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KINDERGARTEN MATHEMATICS

CURRICULUM GUIDE

Loudoun County Public Schools 2014-2015

Overview, Scope and Sequence, Unit Summaries, The First 20 Days Classroom Routines, Curriculum Framework, Learning Progressions

(additional attachments: Intervention Ideas, NCSM Great Tasks SOL alignment, Math Literature Connections)

INTRODUCTION TO LOUDOUN COUNTY’S MATHEMATICS CURRICULUM GUIDE

This CURRICULUM GUIDE is a merger of the Virginia Standards of Learning (SOL) and the Mathematics Achievement Standards for Loudoun County Public Schools. The CURRICULUM GUIDE includes

excerpts from documents published by the Virginia Department of Education. Other statements, such as suggestions on the incorporation of technology and essential questions, represent the professional

consensus of Loudoun’s teachers concerning the implementation of these standards. This CURRICULUM GUIDE is the lead document for planning, assessment, and curriculum work.

NAVIGATING THE LCPS MATHEMATICS CURRICULUM GUIDE

The Curriculum Guide is created to link different components of the guide to related information from the Virginia Department of Education, resources created by Loudoun County Public Schools, as well as vetted outside resources.

To navigate the curriculum guide, click on the hyperlink (if in MSWord, hold the [ctrl] button and left click with the mouse on the hyperlink). It will direct you to either another resource within the curriculum guide, or to a website resource.

If you’re directed to a resource within the curriculum guide, to “go back,” hold the [alt] key and press the left arrow button. Mathematics Internet Safety Procedures 1. Teachers should review all Internet sites and links prior to using it in the classroom. During this review, teachers need to ensure the appropriateness of the content on the site, checking for broken links, and paying attention to any inappropriate pop-ups or solicitation of information. 2. Teachers should circulate throughout the classroom while students are on the internet checking to make sure the students are on the appropriate site and are not minimizing other inappropriate sites. 3. Teachers should periodically check and update any web addresses that they have on their LCPS web pages. 4. Teachers should assure that the use of websites correlate with the objectives of the lesson and provide students with the appropriate challenge.

LCPS Grade K Mathematics Curriculum Guide 2014-2015

Dates of LCPS Quarters

2014 – 2015 School Calendar

Starts Ends

First Quarter September 2 October 31

Second Quarter November 5 January 23

Third Quarter January 27 March 27

Fourth Quarter April 7 June 16

Quarter 1 Quarter 2 Quarter 3 Quarter 4

AUGUST

S M T W R F S

1 2

3 4 5 6 7 8 9

10 11 12 TI TI NH 16

17 NH NH SD SD P 23

24 CS CS CS P P 30

31

SEPTEMBER

S M T W R F S

H F 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

OCTOBER

S M T W R F S

1 2 3 4

5 6 7 8 9 10 11

12 H 14 15 16 17 18

19 20 21 22 23 24 25

26 27 28 29 30 31

NOVEMBER

S M T W R F S

1

2 P P 5 6 7 8

9 10 11 12 13 14 15

16 17 18 19 20 21 22

23 24 25 H H H 29

30

DECEMBER

S M T W R F S

1 2 3 4 5 6

7 8 9 10 11 12 13

14 15 16 17 18 19 20

21 H H H H H 27

28 H H H

JANUARY

S M T W R F S

H H 3

4 5 6 7 8 9 10

11 12 13 14 15 16 17

18 H 20 21 22 23 24

25 MP 27 28 29 30 31

JANUARY

S M T W R F S

H H 3

4 5 6 7 8 9 10

11 12 13 14 15 16 17

18 H 20 21 22 23 24

25 MP 27 28 29 30 31

FEBRUARY

S M T W R F S

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 H 17 18 19 20 21

22 23 24 25 26 27 28

MARCH

S M T W R F S

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 H H

APRIL

S M T W R F S

H H H 4

5 P 7 8 9 10 11

APRIL

S M T W R F S

H H H 4

5 P 7 8 9 10 11

12 13 14 15 16 17 18

19 20 21 22 23 24 25

26 27 28 29 30

MAY

S M T W R F S

1 2

3 4 5 6 7 8 9

10 11 12 13 14 15 16

17 18 19 20 21 22 23

24 H 26 27 28 29 30

31

JUNE

S M T W R F S

1 2 3 4 5 6

7 8 9 10 11 12 13

14 15 L P P 19 20

21 22 23 24 25 26 27

28 29 30

P = Teacher Workday/Planning Day H = Holiday/ No School F = First Day of School TI = Teacher Institute for new professionals NH = New Hire Workday SD = In School Staff Development days CS = County Wide Staff Development Days


Grade K Nine Weeks Overview

1st Quarter 2nd Quarter 3rd Quarter 4th Quarter

Unit 1-Classroom Routines: “The First 20 Days Classroom Routines” NUMBER TALKS K.3 Ordinal Position K.4 Count Forward & Backward K.8 Msmt Instruments K.9 Time K.13 Count/Tally Data K.14 Display Data K.15 Sort & Classify Unit 2-Counting K.4a Count to 100 K.2 Count Sets, Write & Identify Numerals K.13 Count/Tally Data K.4b One More/One Less K.16 Patterns Unit 3-Comparing Sets K.1 One-to-One Correspondence, More, Fewer, Same K.3 Ordinal Position K.13 Count/Tally Data K.14 Display Data

Unit 1-Classroom Routines: NUMBER TALKS K.3 Ordinal Position K.4 Count Forward & Backward K.8 Msmt Instruments K.9 Time K.13 Count/Tally Data K.14 Display Data K.15 Sort & Classify Unit 4-Geometry & Sorting K.15 Sort and Classify K.7 Recognize Coins & Value K.11 Identify & Compare Plane Geometric Figures Unit 5-Shapes in Space K.12 Location of Objects and Plane Geometric Figures K.16 Repeating Patterns

Unit 1-Classroom Routines: NUMBER TALKS K.3 Ordinal Position K.4 Count Forward & Backward K.7 Money K.8 Msmt Instruments K.9 Time K.13 Count/Tally Data K.14 Display Data K.15 Sort & Classify Unit 6-Geometry & Fractions K.11 Identify & Compare Plane Geometric Figures K.5 Fractions K.14 Display Data Unit 7-Measuring My World K.8 Measurement Instruments K.10 Non-standard Msmt K.9 Time Unit 8-Skip Counting & Money K.4c Count by 5’s and 10’s to 100 K.7 Recognize Coins & Value K.16 Repeating Patterns

Unit 1-Classroom Routines: NUMBER TALKS K.3 Ordinal Position K.4 Count Forward & Backward K.7 Money K.8 Msmt Instruments K.9 Time K.13 Count/Tally Data K.14 Display Data K.15 Sort & Classify Unit 8 (cont’d)-Skip Counting & Money K.4c Counting by 5’s and 10’s to 100 K.7 Recognize Coins and Value K.16 Repeating Patterns Unit 9-Combining & Separating K.4b One More/One Less K.6 Model Addition & Subtraction K.7 Recognize Coins & Value

43 days 44 days 43 days 50 days


Kindergarten Scope & Sequence Quarter 1: 43 days

Days Unit Standard Content Strand Topic

All

year

Unit 1: Classroom

Routines

“The First 20 Days Classroom Routines”

and NUMBER TALKS, Ordinal Numbers, Counting, Measurement, Time, Data, Sorting, Money

25

Unit 2: Counting

K.4a Number and

Number Sense

Counting to 100

K.2 Number and

Number Sense

Count Sets, Write, & Identify Numerals

K.13 Probability and

Statistics

Count/Tally Data

K.4b Number and

Number Sense

One more/ One Less

K.16 Patterns, Functions,

Algebra

Patterns

15

Unit 3: Comparing

Sets

K.1 Number and

Number Sense

One-to-one Correspondence, More, Fewer,

Same

K.3 Number and

Number Sense

Ordinal Position


Statistics

Count/Tally Data


Statistics

Display Data

3 Assessment, Review, and Intervention


Quarter 2: 44 days

Days Unit Standard Content Strand Topic All year Unit 1: Classroom Routines NUMBER TALKS, Ordinal Numbers, Counting, Measurement, Time, Data, Sorting, Money

21

Unit 4: Geometry & Sorting

K.15 Patterns, Functions, & Algebra

Sort and Classify

K.7 Measurement Recognize Coins & Value

K.11 Geometry Identify & Compare Plane Geometric Figures

17

Unit 5: Shapes in Space

K.12 Geometry Location of Objects and Plane Geometric Figures


Repeating Patterns



Quarter 3: 43 days


15

Unit 6: Geometry & Fractions

K.11 Geometry Identify & Compare Plane Geometric Figures

K.5 Number and Number Sense Fractions

K.14 Probability and Statistics Display Data

15

Unit 7: Measuring My World

K.8 Measurement Measurement Instruments

K.10 Measurement Non-standard Measurement

K.9 Measurement Time

10

Unit 8: Skip Counting & Money

K.4c Number and Number Sense Counting by 5’s and 10’s to 100


K.16 Patterns, Functions, & Algebra Repeating Patterns



Quarter 4: 50 days


10

Unit 8 (cont’d): Skip Counting & Money

K.4c Number and Number Sense

Counting by 5’s and 10’s to 100



Repeating Patterns

20

Unit 9: Combining & Separating

K.4b Number and Number Sense

One More/One Less

K.6 Computation & Estimation

Model Addition & Subtraction



LCPS MATH Unit Summary Kindergarten 2014-15

Unit: 1 Quarters 1-4

Classroom Routines

VDOE Standards of Learning:

1st quarter: The First 20 Days Classroom Routines K.4 The student will

a) count forward to 100 and backward from 10; b) identify one more than a number and one less than a number; and c) count by fives and tens to 100.

K.3 The student, given an ordered set of ten objects and/or pictures, will indicate the ordinal position of each object, first through tenth, and the ordered position of each object.

K.7 The student will recognize a penny, nickel, dime, and quarter and will determine the value of a collection of pennies and/or nickels whose total value is 10 cents or less (beginning 3rd quarter).

K.8 The student will identify the instruments used to measure length (ruler), weight (scale), time (clock: digital and analog; calendar: day, month, and season), and temperature (thermometer).

K.9 The student will tell time to the hour, using analog and digital clocks.

K.13 The student will gather data by counting and tallying.

K.14 The student will display gathered data in object graphs, picture graphs, and tables, and will answer questions related to the data.

K.15 The student will sort and classify objects according to attributes.

VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations

Learning Targets:

I can count forward to 100 by ones, fives, and tens and I can count backward from 10.

I can identify the ordinal positions for each object in a set of 10 objects that are in order (i.e. from left–to–right, right–to–left, top–to–bottom, and bottom–to–top).

Recognizes coins, and determines value of several coins.

I can identify one more than a number and one less than a number and show the relationship using objects.

I can identify the patterns of counting by ones, fives, and tens using different models (hundreds chart, number line, etc.).

I can identify instruments used to measure length, weight, time, and temperature.

I can tell time to the hour on an analog and digital clock and relate the time to daily routines.

I can collect answers to a question, keep track of the answers by using tally marks, and organize the answers in categories.

I can analyze data I have displayed in graphs and tables.

I can sort and classify a set of objects in at least two different ways and explain my reasoning.


Big Ideas Essential Questions

Taking daily attendance and regular use of a counting jar gives students repeated practice of counting and helps make the connection of the number names and the quantities they represent.

Use temperature data for seasonal changes, patterns, and graphing.

Daily practice of counting aloud and working with

numbers on the hundreds chart and other forms of

representing numerals (number line, place value

straws, graphs, tallies).

Real world application of mathematics concepts.

What does a calendar measure?

How does calendar measure time?

Yesterday was Tuesday. What day is today? What day is tomorrow?

How many days are in this month?

What time will we be going to library? How will that look on an analog and digital clock?

Why do we collect data?

What are some strategies used to gather data?

Say the number name sequence to 100.

Show one more than a number and one less than a number.

How can we show an amount in tallies?

How can we show data in a graph? With pictures?

How can we sort objects in two different ways?

While we are in line for lunch, please count off using your ordinal numbers.

What patterns can we find on the hundreds chart? How do those patterns relate to skip counting?

Prerequisite Skills Vocabulary

VDOE Vertical Alignment document K-3

VDOE Vocabulary Word Wall Cards forward backward sort ones fives classify tens hundreds graph ordinal number pattern table more less tally hundreds chart number line data time temperature month clock thermometer day digital analog season calendar

Achievement Criteria How to Assess Achievement

“The content of the mathematics standards is intended to support the following five process goals for students:

• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and

interpret practical situations.” -2009 Mathematics Standards of Learning

Sample Math Tasks are available in VISION: Search: LCPS-Math: K-12 Math Tasks

Enrollment key: mathisfun http://loudounvision.net/

NCSM Great Tasks (available in all LCPS Elementary Schools—click link)

Click here for a brief audio powerpoint slide

with more information about the Process Goals

http://www.doe.virginia.gov/instruction/mathematics/professional_development/institutes/2011/opening_session/2009sol_vertical_articulation_by_topic_k-3_9-15-11.pdf

http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/math_vocab_cards_k.pdf

http://loudounvision.net/

https://www.dropbox.com/s/ve7sxlqo2ps6cyj/Process%20Goals%20audio%20slide.pptx



Classroom Routines

1st quarter: The First 20 Days Classroom Routines NUMBER TALKS: Example: http://www.mathsolutions.com/videopage/videos/Final/Guess_My_Number.swf Number Talks sample flipcharts available on the Elementary Math Resources VISION site INVESTIGATIONS: Mathematical Thinking in Kindergarten Investigation 1: Attendance Investigation 3: Calendar Investigation 2: Counting Jars Investigation 4: Today’s Question

Utilize hands-on objects and visual (promethean) activities.

Have students take turns manipulating different calendar components.

Utilize student groupings to involve all children in discussions and problem solving.

Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)

http://www.mathsolutions.com/videopage/videos/Final/Guess_My_Number.swf



Unit: 2 Quarter 1

Counting


K.4a The student will a) count forward to 100 and backward from 10;

K.2 The student, given a set containing 15 or fewer concrete objects, will a) tell how many are in the set by counting the number of objects orally; b) write the numeral to tell how many are in the set; and c) select the corresponding numeral from a given set of numerals.

Selecting on a number line

Selecting on a number chart


K.4b The student will b) identify one more than a number and one less than a number;

K.16 The student will identify, describe, and extend repeating patterns.


Learning Targets:

I can count forward to 100 by ones, fives, and tens and I can count backward from 10.

I can identify the number of objects in a set by counting the objects orally, selecting the numeral, and writing the numeral that matches the number of objects in the set. I can create a set of objects that matches a number from 0 through 15.



