5th grade mathematics pacing guide and curriculum map

Scott County Public Schools

TO CREATE A COLLABORATIVE CULTURE WITH A FOCUS ON STUDENT LEARNING

2011-2012 5th

Mathematics Grade

Pacing Guide and Curriculum Map

Scott County Public Schools

TO CREATE A COLLABORATIVE CULTURE WITH A FOCUS ON STUDENT LEARNING

Introduction Scott County Elementary Teachers, It is my hope that this new pacing guide and curriculum map for the Kentucky Core Academic Standards (KCAS)

will provide you with a wealth of instructional material to ensure at least one year’s worth of growth for every single

child that you come into contact with over the course of the school year. As you begin to look through the document, you

will first see that it is designed differently than what we have used before. Please allow me to describe each of the

different sections in detail.

Pacing Guide Each grade level and content area will begin with a one-page pacing guide overview for the year. This pacing guide is

designed with a few different purposes in mind: a) Provide continuity within all elementary schools in Scott County so

that students who transfer from school to school will not miss large chunks of instruction, b) Allow each school to have

the flexibility to group concepts within a specific 9 weeks in a sequence that is most appropriate for them. You will

notice that for each 9 weeks, the specific clusters (math) and strands/clusters (ELA) that the students need to learn are

listed. The strands and clusters are listed in a suggested order for each 9 weeks, however, as long as all concepts are

covered within that specific 9 week period, each school may determine a slightly different sequence within the 9 weeks.

This, hopefully, will allow schools to continue, as necessary, any specific scope and sequence within a strong

instructional program that has proven success in raising student achievement (Everyday Math, etc.). The pacing guide

provides a broad overview of when during the year, specific concepts should be taught.

Curriculum Map The curriculum map is a much more specific piece of the document. The curriculum map provides each standard

deconstructed into smaller learning targets. Each of these learning targets has then been rewritten in student friendly

language and, in some cases, has success criteria added. The purpose of having the specific learning targets in student

friendly language with success criteria is to communicate it to the students at the beginning of each lesson (verbally and by

posting on the board) in order to help them take more ownership and accountability for their own learning. Words and

phrases that show up in parentheses in the student friendly targets are teacher information and can be removed before

posting on the board.

You will notice that in some cases, a specific standard shows up in multiple 9 week blocks. When that happens, please

pay special attention as it may mean that the intent is to review previously learned content or it may mean that different

targets within that standard are being taught each time.

Within the curriculum map you will also see additional columns that have been intentionally left blank for the 2011-2012

school year. Please use the columns for assessments, resources, and differentiation to record what you do for each during

this school year. At the end of the year, we will begin to add them to the district document.

As always, please keep in mind that this is a living, breathing document and as such will never be “finished.” We will

continually work to improve it as we collaborate together for the benefit of our students.

- Matt Thompson, Director of Elementary Schools 6/24/11

This document would not have been possible without the tireless efforts of the following teachers and administrators: Thank you so much for all your work!!!

Anne Mason Eastern Garth Northern Southern Stamping Ground Western Ruthie Adams

Maria Bennett

Amy Brannock

Crissy Ellison

Elizabeth Gabehart

Jessica Grant

Missie Hickey

Christa Kelly

Robin Lowe

Ashlee McCullough

Carla Prather

Paula Richey

Leah Riney

Annie Starnes

Ashley Beckett

Dana Boggs

Andrea Caudill

Stephanie Chenault

Ed Denney

Amanda Ford

Meghan Hillman

Lori Beth Mays

Jaime Moore

Rebecca Sargent

Morganne Vance

Rusty Andes

Ginny Barnes

Lori Bergman

Donna Cox

Amanda Featherston

Lisa Hanson

Rachel Lukacsko

Melissa Mullins

Angela Perkins

Misty Portwood

Theresa Shoup

Mary Frances Watts

Lori Wise

Kelley Bush

Monica Campbell

Melissa Chandler

Stephanie Foley

Debra Hunley

Judi Hunter

Wanda Johnson

Micah Rumer

Brittany Thomas

Marcie Ward

Tracey Werkheiser

Olivia Winkle

Dana Young

Bryan Blankenship

Laura Brock

Brooke Donovan

Marsha Downey

Jennifer Fraley

Jean Gillespie

Lori Graves

Judy Halasek

Shannon Marshall

Tammy Moore

Angela Schmidt

Angie Wallace

Robyn Bays

Stacey Carpenter

Kim Duncan

Betsy Fredericks

Amy Fryman

Wendy Holbrook

Jill Ingram

Paul Krueger

Bettie Ann Monroe

Jessica Napier

Kendle Nicholson

Sarah Price

Debbie Walker

Amy Baker

Corbie Bennett

Tammy Bisotti

Cari Bradley

Shannon Christopher

Peggy Cullen

Dorothy Daley

Cathy Gaebler

Deborah Haddad

Laura Johnson

Jeanne Keller

Amy McGuire

Heidi Mullins

Janet Parker

Lerin Parker

Terri Sutton

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Domain Key CC OA NBT NF MD G

