right next door to 21

0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




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Ask students to pick an even number and explain how they know the number is even Ask

students to pick an odd number and explain how they know it is odd Ask students to count

by 2rsquos 5rsquos or 10rsquos Tell them to describe any patterns that they see (Accept any patterns that

students are able to justify There are many right answers)

Number Lines

The use of number lines in elementary mathematics is crucial in studentsrsquo development of

number and mathematical proficiency While the MGSEK explicitly state use number lines in

grades 2-5 number lines should be used in all grade levels and in multiple settings

According to John Van de Walle

A number line is also a worthwhile model but can initially present conceptual difficulties

for children below second grade and students with disabilities (National Research

Council Committee 2009) This is partially due to their difficulty in seeing the unit

which is a challenge when it appears in a continuous line A number line is also a shift

from counting a number of individual objects in a collection to continuous length units

There are however ways to introduce and model number lines that support young

learners as they learn this representation Familiarity with a number line is essential

because third grade students will use number lines to locate fractions and add and

subtract time intervals fourth graders will locate decimals and use them for

measurement and fifth graders will use perpendicular number lines in coordinate grids

(CCSSO2010)

A number line measures distance from zero the same way a ruler does If you donrsquot

actually teach the use of the number line through emphasis on the unit (length) students

may focus on the hash marks or numerals instead of the spaces (a misunderstanding that

becomes apparent when their answers are consistently off by one) At first students can

build a number path by using a given length such as a set of Cuisenaire rods of the same

color to make a straight line of multiple single units (Van de Walle and Lovin Teaching

Student-Centered Mathematics 3-5 pg 106-107)

Open number lines are particularly useful for building studentsrsquo number sense They can also

form the basis for discussions that require the precise use of vocabulary and quantities and are

therefore a good way to engage students in the Standards for Mathematical Practice

While the possibilities for integrating number lines into the mathematics classroom are endless

the following are some suggestionsideas

On a bulletin board attach a string which will function as an open number line Each

morning (or dedicated time for math routines) put a new number on each studentrsquos desk

Using some type of adhesive (thumb tack tape etc) students will place the number in

the appropriate location on the string In the beginning of the year provide students with

numbers that are more familiar to them As the year progresses move through more

complex problems such as skip counting fractions decimals or other appropriate grade




All Rights Reserved

level problems Through daily integration the number line becomes part of the routine

Following the number placement have a brief discussiondebriefing of the reasoning

used by students to place the numbers

In the 3-Act tasks placed throughout the units students will be provided opportunities to

use an open number line to place estimates that are too low too high and just right as

related to the posed problem Similar opportunities can also be used as part of a daily

routine

Math Maintenance Activities

In addition to instruction centered on the current unit of study the math instructional block

should include time devoted to reviewing mathematics that have already been taught previewing

upcoming mathematics and developing mental math and estimation skills There is a saying that

if you donrsquot use it yoursquoll lose it If students donrsquot have opportunities to continuously apply and

refine the math skills theyrsquove learned previously then they may forget how to apply what

theyrsquove learned Unlike vocabulary words for literacy math vocabulary words are not used

much outside math class so it becomes more important to use those words in discussions

regularly Math maintenance activities incorporate review and preview of math concepts and

vocabulary and help students make connections across domains Itrsquos recommended that 15 to 30

minutes of the math instructional block be used for these math maintenance activities each day

Itrsquos not necessary nor is it recommended that teachers do every activity every day Teachers

should strive for a balance of math maintenance activities so that over the course of a week

students are exposed to a variety of these activities Math maintenance time may occur before or

after instruction related to the current math unit or it can occur at a different time during the day

The goals of this maintenance time should include

Deepening number sense including subitizing flexible grouping of quantities counting

forward and backward using whole numbers fractions decimals and skip counting

starting at random numbers or fractional amounts

Developing mental math skills by practicing flexible and efficient numerical thinking

through the use of operations and the properties of operations

Practicing estimation skills with quantities and measurements such as length mass and

liquid volume depending on grade level

Practicing previously-taught skills so that students deepen and refine their understanding

Reviewing previously-taught concepts that students struggled with as indicated on their

assessments including gaps in math concepts taught in previous grade levels

Using a variety of math vocabulary terms especially those that are used infrequently

Practicing basic facts using strategies learned in previous grade levels or in previous units

to develop or maintain fluency

Previewing prerequisite skills for upcoming math units of study




All Rights Reserved

Participating in mathematical discussions with others that require students to construct

viable arguments and critique the reasoning of others

To accomplish these goals math maintenance activities can take many different forms Some

activities include

Number Corner or Calendar Time

Number Talks

Estimation ActivitiesEstimation 180

Problem of the Day or Spiraled Review Problems

In addition math discussions math journals and math games are appropriate not only for the

current unit of study but also for maintaining math skills that were previously taught

Although there are commercially-available materials to use for math maintenance activities

there are also many excellent websites and internet resources that are free for classroom use

Here is a partial list of some recommended resources A more detailed explanation of some of

these components follows below

Math Maintenance Activity Possible Resources

Number Corner or Calendar Time bull httpteachelemmathweeblycomcalendarhtml

bull Every Day Counts Calendar Math from Houghton Mifflin

Harcourt

bull Number Corner from The Math Learning Center

Number Talks Number Talks by Sherry Parrish

httpkentuckymathematicsorgnumber_talk_resourcesphp

Estimation ActivitiesEstimation 180 httpwwwestimation180com

Problem of the DaySpiraled Review

Problems

wwwinsidemathematicsorg

httpnzmathsconzteaching-material

httpwwwk-5mathteachingresourcescom

httpmathlearnncsharpschoolcomcmsOneaspxportalId=

4507283amppageId=5856325

Childrenrsquos Mathematics Cognitively Guided Instruction by

Thomas Carpentar et Al

Extending Childrenrsquos Mathematics Fractions and Decimals

by Epson and Levi

Number CornerCalendar Time

Number Corner is a time set aside to go over mathematics skills (Standards for calendar can be

found in Social Studies) during the primary classroom day This should be an interesting and

motivating time for students A calendar board or corner can be set up and there should be




All Rights Reserved

several elements that are put in place The following elements should be set in place for students

to succeed during Number Corner

1 a safe environment

2 concrete models or math tools

3 opportunities to think first and then discuss

4 student interaction

Number Corner should relate several mathematics conceptsskills to real life experiences This

time can be as simple as reviewing the months days of the week temperature outside and the

schedule for the day but some teachers choose to add other components that integrate more

standards Number Corner should be used as a time to engage students in a discussion about

events which can be mathematized or as a time to engage in Number Talks

bull Find the number ___

bull If I have a nickel and a dime how much money do I have (any money combination)

bull What is ___ more than ___

bull What is ___ less than ___

bull Mystery number Give clues and they have to guess what number you have

bull This number has ___tens and ___ ones What number am I

bull What is the difference between ___ and ____

bull What number comes after ___ before ___

bull Tell me everything you know about the number ____ (Anchor Chart)