I can compare the similarities and differences between patterns.


Counting forward to 100 and backward from 10.

Counting aloud the number of objects in a set.

Matching a numeral to represent the amount in a set.

Writing a numeral to represent the amount in a set.

Show understanding of tallying and counting tallies.

Demonstrate one more and one less than a number

Recognize patterns in counting with number chart.

How can we count the quantity of items in a group? How can we count the quantity in another way?

How can you represent the quantity with a numeral?

How can you identify the quantity on a hundreds chart?

How can you identify the quantity on a number line?



Why do you think someone might use tally marks to record data as it is collected?”

Prove which of two sets has more, fewer, or the same objects as the other set.

Prove one more than a number and one less than a number.

What is a pattern?




Introduction to counting in Classroom Routines

Introduction to tallying in Classroom Routines

Introduction to one more and one less than a number

in Classroom Routines

VDOE Vocabulary Word Wall Cards number line number chart tally forward backward more less data pattern numeral set empty set number fewer same numerals 0-15 number words 0-15





Click here for a brief audio powerpoint slide with more information about the Process Goals

Sample Math Tasks are available in VISION:

Search: LCPS-Math: K-12 Math Tasks

Enrollment key: mathisfun



Differentiation Resources

Lead students in creating a picture chart of classroom items to count and record. The chart might include items such as desks, chairs, flags, computers, trash cans, and pencil sharpeners.

Use a highlighter to provide a guide for students to trace tally marks.

Use coffee stirrers or ice cream sticks to make physical models of tally marks.

ELL Model Performance Indicators

(click to link)

Investigations: Collecting, Counting, and Measuring Investigation 1: Counting Books Investigation 2: Taking Inventory Investigation 3: Comparing Towers Patterns, Trains, and Hopscotch Paths Investigation 2: What Comes Next? Counting Ourselves and Others Investigation 1: How Many Are We? ESS Lessons: K.2 - Counting Centers K.2 - Counting 15 Dots K.13 - Using Tally Marks BrainPOP Jr.: Tally Marks and Bar Graphs Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)






http://www.doe.virginia.gov/testing/sol/scope_sequence/mathematics_2009/index.php

http://www.doe.virginia.gov/testing/solsearch/sol/math/K/mess_k-2a.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/K/mess_k-2abc.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/K/mess_k-13.pdf

http://www.brainpopjr.com/math/data/tallychartsandbargraphs/



Unit: 3 Quarter 1

Comparing Sets


K.1 The student, given two sets, each containing 10 or fewer concrete objects, will identify and describe one set as having more, fewer, or the same number of members as the other set, using the concept of one-to-one correspondence.

K.3 The student, given an ordered set of ten objects and/or pictures, will indicate the ordinal position of each object, first through tenth, and the ordered position of each object. * In context of collecting data.




Learning Targets:

I can compare two sets of objects and describe a set as having more, fewer, or the same quantity of objects. I can create a set of objects which has more, fewer, or the same quantity as a given set.





Compare sets as having more, fewer, or the same number of items.

Create a set of objects with more, fewer, or the same number of items as another set.

Identify the ordinal position (first through tenth) of objects in a set.

Identify the ordinal position (first through tenth) from most to least of a depicted set of data (ex. graph, groups of items)

Demonstrate understanding of the concept of tallies representing the amount in a set.

Create tables or graphs with objects or pictures to display data collected.

Answer questions or make observations aloud regarding data displayed in graphs or tables.

How can the quantity of two sets of objects be compared?

What strategies can be used to sort and sequence objects?

How can we display gathered data?



What is an ordinal position?

Give examples of how ordinal numbers are used in real life situations.

Compare and contrast the counting sequence and ordinal positions.

Prove which of two sets has more, fewer, or the same objects as the other set.

Have students make a train with 10 cubes. What color is the sixth cube? What is the position of the green cube?

What is the difference between five and fifth?

How do you know when both groups of counters are the same?

If the arrangement of the counters in two groups is different, can the number of counters be the same?




Introduction to counting in Classroom Routines

Introduction to tallying in Classroom Routines

Introduction to more, less, equal to in Classroom Routines

Introduction to data collection and graphs in Classroom Routines

VDOE Vocabulary Word Wall Cards set more fewer same ordinal position cardinal number first second third fourth fifth sixth seventh eighth ninth tenth tally mark data graph table less equal last compare picture graph












Divide students into groups, and ask each group to observe and graph such things as hair colors, types of shoes, colors of shirts, numbers of brothers and sisters, etc. This could also be done in cooperation with another class in the school, with the classes placing themselves into human graphs by class and transferring the information to a pictorial or object graph for comparison purposes.

Lead students in using the computer to type and print positional words to use for labeling items in the classroom.

As a large group, have students place positional words to label areas within the classroom. For example, have students place the word top to label the top of the door, the word middle to label the middle of the door, and the word bottom to label the bottom of the door.


(click to link)

Investigations: Collecting, Counting, and Measuring Investigation 1: Counting Books Investigation 2: Taking Inventory Investigation 3: Comparing Towers Investigation 5: Least to Most Counting Ourselves and Others Investigation 2: What Did You Eat for Lunch? ESS Lessons: K.1 - More, Fewer, or the Same? K.3 - Counting on the Bus K.14 - My Favorite Things BrainPOP Jr.: Making Equal Groups Pictographs Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)










http://www.brainpopjr.com/math/multiplicationanddivision/makingequalgroups/

http://www.brainpopjr.com/math/data/pictographs/



Unit: 4 Quarter 2

Geometry & Sorting



K.7 The student will recognize a penny, nickel, dime, and quarter and will determine the value of a collection of pennies and/or nickels whose total value is 10 cents or less.

K.11 The student will a) identify, describe, and trace plane geometric figures (circle, triangle,

square, and rectangle); and b) compare the size (larger, smaller) and shape of plane geometric

figures (circle, triangle, square, and rectangle).


Learning Targets:


I can identify and describe a penny, nickel, dime, and quarter and determine the value of a collection of coins (10 cents or less) and equivalent amounts (a nickel is the same as 5 pennies).

I can name geometric shapes and tell how they are different.

I can tell (compare) which shape is larger and which is smaller.


Sort and classify objects in multiple ways.

Sort coins by characteristics and label the groupings.

Sort shapes by characteristics and identify differences.

How can objects be sorted and classified according to attributes?

Use the coin names to label various groups of sorted coins.

Compare and contrast a variety of sorts for a set of objects.

Identify and describe plane geometric figures.

Compare and contrast the size and shape of plane geometric figures.



VDOE Vocabulary Word Wall Cards sort classify coin penny nickel dime quarter larger smaller circle triangle square rectangle










Search: LCPS-Math: K-12 Math Tasks Enrollment key: mathisfun


NCSM Great Tasks

(available in all LCPS Elementary Schools—click link)


Have students use a Venn diagram to sort objects.

Have students use a drawing program on the computer to practice drawing geometric figures. Allow them to print their drawings.

Use larger objects for students who have trouble handling small ones.

Give students a way of sorting objects, then ask them to come up with another way.

Have students share different ways of sorting.

ELL Model Performance Indicators (click to link)

Investigations: Making Shapes and Building Blocks Investigation 1: 2-D Shapes Around Us Investigation 2: Exploring Shapes with the Computer ESS Lessons: K.11 - Geometric Figures in Our Classroom K.15 - The Button Box BrainPOP Jr.: Plane Shapes Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)





http://www.doe.virginia.gov/testing/solsearch/sol/math/K/mess_k-11ab.pdf


http://www.brainpopjr.com/math/geometry/planeshapes/



Unit: 5 Quarter 2

Shapes in Space


K.12 The student will describe the location of one object relative to another (above, below, next to) and identify representations of plane geometric figures (circle, triangle, square, and rectangle) regardless of their positions and orientations in space.

(In contexts with Art, Social Science, Language Arts, and patterns)



Learning Targets:

I can identify a triangle, circle, square, and rectangle and describe if one of them is above or below or next to another one.



Describe the location of one object relative to another.

Identify shapes regardless of position.

Utilize basic maps to encourage positional word use.

Compare patterns among shapes and positions.

Utilize Art, Social Science, and Language Arts lessons to develop vocabulary use of positional words and create a better understanding of real world use.

Identify and describe the location of one object relative to another.

Prove orientation does not change the identity of plane geometric figures.

What is a pattern?

Demonstrate and justify a pattern.

Compare and contrast student created pattern.



Introduction to patterns in Classroom Routines

Shape identification and classification in Geometry and Shapes Unit

VDOE Vocabulary Word Wall Cards shape square rectangle circle triangle trace compare alike/same different smaller larger describe above below next to pattern core repeating predict describe















As a large group, have students place positional words to label areas within the classroom. For example, have students place the word top to label the top of the door, the word middle to label the middle of the door, and the word bottom to label the bottom of the door.

Work with students to create an “Orientation Book,” as follows. Have students trace a rectangle on a left-hand page of their books. Then, have them rotate the rectangle a little and trace it on the opposing right-hand page. Direct them to turn the page and repeat the process, using another geometric figure. Continue until all figures have been traced.

Have students work in pairs to create shapes on a geoboard. Have student pairs explain how they created their shapes and how they know what each shape is.

Give students a wide variety of materials (e.g., buttons, toy cars, socks, seeds, noodles, crayons, wooden blocks), and ask them to use the materials to create different patterns. Encourage students to create patterns other than A-B-A-B.


Investigations: Making Shapes and Building Blocks Investigation 1: 2-D Shapes Around Us Investigation 2: Exploring Shapes with the Computer Investigation 3: Looking at 3D Shapes ESS Lessons: K.12 – Geometric Games K.16 – Repeating Patterns BrainPop Jr.: Congruent and Similar Shapes Patterns Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)







http://www.brainpopjr.com/math/geometry/congruentandsimilarshapes/

http://www.brainpopjr.com/math/geometry/patterns/



Unit: 6 Quarter 3

Geometry & Fractions


K.11 The student will a) identify, describe, and trace plane geometric figures (circle, triangle,

square, and rectangle); and b) compare the size (larger, smaller) and shape of plane geometric

figures (circle, triangle, square, and rectangle).

K.5 The student will identify the parts of a set and/or region that represent fractions for halves and fourths.



Learning Targets:

I can name geometric shapes and tell how they are different.

I can tell (compare) which shape is larger and which is smaller.

I can show (represent) halves and fourths as parts of sets and parts of regions.



Utilize various shapes within other shapes (pattern blocks) to depict parts of a whole.

Discuss fractions in sets utilizing graphs and tables.

Area models (fraction circles, fraction squares), Set

models (two-color counters or any discrete objects), and Linear models (number lines, rope, etc.) should all be introduced as representations for fractions.

Identify and describe plane geometric figures.

Compare and contrast the size and shape of plane geometric figures.

What does a fraction represent?

How can we display gathered data?

Using an example of the region/area model and the set model for fractions, demonstrate an unfair sharing situation among four students. “Does each student have a fourth? How do you know?

What does it mean to be “fair” when working with fractions?



Introduction to collecting data and graphs in Classroom Routines

Shape identification and classification in Geometry and Shapes Unit

VDOE Vocabulary Word Wall Cards

larger smaller circle rectangle triangle square set table region fraction halves fourths data graph












NCSM Great Tasks



Extend sharing problems to involve more than one whole. For example, three students sharing two cookies.

Give students opportunities to work with many different wholes and sharing situations. Always identify the whole, or show students a fraction and ask them to describe what the whole would be.

Incorporate fractions into everyday classroom tasks. For example, choose a group of students to represent halves or fourths based on clothing items. During graphing, use fraction vocabulary when possible to describe data. For example, “Half of the class has pets. Our whole class is made up of 24 children.” During snack time, discuss whether sharing is or is not “fair”—whether students get equal amounts.


Investigations: Making Shapes and Building Blocks Investigation 4: Making Shapes and Building Blocks

ESS Lessons: K.5 - Sharing Snacks BrainPOP Jr.: Basic Parts of a Whole Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)






http://www.brainpopjr.com/math/fractions/basicpartsofawhole/



Unit: 7 Quarter 3

Measuring My World


K.8 The student will identify the instruments used to measure length (ruler), weight (scale), time (clock: digital and analog; calendar: day, month, and season), and temperature (thermometer).

K.10 The student will compare two objects or events, using direct comparisons or nonstandard units of measure, according to one or more of the following attributes: length (shorter, longer), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder). Examples of nonstandard units include foot length, hand span, new pencil, paper clip, and block.



Learning Targets:


I can compare and measure objects using foot length, hand span, new pencil, paper clip, and/or block.



Identify different uses of measurement instruments.

Compare different instruments and how to distinguish between when to use the correct instrument.

Utilize nonstandard units and provide opportunities to choose the appropriate nonstandard unit depending on the item being measured.

Show a digital clock and an analog clock. “What is the same about these two clocks? What is different about these two clocks?”

What tool or tools would you use to measure the length of your foot? What tool or tools would you use to measure the length of the cafeteria?”

Display two different objects. “Which of these objects is heavier? How do you know?”

“When do you weigh things in your everyday life? What kinds of things do you weigh?”

What does a calendar measure?

How does calendar measure time?



Introduction to calendar, clock, and thermometer in Classroom Routines

VDOE Vocabulary Word Wall Cards clock ruler thermometer scale weight digital analog calendar day season month temperature length shorter longer height taller heavier lighter hotter colder measure hour minute hands o’clock balance















Guide students in creating a daily classroom schedule that pairs a symbol representing a daily classroom activity with a visual of a clock showing the time when the activity takes place.

Lead the class in singing songs that develop vocabulary for associations with different times of day and require physical modeling of the movement of the clock hands.

Use the body to model or represent “long” by spreading arms wide and “short” by using fingers. For example, ask, “Show me what ‘long’ looks like.” or “Show me how long an elephant’s trunk is.” “Show me what ‘short’ looks like.” or “Show me how short a worm is.”

Have students draw the classroom objects they measured and place their drawings on a class chart divided into columns by lengths: Longer and Shorter.

Lead students in creating minibooks with patterned sentences following instruction in the concepts. The patterned sentences could be placed one per page and might read as follows: “The pencil is longer than the eraser.” “The bookshelf is shorter than the door.” “The bike is shorter than the bus.” Guide students in illustrating their minibooks to show shorter and longer.


(click to link)

ESS Lessons: K.9 - What Time Is It? K.10 - How Long Is It? K.10 – How Tall Are You? K.10 - How Heavy Is It? K.10 – Hot or Cold? BrianPOP Jr.: Time to the Hour Ounces Pounds and Tons Inches and Feet Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)






http://www.doe.virginia.gov/testing/solsearch/sol/math/K/mess_k-10_1.pdf




http://www.brainpopjr.com/math/time/timetothehour/

http://www.brainpopjr.com/math/measurement/ouncespoundsandtons/

http://www.brainpopjr.com/math/measurement/inchesandfeet/



Unit: 8 Quarters 3-4

Skip Counting & Money


K.4 The student will c) count by fives and tens to 100.