Counting and Cardinality Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations – Fractions Measurement and Data Geometry

Scott County Pacing Guide

Fifth Grade Mathematics

1Nine

Weeks

st 5.OA: Write and interpret numerical expressions

• 5.OA.1 • 5.OA.2

5.OA: Analyze patterns and relationships • 5.OA.3

5.NBT: Perform operations with multi-digit whole numbers and with decimals to hundredths

• 5.NBT.5 • 5.NBT.6

5.NBT: Understand the place value system • 5.NBT.1 • 5.NBT.2 • 5.NBT.3a • 5.NBT.3b • 5.NBT.4

2Nine

Weeks

nd 5.NBT: Perform operations with multi-digit whole numbers and with decimals to hundredths

• 5.NBT.7

5.NF: Use equivalent fractions as a strategy to add and subtract fractions

• 5.NF.1

5.NF: Apply and extend previous understandings of multiplication and division to multiply and divide fractions

• 5.NF.3 • 5.NF.5b

5.NF: Use equivalent fractions as a strategy to add and subtract fractions

• 5.NF.1 • 5.NF.2

5.NF: Apply and extend previous understandings of multiplication and division to multiply and divide fractions

• 5.NF.4a • 5.NF.4b • 5.NF.5a • 5.NF.5b

3Nine

Weeks

rd 5.NF: Apply and extend previous understandings of multiplication and division to multiply and divide fractions

• 5.NF.6 • 5.NF.3 • 5.NF.7

5.MD: Convert like measurement units within a given measurement system

• 5.MD.1

5.MD: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition

• 5.MD.3ab • 5.MD.4 • 5.MD.5a • 5.MD.5b • 5.MD.5c

4Nine

Weeks

th 5MD: Represent and interpret data

• 5.MD.2 5.G: Graph points on the coordinate plane to solve real-world and mathematical problems

• 5.G.1 • 5.G.2

5.G: Classify two-dimensional figures into categories based on their properties

• 5.G.3 • 5.G.4

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Make sense of problems and persevere in solving

them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning

of others.

Model with mathematics. Use appropriate tools strategically.

Attend to precision. Look for and make use of structure.

Look for and express regularity in repeated

reasoning.

Scott County Schools 5th Grade Mathematics

9 Weeks Grade.Content.Standard Overall Standard Type 1st 2nd 3rd 4th 5.OA.1 K R S P

Domain Standard Operations and Algebraic Thinking Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Cluster Write and interpret numerical expressions

Assessments Vocabulary Resources Differentiation Target

# Target Type

State Target Student Friendly Target Success Criteria (If Appropriate)

Bold = First time ever Plain = previously introduced * = defined in glossary

Printed Resources

Technology Manipulatives Strategies Remediation Extension ESL

1 K Use order of operations including parentheses, brackets, or braces.

I can use multiplication/division and addition/subtraction to solve basic problems.

Order of operations

parenthesis

brackets

braces

numerical

expression

evaluate

interpret

2 K I can use parentheses in the order of operations to solve basic problems.

3 K I can use brackets in the order of operations to solve basic problems.

4 K I can use braces in the order of operations to solve basic problems.

5 R Evaluate expressions using the order of operations (including using parentheses, brackets, or braces).

I can evaluate equations using the order of operations. (Including parentheses, brackets, or braces)

This means I can solve equations using the algorithm: PBBEMDAS (Please Brother Bob Excuse My Dear Aunt Sally) Parentheses, Brackets, Braces, Exponents, Multiplication or Division, Addition or Subtraction.

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of others.




reasoning.



Domain Standard Operations and Algebraic Thinking Write simple expressions that record calculations with numbers, and interpret numerical expressions

without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 x (8+7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum of product.

Cluster Write and interpret numerical expressions


# Target Type


Bold = First time ever Plain = previously introduced

Printed Resources


1 K Write numerical expressions for given numbers with operation words.

I can write numerical expressions for given numbers with operation words.

operation words

numerical

expressions

interpret

2 K Write operation words to describe a given numerical expression.

I can write operation words to describe a given numerical expression (addition, subtraction, multiplication, division).