Number Corner is also a chance to familiarize your students with Data Analysis This creates an

open conversation to compare quantities which is a vital process that must be explored before

students are introduced to addition and subtraction

At first choose questions that have only two mutually exclusive answers such as yes or

no (eg Are you a girl or a boy) rather than questions that can be answered yes no or

maybe (or sometimes) This sets up the part-whole relationship between the number of

responses in each category and the total number of students present and it provides the

easiest comparison situation (between two numbers eg Which is more How much

more is it) Keep in mind that the concept of less than (or fewer) is more difficult than

the concept of greater than (or more) Be sure to frequently include the concept of less in

your questions and discussions about comparisons

Later you can expand the questions so they have more than two responses Expected

responses may include maybe Irsquom not sure I donrsquot know or a short predictable list of

categorical responses (eg In which season were you born)

Once the question is determined decide how to collect and represent the data Use a

variety of approaches including asking students to add their response to a list of names or

tally marks using Unifix cubes of two colors to accumulate response sticks or posting 3

x 5 cards on the board in columns to form a bar chart

The question should be posted for students to answer For example ldquoDo you have an

older sisterrdquo Ask students to contribute their responses in a way that creates a simple

visual representation of the data such as a physical model table of responses bar graph

etc




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Each day ask students to describe compare and interpret the data by asking questions

such as these ldquoWhat do you notice about the data Which group has the most Which

group has the least How many more answered [this] compared to [that] Why do you

suppose more answered [this]rdquo Sometimes ask data gathering questions ldquoDo you think

we would get similar data on a different day Would we get similar data if we asked the

same question in another class Do you think these answers are typical for first graders

Why or why notrdquo

Ask students to share their thinking strategies that justify their answers to the questions

Encourage and reward attention to specific details Focus on relational thinking and

problem-solving strategies for making comparisons Also pay attention to identifying

part-whole relationships and reasoning that leads to interpretations

Ask students questions about the ideas communicated by the representation used What

does this graph represent How does this representation communicate this information

clearly Would a different representation communicate this idea better

The representation analysis and discussion of the data are the most important parts of

the routine (as opposed to the data gathering process or the particular question being

asked) These mathematical processes are supported by the computational aspects of

using operations on the category totals to solve part-whole or ldquocomparerdquo problems

Number Talks

In order to be mathematically proficient students must be able to compute accurately efficiently

and flexibly Daily classroom number talks provide a powerful avenue for developing ldquoefficient

flexible and accurate computation strategies that build upon the key foundational ideas of

mathematicsrdquo (Parrish 2010) Number talks involve classroom conversations and discussions

centered upon purposefully planned computation problems

In Sherry Parrishrsquos book Number Talks Helping Children Build Mental Math and Computation

Strategies teachers will find a wealth of information about Number Talks including

bull Key components of Number Talks

bull Establishing procedures

bull Setting expectations

bull Designing purposeful Number Talks

bull Developing specific strategies through Number Talks

There are four overarching goals upon which K-2 teachers should focus during Number Talks

These goals are

1 Developing number sense

2 Developing fluency with small numbers

3 Subitizing

4 Making Tens

Number talks are a great way for students to use mental math to solve and explain a variety of

math problems A Number Talk is a short ongoing daily routine that provides students with

meaningful ongoing practice with computation Number Talks should be structured as short

sessions alongside (but not necessarily directly related to) the ongoing math curriculum A great




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place to introduce a Number Talk is during Number CornerCalendar Time It is important to

keep Number Talks short as they are not intended to replace current curriculum or take up

the majority of the time spent on mathematics In fact teachers only need to spend 5 to 15

minutes on Number Talks Number Talks are most effective when done every day The primary

goal of Number Talks is to build computational fluency Children develop computational fluency

while thinking and reasoning like mathematicians When they share their strategies with others

they learn to clarify and express their thinking thereby developing mathematical language This

in turn serves them well when they are asked to express their mathematical processes in writing

In order for children to become computationally fluent they need to know particular

mathematical concepts that go beyond what is required to memorize basic facts or procedures

Students will begin to understand major characteristics of numbers such as

bull Numbers are composed of smaller numbers

bull Numbers can be taken apart and combined with other numbers to make new numbers

bull What we know about one number can help us figure out other numbers

bull What we know about parts of smaller numbers can help us with parts of larger numbers

bull Numbers are organized into groups of tens and ones (and hundreds tens and ones and so

forth)

bull What we know about numbers to 10 helps us with numbers to 100 and beyond

All Number Talks follow a basic six-step format The format is always the same but the

problems and models used will differ for each number talk

1 Teacher presents the problem Problems are presented in many different ways as dot

cards ten frames sticks of cubes models shown on the overhead a word problem or a

numerical expression Strategies are not explicitly taught to students instead the

problems presented lead to various strategies

2 Students figure out the answer Students are given time to figure out the answer To

make sure students have the time they need the teacher asks them to give a ldquothumbs-uprdquo

when they have determined their answer The thumbs up signal is unobtrusive- a message

to the teacher not the other students

3 Students share their answers Four or five students volunteer to share their answers and

the teacher records them on the board

4 Students share their thinking Three or four students volunteer to share how they got

their answers (Occasionally students are asked to share with the person(s) sitting next to

them) The teacher records the students thinking

5 The class agrees on the real answer for the problem The answer that together the

class determines is the right answer is presented as one would the results of an

experiment The answer a student comes up with initially is considered a conjecture

Models andor the logic of the explanation may help a student see where their thinking

went wrong may help them identify a step they left out or clarify a point of confusion

There should be a sense of confirmation or clarity rather than a feeling that each problem

is a test to see who is right and who is wrong A student who is still unconvinced of an

answer should be encouraged to keep thinking and to keep trying to understand For some

students it may take one more experience for them to understand what is happening with

the numbers and for others it may be out of reach for some time The mantra should be

If you are not sure or it doesnt make sense yet keep thinking




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6 The steps are repeated for additional problems Similar to other procedures in your

classroom there are several elements that must be in place to ensure students get the most from

their Number Talk experiences These elements are

1 A safe environment

2 Problems of various levels of difficulty that can be solved in a variety of ways

3 Concrete models

4 Opportunities to think first and then check

5 Interaction

6 Self-correction

Estimation 180

Estimation is a skill that has many applications such as checking computation answers quickly