Learning Targets:

I can identify the patterns of counting by ones, fives, and tens using different models (hundreds chart, number line, etc.).




Skip counting can be used to count different sets of object.

Skip counting numbers is creating number patterns.

Counting coins utilizes skip counting.

Describe patterns in skip counting and use those patterns to predict the next number or numbers in the skip counting sequence.

What is a pattern?

What patterns can we make when counting?

Demonstrate and justify a pattern.

Compare and contrast student created patterns.

Demonstrate strategies for counting the quantity of items in a group then represent it with a numeral.

Prove one more than a number and one less than a number.

How does skip counting help us count coins?



Introduction to skip counting in Classroom Routines

Coin identification and sorting in Geometry and Sorting Unit

Patterns in Shapes in Space Unit

VDOE Vocabulary Word Wall Cards

count skip counting ones fives tens one more than one less than patterns penny nickel dime quarter cents value one cent five cents ten cents twenty-five cents












NCSM Great Tasks



Use manipulatives for counting experiences that include a variety of textures, e.g., foam shapes, plastic straws, ceramic tiles, plastic and metal bottle caps. Use grid paper to assist students in lining up objects into vertical columns.

Provide sorting charts (T-table or chart) to sort coins by coin name and by value.

Create a large T-table or chart to sort large images of coins by coin name and by value.


Investigations: Patterns, Trains, and Hopscotch Paths Investigation 2: What Comes Next? Investigation 3: Hopscotch Paths Investigation 4: Pattern Borders ESS Lessons: K.4 - Hundreds Board Math K.7 - Money Math BrainPOP Jr.: Counting Coins Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)





http://www.doe.virginia.gov/testing/solsearch/sol/math/K/mess_k-4abc.pdf


http://www.brainpopjr.com/math/money/countingcoins/preview.weml



Unit: 9 Quarter 4

Combining & Separating


K.4 The student will b) identify one more than a number and one less than a number; and

K.6 The student will model adding and subtracting whole numbers, using up to 10 concrete objects.



Learning Targets:


I can use manipulatives to model and describe addition and subtraction.



Recognize the relationship of one more than and one less than a number using objects (i.e., five and one more is six; and one less than ten is nine).

Understand that addition means putting things together and that subtraction is the inverse of addition and means to separate things out.

Understand how different groups of coins can equal the same amount.

Demonstrate and justify strategies for a solution within story problem.

What strategies do you use to find the sum of two numbers?

What strategies do you use to find the difference between two numbers?

How can you show the same amount of money using different coins?



Introduction to one more and one less in Classsroom Routines

Coin identification and sorting in Geometry and Sorting Unit

Coin values and counting in Skip Counting & Money Unit

VDOE Vocabulary Word Wall Cards penny nickel dime quarter cents value one cent five cents ten cents twenty-five cents add add on adding sum subtract difference equal plus minus total more fewer same












NCSM Great Tasks



Draw pictures to ‘write’ your own number story. Use your pictures to show both the words and the numbers in your story.

Have students act out number stories provide by teacher or created by students.


Investigations: How Many In All? Investigation 2: Six Tiles Investigation 3: Story Problems Investigation 4: Blue and Red Crayons ESS Lessons: K.6 - Math Stories K.7 - Money Math BrainPOP Jr.: Basic Adding Basic Subtraction Equivalent Coins Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)







http://www.brainpopjr.com/math/additionandsubtraction/basicadding/preview.weml

http://www.brainpopjr.com/math/additionandsubtraction/basicsubtraction/preview.weml

http://www.brainpopjr.com/math/money/equivalentcoins/preview.weml


The First 20 Days Classroom Routines: Establishing a Mathematics Classroom Community

Overview: The mini lessons included in this guide are intended to be used in conjunction with your first unit of study. The daily 10-15 minute lessons will help

you set routines, develop references for students, establish protocols, and create norms for an engaging math classroom community. The lessons may be

modified or extended based on students’ need or grade level. The routines, protocols, and experiences should be revisited throughout the school year in order

to maintain a productive math community.

Goals:

Build a classroom community of learners

Support students’ understanding of math content by establishing guidelines related to the VA process goals (problem solving, communication,

reasoning, connections, and representation).

Develop routines that will help students become reflective problem solvers and engage in a rigorous study of mathematics.

Background: This guide is based on a document developed by Austin Independent School District. Their document was modeled after the First 20 Days of Independent Reading by Fountas & Pinnell. Many of the suggested routines will also connect to other effective protocols used in Being a Writer and Responsive Classroom. This guide was adapted from a resource created by Arlington Public Schools.

Mini Lesson Key Ideas Essential Understandings

Anchor Charts/Supports Resources Teacher Notes

Day 1 Management: Classroom Procedures/ Community Guidelines

Establish routines, procedures, and student expectations for daily math lessons.

Students develop criteria for a “Being a Mathematician” chart that will be posted in the classroom. Students understand that the information posted in the classroom will be a valuable reference for them.

Develop a “Being a Mathematician” anchor chart to which students can refer. The chart should have less than 6 criteria to be effective and manageable. Example behaviors:

• Remain on task • Participate/stay engaged • Listen actively • Discuss math ideas • Treat materials with respect • Always try your best

*Brainstorm the list with the students

Chart paper, Markers Have a discussion about routines and procedures with the students. This is a good time to have students talk about expectations for engaging in classroom discussions and completing their work.

Day 2 Management: Mathematical Tools VA Process Goals: Problem Solving & Representation

Mathematicians can utilize math tools to help them solve problems.

Tools are a valuable resource for mathematicians. Students are aware of the tools that are available in the classroom.

Brainstorm a list of mathematical tools and discuss how they can be used and stored. Add additional information to the “Being a Mathematician” chart about placing materials in their proper storage containers and location after use. Examples: Base ten blocks Cubes Number cubes Hundreds chart Two-colored counters

Emphasize how and why materials are to be used during math instruction.



Day 3 Math Talk/ Classroom Discourse VA Process Goal: Communication

Mathematicians communicate orally about their work. Norms for classroom discussions need to be established in order to engage in respectful discourse and have equitable participation.

In order to communicate and learn from each other, mathematicians must listen to, as well as speak, with their classmates. We will function as a respectful classroom community in order to learn.

Create an anchor chart for “Norms for a Math Discussion” or “Rights and Obligations During Discussions” Example norms include: Speak respectfully Take turns (equitable participation) Give others time to think Eyes on the speaker

Norms may be similar to those you establish in other content areas. These established routines should be revisited all year long.

Day 4 Math Talk/ Classroom Discourse VA Process Goal: Communication

Mathematicians communicate orally about their work. Different talk moves can be used while facilitating classroom discussions. Students learn content through the process goal of communication.

Math can be more rigorous when you communicate with others. There are sentence starters that can be used to help one engage in discussions.

Post and discuss Talk Moves to encourage students to share their thinking. Identify 1 or 2 moves to begin the year with (based on your first units of study).

- Talk bubbles or Talk move sticks

Introduce talk moves

- Turn and Talk (also called partner talk, or think-pair-share)

- Say More: You ask an individual student to expand on what he or she said

- Revoicing (also called verify and clarify)

- Repeat - Agree/Disagree and why?

Encourage students to speak in complete thoughts when communicating orally. The utilization and introduction of talk moves is a continuous process. This day is one way to introduce moves, but it should be ongoing.



Day 5 Collaboration (Game) VA Process Goal: Communication

Mathematicians can work collaboratively while playing a game in order to learn important math concepts.

Students understand that they can work with others to explore math content. Cooperation is a key component of working with a partner.

Establish rules for working with a partner while playing a math game. Try the “Say it to Play it” guideline: When playing a game in partners, the students must state their move and/or provide an explanation for why they are playing that move (Ex: In the game Compare, a student may say “9 is greater than 5, so I win the cards”).

Post rules and directions for engaging in a game with a partner. Consider utilizing a fact fluency game for this mini lesson.

Rules and clear directions will help make group work successful. After the mini lesson, have students practice a game during the math lesson for the day.

Day 6 Collaborative/ Independent Work (Rotations) VA Process Goal: Communication

Mathematicians can explore/ engage in a variety of experiences within a math period. Work may be collaborative or independent.

In order to have a variety of activities during a math block, it is important to be mindful of procedures, noise level, expectations, etc.

Review procedures for moving around the classroom to different centers Consider utilizing visual time reminders Use cues for sound control/reminders

Post clear directions at independent centers. Provide a materials checklist.



Day 7 Real Life Connections to Math VA Process Goal: Connections

Mathematicians make connections between math ideas and the world around them.

Math connects to other content areas/disciplines (i.e. Science). Students relate math to the world around them.

Brainstorm a list of math concepts that relate to the real world. Consider using the following discussion prompts: Where in the world do you see numbers? When do you use math in your everyday life?

Chart paper Calendar / Daily Schedule

Consider connecting this discussion to everyday events in their life.

Day 8 Representing Thinking VA Process Goals: Representation, Communication

Mathematicians can represent ideas in multiple ways. Mathematicians use words to explain their thinking. Mathematicians can explain their thinking verbally or in writing in order to process information.

Students will become more familiar with ways they can represent math ideas. Students can show their math thinking in written words.

In order to fully communicate their understanding, mathematicians may provide written explanations of their reasoning.

Brainstorm ways that students can represent their thinking. Ex: Pictures/drawing Words Numbers Symbols Manipulative models

Utilize sentence frames: “This is a ______________. It is a ______ because it ______________. “ This example shows a picture, numbers, and a written explanation.

Encourage students to show math concepts in a variety of ways. Encourage students to write about their understanding or show their thinking using words, pictures, numbers, etc.



Day 9 Recording & Reflecting in Math

VA Process Goal: Communication

Mathematicians keep a record of their daily experiences (i.e. math game).

Students will understand how to utilize a recording sheet or guide as they play a game or solve a problem. Students will record and reflect upon their work to communicate their understanding in writing.

Example of Game Recording Sheet:

Introduce a Recording Sheet as a student tool.

Day 10 Academic Language of Math VA Process Goal: Communication

Specialized language is used in math. Mathematical language can be modeled and explicitly taught.

Students will develop an understanding of specific math terminology. Conceptual understanding is developed as students use math terminology.

Post examples of key vocabulary terms with visual examples.

Math Word Wall, Word Banks, VDOE Vocabulary Cards http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/index.shtml The vocabulary terms introduced are then posted for class reference.

New vocabulary should be explicitly introduced and utilized within daily lessons. This is a continuous routine/ element for all units of study.

http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/index.shtml





Day 11 Vocabulary Development VA Process Goals: Representation, Communication, Connections

Mathematicians use a variety of strategies to build vocabulary.

Students will utilize a tool to reinforce their math vocabulary.

Select model to implement with students (i.e. Frayer).

Student math journal VDOE Math Vocabulary Cards Frayer Model

Students can utilize math journals to keep a record of math vocabulary. Their journals can also serve as a valuable resource in addition to the Word Wall or class references (see Day 10).

Day 12 Math Strategies

VA Process Goals: Problem Solving, Representation, Connections

A variety of strategies can be used to solve problems and explore mathematical concepts.

Students develop a repertoire of strategies. Students see connections between different strategies used to solve problems.

Build or add to a strategy wall showing models of strategies for various skills or concepts.

Anchor charts can be developed for a wide variety of strategies depending on the grade level. Examples are shown to the left.



Day 13 Connections VA Process Goals: Connections, Communication

Mathematicians make and recognize connections among mathematical ideas.

Students understand that they can make connections among math ideas. Math can be related to the world outside the classroom.

Discussion questions: How is that answer like the one you modeled yesterday? Where have you seen that before?

Consider having students glue question/ comment starters in the back of their math journal. They can refer to it during class discussions.

Day 14 Justification VA Process Goals: Reasoning, Representation

Mathematicians verify their thinking by showing it multiple ways.

Students will develop a deeper understanding of content when asked to justify their thinking.

Create an anchor chart that depicts ways that students can justify their thinking.

Justify means: explain, defend,

describe, prove, give reasons, show

you understand, validate…

Using verbal explanation first can help facilitate written justification.



Day 15 Problem Solving Strategies VA Process Goals: Problem Solving, Communication

Mathematicians choose from a variety of strategies to solve problems.

Students have a resource of strategies to help them solve problems . Sample strategies: -find a pattern - estimate and check -make an organized list -draw a diagram -write an equation -work backward -solve a simpler problem -read a table/chart

Introduce problem solving strategies (a variety of strategies can be used). Explain that the different strategies can be used to help students with problem solving. Choose 1 strategy to explain/highlight for the mini lesson. You will continue to model/introduce/use the strategies throughout the year.

Students can create their own problem solving strategy icons or bookmarks as well as refer to a class anchor chart of strategies.

During classroom instruction, teachers can engage students in discourse about their problem solving strategy.

Day 16 Problem Solving Protocol VA Process Goals: Problem Solving, Communication

There are processes that can be used to help solve problems.

Students will be introduced to a problem solving protocol. Students will become familiar with the protocol steps.

Develop and post a problem solving protocol.

Post the protocol in the classroom for student reference.

Consider trying a problem as a class to model how the protocol is used. The emphasis should be on the steps, so it may be easiest to select content that is readily accessible to all learners.

Step 1: Read and quietly think on your own – release your pencils. Step 2: Talk about the problem. What is your plan to solve? Pick your strategy. Step 3: Share your strategy. Step 4: Solve the problem and communicate your thinking.



Day 17 Rubric Familiarization VA Process Goals: Reasoning, Connections

There are tools mathematicians use to monitor and assess their work or behavior.

Students understand how to use a rubric to assess themselves/ their work.

Create a class rubric that is not math related. The topic should be something relevant to an everyday student activity in the classroom or school. Examples include: Lunchroom behavior Morning routine Dismissal Cubbie/desk organization

Day 18 Reflection/ Self-Monitoring VA Process Goal: Reasoning

Mathematicians modify their work as needed.

Students reflect upon and revise their work to demonstrate their full understanding.

Introduce a criteria chart and rubric for self- monitoring of work.

Sample Rubric:

Rubric & Problem Solving Protocol Create an anchor chart with “How to Self-Correct or Modify Your Work”

Help students develop a clear understanding of the criteria and how upcoming math tasks will be scored. Emphasize how this is similar to the revisions they do during the writing process.