3 R Interpret numerical expressions without evaluating them.

I can interpret key words to tell what operation to use and write a numerical expression.

This means I can read a word problem and then combine number and operation signs (+, -, x, ÷) to show the problem. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 x (8+7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum of product.

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reasoning.



Domain Standard Operations and Algebraic Thinking Generate two numerical patterns using two given rules. Identify apparent relationships between

corresponding terms. From ordered pairs consisting of corresponding terms for two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule, “Add 3” and the starting number 0, and the given rule “Add 6” and the starting number 0, generate the terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Cluster Analyze patterns and relationships


# Target Type



Printed Resources


1 K Generate two numerical patterns using two given rules.

I can generate (create) two numerical patterns using two given rules.

generate

numerical patterns

corresponding

terms

coordinate grid

(graph)

ordered pairs

x-coordinate

y-coordinate

x-axis

y-axis

2

K

From ordered pairs consisting of corresponding terms for the two patterns

I can define corresponding terms.

3 I can form ordered pairs consisting of corresponding terms for the two patterns.

This mean I can write an ordered pair in the (x,y) pattern.

4

K Graph generated ordered pairs on a coordinate plane.

I can generate ordered pairs on a coordinate plane.

5 I can graph ordered pairs on a coordinate plane.

7

R

Analyze and explain the relationship between corresponding terms in the two numerical patterns.

I can analyze the relationships between corresponding terms in the two numerical patterns.

This means I can find the rule in a series of numbers, write the ordered pairs, and then graph the values on a coordinate plane.

8 I can explain the relationship between corresponding terms in the two numerical patterns.

This means I can explain the relationship between at least two numbers.

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of others.




reasoning.


9 Weeks Grade.Content.Standard Overall Standard Type 1st 2nd 3rd 4th 5.NBT.5 K R S P

Domain Standard Number and Operations in Base Ten Fluently multiply multi-digit whole numbers using the standard algorithm.

Cluster Perform operations with multi-digit whole numbers and with decimals to hundredths


# Target Type



Printed Resources


1 K Fluently multiply multi-digit whole numbers using the standard algorithm

I can multiply four-digit by two-digit whole numbers using the standard algorithm (a step by step process).

This means I can use the steps to multiply starting with the ones place.

algorithm

product

factors

addends

distributive

property

equation

variable

partial product

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reasoning.



Domain Standard Number and Operations in Base Ten Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors,

using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Cluster Perform operations with multi-digit whole numbers and with decimals to hundredths


# Target Type



Printed Resources


1 K Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors

I can divide up to four-digit dividends and two-digit divisors to find a quotient.

division

dividend

divisor

quotient/remainder

associative property

commutative

property

distributive property

inverse operation

rectangular array

equation

area models

mixed numbers

2

R

Use strategies based on place value, the properties of operations, and/or the relationship between multiplication and division to solve division problems

I can solve division problems using the inverse operation of multiplication.

3 I can solve division problems using the distributive property, associative property, commutative property, identity and property of zero.

4 R Illustrate and explain division calculations by using equations, rectangular arrays, and/or area models.

I can explain division problems by using equations, rectangular arrays, and/or area models.

This means I can use words or pictures to explain how I solved division problems.

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reasoning.



Domain Standard Number and Operations in Base Ten Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in

the place to its right and 1/10 of what it represents in the place to its left. Cluster Understand the place value system


# Target Type



Printed Resources


1 K

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left

I can identify the value of any digit based on its place value.

digit/multi-digit

I can understand that in a multi-digit whole number each digit is ten times the digit to the right.

This means I know the hundreds place is ten times greater than the tens place.

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reasoning.



Domain Standard Number and Operations in Base Ten Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and

explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Cluster Understand the place value system


# Target Type



Printed Resources


1 K Represent powers of 10 using whole number exponents

I can represent powers of 10 using whole number exponents.

decimal point

exponents

explain

2 K Fluently translate between powers of ten written as ten raised to a whole number exponent, the expanded form, and standard notation (103 = 10 x 10 x 10 = 1000)

I can fluently translate between powers of ten.

3 R Explain the patterns in the number of zeros of the product when multiplying a number by powers of 10.

I can explain the patterns in the number of zeros of the product when multiplying by 10.

This means I can explain how to multiply a whole number by a power of 10 (add on zeros at the end of the whole number. For example, 12 x 10 = 120, 12 x 100 = 1,200)

4 R Explain the relationship of the placement of the decimal point when a decimal is multiplied or divided by a power of 10.