Engaging in regular estimation activities will develop studentsrsquo reasoning skills number sense

and increase their repertoire of flexible and efficient strategies As students gain more

experiences with estimation their accuracy will improve

According to John Van de Walle there are three types of estimation that students should

practice

Measurement estimation ndash determining an approximate measurement such as weight

length or capacity

Quantity estimation ndash approximating the number of items in a collection

Computational estimation ndash determining a number that is an approximation of a

computation

One resource which provides contexts for all three types of estimation is Andrew Stadelrsquos

website httpwwwestimation180com In his website Mr Stadel has posted daily estimation

contexts Here are his directions for using his website

1 Click on a picture

2 Read the question

3 Look for context clues

4 Make an estimate

5 Tell us how confident you are

6 Share your reasoning (what context clues did you use)

7 See the answer

8 See the estimates of others




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The most important part is step 6 After you make an estimate feel free to give a brief

description Its so valuable to a classroom when students share their logic or use of context

clues when formulating an estimate

Andrew Stadel has collaborated with Michael Fenton to create a recording sheet for students to

use with the estimation contexts on the website The recording sheet can also be found at

httpwwwestimation180com Here are his directions for the recording sheet

Column use descriptions from Andrew Stadel

Day

In Estimation 180s first year I was just trying to keep up with creating these estimation

challenges in time for use in my own classroom There really wasnt a scope and

sequence involved That said now that there are over 160 estimation challenges

available teachers and students can use them at any time throughout the school year and

without completing them in sequential order Therefore use the Day column simply to

number your daily challenges according to the site Tell your students or write it up on

the board that youre doing the challenge from Day 135 even though you might be on the

fifth day of school

Description

In my opinion this column is more important than the Day column Dont go crazy

here Keep it short and sweet but as specific as possible For example theres a lot of

scattered height estimates on the site Dont write down How tall for Day 110 Instead

write Bus height because when you get to Day 111 Id write in Parking structure

height I believe the teacher has the ultimate say here but it can be fun to poll your

students for a short description in which you all can agree Give students some

ownership right If unit measurement is involved try and sneak it in here Take Day

125 for instance Id suggest entering Net Wt (oz) of lg Hersheys bar Keep in mind

that Day 126 asks the same question but Id suggest you encourage your class to use

pounds if they dont think of it

By the way sometimes unit measurement(s) are already included in the question Use

discretion

Too Low

Think of an estimate that is too low




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Dont accept one (1) thats just rubbish unless one (1) is actually applicable to the

context of the challenge Stretch your students Think of it more as an answer thats too

low but reasonably close After all this is a site of estimation challenges not gimmes

Too High

Refer to my notes in Too Low Just dont accept 1 billion unless its actually applicable

Discuss with students the importance of the Too Low and Too High sections we are

trying to eliminate wrong answers while creating a range of possible answers

My Estimate

This is the place for students to fill in their answer If the answer requires a unit of

measurement we better see one Not every estimation challenge is How

many marshmallows or Christmas lights or cheese balls

Even if a unit of measurement has already been established (see the Description notes)

Id still encourage your students to accompany their numerical estimate with a unit of

measurement

For example on Day 41 Whats the height of the Giant [Ferris] Wheel use what

makes sense to you your students and your countrys customary unit of measurement

Discuss the importance of unit measurements with students Dont accept 108 What does

that 108 represent Pancakes Oil spills Bird droppings NO It represents 108 feet

My Reasoning

The My Reasoning section is the most recent addition to the handout and Im extremely

thrilled about it This is a students chance to shine Encourage their reasoning to be short

and sweet When a student writes something down theyll be more inclined to share it or

remember it Accept bullet points or phrases due to the limited space We dont need

students to write paragraphs However we are looking for students to identify any

context clues they used personal experiences andor prior knowledge Hold students

accountable for their reasoning behind the estimate of the day

Dont let student reasoning go untapped If youre doing a sequence of themed

estimation challenges dont accept I just guessed after the first day in the sequence

For example if youre doing the flight distance themed estimate challenges starting

on Day 136 you will establish the distance across the USA on the first day Sure go

ahead and guess on Day 136 but make sure you hold students accountable for their

reasoning every day thereafter

Have students share their reasoning before and after revealing the answer Utilize Think-

Pair-Share This will help create some fun conversations before revealing the answer

After revealing the answer get those who were extremely close (or correct) to share their




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reasoning I bet youll have some great mathematical discussions Im also curious to hear

from those that are way off and how their reasoning could possibly be improved

Id say the My Reasoning section was born for Mathematical Practice 3 Construct viable

arguments and critique the reasoning of others Keep some of these thoughts in mind

regarding Mathematical Practice 3

Explain and defend your estimate

Construct a detailed explanation referencing context clues prior knowledge or

previous experiences

Invest some confidence in it

Try to initiate a playful and respectful argument in class

Ask Was anyone convinced by this explanation Why Why not or Are you

guys going to let [student name] off the hook with that explanation

Theres reasoning behind every estimate (not guess)

Find out what that reasoning is

DONT let student reasoning go untapped

Answer

Jot down the revealed answer Id also encourage students to write down the unit of

measurement used in the answer The answer might use a different unit of measurement

than what you and your class agreed upon Take the necessary time to discuss the most

relative unit of measurement I might be subjectively wrong on some of the answers

posted As for more thoughts on unit of measurement refer to the My Estimate notes

above Continue having mathematical discussion after revealing the answer Refer to my

notes regarding the use of Mathematical Practice 3 in the My Reasoning section

Error

Find the difference between My Estimate and Answer Have students circle either the +

or the - if they didnt get it exactly correct

+ Your estimate was greater than (above) the actual answer

- Your estimate was less than (below) the actual answer

Mathematize the World through Daily Routines

The importance of continuing the established classroom routines cannot be overstated Daily

routines must include such obvious activities such as taking attendance doing a lunch count

determining how many items are needed for snack lining up in a variety of ways (by height age

type of shoe hair color eye color etc) daily questions 99 chart questions and calendar

activities They should also include less obvious routines such as how to select materials how to

use materials in a productive manner how to put materials away how to open and close a door

etc An additional routine is to allow plenty of time for children to explore new materials before

attempting any directed activity with these new materials The regular use of the routines are

important to the development of studentsrsquo number sense flexibility and fluency which will

support studentsrsquo performances on the tasks in this unit




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Workstations and Learning Centers

It is recommended that workstations be implemented to create a safe and supportive environment

for problem solving in a standards-based classroom These workstations typically occur during

the ldquoexploringrdquo part of the lesson which follows the mini-lesson Your role is to introduce the

concept and allow students to identify the problem Once students understand what to do and you

see that groups are working towards a solution offer assistance to the next group

Groups should consist of 2-5 students and each student should have the opportunity to work with

all of their classmates throughout the year Avoid grouping students by ability Students in the

lower group will not experience the thinking and language of the top group and top students will

not hear the often unconventional but interesting approaches to tasks in the lower group (28 Van

de Walle and Lovin 2006)

In order for students to work efficiently and to maximize participation several guidelines must

be in place (Burns 2007)

1 You are responsible for your own work and behavior

2 You must be willing to help any group member who asks

3 You may ask the teacher for help only when everyone in your group has the same question

These rules should be explained and discussed with the class so that each student is aware of the

expectations you have for them as a group member Once these guidelines are established you

should be able to successfully lead small groups which will allow you the opportunity to engage

with students on a more personal level while providing students the chance to gain confidence as

they share their ideas with others

The types of activities students engage in within the small groups will not always be the same

Facilitate a variety of tasks that will lead students to develop proficiency with numerous concepts

and skills Possible activities include math games related previous Framework tasks problems

and computer-based activities With all tasks regardless if they are problems games etc include

a recording sheet for accountability This recording sheet will serve as a means of providing you

information of how a child arrived at a solution or the level at which they can explain their

thinking (Van de Walle 2006)