Day 19 Collaboration (Task) VA Process Goal: Communication

Mathematicians can work collaboratively on a problem solving task to learn important math concepts.

Students understand that they can work with others to solve problems and learn new information.

Review roles that pairs or small groups should follow/hold when working together on a task. Examples: Materials manager Recorder Reporter Time keeper

Develop an anchor chart with roles/procedures for group work on a task/problem. Self-assess/reflect upon collaborative work experiences. Students can use the problem solving protocol together (See Day 16).

Save time at the end of the lesson to debrief the experience. What went well? What could be improved next time they are working in a group?

Day 20

Process Goals

VA Process Goals: Problem Solving, Reasoning, Communication, Connections, & Representation

“The content of the mathematics standards is intended to support the following five process goals for students: *becoming mathematical problem solvers *communicating mathematically *reasoning mathematically *making mathematical connections and *using mathematical representations to model and interpret practical situations.”

-2009 Mathematics Standards of Learning

Student-friendly process goals poster (can be a poster for the classroom and/or a small version can be taped to desks or in math journals) Process Goals bookmark (click on picture to the left to access the file for the poster and bookmark)

Students should be engaged in process goals throughout every mathematical task and lesson throughout the year.

https://www.dropbox.com/s/t2pvle6rn86heu2/Process Goals student-friendly.docx

VDOE Technical Assistance Document

to be used in conjunction with the VDOE Curriculum Framework (click title above to link to document)

Virginia Mathematics Standards of Learning

Curriculum Framework 2009 Introduction

The 2009 Mathematics Standards of Learning Curriculum Framework is a companion document to the 2009 Mathematics Standards of Learning and

amplifies the Mathematics Standards of Learning by defining the content knowledge, skills, and understandings that are measured by the Standards

of Learning assessments. The Curriculum Framework provides additional guidance to school divisions and their teachers as they develop an

instructional program appropriate for their students. It assists teachers in their lesson planning by identifying essential understandings, defining

essential content knowledge, and describing the intellectual skills students need to use. This supplemental framework delineates in greater specificity

the content that all teachers should teach and all students should learn.

Each topic in the Mathematics Standards of Learning Curriculum Framework is developed around the Standards of Learning. The format of the

Curriculum Framework facilitates teacher planning by identifying the key concepts, knowledge and skills that should be the focus of instruction for

each standard. The Curriculum Framework is divided into three columns: Understanding the Standard; Essential Understandings; and Essential

Knowledge and Skills. The purpose of each column is explained below.

Understanding the Standard

This section includes background information for the teacher (K-8). It contains content that may extend the teachers’ knowledge of the standard

beyond the current grade level. This section may also contain suggestions and resources that will help teachers plan lessons focusing on the standard.

Essential Understandings

This section delineates the key concepts, ideas and mathematical relationships that all students should grasp to demonstrate an understanding of the

Standards of Learning. In Grades 6-8, these essential understandings are presented as questions to facilitate teacher planning.

Essential Knowledge and Skills

Each standard is expanded in the Essential Knowledge and Skills column. What each student should know and be able to do in each standard is

outlined. This is not meant to be an exhaustive list nor a list that limits what is taught in the classroom. It is meant to be the key knowledge and skills

that define the standard.

The Curriculum Framework serves as a guide for Standards of Learning assessment development. Assessment items may not and should not be a

verbatim reflection of the information presented in the Curriculum Framework. Students are expected to continue to apply knowledge and skills

from Standards of Learning presented in previous grades as they build mathematical expertise.

http://www.doe.virginia.gov/instruction/mathematics/resources/mathematics_sol_technical_assistance.pdf

FOCUS K–3 STRAND: NUMBER AND NUMBER SENSE GRADE LEVEL K

Students in grades K–3 have a natural curiosity about their world, which leads them to develop a sense of number. Young children are motivated to

count everything around them and begin to develop an understanding of the size of numbers (magnitude), multiple ways of thinking about and

representing numbers, strategies and words to compare numbers, and an understanding of the effects of simple operations on numbers. Building on

their own intuitive mathematical knowledge, they also display a natural need to organize things by sorting, comparing, ordering, and labeling objects

in a variety of collections.

Consequently, the focus of instruction in the number and number sense strand is to promote an understanding of counting, classification, whole

numbers, place value, fractions, number relationships (“more than,” “less than,” and “equal to”), and the effects of single-step and multistep

computations. These learning experiences should allow students to engage actively in a variety of problem solving situations and to model numbers

(compose and decompose), using a variety of manipulatives. Additionally, students at this level should have opportunities to observe, to develop an

understanding of the relationship they see between numbers, and to develop the skills to communicate these relationships in precise, unambiguous

terms.

K.1 The student, given two sets, each containing 10 or fewer concrete objects, will identify and describe one set as having more,

fewer, or the same number of members as the other set, using the concept of one-to-one correspondence.

UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)

ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS

A set is a collection of distinct elements or items.

A one-to-one correspondence exists when two sets

have an equal number of items.

Strategies for developing the concept of one-to-one

matching involve set comparisons without

counting. Hands-on experiences in matching

items between two sets by moving, touching, and

aligning objects, using one-to-one

correspondence, enable visual as well as

kinesthetic comparisons of the number of items in

the two sets.

Students can also count to make comparisons between

two sets without matching the sets, using one-to-

one correspondence.

Students are generally familiar with the concept of

more, but have had little experience with the term

less. It is important to use the terms together to

build an understanding of their relationship. For

example, when asking which group has more,

follow with which group has less and vice versa.

All students should

Understand how quantities relate to each other,

which leads to an understanding of how

numbers are related to each other.

The student will use problem solving, mathematical

communication, mathematical reasoning, connections, and

representations to

Match each member of one set with each member of another

set, using the concept of one-to-one correspondence to

compare the number of members between sets, where each

set contains 10 or fewer objects.

Compare and describe two sets of 10 or fewer objects, using

the terms more, fewer, and the same.

Given a set of objects, construct a second set which has more,

fewer or the same number of objects.

K.2 The student, given a set containing 15 or fewer concrete objects, will

a) tell how many are in the set by counting the number of objects orally;

b) write the numeral to tell how many are in the set; and

c) select the corresponding numeral from a given set of numerals.



Counting involves two separate skills: verbalizing the

list of standard number words in order (“one,

two, three, ”) and connecting this sequence

with the objects in the set being counted, using

one-to-one correspondence. Association of

number words with collections of objects is

achieved by moving, touching, or pointing to

objects as the number words are spoken. Objects

may be presented in random order or arranged for

easy counting.

Kinesthetic involvement (e.g., tracing the numbers,

using tactile materials, such as sand, sandpaper,

carpeting, or finger paint) facilitates the writing

of numerals.

Articulating the characteristics of each numeral when

writing numbers has been found to reduce the

amount of time it takes to learn to write numerals.

Zero (0) is both a number and a digit. As a number, it

plays a central role in mathematics as the additive

identity of the integers, real numbers, and many

other algebraic structures. As a digit, zero is used

as a placeholder in systems.

Conservation of number and cardinality principle are

two important milestones in development to

attaching meaning to counting.

The cardinality principle refers to the concept that the

last counted number describes the total amount of

the counted set. It is an extension of one-to-one

correspondence.

All students should

Read and write numerals from 0 through 15.

Understand that the total number of objects can

be found by counting.

Understand that the last counted number

describes the total amount in the set.

Understand that if the set is empty, it has 0

elements.

Understand that changing the spatial arrangement

of a set of objects does not change the total

amount of the set.



representations to

Count orally the number of objects in a set containing 15 or

fewer concrete objects, using one-to-one correspondence,

and identify the corresponding numeral.

Identify written numerals from 0 through 15 represented in

random order.

Select the numeral from a given set of numerals that

corresponds to a set of 15 or fewer concrete objects.

Write the numerals from 0 through 15.

Write a numeral that corresponds to a set of 15 or fewer

concrete objects.

Construct a set of objects that corresponds to a given numeral,

including an empty set.

K.2 The student, given a set containing 15 or fewer concrete objects, will

a) tell how many are in the set by counting the number of objects orally;

b) write the numeral to tell how many are in the set; and

c) select the corresponding numeral from a given set of numerals.



Conservation of number is the understanding that the

number of objects remains the same when they

are rearranged spatially.

K.3 The student, given an ordered set of ten objects and/or pictures, will indicate the ordinal position of each object, first through

tenth, and the ordered position of each object.



Understanding the cardinal and ordinal meanings of

numbers are necessary to quantify, measure, and

identify the order of objects.

An ordinal number is a number that names the place

or position of an object in a sequence or set (e.g.,

first, third). Ordered position, ordinal position,

and ordinality are terms that refer to the place or

position of an object in a sequence or set.

The ordinal position is determined by where one starts

in an ordered set of objects or sequence of

objects.

The ordinal meaning of numbers is developed by

identifying and verbalizing the place or position

of objects in a set or sequence (e.g., the student’s

position in line when students are lined up

alphabetically by first name).

All students should

Use ordinal numbers to describe the position of

objects in a sequence.



representations to

Identify the ordinal positions first through tenth using ordered

sets of ten concrete objects and/or pictures of such sets

presented from

left-to-right;

right-to-left;

top-to-bottom; and/or

bottom-to-top.

K.4 The student will

a) count forward to 100 and backward from 10;

b) identify one more than a number and one less than a number; and

c) count by fives and tens to 100.



Counting skills are essential components of the

development of number ideas; however, they are

only one of the indicators of the understanding of

numbers.

Counting forward by rote advances the child’s

development of sequencing. The natural numbers

are 1, 2, 3, 4…. The whole numbers are 0, 1, 2, 3,

4…. Students should count the whole numbers 0,

1, 2, 3, 4,.

Counting backward by rote lays the foundation for

subtraction. Students should count backward

beginning with 10, 9, 8, through 3, 2, 1, 0.

Counting forward and backward leads to the

development of counting on and counting back.

The patterns developed as a result of skip counting are

precursors for recognizing numeric patterns,

functional relationships, and concepts underlying

money, time telling, and multiplication. Powerful

models for developing these concepts include, but

are not limited to, counters, hundred chart, and

calculators.

Skip counting by fives lays the foundation for reading

a clock effectively and telling time to the nearest

five minutes, counting money, and developing the

multiplication facts for five.

Skip counting by tens is a precursor for use of place

value, addition, counting money, and multiplying

by multiples of 10.

All students should

Use the correct oral counting sequence in both

forward and backward counting situations.

Understand that skip counting can be used to

count a collection of objects.

Describe patterns in skip counting and use those

patterns to predict the next number or

numbers in the skip counting sequence.

Understand that numeric relationships include one

more than, one less than, two more than, two

less than, etc.

Understand benchmarks of five and ten.



representations to

Count forward from 0 to 100.

Count backward from 10 to 0.

Recognize the relationship of one more than and one less than a

number using objects (i.e., five and one more is six; and

one less than ten is nine).

Group 100 or fewer objects together into sets of fives or tens

and then count them by fives or by tens.

Investigate and recognize the pattern of counting by fives to

100, using a variety of tools.

Investigate and recognize the pattern of counting by tens to

100, using a variety of tools.


a) count forward to 100 and backward from 10;

b) identify one more than a number and one less than a number; and

c) count by fives and tens to 100.



Calculators can be used to display the numeric

patterns that result from skip counting.

K.5 The student will identify the parts of a set and/or region that represent fractions for halves and fourths.



A fraction is a way of representing part of a whole (as

in a region/area model) or part of a group (as in a

set model).

In each fraction model, the parts must have the same

area.

The fractional parts of a set model are subsets of an

equal number. For example, in a set of ten cubes,

each half would be a subset of five cubes.

Informal, integrated experiences with fractions at this

level will help students develop a foundation for

deeper learning at later grades. Understanding the

language of fractions furthers this development

(e.g., fourths means “four equal parts of a whole”

or 1

4 represents one of four parts of equal size

when a pizza is shared among four students).

All students should

Understand that fractional parts are equal shares

of a whole region or a whole set.

Understand that the fraction name (half, fourth)

tells the number of equal parts in the whole.

Understand that the fraction name (half, fourth) of

the set model is a subset of the whole set with

equal numbers.



representations to

Recognize fractions as representing parts of equal size of a

whole.

Given a region, identify half and/or a fourth of the region.

Given a set, identify half and/or a fourth of the set.

FOCUS K–3 STRAND: COMPUTATION AND ESTIMATION GRADE LEVEL K

A variety of contexts are necessary for children to develop an understanding of the meanings of the operations such as addition and subtraction.

These contexts often arise from real-life experiences in which they are simply joining sets, taking away or separating from a set, or comparing sets.

These contexts might include conversations, such as “How many books do we have altogether?” or “How many cookies are left if I eat two?” or “I

have three more candies than you do.” Although young children first compute using objects and manipulatives, they gradually shift to performing

computations mentally or using paper and pencil to record their thinking. Therefore, computation and estimation instruction in the early grades

revolves around modeling, discussing, and recording a variety of problem situations. This approach helps students transition from the concrete to the

representation to the symbolic in order to develop meaning for the operations and how they relate to each other.

In grades K–3, computation and estimation instruction focuses on

relating the mathematical language and symbolism of operations to problem situations;

understanding different meanings of addition and subtraction of whole numbers and the relation between the two operations;

developing proficiency with basic addition, subtraction, multiplication, division and related facts;

gaining facility in manipulating whole numbers to add and subtract and in understanding the effects of the operations on whole numbers;

developing and using strategies and algorithms to solve problems and choosing an appropriate method for the situation;

choosing, from mental computation, estimation, paper and pencil, and calculators, an appropriate way to compute;

recognizing whether numerical solutions are reasonable;

experiencing situations that lead to multiplication and division, such as equal groupings of objects and sharing equally; and

performing initial operations with fractions.

FOCUS K–3 STRAND: COMPUTATION AND ESTIMATION GRADE LEVEL K

K.6 The student will model adding and subtracting whole numbers, using up to 10 concrete objects.



Whole numbers are 0, 1, 2, 3, 4, 5, 6, and so on.

Addition is the process of combining or joining sets.

Subtraction can be viewed as a taking away or

separating process or as comparing to find the

difference between two sets.

Counting on from the larger set to determine the sum

of the combined sets is a strategy for finding a

sum.

Counting backward from the larger set to determine

the difference between two sets is a strategy for

subtraction.

Number relationships, including the following, help

students develop strategies for adding and

subtracting.

Instant recognition of the amount in a set of

objects that are arranged in a familiar

pattern such as the dots on number cubes

One more than, one less than, two more than,

two less than

All students should

Understand that addition means putting things

together and that subtraction is the inverse of

addition and means to separate things out.



representations to

Combine two sets with known quantities in each set, and count

the combined set using up to 10 concrete objects, to

determine the sum, where the sum is not greater than 10.