I can explain the relationship of the placement of the decimal point when a decimal is multiplied or divided by a power of 10.

This means I can: • Decide which

direction to move the decimal point

• Find the number of places to move the decimal point in the product

• Write the product

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Make sense of problems

and persevere in solving

them.

Reason abstractly and

quantitatively.

Construct viable arguments

and critique the reasoning

of others.

Model with mathematics. Use appropriate tools

strategically.

Attend to precision. Look for and make use of

structure.

Look for and express

regularity in repeated

reasoning.


9 Weeks Grade.Content.Standard Overall Standard Type

1st 2

nd 3

rd 4

th 5.NBT.3a K R S P

Domain Standard

Number and Operations in Base Ten Read, write, and compare decimals to thousandths:

a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded

form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). Cluster

Understand the place value system

Assessments Vocabulary Resources Differentiation

Target

#

Target

Type

State Target Student Friendly Target Success Criteria

(If Appropriate)

Bold = First time ever

Plain = previously

introduced

Printed

Resources


1

K

Read and write decimals to

thousandths using base-ten

numerals, number names,

and expanded form

I can read and write

decimals to thousandths

using base-ten numerals in

standard form.

place value

decimals

decimal point

base ten system

base-ten numerals

(standard form)

number name

(word form)

expanded form

tenth

hundredth

thousandth

2 I can read and write



word form.

3 I can read and write



expanded form.

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reasoning.


9 Weeks Grade.Content.Standard Overall Standard Type 1st 2nd 3rd 4th 5.NBT.3b K R S P

Domain Standard Number and Operations in Base Ten Read, write, and compare decimals to thousandths:

b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.



# Target Type



Printed Resources


1 K Use >, =, and < symbols to record the results of comparisons between decimals.

I can compare decimals using >, =, and < symbols.

compare

place value

decimal point

decimal

greatest to least (>)

least to greatest (<)

equal to (=)

greatest place value

(<, >, =)

digits

2 R Compare two decimals to the thousandths on the place value of each digit

I can compare two decimals to the thousandths place.

This means I can align numbers with a decimal point and compare the digits starting with the greatest/least place value.

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reasoning.



Domain Standard Number and Operations in Base Ten Use place value understanding to round decimals to any place.



# Target Type



Printed Resources


1 K Use knowledge of base ten and place value to round decimals to any place

I can round decimals to the thousandths place using the base ten system.

place value

rounding

base ten system

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reasoning.



Domain Standard Number and Operations in Base Ten Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and

strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Cluster Perform operations with multi-digit whole numbers and with decimals to hundredths.


# Target Type



Printed Resources


1 K Add, subtract, multiply, and divide decimals to hundredths using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

I can add decimals to hundredths using models and/or drawings.

concrete model grid hundredths thousandths inverse operation addition identity property of 0 commutative property of addition associative property of addition multiplicative identity property of 1 commutative property of multiplication associative property of multiplication

2 K I can subtract decimals to hundredths using models and/or drawings.

3 K I can multiply decimals to hundredths using models and/or drawings.

4 K I can divide decimals to hundredths using models and/or drawings.

5 K I can use the properties of operations and/or inverse operations to solve problems using decimals.

6 R Relate the strategy to a written method and explain the reasoning used to solve decimal operation calculations.

I can write and explain the strategy I used to solve operations using decimals.

This means I can draw, use words, or create a model to explain how to solve problems using decimals.

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reasoning.


9 Weeks Grade.Content.Standard Overall Standard Type 1st 2nd 3rd 4th 5.NF.1 K R S P

Domain Standard Number and Operations – Fractions Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given

fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc) /bd)

Cluster Use equivalent fractions as a strategy to add and subtract fractions.


# Target Type



Printed Resources


1 K Generate equivalent fractions to find the like denominator

I can generate (create) equivalent fractions to find like denominators.

numerator denominator (like/unlike) common denominator least common denominator (LCD) least common multiple (LCM) fraction mixed number generate equivalent convert simplest form simplify Greatest Common Factor (GCF) improper fraction

2 R Solve addition and subtraction problems involving fractions (including mixed numbers) with like and unlike denominators using an equivalent fraction strategy

I can solve addition and subtraction problems involving fractions with like denominators.

3 R I can solve addition and subtraction problems involving fractions with unlike denominators.

This means I can convert fractions with unlike denominators to fractions with like denominators before adding and subtracting.

4 R I can solve addition and subtraction problems involving mixed numbers with like and unlike denominators.

This means I can convert a mixed number to an improper fraction, find a common denominator, and then solve.