Games

ldquoA game or other repeatable activity may not look like a problem but it can nonetheless be

problem based The determining factor is this Does the activity cause students to be reflective

about new or developing relationships If the activity merely has students repeating procedure

without wrestling with an emerging idea then it is not a problem-based experience However

the few examples just mentioned and many others do have children thinking through ideas that

are not easily developed in one or two lessons In this sense they fit the definition of a problem-

based task

Just as with any task some form of recording or writing should be included with stations

whenever possible Students solving a problem on a computer can write up what they did and

explain what they learned Students playing a game can keep records and then tell about how

they played the game- what thinking or strategies they usedrdquo (Van de Walle and Lovin

Teaching Student-Centered Mathematics K-3 page 26)




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Journaling

Students should be writing and talking about math topics every day Putting thoughts into words

helps to clarify and solidify thinking By sharing their mathematical understandings in written

and oral form with their classmates teachers and parents students develop confidence in

themselves as mathematical learners this practice also enables teachers to better monitor student

progress NJ DOE

Language whether used to express ideas or to receive them is a very powerful tool and should

be used to foster the learning of mathematics Communicating about mathematical ideas is a way

for students to articulate clarify organize and consolidate their thinking Students like adults

exchange thoughts and ideas in many waysmdashorally with gestures and with pictures objects

and symbols By listening carefully to others students can become aware of alternative

perspectives and strategies By writing and talking with others they learn to use more-precise

mathematical language and gradually conventional symbols to express their mathematical

ideas Communication makes mathematical thinking observable and therefore facilitates further

development of that thought It encourages students to reflect on their own knowledge and their

own ways of solving problems Throughout the early years students should have daily

opportunities to talk and write about mathematics NCTM

When beginning math journals the teacher should model the process initially showing

students how to find the front of the journal the top and bottom of the composition book how

to open to the next page in sequence (special bookmarks or ribbons) and how to date the

page Discuss the usefulness of the book and the way in which it will help students retrieve

their math thinking whenever they need it

When beginning a task you can ask What do we need to find out and then How do we

figure it out Then figure it out usually by drawing representations and eventually adding

words numbers and symbols During the closing of a task have students show their journals

with a document camera or overhead when they share their thinking This is an excellent

opportunity to discuss different ways to organize thinking and clarity of explanations

Use a composition notebook (the ones with graph paper are terrific for math) for recording or

drawing answers to problems The journal entries can be from Frameworks tasks but should

also include all mathematical thinking Journal entries should be simple to begin with and

become more detailed as the childrens problem-solving skills improve Children should

always be allowed to discuss their representations with classmates if they desire feedback

The childrens journal entries demonstrate their thinking processes Each entry could first be

shared with a buddy to encourage discussion and explanation then one or two children

could share their entries with the entire class Dont forget to praise children for their thinking

skills and their journal entries These journals are perfect for assessment and for parent

conferencing The studentrsquos thinking is made visible




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GENERAL QUESTIONS FOR TEACHER USE

Adapted from Growing Success and materials from Math GAINS and TIPS4RM

Reasoning and Proving

bull How can we show that this is true for all cases

bull In what cases might our conclusion not hold true

bull How can we verify this answer

bull Explain the reasoning behind your prediction

bull Why does this work

bull What do you think will happen if this pattern continues

bull Show how you know that this statement is true

bull Give an example of when this statement is false

bull Explain why you do not accept the argument as proof

bull How could we check that solution

bull What other situations need to be considered

Reflecting

bull Have you thought abouthellip

bull What do you notice abouthellip

bull What patterns do you see

bull Does this problemanswer make sense to you

bull How does this compare tohellip

bull What could you start with to help you explore the possibilities

bull How can you verify this answer

bull What evidence of your thinking can you share

bull Is this a reasonable answer given thathellip

Selecting Tools and Computational Strategies

bull How did the learning tool you chose contribute to your understandingsolving of the

problem How did they assist in your communication

bull In what ways would [name a tool] assist in your investigationsolving of this problem

bull What other tools did you consider using Explain why you chose not to use them

bull Can you think of a different way to do the calculation that may be more efficient

bull What estimation strategy did you use

Connections

bull What other math have you studied that has some of the same principles properties or

procedures as this

bull How do these different representations connect to one another

bull When could this mathematical concept or procedure be used in daily life

bull What connection do you see between a problem you did previously and todayrsquos problem

Representing

bull What would other representations of this problem demonstrate

bull Explain why you chose this representation




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bull How could you represent this idea algebraically Graphically

bull Does this graphical representation of the data bias the viewer Explain

bull What properties would you have to use to construct a dynamic representation of this

situation

bull In what way would a scale model help you solve this problem

QUESTIONS FOR TEACHER REFLECTION

bull How did I assess for student understanding

bull How did my students engage in the 8 mathematical practices today

bull How effective was I in creating an environment where meaningful learning could take

place

bull How effective was my questioning today Did I question too little or say too much

bull Were manipulatives made accessible for students to work through the task

bull Name at least one positive thing about todayrsquos lesson and one thing you will change

bull How will todayrsquos learning impact tomorrowrsquos instruction




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MATHEMATICS DEPTH-OF-KNOWLEDGE LEVELS

Level 1 (Recall) includes the recall of information such as a fact definition term or a simple

procedure as well as performing a simple algorithm or applying a formula That is in

mathematics a one-step well-defined and straight algorithmic procedure should be included at

this lowest level Other key words that signify a Level 1 include ldquoidentifyrdquo ldquorecallrdquo ldquorecognizerdquo

ldquouserdquo and ldquomeasurerdquo Verbs such as ldquodescriberdquo and ldquoexplainrdquo could be classified at different

levels depending on what is to be described and explained

Level 2 (SkillConcept) includes the engagement of some mental processing beyond a habitual

response A Level 2 assessment item requires students to make some decisions as to how to

approach the problem or activity whereas Level 1 requires students to demonstrate a rote

response perform a well-known algorithm follow a set procedure (like a recipe) or perform a

clearly defined series of steps Keywords that generally distinguish a Level 2 item include

ldquoclassifyrdquo ldquoorganizerdquo rdquoestimaterdquo ldquomake observationsrdquo ldquocollect and display datardquo and

ldquocompare datardquo These actions imply more than one step For example to compare data requires

first identifying characteristics of the objects or phenomenon and then grouping or ordering the

objects Some action verbs such as ldquoexplainrdquo ldquodescriberdquo or ldquointerpretrdquo could be classified at

different levels depending on the object of the action For example if an item required students

to explain how light affects mass by indicating there is a relationship between light and heat this

is considered a Level 2 Interpreting information from a simple graph requiring reading

information from the graph also is a Level 2 Interpreting information from a complex graph that

requires some decisions on what features of the graph need to be considered and how

information from the graph can be aggregated is a Level 3 Caution is warranted in interpreting

Level 2 as only skills because some reviewers will interpret skills very narrowly as primarily

numerical skills and such interpretation excludes from this level other skills such as

visualization skills and probability skills which may be more complex simply because they are

less common Other Level 2 activities include explaining the purpose and use of experimental

procedures carrying out experimental procedures making observations and collecting data

classifying organizing and comparing data and organizing and displaying data in tables

graphs and charts

Level 3 (Strategic Thinking) requires reasoning planning using evidence and a higher level of

thinking than the previous two levels In most instances requiring students to explain their

thinking is a Level 3 Activities that require students to make conjectures are also at this level