Given a set of 10 or fewer concrete objects, remove, take away,

or separate part of the set and determine the result.

FOCUS K–3 STRAND: MEASUREMENT GRADE LEVEL K

Measurement is important because it helps to quantify the world around us and is useful in so many aspects of everyday life. Students in grades K–3

should encounter measurement in many normal situations, from their daily use of the calendar and from science activities that often require students

to measure objects or compare them directly, to situations in stories they are reading and to descriptions of how quickly they are growing.

Measurement instruction at the primary level focuses on developing the skills and tools needed to measure length, weight/mass, capacity, time,

temperature, area, perimeter, volume, and money. Measurement at this level lends itself especially well to the use of concrete materials. Children can

see the usefulness of measurement if classroom experiences focus on estimating and measuring real objects. They gain deep understanding of the

concepts of measurement when handling the materials, making physical comparisons, and measuring with tools.

As students develop a sense of the attributes of measurement and the concept of a measurement unit, they also begin to recognize the differences

between using nonstandard and standard units of measure. Learning should give them opportunities to apply both techniques and nonstandard and

standard tools to find measurements and to develop an understanding of the use of simple U.S. Customary and metric units.

Teaching measurement offers the challenge to involve students actively and physically in learning and is an opportunity to tie together other aspects

of the mathematical curriculum, such as fractions and geometry. It is also one of the major vehicles by which mathematics can make connections

with other content areas, such as science, health, and physical education.

K.7 The student will recognize a penny, nickel, dime, and quarter and will determine the value of a collection of pennies and/or

nickels whose total value is 10 cents or less.



Involvement in varied activities such as physically

manipulating coins and making comparisons

about their sizes, colors, and values is prerequisite

to the skills of coin recognition and valuation.

Counting money helps students gain an awareness of

consumer skills and the use of money in everyday

life.

A variety of classroom experiences in which students

manipulate physical models of money and count

forward to determine the value of a collection of

coins are important activities to ensure

competence with using money.

Students need experiences to develop the concept that

a nickel has a value of five cents even though it is

one object.

All students should

Develop common referents for identifying

pennies, nickels, dimes, and quarters.

Understand the value of a collection of coins

whose value is 10 cents or less.



representations to

Describe the properties/characteristics (e.g., color, relative size)

of a penny, nickel, dime, and quarter.

Identify a penny, nickel, dime, and quarter.

Identify that a nickel is the same value as five pennies.

Count a randomly placed collection of pennies and/or nickels

(or models of pennies and/or nickels) whose value is 10

cents or less, and determine the value of the collection.

K.8 The student will identify the instruments used to measure length (ruler), weight (scale), time (clock: digital and analog;

calendar: day, month, and season), and temperature (thermometer).



Many experiences in measuring physical objects,

using nonstandard and standard units of measure,

help to develop an intuitive understanding of

measurement and will help students connect a

tool with its purpose in measuring.

Selecting from among various measuring instruments

and determining which can be used to solve

various real-life problems are introduced at this

level.

A precursor to connecting tools to a type of

measurement is an introduction to the concepts of

length, weight, time, and temperature.

All students should

Identify an appropriate measuring tool for a given

unit of measure.



representations to

Identify a ruler as an instrument to measure length.

Identify different types of scales as instruments to measure

weight.

Identify different types of clocks (analog and digital) as

instruments to measure time.

Identify the components of a calendar, including days, months,

and seasons.

Identify different types of thermometers as instruments used to

measure temperature.




Many experiences in relating time on the hour to daily

routines and school schedules (e.g., catching the

bus, lunch time, recess time, and resource time)

help students develop personal referents for time.

Making sense of telling time to the nearest hour is

reinforced when students recognize the positions

of the hands on an analog clock and identify the

corresponding time to the hour.

All students should

Apply an appropriate technique, depending on the

type of clock, to determine time to the nearest

hour.



representations to

Tell time on an analog clock to the hour.

Tell time on a digital clock to the hour.

K.10 The student will compare two objects or events, using direct comparisons or nonstandard units of measure, according to one or

more of the following attributes: length (shorter, longer), height (taller, shorter), weight (heavier, lighter), temperature (hotter,

colder). Examples of nonstandard units include foot length, hand span, new pencil, paper clip, and block.



Length is the distance between two points.

Height is the vertical length of a perpendicular to its

base.

Weight is a measure of the heaviness of an object.

Temperature is the degree of hotness or coldness of an

object (e.g., a body) or environment.

Students need to identify the attribute that they are

measuring (e.g., length, height, weight,

temperature) before they begin to measure.

Multiple hands-on experiences are needed to gain the

ability to compare the attributes of objects.

All students should

Compare and order objects according to their

attributes.

Develop an understanding of measuring with

nonstandard and standard units of measure.

Recognize attributes (length, height, weight,

temperature) that can be measured.



representations to

Compare and describe lengths of two objects (as shorter or

longer), using direct comparison or nonstandard units of

measure (e.g., foot length, hand span, new pencil, paper

clip, block).

Compare and describe heights of two objects (as taller or

shorter), using direct comparison or nonstandard units of

measure (e.g., book, hand span, new pencil, paper clip,

block).

Compare and describe weights of two objects (as heavier or

lighter), using direct comparison or nonstandard units of

measure (e.g., book, cubes, new pencil, paper clip, block).

Compare and describe temperatures of two objects or

environment (as hotter or colder), using direct comparison.

FOCUS K–3 STRAND: GEOMETRY GRADE LEVEL K

Children begin to develop geometric and spatial knowledge before beginning school, stimulated by the exploration of figures and structures in their

environment. Geometric ideas help children systematically represent and describe their world as they learn to represent plane and solid figures

through drawing, block constructions, dramatization, and verbal language.

The focus of instruction at this level is on

observing, identifying, describing, comparing, contrasting, and investigating solid objects and their faces;

sorting objects and ordering them directly by comparing them one to the other;

describing, comparing, contrasting, sorting, and classifying figures; and

exploring symmetry, congruence, and transformation.

In the primary grades, children begin to develop basic vocabulary related to figures but do not develop precise meanings for many of the terms they

use until they are thinking beyond Level 2 of the van Hiele theory (see below).

The van Hiele theory of geometric understanding describes how students learn geometry and provides a framework for structuring student

experiences that should lead to conceptual growth and understanding.

Level 0: Pre-recognition. Geometric figures are not recognized. For example, students cannot differentiate between three-sided and four-sided

polygons.

Level 1: Visualization. Geometric figures are recognized as entities, without any awareness of parts of figures or relationships between

components of a figure. Students should recognize and name figures and distinguish a given figure from others that look somewhat the same.

(This is the expected level of student performance during grades K and 1.)

Level 2: Analysis. Properties are perceived but are isolated and unrelated. Students should recognize and name properties of geometric figures.

(Students are expected to transition to this level during grades 2 and 3.


a) identify, describe, and trace plane geometric figures (circle, triangle, square, and rectangle); and

b) compare the size (larger, smaller) and shape of plane geometric figures (circle, triangle, square, and rectangle).



An important part of the geometry strand in grades K

through 2 is the naming and describing of figures.

Children move from their own vocabulary and

begin to incorporate conventional terminology as

the teacher uses geometric terms.

A plane geometric figure is any plane, closed figure.

Circles and polygons are examples of plane

geometric figures.

Presentation of triangles, rectangles, and squares

should be made in a variety of spatial orientations

so that students do not develop the common

misconception that triangles, rectangles, and

squares must have one side parallel to the bottom

of the page on which they are printed.

The van Hiele theory of geometric understanding

describes how students learn geometry and

provides a framework for structuring student

experiences that should lead to conceptual growth

and understanding.

Level 0: Pre-recognition. Geometric figures

are not recognized. For example, students

cannot differentiate between three-sided

and four-sided polygons.

Level 1: Visualization. Geometric figures are

recognized as entities, without any

awareness of parts of figures or

relationships between components of a

figure. Students should recognize and

name figures and distinguish a given

figure from others that look somewhat the

same (e.g., “I know it’s a rectangle

because it looks like a door, and I know

All students should

Use their knowledge of plane figures to help them

systematically represent and describe their

world.

Identify the characteristics of plane geometric

figures (circle, triangle, square, and

rectangle).

Compare the size and shape of plane

geometric figures by using strategies to sort

and/or group and begin to refine the

vocabulary used to explain their strategies.



representations to

Identify a circle, triangle, square, and rectangle.

Describe the characteristics of triangles, squares, and

rectangles, including number of sides and number of

angles.

Describe a circle using terms such as round and curved.

Trace a circle, triangle, square, and rectangle.

Compare and group plane geometric figures (circle, triangle,

square, and rectangle) according to their relative sizes

(larger, smaller).

Compare and group plane geometric figures (circle, triangle,

square, and rectangle) according to their shapes.

Distinguish between examples and nonexamples of identified

geometric figures (circle, triangle, square, and rectangle).






that a door is a rectangle.”)

Level 2: Analysis. Properties are perceived,

but are isolated and unrelated. Students

should recognize and name properties of

geometric figures (e.g., “I know it’s a

rectangle because it is closed; it has four

sides and four right angles.”).

A polygon is a geometric figure that

has sides that are line segments;

is simple (its sides do not cross);

is closed; and

is two-dimensional (lies in a plane).

A triangle is a polygon with three angles and three

sides. Children should be shown different types of

triangles such as equilateral, isosceles, scalene,

right, acute, and obtuse; however, they are not

expected to name the various types.

A quadrilateral is a polygon with four sides.

A rectangle is a quadrilateral with four right angles.

A square is a rectangle with all four sides of equal

length.

A circle is a closed curve with all points in one plane

and the same distance from a fixed point (the

center).

Early experiences with comparing and sorting figures

assist students in analyzing the characteristics of

plane geometric figures.






Attribute blocks, relational attribute blocks, and

tangrams are among the manipulatives that are

particularly appropriate for sorting and comparing

size.

Clay, straws, and paper and scissors are

several manipulatives that are appropriate

for constructing geometric figures.

K.12 The student will describe the location of one object relative to another (above, below, next to) and identify representations of

plane geometric figures (circle, triangle, square, and rectangle) regardless of their positions and orientations in space.



Representations of circles, squares, rectangles, and

triangles can be found in the students’

environment at school and at home. Students

should have opportunities to identify/classify

things in their environment by the type of figures

those things represent.

Children are often confused when a figure such as a

square is rotated: they frequently refer to the

rotated square as a diamond. Clarification needs

to be ongoing — i.e., a square is a square

regardless of its location in space; there is no such

geometric figure as a diamond.

All students should

Understand that objects can have different

orientations in space.



representations to

Identify pictorial representations of a circle, triangle, square,

and rectangle, regardless of their position and orientation

in space.

Describe the location of one object relative to another, using

the terms above, below, and next to.

FOCUS K–3 STRAND: PROBABILITY AND STATISTICS GRADE LEVEL K

Students in the primary grades have a natural curiosity about their world, which leads to questions about how things fit together or connect. They

display their natural need to organize things by sorting and counting objects in a collection according to similarities and differences with respect to

given criteria.

The focus of probability instruction at this level is to help students begin to develop an understanding of the concept of chance. They experiment with

spinners, two-colored counters, dice, tiles, coins, and other manipulatives to explore the possible outcomes of situations and predict results. They

begin to describe the likelihood of events, using the terms impossible, unlikely, equally likely, more likely, and certain.

The focus of statistics instruction at this level is to help students develop methods of collecting, organizing, describing, displaying, and interpreting

data to answer questions they have posed about themselves and their world.




Data are pieces of information collected about people

or things. The primary purpose of collecting data

is to answer questions.

Tallying is a method for gathering information. Tally

marks are used to show how often something

happens or occurs. Each tally mark represents one

occurrence. Tally marks are clustered into groups

of five, with four vertical marks representing the

first four occurrences and the fifth mark crossing

the first four on a diagonal to represent the fifth

occurrence.

When data are presented in an organized manner,

students can describe the results of their

investigation (i.e., identifying parts of the data

that have special characteristics, including

categories with the greatest, the least, or the same

number of responses).

In the process of gathering data, students make

decisions about what is relevant to their

investigation (e.g., when collecting data on their

classmates’ favorite pets, deciding to limit the

categories to common pets).

When students begin to collect data, they recognize

the need to categorize, which helps develop the

understanding of “things that go together.”

Categorical data are used when constructing

picture graphs and bar graphs.

All students should

Pose questions and gather data.

Understand how data are collected and presented

in an organized manner by counting and

tallying.



representations to

Use counting and tallying to gather data on categories

identified by the teacher and/or student (e.g., favorites,

number of days of various types of weather during a given

month, types of pets, types of shoes).

K.14 The student will display gathered data in object graphs, picture graphs, and tables, and will answer questions related to the

data.



Object graphs are graphs that use concrete materials to

represent the categorical data that are collected

(e.g., cubes stacked by the month, with one cube

representing the birthday month of each student).

Picture graphs are graphs that use pictures to show

and compare information.

Tables are an orderly arrangement of data in which the

data are arranged in columns and rows in an

essentially rectangular format. Tables may be

used to display some type of numerical

relationship or organized lists (e.g., input/output

functions, tables showing one candy costs five

cents and two candies cost 10 cents).

Students represent data to convey results of their

investigations at a glance, using concrete objects,

pictures, and numbers to give a “picture” of the

organized data.

When data are displayed in an organized manner,

children can describe the results of their

investigations.

Graphs can be used to make connections between

mathematics and social studies and/or science

(e.g., job areas and the different people that work

in these areas: health — doctors and nurses;

education — teachers and principals).

Statements representing an analysis and interpretation

of the characteristics of the data in the graph (e.g.,

similarities and differences, least and greatest, the

categories, and total number of responses) should

be asked.

All students should

Understand that data can be represented using

concrete objects, pictures, and graphs.

Understand that different types of representations

emphasize different things about the same

data.

Understand that picture graphs use pictures to

show and compare information; object graphs

use concrete materials to represent

categorical data; and tables can be used to

show an orderly arrangement of data in

columns and rows.

Answer questions related to the gathered data

from object graphs, picture graphs, and

tables.

Relate their ideas about the data to concepts such

as part-part-whole and number relationships.



representations to

Display data by arranging concrete objects into organized

groups to form a simple object graph.

Display gathered data, using pictures to form a simple picture

graph (e.g., a picture graph of the types of shoes worn by

students on a given day).

Display gathered data in tables, either in rows or columns.

Answer questions related to the gathered data displayed in

object graphs, picture graphs, and tables by:

Describing the categories of data and the data as a

whole (e.g., the total number of responses) and its

parts.