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them.


quantitatively.



of others.


strategically.


structure.



reasoning.



1st 2

nd 3

rd 4

th 5.NF.3 K R S P

Domain Standard

Number Operations – Fractions Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems

involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by

using visual fraction models or equations to represent the problem. For example, interpret ¾ as the result of

dividing 3 by 4, noting that ¾ multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4

people each person has a share of size ¾. If 9 people want to share a 50-pound sack of rice equally by

weight, how many pounds of rice should each person get? Between what two whole numbers does your

answer lie?

Cluster

Apply and extend previous understandings of multiplication and division to multiply an

divide fractions.


Target

#

Target

Type


(If Appropriate)


Plain = previously introduced

Printed

Resources


1 K Interpret a fraction as

division of the numerator

by the denominator (a/b = a

÷ b).

I can interpret (show) that a

fraction is the numerator

divided by the

denominator.

interpret

fractions

numerator

denominator

inverse operation

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quantitatively.



of others.


strategically.


structure.



reasoning.



1st 2

nd 3

rd 4

th 5.NF.5b K R S P

Domain Standard

Number and Operations-Fractions Interpret multiplication as scaling (resizing), by:

b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than

the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case);

explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the

given number; and relating the principle of fraction equivalence a/b = (n x a)/(n x b) to the effect of

multiplying a/b by 1

Cluster

Apply and extend previous understandings of multiplication and division to multiply and

divide fractions


Target

#

Target

Type


(If Appropriate)



Printed

Resources


1 K

Know that multiplying

whole numbers and

fractions result in products

greater than or less than

one depending upon the

factors

I can show that multiplying

whole numbers and

fractions results in products

greater than or less than

one depending on the

factors

This means if I multiply a

whole number by a proper

fraction, my answer will be

less than the whole

number.

conclusion

explain

This means if I multiply a

whole number by an

improper fraction, my

answer will be greater than

the whole number.

2 R Draw a conclusion

multiplying a fraction

greater than one will result

in a product greater than

the given number

I can explain that

multiplying a fraction by

anything greater than one

will give me a product

greater than my original

number

This means I can show that

when multiply a fraction y

a number greater than one

gets a number greater than

the original number by

using pictures, models, or

equations

3 R Draw a conclusion that

when you multiply a

fraction by one (which can

I can explain that when you

multiply a fraction by one

(can be represented by a

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quantitatively.



of others.


strategically.


structure.



reasoning.


be written as various

fraction, i.e. 2/2, 3/3, etc)

the resulting fraction is

equivalent

whole number or a

fraction) you will get an

equivalent fraction

4 R Draw a conclusion that

when you multiply a

fraction by a fraction, the

product will be smaller

than the given number

I can explain that when you

multiply two fractions

together you get a product

smaller than the given

factors.

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them.



of others.




reasoning.



Domain Standard Number and Operations – Fractions Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given

fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc) /bd)



# Target Type



Printed Resources


1 K Generate equivalent fractions to find the like denominator


numerator denominator (like/unlike) common denominator least common denominator (LCD) least common multiple (LCM) fraction mixed number generate equivalent convert simplest form simplify Greatest Common Factor (GCF) improper fraction

2 R Solve addition and subtraction problems involving fractions (including mixed numbers) with like and unlike denominators using an equivalent fraction strategy

I can solve addition and subtraction problems involving fractions with like denominators.

3 R I can solve addition and subtraction problems involving fractions with unlike denominators.

This means I can convert fractions with unlike denominators to fractions with like denominators before adding and subtracting.

4 R I can solve addition and subtraction problems involving mixed numbers with like and unlike denominators.

This means I can convert a mixed number to an improper fraction, find a common denominator, and then solve.

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them.



of others.




reasoning.



Domain Standard Number and Operations – Fractions Solve word problems involving addition and subtraction of fractions referring to the same whole, including

cases of unlike denominators, e.g. by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + ½ = 3/7, by observing that 3/7 < ½.



# Target Type



Printed Resources


1 K Generate equivalent fractions to find like denominators.


fractions

numerator

denominator

(like/unlike)

common

denominator

least common

denominator

benchmarks (0, ½,

1)

estimate

inverse operations

2 R Solve word problems involving addition and subtraction of fractions with unlike denominators referring to the same whole (e.g. by using visual fraction models or equations to represent the problem)

I can solve word problems using addition and subtraction of fractions with unlike denominators referring to the same whole.

This means I can illustrate a model or create equations to show how different size fractional parts fit together to equal a whole.