The cognitive demands at Level 3 are complex and abstract The complexity does not result from

the fact that there are multiple answers a possibility for both Levels 1 and 2 but because the task

requires more demanding reasoning An activity however that has more than one possible

answer and requires students to justify the response they give would most likely be a Level 3

Other Level 3 activities include drawing conclusions from observations citing evidence and

developing a logical argument for concepts explaining phenomena in terms of concepts and

using concepts to solve problems




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DOK contrsquodhellip

Level 4 (Extended Thinking) requires complex reasoning planning developing and thinking

most likely over an extended period of time The extended time period is not a distinguishing

factor if the required work is only repetitive and does not require applying significant conceptual

understanding and higher-order thinking For example if a student has to take the water

temperature from a river each day for a month and then construct a graph this would be

classified as a Level 2 However if the student is to conduct a river study that requires taking

into consideration a number of variables this would be a Level 4 At Level 4 the cognitive

demands of the task should be high and the work should be very complex Students should be

required to make several connectionsmdashrelate ideas within the content area or among content

areasmdashand have to select one approach among many alternatives on how the situation should be

solved in order to be at this highest level Level 4 activities include designing and conducting

experiments making connections between a finding and related concepts and phenomena

combining and synthesizing ideas into new concepts and critiquing experimental designs




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DEPTH AND RIGOR STATEMENT

By changing the way we teach we are not asking children to learn less we are asking them to

learn more We are asking them to mathematize to think like mathematicians to look at numbers

before they calculate to think rather than to perform rote procedures Children can and do

construct their own strategies and when they are allowed to make sense of calculations in their

own ways they understand better In the words of Blaise Pascal ldquoWe are usually convinced

more easily by reasons we have found ourselves than by those which have occurred to othersrdquo

By changing the way we teach we are asking teachers to think mathematically too We are

asking them to develop their own mental math strategies in order to develop them in their

students Catherine Twomey Fosnot and Maarten Dolk Young Mathematicians at Work

While you may be tempted to explain and show students how to do a task much of the learning

comes as a result of making sense of the task at hand Allow for the productive struggle the

grappling with the unfamiliar the contentious discourse for on the other side of frustration lies

understanding and the confidence that comes from ldquodoing it myselfrdquo

DIFFERENTIATION

Information and instructional strategies for gifted students English Language Learners and

students with disabilities is available at httpeducationohiogovTopicsAcademic-Content-

StandardsNew-Learning-Standards




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Problem Solving Rubric (K-2)

SMP 1-Emergent 2-Progressing 3- MeetsProficient 4-Exceeds

Make sense of

problems and

persevere in

solving them

The student was unable to

explain the problem and

showed minimal perseverance

when identifying the purpose

of the problem

The student explained the

problem and showed some

perseverance in identifying the

purpose of the problem AND

selected and applied an

appropriate problem-solving

strategy that led to a partially

complete andor partially accurate

solution


problem and showed

perseverance when identifying

the purpose of the problem

AND selected and applied an


strategy that led to a generally

complete and accurate solution

The student explained the problem

and showed perseverance by

identifying the purpose of the problem

and selected and applied an

appropriate problem-solving strategy

that led to a thorough and accurate

solution

Attends to

precision

The student was unclear in

their thinking and was unable

to communicate

mathematically

The student was precise by

clearly describing their actions

and strategies while showing

understanding and using

appropriate vocabulary in their

process of finding solutions




understanding and using grade-

level appropriate vocabulary in

their process of finding

solutions

The student was precise by clearly

describing their actions and strategies

while showing understanding and

using above-grade-level appropriate

vocabulary in their process of finding

solutions

Reasoning and

explaining


express or justify their opinion

quantitatively or abstractly

using numbers pictures charts

or words

The student expressed or justified

their opinion either quantitatively

OR abstractly using numbers

pictures charts OR words

The student expressed and

justified their opinion both

quantitatively and abstractly


andor words

The student expressed and justified

their opinion both quantitatively and

abstractly using a variety of numbers

pictures charts and words

Models and use

of tools


select an appropriate tool draw

a representation to reason or

justify their thinking

The student selected an

appropriate tool or drew a correct

representation of the tools used to

reason and justify their response

The student selected an efficient

tool andor drew a correct

representation of the efficient

tool used to reason and justify

their response

The student selected multiple efficient

tools and correctly represented the

tools to reason and justify their

response In addition this student was

able to explain why their tool model

was efficient

Seeing

structure and

generalizing


identify patterns structures or

connect to other areas of

mathematics andor real-life

The student identified a pattern or

structure in the number system

and noticed connections to other

areas of mathematics or real-life

The student identified patterns or

structures in the number system


areas of mathematics and real-

life

The student identified various patterns

and structures in the number system

and noticed connections to multiple

areas of mathematics and real-life

Many thanks to Richmond County Schools for sharing this rubric




All Rights Reserved

SUGGESTED LITERATURE

bull The Greedy Triangle by Marilyn Burns

bull When a Line BeginshellipA Shape Begins by Rhonda Gowler Greene

bull Round Trip by Ann Jonas

bull Eight Hands Round by Ann Whitford Paul

bull Pattern by Henry Arthur Pluckrose

bull Shape by Henry Arthur Pluckrose

bull The Shape of Things by Dayle Ann Dobbs

bull Grandfather Tangrsquos Story by Ann Tompert and Robert Andrew Parker

bull Three Pigs One Wolf and Seven Magic Shapes by Maccarone and Neuhaus and

bull The Tangram Magician by Lisa Campbell Ernst

bull Measuring Penny by Loreen Leedy or

bull Me and the Measure of Things by Joan Sweeney

bull The Best Bug Parade by Stuart J Murphy

bull Chrysanthemum by Kevin Henkes

bull Mighty Maddie by Stuart Murphy

bull If You Give a Mouse a Cookie by Laura Numeroff

bull Ten Black Dots by Donald Crews

bull Annorsquos Counting House by Mitsumasa Anno

bull The Penny Pot by Barbara Derubertis

bull Ten Flashing Fireflies by Philemon Sturges

bull 12 Ways to Get to 11 by Eve Merriam

bull One Is a Snail Ten Is a Crab by April Pulley Sayre and Jeff Sayre

bull Two of Everything by Lily Toy Hong


httpkentuckymathematicsorgpimser_printablesphp

TECHNOLOGY LINKS

httpcatalogmathlearningcenterorgapps

httpnzmathsconzdigital-learning-objects

httpwwwgadoeorgTechnology-ServicesSLDSPagesTeacher-Resource-Linkaspx

httpswwwgeorgiastandardsorgGeorgia-StandardsPagesMathaspx




All Rights Reserved

RESOURCES CONSULTED

Content

Mathematics Progressions Documents httpimematharizonaeduprogressions

Illustrative Mathematics httpswwwillustrativemathematicsorgcontent-standardsK

NZ Maths

httpnzmathsconz

TeacherStudent Sense-making

httpwwwyoutubecomusermitcccnyorgfeature=watch

httpswwwgeorgiastandardsorgGeorgia-StandardsPagesMathaspx or

httpseccsedlorgcommon_core_videos

Journaling

httpwwwkindergartenkindergartencom201007setting-up-math-problemsolving-notebookshtml