Identifying parts of the data that represent numerical

relationships, including categories with the greatest,

the least, or the same.

FOCUS K–3 STRAND: PATTERNS, FUNCTIONS, AND ALGEBRA GRADE LEVEL K

Stimulated by the exploration of their environment, children begin to develop concepts related to patterns, functions, and algebra before beginning

school. Recognition of patterns and comparisons are important components of children’s mathematical development.

Students in kindergarten through third grade develop the foundation for understanding various types of patterns and functional relationships through

the following experiences:

sorting, comparing, and classifying objects in a collection according to a variety of attributes and properties;

identifying, analyzing, and extending patterns;

creating repetitive patterns and communicating about these patterns in their own language;

analyzing simple patterns and making predictions about them;

recognizing the same pattern in different representations;

describing how both repeating and growing patterns are generated; and

repeating predictable sequences in rhymes and extending simple rhythmic patterns.

The focus of instruction at the primary level is to observe, recognize, create, extend, and describe a variety of patterns. These students will experience

and recognize visual, kinesthetic, and auditory patterns and develop the language to describe them orally and in writing as a foundation to using

symbols. They will use patterns to explore mathematical and geometric relationships and to solve problems, and their observations and discussions of

how things change will eventually lead to the notion of functions and ultimately to algebra.




To classify is to arrange or organize a set of materials

according to a category or attribute (a quality or

characteristic). An object has many attributes

such as color, size, shape, thickness, etc.

General similarities and differences among objects are

easily observed by children entering kindergarten,

who are able to focus on any one attribute. The

teacher’s task is to move students toward a more

sophisticated understanding of classification in

which two or more attributes connect or

differentiate sets, such as those found in nature

(e.g., leaves with different colors and different

figures).

All students should

Understand that the same set of objects can be

sorted and classified in different ways.



representations to

Sort objects into appropriate groups (categories) based on one

attribute.

Classify sets of objects into groups (categories) of one attribute.

Label attributes of a set of objects that has been sorted.

Name multiple ways to sort a set of objects.




Pattern recognition is a fundamental cornerstone of

mathematics, particularly algebra.

In a repeating pattern, the core of the pattern is the

string of elements that repeats. By identifying the

core, students demonstrate their understanding of

the pattern.

Students should recognize that the sound pattern

‘snap, clap, snap, clap’ is the same in form as the

color pattern ‘red, blue, red, blue’.

Pattern recognition and the extension of the pattern

allow students to make predictions.

The simplest types of patterns are repeating patterns.

The patterns can be oral, such as the refrain in

“Old MacDonald’s Farm” (“e-i-e-i-o”), or

physical with clapping and snapping patterns, or

combinations of both, such as is found in songs

like the “Hokey Pokey.” In each case, students

need to identify the basic unit of the pattern and

repeat it. Opportunities to create, recognize,

describe, and extend repeating patterns are

essential to the primary school experience.

Sample repeating patterns (repeating the core) are

ABABABAB;

ABCABC;

AABBAABBAABB;

AABAAB;

AABCAABC; and

ABACABAC.

All students should

Understand that patterns are a way to recognize

order and organize their world and to predict

what comes next in an arrangement.

Understand that the sound pattern ‘snap, clap,

snap, clap’ is the same in form as the color

pattern ‘red, blue, red, blue’.



representations to

Observe and identify the basic repeating pattern (core) found in

repeating patterns of common objects, sounds, and

movements that occur in practical situations.

Identify the core in a repeating pattern.

Extend a repeating pattern by adding at least two repetitions to

the pattern.

Create a repeating pattern.

Compare similarities and differences between patterns.

Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade K

Learning Progressions The following pages are the Learning Progressions for the curriculum. More information about the Learning Progressions can be found on VISION. The Grading and Assessment, Module 3: Learning Progressions is about what Learning Progressions are, how they were developed, and how they are used to support instruction and build student learning.


LP K.1 SOL K.1: The student, given two sets, each containing 10 or fewer concrete objects, will identify and describe one set as having more, fewer, or the same number of members as the other set, using the concept of one-to-one correspondence. Learning Target: I can compare two sets of objects and describe a set as having more, fewer, or the same quantity of objects. I can create a set of objects which has more, fewer, or the same quantity as a given set.

Learning Progression The student will use problem solving, mathematical communication,

mathematical reasoning, connections, and representations at each level of the learning progression.

Advanced Proficient

I can count the objects in the two sets and compare the two sets by describing the number as greater than, less than, or the same. *Students begin to develop an understanding of the values associated with numbers.

Proficient

I can compare two sets of objects and describe a set as having more, fewer, or the same quantity of objects. I can create a set of objects which has more, fewer, or the same quantity as a given set.

Intermediate

I can describe two sets of objects as having the same quantity or not.

Beginner

I can match the members from one set to the members of the other set.* *This develops the strategy of one-to-one matching to compare sets and one-to-one correspondence when two sets have an equal number of items.


LP K.2 SOL K.2: The student, given a set containing 15 or fewer concrete objects, will

a) tell how many are in the set by counting the number of objects orally; b) write the numeral to tell how many are in the set; and c) select the corresponding numeral from a given set of numerals.

Learning Target: I can identify the number of objects in a set by counting the objects orally, selecting the numeral, and writing the numeral that matches the number of objects in the set. I can create a set of objects that matches a number from 0 through 15.



Advanced Proficient

I can create a set of objects that is greater than or less than a given number, or I can select or write a number that is greater than or less than a given number.* *This LT focuses on writing or selecting a number equal to the quantity in a set. The Advanced Proficient level extends this to identifying the relationship

between numbers by exploring greater than or less than a given number.

Proficient

I can identify the number of objects in a set by counting the objects orally, selecting the numeral, and writing the numeral that matches the number of objects in the set. I can create a set of objects that matches a number from 0 through 15.

Intermediate

I can recognize, select, and write the numerals that match the numbers I am counting.

Beginner

I can count orally from 0 through 15. I understand that the numbers I am counting tells me how many objects are in a set.


LP K.3 SOL K.3: The student, given an ordered set of ten objects and/or pictures, will indicate the ordinal position of each object, first through tenth, and the ordered position of each object. Learning Target: I can identify the ordinal positions for each object in a set of 10 objects that are in order (i.e. from left–to–right, right–to–left, top–to–bottom, and bottom–to–top).

Learning Progression

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations at each level of the learning progression.

Advanced Proficient

I can identify the ordinal positions for each object in a set of objects that are placed in order (i.e. from left–to–right, right–to–left, top–to–bottom, and bottom–to–top), and at any starting point in the set. For example:

Proficient


Intermediate

I can count* the ten objects that are placed in an order (i.e. from left–to–right, right–to–left, top–to–bottom, and bottom–to–top). *This is about cardinal numbers or counting numbers.

Beginner

I can organize a set of ten objects in order (i.e. from left–to–right, right–to–left, top–to–bottom, and bottom–to–top).


LP K.4ac SOL K.4: The student will:

a) count forward to 100 and backward from 10; c) count by fives and tens to 100.

Learning Target: I can count forward to 100 by ones, fives, and tens and I can count backward from 10. I can identify the patterns of counting by ones, fives, and tens using different models (hundreds chart, number line, etc.).



Advanced Proficient

I can relate counting to 100 in different ways and counting backwards from 10 to real-life situations (counting money, rocket launch, etc.).

Proficient

I can count forward to 100 by ones, fives, and tens and I can count backward from 10. I can identify the patterns of counting by ones, fives, and tens using different models (hundreds chart, number line, etc.).

Intermediate

I can understand that I can count in equal groups to get to the target number more quickly.

Beginner

I can count to 100 by ones and backward from 10.


LP K.4b SOL K.4: The student will: b) identify one more than a number and one less than a number. Learning Target: I can identify one more than a number and one less than a number and show the relationship using objects.



Advanced Proficient

I can identify two more than a number, two less than a number, three more than a number, three less than a number, and show the relationship using objects.

Proficient


Intermediate

I can identify one more than a given number and one less than a given number on a hundreds chart or a number line.

Beginner

I can count the number of objects in a set and identify that number on a hundreds chart or a number line.


LP K.5 SOL K.5: The student will identify the parts of a set and/or region that represent fractions for halves and fourths. Learning Target: I can show (represent) halves and fourths as parts of sets and parts of regions.



Advanced Proficient

I can represent fourths as parts of halves.

Proficient I can show (represent) halves and fourths as parts of sets and parts of regions.

Intermediate I can show (represent) fourths as parts of a region and as part of a set by using manipulatives..

Beginning I can show (represent) halves as parts of a region and part of a set by using manipulatives.


LP K.6 SOL K.6: The studentwill model adding and subtracting whole numbers, using up to 10 concrete objects. Learning Target: I can use manipulative to model and describe addition and subtraction.



Advanced Proficient

I can describe how addition and subtraction are alike and how they are different.

Proficient I can use manipulatives to model and describe addition and subtraction.

Intermediate I can take away a set of objects from a given set and use counting backward OR counting on to find the difference.

Beginning I can combine two sets of concrete objects and count on to find a sum.


LP K.7 SOL K.7: The student will recognize a penny, nickel, dime, and quarter and will determine the value of a collection of pennies and/or nickels whose total value is 10 cents or less. Learning Target: I can identify and describe a penny, nickel, dime, and quarter and determine the value of a collection of coins (10 cents or less)

and equivalent amounts (a nickel is the same as 5 pennies).



Advanced Proficient

I can create a collection of coins based on clues (for example: Create a collection of coins whose value is 23 cents and includes at least 2 nickels).

Proficient

I can identify and describe a penny, nickel, dime, and quarter and determine the value of a collection of coins (10

cents or less) and equivalent amounts (a nickel is the same as 5 pennies).

Intermediate

I can recognize and identify a penny, nickel, dime, and quarter.

Beginner

I can understand that coins represent a specific value of money.


LP K.8 SOL K.8: The student will identify the instruments used to measure length (ruler), weight( scale), time (clock: digital and analog; calendar: day, month, and season), and temperature (thermometer). Learning Target: I can identify instruments used to measure length, weight, time, and temperature.



Advanced Proficient

I can identify a non-standard instrument to measure length, weight, and/or temperature.

Proficient


Intermediate

I can identify the instruments that are used for measurement. (i.e. I can identify a ruler, a scale, a clock, a calendar, and a thermometer).

Beginner

I understand that length, weight, time, and temperature can be measured.


LP K.9 SOL K.9: The student will tell time to the hour, using analog and digital clocks. Learning Target: I can tell time to the hour on an analog and digital clock and relate the time to daily routines.



Advanced Proficient

I can name a time based on clues (for example: What time of day could it be if the hour hand is on the 6 and you are eating dinner?).

Proficient


Intermediate

I can use the hour hand on an analog clock to determine time to the nearest hour.

Beginner

I can recognize an analog and digital clock as a tool to measure time.


LP K.10 SOL K.10: The student will compare two objects or events, using direct comparisons or nonstandard units of measure, according to one or more of the following attributes: Length (shorter, longer), height (shorter, taller), weight (heavier, lighter), temperature (hotter, colder). Examples of nonstandard units include foot length, hand span, new pencil, paper clip, and block. Learning Target: I can compare and measure objects using foot length, hand span, new pencil, paper clip, and/or block.



Advanced Proficient

I can investigate how nonstandard units may be equivalent; i.e. how many hand spans “equal” a foot length?

Proficient I can compare and measure objects using foot length, hand span, new pencil, paper clip, and/or block.

Intermediate I can measure objects using foot length, hand span, new pencil, paper clip, and/or block and tell how many measures the object is (3 hand spans, 2 foot lengths).

Beginning I can compare objects and tell which is longer, taller, heavier, hotter.


LP K.11a SOL K.11: The student will:

a) identify, describe, and trace plane geometric figures (circle, triangle, square, and rectangle); and…

Learning Target: I can name geometric shapes and tell how they are different.



Advanced Proficient

I can tell how squares and rectangles are different and how they are alike.

Proficient I can name geometric shapes and tell how they are different.

Intermediate I can describe the size of bgeometric shapes.

Beginning I can sort, identify, and trace geometric shapes.


LP K.11b SOL K.11: The student will: b) compare the size (larger, smaller) and shape of geometric figures (circle, triangle, square, and rectangle). Learning Target: I can tell (compare) which shape is larger and which is smaller.



Advanced Proficient

I can put three or more shapes in order by size.

Proficient I can tell (compare) which shape is larger and which is smaller.

Intermediate I can tell (compare) which shape is larger.

Beginning I can tell (compare) which shape is smaller.


LP K.12 SOL K.12: The student will describe the location of one object relative to another and identify representations of plane geometric figures regardless of their positions in space. Learning Target: I can describe the location of one object relative to another and identify representations of plane geometric figures regardless of their positions in space.



Advanced Proficient

I can place an object above or below or next to another object.

Proficient

I can identify a triangle, circle, square, and rectangle and describe if one of them is above or below or next to another one.

Intermediate I can identify a triangle, circle, square, and rectangle.

Beginning I can describe an object as above or below or next to another object.


LP K.13 SOL K.13: The student will gather data by counting and tallying. Learning Target: I can collect answers to a question, keep track of the answers by using tally marks, and organize the answers in categories.



Advanced Proficient

I can combine my data with another set of data for the same question and show the combined data by counting and tallying.

Proficient


Intermediate

I can gather data for a question (i.e. Did you bring lunch? How many pets do you have? What type of shoes are you wearing?).

Beginner

I can count by fives and use tally marks to represent the different numbers.


LP K.14 SOL K.14: The student will display gathered data in object graphs, picture graphs, and tables, and will answer questions related to the data. Learning Target: I can analyze data I have displayed in graphs and tables.



Advanced Proficient

I can create multiple ways to represent data and develop questions to analyze the data.

Proficient I can analyze data I have displayed in graphs and tables.

Intermediate I can display data using pictures as counting devices.

Beginning I can display data by arranging manipulatives/objects or into groups (object graph).


LP K.15 SOL K.15: The student will sort and classify objects according to attributes. Learning Target: I can sort and classify a set of objects in at least two different ways and explain my reasoning.



Advanced Proficient

I can sort and classify a set of objects in multiple ways and justify the most efficient way for a real-life situation (for example, sorting food at a grocery store).

Proficient


Intermediate

I can sort and classify a set of objects in at least one way.

Beginner

I can identify characteristics of objects (color, size, shape, etc.).


LP K.16 SOL K.16: The student will identify, describe, and extend repeating patterns. Learning Target: I can compare the similarities and differences between patterns.



Advanced Proficient

I can find examples of repeating patterns in real life situations and connect it to other repeating patterns. (i.e. the colors on a checkerboard – red, black, red, black is a repeating pattern that looks like the AB-AB pattern)

Proficient


Intermediate

I can identify the core of a repeating pattern and extend the pattern (by two repetitions or more).