3 R Evaluate the reasonableness of an answer, using fractional number sense, by comparing it to a benchmark fraction.

I can evaluate a fraction and determine if it is closer to 0, ½, or 1.

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them.


quantitatively.



of others.


strategically.


structure.



reasoning.



1st 2

nd 3

rd 4

th 5.NF.4a K R S P

Domain Standard

Number and Operations – Fractions Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a

fraction.

a. Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as a results of

a sequence of operations a x q / b. For example, use a visual fraction model to show (2/3) x 4 = 8/3, and

create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) =

ac/bd.)

Cluster


divide fractions.


Target

#

Target

Type


(If Appropriate)



Printed

Resources


1 K Multiply fractions by

whole numbers.

I can multiply fractions by

whole numbers.

improper fractions

mixed number

2 R Interpret the product of a

fraction times a whole n

number as total number of

parts of the whole. (for

example ¾ x 3 = ¾ + ¾ +

¾ = 9/4)

I can explain a fraction by

a whole number to find the

product.

This means I can write an

equation for the problem,

rename the whole number

as an improper fraction,

multiply the numerators

and the denominators, use

models to check, and

convert the improper

fraction to a mixed number

in simplest form.

3 R Determine the sequence of

operations that result in the

total number of parts of the

whole (for example ¾ x 3

= (3x3) /4=9/4)

I can use the order of

operations to solve a

multiplication problem

using fractions as total

parts of a whole.

4 K Multiply fractions by

fractions

I can multiply fractions by

fractions.

5 R Interpret the product of a I can interpret if I multiply

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them.


quantitatively.



of others.


strategically.


structure.



reasoning.


fraction times a fraction as

the total number of parts of

the whole.

two fractions together the

product will be a smaller

fraction.

6 R I can multiply mixed

fractions.

This means I can convert

mixed fractions to

improper fractions, then

multiply, and convert back

to a mixed fraction in

simplest form.

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quantitatively.



of others.


strategically.


structure.



reasoning.



1st 2

nd 3

rd 4

th 5.NF.4b K R S P

Domain Standard

Number and Operations – Fractions Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a

fraction.

b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate

unit fraction side lengths, and show that the area is the same as would be found by multiplying the side

lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as

rectangular areas.

Cluster


divide.


Target

#

Target

Type


(If Appropriate)



Printed

Resources


1 K Find area of a rectangle

with fractional side lengths

using different strategies.

(e.g. tiling with unit

squares of the appropriate

unit fraction side lengths,

multiplying side lengths)

I can multiply the

fractional length times the

fractional width to find the

area of a rectangle.

area of a rectangle

multiplicative

identity property

of 1

commutative

property of

multiplication

associative

property of

multiplication

model

tiling

2 R Represent fraction products

as rectangular areas.

I can create a model or

illustration of fractional

products as rectangular

areas.

3 R Justify multiplying

fractional side lengths to

find the area is the same as

tiling a rectangle with unit

squares of the appropriate

unit fraction side lengths.

I can justify area by

showing the multiplication

of fractional sides and

models.

This means I can show that

the picture and the

equation area equal.

4 S Model the area of

rectangles with fractional

side lengths with unit

I can create a model to

show the area of a

rectangle using fractional

This means I can…

Break into tiles based

on a fraction

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them.


quantitatively.



of others.


strategically.


structure.



reasoning.


squares to show the area of

rectangles.

lengths. Find length and

width using

multiplication of

fractions

Find area of

rectangle

unit fraction

fraction model

fractional side

lengths

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them.



of others.




reasoning.


9 Weeks Grade.Content.Standard Overall Standard Type 1st 2nd 3rd 4th 5.NF.5a K R S P

Domain Standard Number and Operations – Fractions Interpret multiplication as scaling (resizing), by:

a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Cluster Apply and extend previous understandings of multiplication and division to multiply and divide fractions.


# Target Type



Printed Resources


1 K Know that scaling (resizing) involves multiplication.

I can show that scaling (resizing) involves the multiplication of fractions. For example: 6 ½ x ¾ = 13/2 x ¾ = 13 x 3 2x4 = 39/8 =4 7/8

scaling/resizing

compare

product

factor

2 R Compare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indication multiplication. For example, a 2x3 rectangle would have an area twice the length of 3.

I can compare the product of two whole numbers and know that it will be greater than the value of either of those factors. For example, a 2x3 rectangle would have an area twice the length of 3.

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them.



of others.




reasoning.