Community of Learners

httpwwwedutopiaorgmath-social-activity-cooperative-learning-video

httpwwwedutopiaorgmath-social-activity-sel

httpwwwyoutubecomuserresponsiveclassroomvideos

Tea



July 2018 of 47

All Rights Reserved

Grade Level Overview

TABLE OF CONTENTS

Curriculum Maphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip4

Unpacking the Standards

bull Standards for Mathematical Practicehelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip5

bull Content Standardshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip8

Mindset and Mathematics helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip18

Vertical Understanding of the Mathematic Learning Trajectory helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip19

Research of Interest to Teachers helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip20

GloSS and IKAN helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip20

Fluencyhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip21

Arc of LessonMath Instructional Frameworkhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip22

Unpacking a Taskhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip23

Routines and Rituals

bull Teaching Math in Context and Through Problemshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip24

bull Use of Manipulativeshelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip24

bull Use of Strategies and Effective Questioninghelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip25

bull 0-99 or 1-100 Charthelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip26

bull Number Lines helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip28

bull Math Maintenance Activities helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip29

o Number CornerCalendar Time helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip30

o Number Talks helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip32

o EstimationEstimation 180 helliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip34




All Rights Reserved

















All Rights Reserved



Kindergarten



mathematical topics




Comparing

Numbers

Counting With

Friends

Sophisticated

Shapes

Measuring and

Analyzing Data

Investigating

Addition and

Subtraction

Further

Investigation of

Addition and

Subtraction

Show What We

Know

MGSEKCC1

MGSEKCC2

MGSEKCC3

MGSEKCC4

MGSEKMD3

MGSEKNBT1

MGSEKCC3

MGSEKCC4a

MGSEKCC5

MGSEKCC6

MGSEKCC7

MGSEKMD3

MGSEKG1

MGSEKG2

MGSEKG3

MGSEKG4

MGSEKG5

MGSEKG6

MGSEKMD3

MGSEKMD1

MGSEKMD2

MGSEKMD3

MGSEKOA1

MGSEKOA2

MGSEKOA3

MGSEKOA4

MGSEKOA5

MGSEKOA1

MGSEKOA2

MGSEKOA3

MGSEKOA4

MGSEKOA5

ALL






All Rights Reserved












































All Rights Reserved













(1OA7)






























All Rights Reserved









sequence





All Rights Reserved

CONTENT STANDARDS





















itself





presented















All Rights Reserved


























larger


















All Rights Reserved

















counting strategies




(Student 2)

Student 1





Student 2






Student 3




















All Rights Reserved














equations



















additional examples












All Rights Reserved


(+ - =)

Example



pictures of










or equation




Example



Student 1

Using a Ten-Frame






10

Student 2

Think Addition






missing

Student 3

Basic Fact






All Rights Reserved

























PLACE VALUE














All Rights Reserved







longrdquo









tallershorter





other
















All Rights Reserved


EACH CATEGORY



10)





each set









representations

GEOMETRY (G)



SPHERES)

















All Rights Reserved








behind and next to





















equal length)












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All Rights Reserved














All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




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Ann Lovin




How




task



















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booksparent_node=








connected










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All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























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quantities together








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0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




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Number Lines















(CCSSO2010)






















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routine


































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activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








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etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








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forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





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Too High




My Estimate






measurement





My Reasoning




















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Answer








Error



















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Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






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situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved

















All Rights Reserved



Kindergarten



mathematical topics




Comparing

Numbers

Counting With

Friends

Sophisticated

Shapes

Measuring and

Analyzing Data

Investigating

Addition and

Subtraction

Further

Investigation of

Addition and

Subtraction

Show What We

Know

MGSEKCC1

MGSEKCC2

MGSEKCC3

MGSEKCC4

MGSEKMD3

MGSEKNBT1

MGSEKCC3

MGSEKCC4a

MGSEKCC5

MGSEKCC6

MGSEKCC7

MGSEKMD3

MGSEKG1

MGSEKG2

MGSEKG3

MGSEKG4

MGSEKG5

MGSEKG6

MGSEKMD3

MGSEKMD1

MGSEKMD2

MGSEKMD3

MGSEKOA1

MGSEKOA2

MGSEKOA3

MGSEKOA4

MGSEKOA5

MGSEKOA1

MGSEKOA2

MGSEKOA3

MGSEKOA4

MGSEKOA5

ALL






All Rights Reserved












































All Rights Reserved













(1OA7)






























All Rights Reserved









sequence





All Rights Reserved

CONTENT STANDARDS





















itself





presented















All Rights Reserved


























larger


















All Rights Reserved

















counting strategies




(Student 2)

Student 1





Student 2






Student 3




















All Rights Reserved














equations



















additional examples












All Rights Reserved


(+ - =)

Example



pictures of










or equation




Example



Student 1

Using a Ten-Frame






10

Student 2

Think Addition






missing

Student 3

Basic Fact






All Rights Reserved

























PLACE VALUE














All Rights Reserved







longrdquo









tallershorter





other
















All Rights Reserved


EACH CATEGORY



10)





each set









representations

GEOMETRY (G)



SPHERES)

















All Rights Reserved








behind and next to





















equal length)












All Rights Reserved














All Rights Reserved














All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




All Rights Reserved
















Ann Lovin




How




task



















All Rights Reserved




















booksparent_node=








connected










All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








All Rights Reserved
































0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved



Kindergarten



mathematical topics




Comparing

Numbers

Counting With

Friends

Sophisticated

Shapes

Measuring and

Analyzing Data

Investigating

Addition and

Subtraction

Further

Investigation of

Addition and

Subtraction

Show What We

Know

MGSEKCC1

MGSEKCC2

MGSEKCC3

MGSEKCC4

MGSEKMD3

MGSEKNBT1

MGSEKCC3

MGSEKCC4a

MGSEKCC5

MGSEKCC6

MGSEKCC7

MGSEKMD3

MGSEKG1

MGSEKG2

MGSEKG3

MGSEKG4

MGSEKG5

MGSEKG6

MGSEKMD3

MGSEKMD1

MGSEKMD2

MGSEKMD3

MGSEKOA1

MGSEKOA2

MGSEKOA3

MGSEKOA4

MGSEKOA5

MGSEKOA1

MGSEKOA2

MGSEKOA3

MGSEKOA4

MGSEKOA5

ALL






All Rights Reserved












































All Rights Reserved













(1OA7)






























All Rights Reserved









sequence





All Rights Reserved

CONTENT STANDARDS





















itself





presented















All Rights Reserved


























larger


















All Rights Reserved

















counting strategies




(Student 2)

Student 1





Student 2






Student 3




















All Rights Reserved














equations



















additional examples












All Rights Reserved


(+ - =)