Beginner

I can recognize repeating patterns around me and in practical situations.

NCSM Great Tasks K-5 (available in all LCPS Elementary Schools)

VA SOL Alignment

Kindergarten Math

Domino Addition and Subtraction

Launch

SOL K.2 The student, given a set containing 15 or fewer concrete objects, will a) tell how many are in the set by counting the number of objects orally; b) write the numeral to tell how many are in the set; and c) select the corresponding numeral from a given set of numerals.

Activity

SOL K.1 The student, given two sets, each containing 10 or fewer concrete objects, will identify and describe one set as having more, fewer, or the same number of members as the other set, using the concept of one-to-one correspondence.

Counting Sheep

Launch

SOL K.2 The student, given a set containing 15 or fewer concrete objects, will a) tell how many are in the set by counting the number of objects orally; d) write the numeral to tell how many are in the set; and e) select the corresponding numeral from a given set of numerals.

Activity SOL K.3 The student, given an ordered set of ten objects and/or

pictures, will indicate the ordinal position of each object, first through tenth, and the ordered position of each object.

How Big is Your Foot?

Launch & Activity

SOL K.10 The student will compare two objects or events, using direct comparisons or nonstandard units of measure, according to one or more of the following attributes: length (shorter, longer), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder). Examples of nonstandard units include foot length, hand span, new pencil, paper clip, and block.

1st Grade Math

Bunny Hip Hop

Launch

SOL 1.1 The student will a) count from 0 to 100 and write the corresponding numerals;

and b) group a collection of up to 100 objects into tens and ones and

write the corresponding numeral to develop an understanding of place value.

Activity

SOL 1.2 The student will count forward by ones, twos, fives, and tens to 100 and backward by ones from 30.

When does it Happen?

Launch & Activity

SOL 1.8 The student will tell time to the half-hour, using analog and digital clocks.

Ten is our Friend!

Launch

SOL 1.5 The student will recall basic addition facts with sums to 18 or less and the corresponding subtraction facts.

Activity SOL 1.6 The student will create and solve one-step story and picture

problems using basic addition facts with sums to 18 or less and the corresponding subtraction facts.

2nd Grade Math

Creative Cards

Launch & Activity

SOL 2.16 The student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and rectangle/rectangular prism).

Piggy Banks

Launch & Activity

SOL 2.10 The student will a) count and compare a collection of pennies, nickels, dimes, and

quarters whose total value is $2.00 or less; and b) correctly use the cent symbol (¢), dollar symbol ($), and

decimal point (.).

Show What You Know!

Launch

SOL 2.2 The student will a) identify the ordinal positions first through twentieth, using an

ordered set of objects; and b) write the ordinal numbers.

Activity

SOL 2.8 The student will create and solve one- and two-step addition and subtraction problems, using data from simple tables, picture graphs, and bar graphs.

SOL 2.9 The student will recognize and describe the related facts that represent and describe the inverse relationship between addition and subtraction.

Pies for Sale

Launch SOL 2.19 The student will analyze data displayed in picture graphs,

pictographs, and bar graphs.

Activity

SOL 2.17 The student will use data from experiments to construct picture graphs, pictographs, and bar graphs.

SOL 2.19 The student will analyze data displayed in picture graphs, pictographs, and bar graphs.

3rd Grade Math

Playful Puppies

Launch

SOL 3.10 The student will a) measure the distance around a polygon in order to determine

perimeter; and b) count the number of square units needed to cover a given

surface in order to determine area.

SOL 3.20 The student will a) investigate the identity and the commutative properties for

addition and multiplication; and b) identify examples of the identity and commutative properties

for addition and multiplication.

Activity

SOL 3.5 The student will recall multiplication facts through the twelves table, and the corresponding division facts.

SOL 3.6 The student will represent multiplication and division, using area, set, and number line models, and create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.

SOL 3.10 The student will a) measure the distance around a polygon in order to determine

perimeter; and b) count the number of square units needed to cover a given

surface in order to determine area.

SOL 3.20 The student will a) investigate the identity and the commutative properties for

addition and multiplication; and b) identify examples of the identity and commutative properties

for addition and multiplication.

Correcting the Calculator

Launch & Activity

SOL 3.1 The student will a) read and write six-digit numerals and identify the place value

and value of each digit; b) round whole numbers, 9,999 or less, to the nearest ten,

hundred, and thousand; and c) compare two whole numbers between 0 and 9,999, using

symbols (>, <, or = ) and words (greater than, less than, or equal to).

SOL 3.2 The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences. The student will use these relationships to solve problems.

Fraction Reactions

Launch & Activity

SOL 3.3 The student will a) name and write fractions (including mixed numbers)

represented by a model; b) model fractions (including mixed numbers) and write the

fractions’ names; and c) compare fractions having like and unlike denominators, using

words and symbols (>, <, or =).

4th Grade Math

Bugs, Giraffes, Elephants, and More

Launch

SOL 4.2 The student will a) compare and order fractions and mixed numbers; b) represent equivalent fractions; and c) identify the division statement that represents a fraction.

SOL 4.7 The student will a) estimate and measure length, and describe the result in

both metric and U.S. Customary units; and b) identify equivalent measurements between units within

the U.S. Customary system (inches and feet; feet and yards; inches and yards; yards and miles) and between units within the metric system (millimeters and centimeters; centimeters and meters; and millimeters and meters).

SOL 4.14 The student will collect, organize, display, and interpret data from a variety of graphs.

Activity

SOL 4.14 The student will collect, organize, display, and interpret data from a variety of graphs.

Does it Make Sense?

Launch

SOL 4.3 The student will a) read, write, represent, and identify decimals expressed

through thousandths; b) round decimals to the nearest whole number, tenth, and

hundredth; c) compare and order decimals; and

SOL 4.4 The student will a) estimate sums, differences, products, and quotients of whole

numbers; b) add, subtract, and multiply whole numbers; c) divide whole numbers, finding quotients with and without

remainders; and d) solve single-step and multistep addition, subtraction, and

multiplication problems with whole numbers.

Activity

SOL 4.4 The student will a) estimate sums, differences, products, and quotients of whole

numbers; b) add, subtract, and multiply whole numbers; c) divide whole numbers, finding quotients with and without

remainders; and d) solve single-step and multistep addition, subtraction, and

multiplication problems with whole numbers.

The Bigger Half

Launch & Activity


Harry’s Hike

Launch


Activity

SOL 4.5 The student will a) determine common multiples and factors, including least

common multiple and greatest common factor; b) add and subtract fractions having like and unlike

denominators that are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fractions, using common multiples and factors;

c) add and subtract with decimals; and d) solve single-step and multistep practical problems involving

addition and subtraction with fractions and with decimals.

5th Grade Math

Packed Parking

Launch

SOL 5.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

Activity

SOL 5.5 The student will a) find the sum, difference, product, and quotient of two numbers

expressed as decimals through thousandths (divisors with only one nonzero digit); and

b) create and solve single-step and multistep practical problems involving decimals.

SOL 5.6 The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form.

Finding Fractions

Launch

SOL 5.2 The student will a) recognize and name fractions in their equivalent decimal form

and vice versa; and b) compare and order fractions and decimals in a given set from

least to greatest and greatest to least.

Activity

SOL 5.17 The student will describe the relationship found in a number pattern and express the relationship.

SOL 5.18 The student will a) investigate and describe the concept of variable; b) write an open sentence to represent a given mathematical

relationship, using a variable; c) model one-step linear equations in one variable, using addition

and subtraction; and d) create a problem situation based on a given open sentence,

using a single variable.

SOL 5.19 The student will investigate and recognize the distributive property of multiplication over addition.

Varying Volumes

Launch & Activity

SOL 5.8 The student will a) find perimeter, area, and volume in standard units of measure; b) differentiate among perimeter, area, and volume and identify

whether the application of the concept of perimeter, area, or volume is appropriate for a given situation;

c) identify equivalent measurements within the metric system; d) estimate and then measure to solve problems, using U.S.

Customary and metric units; and e) choose an appropriate unit of measure for a given situation

involving measurement using U.S. Customary and metric units.

SOL 5.13 The student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will

a) develop definitions of these plane figures; and b) investigate and describe the results of combining and

subdividing plane figures.

Location, Location, Location

Launch

SOL 5.17 The student will describe the relationship found in a number pattern and express the relationship.

Activity

SOL 5.18 The student will a) investigate and describe the concept of variable; b) write an open sentence to represent a given mathematical

relationship, using a variable; c) model one-step linear equations in one variable, using addition

and subtraction; and d) create a problem situation based on a given open sentence,

using a single variable.

SOL 5.19 The student will investigate and recognize the distributive property of multiplication over addition.

Mathematics Literature Connections Organized by Curriculum Units

Grade K Math Literature Connections

Unit 2: Counting

One, Two, Skip a Few: First Number Rhymes by Roberta Arenson

98,99,100! Ready or Not, Here I come! by Marilyn Bums and Teddy Slater

Unit 3: Comparing Sets

20 Hungry Piggies: A Number Book by Trudy Harris

Ten Little Rubber Ducks by Eric Carle

Ten Little Caterpillars by Bill Martin Jr

Henry the Fourth by Stuart J. Murphy

One Monday Morning by Uri Shulevitz

The Napping House by Audrey Wood

Tally O’Malley by Stewart J. Murphy

So you want to be President? By Judith St. George

The Great Graph Contest By Loreen Leedy

Unit 4: Geometry & Sorting

Dave’s Down-to-Earth Rock Shop by Stuart J. Murphy

Unit 5: Shapes in Space

Twizzlers Shapes and Patterns by Jerry Pallotta


Give Me Half by Stuart J. Murphy

Full House by Dayle Ann Dodds


Measuring Up by J.E. Osborne

Dumpling Soup by Jama Kim Rattigan

How Big is a Foot by Rolf Myller

Big and Little by Steven Jenkins

Time to… by Bruce McMillan

Telling Time: How to Tell Time on Digital and Analog Clocks by Jules Older

Telling Time with Big Mama Cat by D. Harper

Biggest, Strongest, Fastest by Steven Jenkins

Inch by Inch by Leo Lionni

Before and After: A Book of Nature Timescapes by Jan Thornhill


Arctic Fives Arrive by Elinor J. Pinczes

26 Letters and 99 Cents by Tana Hoban


More or Less by Stuart J. Murphy

Animals on Board by Stuart J. Murphy

A Quarter from the Tooth Fairy by Caren Holtzman

Grade 1 Math Literature Connections

Unit 2: Sorting, Ordering, & Patterns

Twizzlers Shapes and Patterns by Jerry Pallotta

Unit 3: Developing a Base Ten System

Moira’s Birthday by Robert Munsch

Something Good by Robert Munsch

Is It Larger? Is It Smaller? By T. Hoban

One Hundred Hungry Ants by Elinor J. Pinczes

Ten Sly Piranhas: A Counting Story in Reverse by William Wise

How Many, How Many, How Many by Rick Walton

98, 99, 100! Ready or Not, Here I Come! By Marilyn Burns and Teddy Slater

Stay in Line by Teddy Slater


Three Pigs, One Wolf, and Seven Magic Shapes by Grace Maccarone

Flat Stanley by J. Brown

The Shapes We Eat by Simone T. Ribke

Give Me Half! By Stuart J. Murphy

Gator Pie by L. Mathews

Unit 5: Time & Fractions


Telling Time: How to Tell Time on Digital and Analog Clock by Jules Older


Unit 6: Working With Data

Probably Pistachio by Stuart J. Murphy

So You Want to be President? By Judith St. George

The Great Graph Contest by Loreen Leedy

Ready, Set, Hop! By Stuart J. Murphy

Bunches and Bunches of Bunnies by Mathews and Bassett


Rooster’s Off to See the World by Eric Carle

Round Trip by A. Jonas

Lemonade For Sale by Stuart J. Murphy


How Do You Measure Weight? by Thomas K. and Heather Adamson

The Greedy Triangle by Marilyn Burns


How Big is a Foot? by Rolf Myller


Biggest, Strongest, Fastest by Steven Jenkins



Best Bug Parade by Stuart J. Murphy

Me and the Measure of Things by J. Sweeney

Unit 9: Applying Place Value

Shoes, Shoes, Shoes by A. Morris

Unit 10: Whole Number Computation

Animals on Board by Stuart J. Murphy

Elevator Magic by Stuart J. Murphy

Ten Black Dots by Donald Crew

Rooster’s Off to See the World by Eric Carle


How High Can a Dinosaur Count? by V. Fisher


The Penny Pot by Stuart J. Murphy


Unit 2: Extending Place Value

The Crayon Counting Book by Pam Munoz

Underwater Counting: Even Numbers by Jerry Pallotta

Unit 3: Computational Fluency

Growing Patterns: Fibonacci Numbers in Nature by S.G. and R.P. Campbell

Mission: Addition by Loreen Leedy

Each Orange Had 8 Slices: A Counting Book by Paul Giganti


Unit 4: Applying Place Value to Computation/Problem Solving

Great Estimations by Bruce Goldstone

How Many Seeds in a Pumpkin? By Margaret McNamara and G. Brian Karas

How Many Feet? How Many Tails? A Book of Math Riddles by Marilyn Burns

Sam and the Lucky Money by K. Chinn

Balancing Act by Ellen Stoll Walsh

Betcha by Stuart J. Murphy

Unit 5: Probability & Data

Frog and Toad are Friends by A. Lobel

Polar Bear Math: Learning About Fractions from Klondike and Snow by Nagda and Bickel

Get Up and Go! By Stuart J. Murphy

Unit 6: Data & Problem Solving

So You Want to be President? By Judith St. George

Unit 7: Time & Temperature

Telling Time: How to Tell Time on Digital and Analog Clock by Jules Older


Why Mosquitoes Buzz in People’s Ears: A West African Tale by V. Aardema

The Grouchy Lady Bug by Eric Carle

Chimp Math: Learning About Time from a Baby Chimpanzee by Nagda and Bickel

What Time Is It? A Book of Math Riddles by Sheila Keenan


Eating Fractions by Bruce McMillan


Full House by Dayle Ann Dodds

The Patchwork Quilt by Valerie Flournoy



How Big is a Foot? By Rolf Myller



Biggest, Strongest, and Fastest by Steven Jenkins



Jelly Beans for Sale by Bruce McMillan

The Penny Pot by Stuart J. Murphy

The Coin Counting Book by Rosanne Lanczak Williams

Once Upon a Dime by Nancy Kelly Allen


Unit 2: Place Value

Many Is How Many? By Illa Pondendorf

A Light in the Attic (“How Many, How Much” and “Overdues”) by Shel Silverstein

Counting on Frank by Rod Clement

How Much Is a Million? by David M. Schwartz

If You Made a Million by David M. Schwartz

Moira’s Birthday by Robert Munsch

Something Good by Robert Munsch

Unit 3: Computation With Whole Numbers (addition/subtraction)

Ten Black Dots by Donald Crews

Dealing with Addition Lynette Long

One Duck Stuck by Phyllis Root

One Gorilla by Atsuko Morozumi

A Three Hat Day by Laura Geringer

Unit 4: Money

Alexander, Who Used To Be Rich Last Sunday by Judith Viorst

Penny: The Forgotten Coin by Denise Brenna-Nelson

The Coin Counting Book by Rozanne Lanczak Williams

The Penny Pot by Stuart Murphy

Pigs Will Be Pigs: Fun With Math and Money by Amy Axelrod

Unit 5: Computation With Whole Numbers (multiplication/division)

Amanda Bean’s Amazing Dream by Cindy Neuschwander

A Remainder of One (*extension) by Elinor J. Pinczes

One Hundred Angry Ants by Elinor J. Pinczes

2 x 2 = Boo by Loreen Leedy

7 x 9 Trouble by Claudia Mills

Too Many Kangaroo Things to Do by Stuart Murphy

Divide and Ride by Stuart Murphy

Bananas Jacqueline Farmer

Centipede’s 100 Shoes by Tony Ross

Ten Times Better by Richard Michelson

Unit 6: Patterns & Data

Emma’s Christmas by Irene Trivias

The Doorbell Rang by Pat Hutchins

One Hundred Angry Ants by Elinor Pinczes

She Came Bringing Me That Little Baby Girl by Eloise Greenfield

Knots on a Counting Rope by Bill Martin Jr.