Domain Standard Number and Operations – Fractions Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual

fraction. Cluster Apply and extend previous understandings of multiplication and division to multiply and divide fractions.


# Target Type



Printed Resources


1 K Represent word problems involving multiplication of fractions and mixed numbers (e.g., by using visual fraction models or equations to represent the problem.)

I can represent word problems with fractions and mixed numbers using pictures, models, and/or numbers.

represent visual models simplest forms convert properties of operations

2 R Solve real world problems involving multiplication of fractions and mixed numbers.

I can solve word problems by multiplying fractions and mixed numbers.

This means I can read the problem, decide what to multiply, solve the problem, and decide if my answer makes since using mathematical proof or illustrations.

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them.



of others.




reasoning.



Domain Standard Number Operations – Fractions Interpret a fraction as division of the numerator by the denominator (a/b = a÷b). Solve word problems

involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?



# Target Type



Printed Resources


1 K Interpret a fraction as division of the numerator by the denominator (a/b = a÷b).

I can interpret a fraction as a numerator divided by a denominator.

interpret

fractions

numerator

denominator

inverse operation

2 R Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers (e.g., using visual fraction models or equations to represent the problem.)

I can solve a word problem using division and show the answer as a fraction or mixed number.

This means I can use visual fraction models or equations to represent and solve a problem.

3 R Interpret the remainder as a fractional part of the problem.

I can explain how a remainder is a fractional part of the whole.

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them.



of others.


Attend to precision.

Look for and make use of structure.


reasoning.


9 Weeks Grade.Content.Standard Overall Standard Type 1st 2nd 3rd 4th 5.NF.7abc K R S P

Domain Standard Number and Operations –Fractions Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole

numbers by unit fractions.* *Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade. a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) divided by 4, and use a visual fraction model to show the quotient. Use relationships between multiplication and division to explain that (1/3) ÷4 = 1/12 because (1/12) x 4 = 1/3. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5) = 20 because 20 x (1/5) =4. c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share ½ lb. of chocolate equally? How many 1/3 cup servings are in 2 cups of raisins?



# Target Type



Printed Resources


1 K Know the relationship between multiplication and division.

I can tell that division is the opposite of multiplication (fact families).

This means that I can solve problems such as 3 x 4 = 12 so therefore 12/3 = 4 and 12/4 = 3.

reciprocal

unit fraction

justify

2 K I can define reciprocal. 3 R Interpret division of a unit

fraction by a whole number and justify your answer using the relationship between multiplication and division, and by creating

I can divide a fraction by a whole number and prove the answer using multiplication.

This means I can prove my answer is correct by creating story problems, visual models, and/or other multiplication strategies by multiplying the quotient

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them.



of others.


Attend to precision.

Look for and make use of structure.


reasoning.


story problems, using visual models, and relationship to multiplication, etc.

and divisor.

4 R Interpret division of a whole number by a unit fraction and justify your answer using the relationship between multiplication and division, and by representing the quotient with a visual fraction model.

I can divide a whole number by a fraction with an equation and a fraction model.

This means I can…… *write an equation for the problem. *write the reciprocal. *multiply by the reciprocal. *create a fraction model to show the quotient.

5 R Solve real world problems involving division of unit fractions by whole numbers other than 0 and division of whole numbers by unit fractions using strategies such as visual fractions models and equations.

I can solve a word problem involving division of unit fractions by whole numbers.

This means I can use models and equations to solve division problems with fractions.

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them.


quantitatively.



of others.


strategically.


structure.



reasoning.



1st 2

nd 3

rd 4

th 5.MD.1 K R S P

Domain Standard

Measurement and Data Convert among different-sized standard measurement units within a given measurement system (e.g.,

convert 5cm to 0.05m), and use these conversions in solving multi-step, real world problems. Cluster

Convert like measurement units within a given measurement system.


Target

#

Target

Type


(If Appropriate)

Bold = First time ever Plain = previously

introduced

Printed Resources


1 K Recognize units of

measurement within the

same system.

I can identify units of


same system.

convert

Measurement

System

customary units

metric units

capacity

length

weight (mass)

2 K Divide and multiply to

change units.

I can divide and multiply to

change units.

This means I can multiply

by powers of 10 and move

the decimals as necessary.

3 R Convert units of


same system.

I can convert metric

lengths and weights.

This means that I can

convert between metric

units (m, cm, mm, kg, ml,

etc) by multiplying or

dividing.

4 R I can convert customary

lengths and weights.

This means that I can

convert between inches,

feet, yards, ounces, pounds

and miles and pints,

gallons, quarts, cups, etc.,

by multiplying or dividing.