Example



pictures of










or equation




Example



Student 1

Using a Ten-Frame






10

Student 2

Think Addition






missing

Student 3

Basic Fact






All Rights Reserved

























PLACE VALUE














All Rights Reserved







longrdquo









tallershorter





other
















All Rights Reserved


EACH CATEGORY



10)





each set









representations

GEOMETRY (G)



SPHERES)

















All Rights Reserved








behind and next to





















equal length)












All Rights Reserved














All Rights Reserved














All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




All Rights Reserved
















Ann Lovin




How




task



















All Rights Reserved




















booksparent_node=








connected










All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








All Rights Reserved
































0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved












































All Rights Reserved













(1OA7)






























All Rights Reserved









sequence





All Rights Reserved

CONTENT STANDARDS





















itself





presented















All Rights Reserved


























larger


















All Rights Reserved

















counting strategies




(Student 2)

Student 1





Student 2






Student 3




















All Rights Reserved














equations



















additional examples












All Rights Reserved


(+ - =)

Example



pictures of










or equation




Example



Student 1

Using a Ten-Frame






10

Student 2

Think Addition






missing

Student 3

Basic Fact






All Rights Reserved

























PLACE VALUE














All Rights Reserved







longrdquo









tallershorter





other
















All Rights Reserved


EACH CATEGORY



10)





each set









representations

GEOMETRY (G)



SPHERES)

















All Rights Reserved








behind and next to





















equal length)












All Rights Reserved














All Rights Reserved














All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




All Rights Reserved
















Ann Lovin




How




task



















All Rights Reserved




















booksparent_node=








connected










All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








All Rights Reserved
































0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved













(1OA7)






























All Rights Reserved









sequence





All Rights Reserved

CONTENT STANDARDS





















itself





presented















All Rights Reserved


























larger


















All Rights Reserved

















counting strategies




(Student 2)

Student 1





Student 2






Student 3




















All Rights Reserved














equations



















additional examples












All Rights Reserved


(+ - =)

Example



pictures of










or equation




Example



Student 1

Using a Ten-Frame






10

Student 2

Think Addition






missing

Student 3

Basic Fact






All Rights Reserved

























PLACE VALUE














All Rights Reserved







longrdquo









tallershorter





other
















All Rights Reserved


EACH CATEGORY



10)





each set









representations

GEOMETRY (G)



SPHERES)

















All Rights Reserved








behind and next to





















equal length)












All Rights Reserved














All Rights Reserved














All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




All Rights Reserved
















Ann Lovin




How




task



















All Rights Reserved




















booksparent_node=








connected










All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








All Rights Reserved
































0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








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forth)































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3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





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Day








fifth day of school

Description












discretion

Too Low





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Too High




My Estimate






measurement





My Reasoning




















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Answer








Error



















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Games







based task









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Journaling





progress NJ DOE



































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Reflecting

















Connections


procedures as this




Representing






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situation






place








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graphs and charts














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All Rights Reserved















DIFFERENTIATION







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Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








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RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

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sequence





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CONTENT STANDARDS





















itself





presented















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larger


















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counting strategies




(Student 2)

Student 1





Student 2






Student 3




















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equations



















additional examples












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(+ - =)

Example



pictures of










or equation




Example



Student 1

Using a Ten-Frame






10

Student 2

Think Addition






missing

Student 3

Basic Fact






All Rights Reserved

























PLACE VALUE














All Rights Reserved







longrdquo









tallershorter





other
















All Rights Reserved


EACH CATEGORY



10)





each set









representations

GEOMETRY (G)



SPHERES)

















All Rights Reserved








behind and next to





















equal length)












All Rights Reserved














All Rights Reserved














All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




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Ann Lovin




How




task



















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booksparent_node=








connected










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All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























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quantities together








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0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




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Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








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forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





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Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved

CONTENT STANDARDS





















itself





presented















All Rights Reserved


























larger


















All Rights Reserved

















counting strategies




(Student 2)

Student 1





Student 2






Student 3




















All Rights Reserved














equations



















additional examples












All Rights Reserved


(+ - =)

Example



pictures of










or equation




Example



Student 1

Using a Ten-Frame






10

Student 2

Think Addition






missing

Student 3

Basic Fact






All Rights Reserved

























PLACE VALUE














All Rights Reserved







longrdquo









tallershorter





other
















All Rights Reserved


EACH CATEGORY



10)





each set









representations

GEOMETRY (G)



SPHERES)

















All Rights Reserved








behind and next to





















equal length)












All Rights Reserved














All Rights Reserved














All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




All Rights Reserved
















Ann Lovin




How




task



















All Rights Reserved




















booksparent_node=








connected










All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








All Rights Reserved
































0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved


























larger


















All Rights Reserved

















counting strategies




(Student 2)

Student 1





Student 2






Student 3




















All Rights Reserved














equations



















additional examples












All Rights Reserved


(+ - =)

Example



pictures of










or equation




Example



Student 1

Using a Ten-Frame






10

Student 2

Think Addition






missing

Student 3

Basic Fact






All Rights Reserved

























PLACE VALUE














All Rights Reserved







longrdquo









tallershorter





other
















All Rights Reserved


EACH CATEGORY



10)





each set









representations

GEOMETRY (G)



SPHERES)

















All Rights Reserved








behind and next to





















equal length)












All Rights Reserved














All Rights Reserved














All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




All Rights Reserved
















Ann Lovin




How




task



















All Rights Reserved




















booksparent_node=








connected










All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








All Rights Reserved
































0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved

















counting strategies




(Student 2)

Student 1





Student 2






Student 3




















All Rights Reserved














equations



















additional examples












All Rights Reserved


(+ - =)

Example



pictures of










or equation




Example



Student 1

Using a Ten-Frame






10

Student 2

Think Addition






missing

Student 3

Basic Fact






All Rights Reserved

























PLACE VALUE














All Rights Reserved







longrdquo









tallershorter





other
















All Rights Reserved


EACH CATEGORY



10)





each set









representations

GEOMETRY (G)



SPHERES)

















All Rights Reserved








behind and next to





















equal length)












All Rights Reserved














All Rights Reserved














All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




All Rights Reserved
















Ann Lovin




How




task



















All Rights Reserved




















booksparent_node=








connected










All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








All Rights Reserved
































0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved














equations



















additional examples












All Rights Reserved


(+ - =)

Example



pictures of










or equation




Example



Student 1

Using a Ten-Frame






10

Student 2

Think Addition






missing

Student 3

Basic Fact






All Rights Reserved

























PLACE VALUE














All Rights Reserved







longrdquo









tallershorter





other
















All Rights Reserved


EACH CATEGORY



10)





each set









representations

GEOMETRY (G)



SPHERES)

















All Rights Reserved








behind and next to





















equal length)












All Rights Reserved














All Rights Reserved














All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




All Rights Reserved
















Ann Lovin




How




task



















All Rights Reserved




















booksparent_node=








connected










All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








All Rights Reserved
































0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved


(+ - =)