Berries, Nuts, and Seeds by Diane L. Burns

Lemonade for Sale by Stuart Murphy

Tiger Math: Learning to Graph from a Baby Tiger by Ann Whitehead Nagda

Grapes of Math by Greg Tang

The Quilting Bee by Gail Gibbons

Two Ways to Count to Ten: A Liberian Folktale by Ruby Dee

Unit 7: Geometry

The Important Book by Margaret Wise Brown

Three Pigs, One Wolf, and Severn Magic Shapes by Grace Maccarone

Pablo’s Tree Pat Mora

If You Were a Polygon Marcie Aboff

It Looked Like Spilt Milk by Charles G. Shaw

Mummy Math by Cindy Neuschwander

Shape Up by David Adler

A Cloak for the Dreamer by Aileen Friedman

Unit 8: Fractions, Probability, & Measurement (length) / Unit 9: Computation With Fractions

Eating Fractions by Bruce McMillan

Seven Little Hippos by Mike Thaler

Shoes, Shoes, Shoes by Ann Morris

Biggest, Strongest, Fastest Steve Jenkins

The Wolf’s Chicken Stew Keiko Kasza

A Very Improbably Story: A Math Adventure by Edward Einhorn

The Thirteen Days of Halloween Carool Greene

The Doorbell Rang Pat Hutchins

Whole-y Cow, Fractions are Fun! by Taryn Souders

Apple Fractions by Jerry Pallotta

The Hershey’s Milk Chocolate Bar Fractions BookU by Jerry Pallotta

Fraction Action by Loreen Leedy

Unit 10: Elapsed Time and Temperature

Telling Time: How to Tell Time on Digital and Analog Clocks by Jules Older

What Time is it, Mr. Crocodile? By Judy Sierra

Chimp Math by Ann Whitehead Nagda

Unit 11: Measurement

Spaghetti and Meatballs for All by Marilyn Burns

Perimeter, Area, and Volume David A. Adler

Pastry School in Paris Cindy Neuschwander

Measuring Penny (length) by Loreen Leedy

Biggest, Strongest, Fastest by Steve Jenkins

Is a Blue Whale the Biggest Thing There Is? by Robert E. Wells

Polly’s Pen Pal by Stuart L. Murphy


Room for Ripley by Stuart Murphy


Unit 2: Number Sense: Whole Numbers

A Million Fish…More or Less by Patricia C. McKissack

Unit 3: Whole Number Operations & Applications (adding & subtracting)

Math Curse by Jon Scieszka and Lane Smith

The $1.00 Word Riddle Book by Marilyn Burns

Esio Trot by Roald Dahl

From Seashells to Smart Cards: Money and Currency (everyday economics) by Ernestine

Giesecke

Anno’s Magic Seeds by Mitsumasa Anno

Equal Shmequal by Virginia Kroll

Unit 4: Whole Number Operations & Applications (multiplication & division)

The King’s Chessboard by David Birch

The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan

Math Curse by Jon Scieszka and Lane Smith

Hottest, Coldest, Highest, Deepest by Steve Jenkins

In the Next Three Seconds…Predictions for the Millenium by Comp. Rowland Morgan

Ten Times Better by Richard Michelson

Two Ways to Count to Ten: A Liberian Folktale by Ruby Dee

A Remainder of One by Elinor J. Pinczes

Counting on Frank by Rod Clement

Unit 5: Data & Statistics

The Great Graph Contest by Loreen Leedy

Unit 6: Number Sense: Rational Numbers

The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan

One Riddle, One Answer by Lauren Thompson

Icebergs and Glaciers by Seymour Simon

Tiger Math: Learning to Graph from a Baby Tiger by Ann W. Nagda and Cindy Bickel

Unit 7: Rational Number Operations

Jump, Kangaroo Jump (Math Start) by Stuart Murphy and Kevin O’Malley

Pizza Counting by Christina Dobson

Piece=Part=Portion by Gifford and Thaler

Fractions=Trouble! By Claudia Mills

Unit 8: Probability & Data Using Rational Numbers

Jumanji by Chris Van Allsburg

A Very Improbable Story by Edward Einhorn and Adam Gustavson

Pigs at Odds by Amy Axelrod and Sharon Nally

Unit 9: Patterns & Measurement

G is for Googol: A Math Alphabet Book by David M. Schwartz

How Much, How Many, How Far, How Heavy, How Long, How Tall Is 1000? by Helen

Nolan

Icebergs and Glaciers by Seymour Simon

If You Hopped Like a Frog by David M. Schwartz

Is a Blue Whale the Biggest Thing There Is? By Robert E. Wells

Biggest, Strongest, Fastest by Steve Jenkins

Unit 10: Plane Geometry & Transformations

Marvelous Math by Lee Bennett Hopkins

The Warlord’s Puzzle by Virginia Walton Pilegard

Shape Up! Fun with Triangles and Other Polygons by David Adler and Nancy Tobin

Spaghetti and Meatballs for All! by Marilyn Burns and Debbie Tilley

Chickens on the Move (Math Matters!) by Pamela Pollack


Unit 2

A Remainder of One by Elinor Pinczes

My Even Day by Doris Fisher

The Grapes of Math by Greg Tang

Math Appeal by Greg Tang

Among the Odds and Evens by Prescilla Turner


Unit 3

Germs Make Me Sick by Melvin Berger

Bats on Parade by Kathi Appelt

Unit 4

Alexander Who Used to Be Rich Last Sunday by Judith Viorst

Fraction Fun by David Adler

Unit 5

Measuring Penny by Loreen Leedy

Alexander Who Used to Be Rich Last Sunday by Judith Viorst

Counting On Frank by Rod Clements

How Long? How Wide? by Brian Cleary

Millions to Measure by David Schwartz

Fractions, Decimals, and Percents by David Adler

Unit 6

The Greedy Triangle by Marilyn Burns

Sir Cumference and the Dragon of Pi by Cindy Neuschwander

Unit 7

Chimp Math, Tiger Math, Polar Bear Math, and Cheetah Math (series) by Anne Nagda

A More Perfect Union by Betsy Maestro

Model Performance Indicator Information for Curriculum Guides

Embedded in the LCPS curriculum guides are sample Model Performance Indicator (MPI) tables (below).

These tables will be useful as you differentiate instruction for all of your learners, but they are especially

helpful for English Language Learners. Below are frequently asked questions about MPI.

What is a Model Performance Indicator (MPI)?

An MPI is a tool that can be used to show examples of how language is processed or produced within a

particular context, including the language with which students may engage during classroom instruction and

assessment.

Each MPI contains three main parts:

Language Function: The first part of an MPI, this shows how students are processing/producing

language at each level of language proficiency

Content Stem: This will remain consistent throughout an MPI strand and should reflect the knowledge

and skills of the state’s content standards

Support: The final part of an MPI, this highlights the differentiation that should be incorporated for

students at each language level by suggesting appropriate instructional supports for students at each

level of language proficiency

The samples provided also include an example context for language use that provides a brief descriptor of the

activity or task in which students would be engaged, while the inclusion of topic-related language helps to

support the emphasis on imbedding academic language instruction into our content-area teaching practices.

How can these sample MPIs help me?

Educators can use MPI strands in several ways:

to align students’ performance to levels of language development

as a tool for creating language objectives/targets that will help extend students’ level of language

proficiency

as a means for differentiating instruction that incorporates the language of the content area in a way that

meets the needs of students’ levels of language proficiency

An MPI strand helps illustrate the progression of language development from one proficiency level to the next

within a particular context. As these strands are examples, they represent one of many possibilities; therefore,

they can be transformed in order to be made more relevant to the individual classroom context.

Where can I get more information about WIDA, MPIs, etc.?

See My Learning Plan for several WIDA training modules

Introduction to the WIDA ELD Standards

Transforming the WIDA ELD Standards

Interpreting the WIDA ACCESS Score Report

The information above was adapted from the 2012 Amplification of the English Development Standards Kindergarten-Grade 12 resource guide and can be accessed at www.wida.us

http://www.wida.us/

SOL K.13 The student will gather data by counting and tallying.

Example Context for Language Use: Students will count tally marks to organize data gathered on the number of girls and the number of boys in

each of two kindergarten classrooms in the school.

COGNITIVE FUNCTION: Students at all levels of English proficiency will ANALYZE information by counting and tallying data gathered.

LIS

TE

NIN

G

Level 1

Entering

Level 2

Emerging

Level 3

Developing

Level 4

Expanding

Level 5

Bridging

Lev

el 6-R

each

ing

Apply teacher-modeled

oral directions on

counting and tallying

data gathered using

illustrated graphic

organizers in small

groups using L1 or L2

Apply teacher-modeled

oral directions on


data gathered based on

simple oral commands

in small groups

Organize counting and

tallying data gathered

based on teacher-modeled

oral directions using

illustrated graphic

organizers with a partner



based on teacher-

modeled oral directions

using illustrated graphic

organizers



based on teacher-


SP

EA

KIN

G

Describe counting and


using teacher modeling,

illustrated graphic

organizers, and

illustrated word banks in

small groups using L1 or

L2

Present counting and


using teacher modeling,

illustrated graphic

organizers, and

illustrated word banks

with a partner

Explain counting and


using teacher modeling

and illustrated graphic


Discuss counting and




Compare and contrast


data gathered using

illustrated graphic

organizers with a

partner

RE

AD

ING

Level 1

Entering

Level 2

Emerging

Level 3

Developing

Level 4

Expanding

Level 5

Bridging

Lev

el 6-R

each

ing

Identify counting and



organizers and illustrated

word banks in small

groups using L1 or L2

Associate with objects

the counting and tallying

data gathered using

illustrated graphic

organizers and word

banks with a partner

Develop questions about

counting and tallying data

gathered using labeled and

illustrated graphic


Categorize counting and


with using labeled and

illustrated graphic


Compare and contrast

categories of objects

from counting and


using labeled and

illustrated graphic

organizers

WR

ITIN

G Identify counting and


using illustrated word

cards in small groups

using L1 or L2

Describe counting and


using sentence frames

and illustrated word

cards with a partner

Explain counting and


using sentence fames and

illustrated word cards with

a partner

Formulate questions

about counting and


using sentence frames

with a partner

Create a chart to show


data gathered with a

partner

TOPIC-RELATED LANGUAGE: Students at all levels of English language proficiency interact with grade level words and expressions such as:

data, data collection, tally marks, tallying, apply, organize, describe, present, explain, discuss, compare and contrast, identify, associate, develop,

categorize, identify, explain, formulate, create

SOL K.14 The student will display gathered data in object graphs, picture graphs, and tables, and will answer questions related to the data.

Example Context for Language Use: Students will answer questions about data gathered and displayed on a picture graph of the class’ favorite ice

cream.

COGNITIVE FUNCTION: Students at all levels of English language proficiency will EVALUATE data in tables, object graphs, or picture

graphs.

LIS

TE

NIN

G

Level 1

Entering

Level 2

Emerging

Level 3

Developing

Level 4

Expanding

Level 5

Bridging

Lev

el 6-R

each

ing

Identify data on a table,

object graph, or picture

graph based on teacher-


during whole group

instruction using

manipulatives and

illustrated examples





using illustrated examples

and visual supports in a

small group

Classify data on a table,


graph following one-step

oral commands using

illustrated examples in small

groups

Compare data on a table,


graph following multi-step

oral commands using visual

supports and graphic


Evaluate data on a table,


graph in response to oral

questions from the

teacher using graphic


SP

EA

KIN

G

Present data on a table,




using manipulatives and

illustrated examples during

whole group instruction

Present data on a table,


graph following simple

oral commands using

illustrated examples and

visual supports in small

groups

Describe data on a table,


graph using visual supports

and graphic organizers in

small groups

Discuss data on a table,


graph using visual supports

and graphic organizers with

a partner

Explain data on a table,


graph using visual

supports and graphic


R

EA

DIN

G

Level 1

Entering

Level 2

Emerging

Level 3

Developing

Level 4

Expanding

Level 5

Bridging

Lev

el 6-R

each

ing



graph based on labeled

illustrations during whole

group instruction




illustrations in small

groups




illustrations in a small group




illustrations with a partner

Draw conclusions about

data on a table, object

graph, or picture graph

based on labeled

illustrations with a

partner

WR

ITIN

G Identify data on a table,


graph using labeled

illustrations and graphic

support during whole group

instruction

Describe data on a table,


graph using models and

illustrated word cards in a

small group

Explain data on a table,


graph using models and

illustrated word cards in a

small group



graph using word banks and

illustrated graphic


Compile data on a table,


graph using word banks

and graphic organizers

with a partner

TOPIC-RELATED LANGUAGE: TOPIC-RELATED LANGUAGE: Students at all levels of English language proficiency interact with grade

level words and expressions such as gather, tables, picture graph, object graph, data, data collection, more, less, equal, identify, classify, compare,

evaluate, present, describe, discuss, explain, draw conclusions, explain, compile

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