Example



pictures of










or equation




Example



Student 1

Using a Ten-Frame






10

Student 2

Think Addition






missing

Student 3

Basic Fact






All Rights Reserved

























PLACE VALUE














All Rights Reserved







longrdquo









tallershorter





other
















All Rights Reserved


EACH CATEGORY



10)





each set









representations

GEOMETRY (G)



SPHERES)

















All Rights Reserved








behind and next to





















equal length)












All Rights Reserved














All Rights Reserved














All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




All Rights Reserved
















Ann Lovin




How




task



















All Rights Reserved




















booksparent_node=








connected










All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








All Rights Reserved
































0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved

























PLACE VALUE














All Rights Reserved







longrdquo









tallershorter





other
















All Rights Reserved


EACH CATEGORY



10)





each set









representations

GEOMETRY (G)



SPHERES)

















All Rights Reserved








behind and next to





















equal length)












All Rights Reserved














All Rights Reserved














All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




All Rights Reserved
















Ann Lovin




How




task



















All Rights Reserved




















booksparent_node=








connected










All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








All Rights Reserved
































0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


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Representing






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situation






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graphs and charts














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DIFFERENTIATION







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Make sense of

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solving them





of the problem









solution


problem and showed













solution

Attends to

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to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









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longrdquo









tallershorter





other
















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EACH CATEGORY



10)





each set









representations

GEOMETRY (G)



SPHERES)

















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behind and next to





















equal length)












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All Rights Reserved














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math achievement




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you Katherine


TRAJECTORY




Yoursquoll












come



understand










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Resources

The Coherence Map






subtraction









eportpdf



















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FLUENCY




number











developed





Fluent students




them






testspdf




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Ann Lovin




How




task



















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booksparent_node=








connected










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reasoning




the classroom



intended


problems



page 8-9)


























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quantities together








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40 41 42 43 44 45 46 47 48 49

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60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

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90 91 92 93 94 95 96 97 98 99




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Number Lines















(CCSSO2010)






















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routine


































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activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








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etc




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Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








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forth)































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3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





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Day








fifth day of school

Description












discretion

Too Low





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Too High




My Estimate






measurement





My Reasoning




















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Answer








Error



















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Games







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Journaling





progress NJ DOE



































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Reflecting

















Connections


procedures as this




Representing






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situation






place








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graphs and charts














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Make sense of

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persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









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Content



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Journaling






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July 2018 of 47

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EACH CATEGORY



10)





each set









representations

GEOMETRY (G)



SPHERES)

















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behind and next to





















equal length)












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All Rights Reserved














All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










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Resources

The Coherence Map






subtraction









eportpdf



















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FLUENCY




number











developed





Fluent students




them






testspdf




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Ann Lovin




How




task



















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booksparent_node=








connected










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All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























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quantities together








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0 1 2 3 4 5 6 7 8 9

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40 41 42 43 44 45 46 47 48 49

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60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

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(CCSSO2010)






















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routine


































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activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








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etc




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Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








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forth)































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3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





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Day








fifth day of school

Description












discretion

Too Low





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Too High




My Estimate






measurement





My Reasoning




















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Answer








Error



















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Games







based task









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Journaling





progress NJ DOE



































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Reflecting

















Connections


procedures as this




Representing






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situation






place








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graphs and charts














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All Rights Reserved















DIFFERENTIATION







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Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








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RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

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behind and next to





















equal length)












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All Rights Reserved














All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




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Ann Lovin




How




task



















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booksparent_node=








connected










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All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























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quantities together








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0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








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etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








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forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





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Day








fifth day of school

Description












discretion

Too Low





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Too High




My Estimate






measurement





My Reasoning




















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Answer








Error



















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Games







based task









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Journaling





progress NJ DOE



































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Reflecting

















Connections


procedures as this




Representing






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situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

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All Rights Reserved














All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




All Rights Reserved
















Ann Lovin




How




task



















All Rights Reserved




















booksparent_node=








connected










All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























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quantities together








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0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved














All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




All Rights Reserved
















Ann Lovin




How




task



















All Rights Reserved




















booksparent_node=








connected










All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








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0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved




math achievement




httpswwwyoucubedorg


you Katherine


TRAJECTORY




Yoursquoll












come



understand










All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




All Rights Reserved
















Ann Lovin




How




task



















All Rights Reserved




















booksparent_node=








connected










All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








All Rights Reserved
































0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved

Resources

The Coherence Map






subtraction









eportpdf



















All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




All Rights Reserved
















Ann Lovin




How




task



















All Rights Reserved




















booksparent_node=








connected










All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








All Rights Reserved
































0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved

FLUENCY




number











developed





Fluent students




them






testspdf




All Rights Reserved
















Ann Lovin




How




task



















All Rights Reserved




















booksparent_node=








connected










All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








All Rights Reserved
































0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved
















Ann Lovin




How




task



















All Rights Reserved




















booksparent_node=








connected










All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








All Rights Reserved
































0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






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situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

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booksparent_node=








connected










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All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























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quantities together








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0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








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etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








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forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved











































All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








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0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved








reasoning




the classroom



intended


problems



page 8-9)


























All Rights Reserved





































quantities together








All Rights Reserved
































0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved





































quantities together








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0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved
































0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99




All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved





Number Lines















(CCSSO2010)






















All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved







routine


































All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved




activities include


Number Talks












Harcourt






Problems





4507283amppageId=5856325




by Epson and Levi








All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved










































etc




All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved







Why or why notrdquo












Number Talks














These goals are



3 Subitizing

4 Making Tens








All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved

















forth)































All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved






3 Concrete models


5 Interaction

6 Self-correction

Estimation 180






practice


length or capacity



computation





2 Read the question


4 Make an estimate



7 See the answer





All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved








Day








fifth day of school

Description












discretion

Too Low





All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved




Too High




My Estimate






measurement





My Reasoning




















All Rights Reserved
















Answer








Error



















All Rights Reserved





























Games







based task









All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














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All Rights Reserved















DIFFERENTIATION







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Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









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Journaling






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July 2018 of 47

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Answer








Error



















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Games







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Journaling





progress NJ DOE



































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Reflecting

















Connections


procedures as this




Representing






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situation






place








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graphs and charts














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DIFFERENTIATION







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Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









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TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

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Games







based task









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Journaling





progress NJ DOE



































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Reflecting

















Connections


procedures as this




Representing






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situation






place








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graphs and charts














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All Rights Reserved















DIFFERENTIATION







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Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved

Journaling





progress NJ DOE



































All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






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situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved















Reflecting

















Connections


procedures as this




Representing






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situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved




situation






place








All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved





























graphs and charts














All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved


















All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved















DIFFERENTIATION







All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea



July 2018 of 47

All Rights Reserved



Make sense of

problems and

persevere in

solving them





of the problem









solution


problem and showed













solution

Attends to

precision



to communicate

mathematically













solutions






solutions

Reasoning and

explaining





or words









andor words





Models and use

of tools













their response






was efficient

Seeing

structure and

generalizing













life









All Rights Reserved



























TECHNOLOGY LINKS








All Rights Reserved

RESOURCES CONSULTED

Content



NZ Maths

httpnzmathsconz





Journaling






Tea