5 R Solve multi-step, real

world problems that

involve converting units.

I can solve multi-step word

problems that involve

converting units.

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reasoning.


9 Weeks Grade.Content.Standard Overall Standard Type 1st 2nd 3rd 4th 5.MD.3ab K R S P

Domain Standard Measurement and Data Recognize volume as an attribute of solid figures and understands concepts of volume measurement.

a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

Cluster Geometric measurement: understand concepts of volume and relate volume and relate volume to multiplication and to addition.


# Target Type



Printed Resources


1 K

Recognize that volume is the measurement of the space inside a solid three-dimensional figure.

I can define volume as the space inside of a solid 3D shape.

volume

attribute

cubic unit

cube

rectangular prism

gaps

overlaps

3-deminsional

Unit cube

2 K

Recognize a unit cube has 1 cubic unit of volume and is used to measure volume of three-dimensional shapes.

I can identify that a unit cube is the same as 1 cubic unit of volume in a 3D shape.

3 K

Recognize any solid figure packed without gaps or overlaps and filled with (n) “unit cubes” indicates the total cubic units or volume.

I can find the volume of any solid figure by counting the number of unit cubes.

I can identify the volume is the same as the number of total “unit cubes”.

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quantitatively.



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strategically.


structure.



reasoning.



1st 2

nd 3

rd 4

th 5.MD.4 K R S P

Domain Standard

Measurement and Data Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and improvised units.

Cluster

Geometric measurement: understand concepts of volume and relate volume to

multiplication and to addition.


Target

#

Target

Type


(If Appropriate)


introduced

Printed Resources


1 K Measure volume by

counting unit cubes, cubic

cm, cubic in., cubic ft., and

improvised units.

I can measure the volume

of a solid by counting the

units and recording it as

units cubes.

unit cubes

cubed

cubic units of

measure (cm., in.,

ft., etc.)

improvised unit

(non-standard)

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reasoning.


9 Weeks Grade.Content.Standard Overall Standard Type 1st 2nd 3rd 4th 5.MD.5a K R S P

Domain Standard Measurement and Data Relate volume to the operations of multiplication and addition and solve real world and mathematical

problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit

cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number procedures as volumes, e.g., to represent the associative property of multiplication.

Cluster Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.


Target #

Target Type


Bold = First time ever Plain = previously introduced * = defined in glossary

Printed Resources


1 K Identify a right rectangular prism.

I can identify a right rectangular prism by its characteristics.

volume

right rectangular

prism

volume (length x

width x height =

volume cubed)

2 R Develop volume formula for a rectangle prism by comparing volume when filled with cubes to volume by multiplying the height by the area of the base, or when multiplying the edge lengths (LxWxH).

I can develop a formula to find volume.

This means I can fill a 3D shape with cubes and then count the number of cubes in the height, width, and length to find the formula (This will lead to LxWxH).

3 K Multiply the three dimensions in any order to calculate volume (Commutative and associative properties).

I can calculate the volume of a three dimensional shape by using the formula: LxWxH (associative and commutative properties of multiplication)

4 S Find the volume of a right rectangular prism with whole number side lengths by packing it with unit cubes.

I can find the volume of a right rectangular prism using the formula LxWxH and compare it to the number of cubes I counted.

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reasoning.


9 Weeks Grade.Content.Standard Overall Standard Type 1st 2nd 3rd 4th 5.MD.5b K R S P


problems involving volume. b. Apply the formula V = l x w x h and V = B x h for rectangular prisms to find volume of right rectangular prisms with whole-number lengths in the context of solving real world and mathematical problems.

Cluster Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition


# Target Type



Printed Resources


1 K Know that “B” is the area of the Base

I know that “B” stands for the area of the base.

This means to find “B” I calculate L x W.

base = area

squared (length x

width = area

squared)

volume formula:

(base x height =

volume cubed)

apply

2

R

Apply the following formulas to right rectangular prisms having whole number edge lengths in the context of real world mathematical problems: Volume = length x width x height Volume = area of base x height

I can find the volume of a right rectangular prism using length x width x height.

3 I can find the volume of a right rectangular prism using area of base x height.

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reasoning.


9 Weeks Grade.Content.Standard Overall Standard Type 1st 2nd 3rd 4th 5.MD.5c K R S P


problems involving volume. c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

Cluster Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition


# Target Type



Printed Resources


1 K Recognize volume as additive

I can identify when you add base on base on base that your volume is increasing.

This means if I have a base of 10 and I add 3 more bases to the original – my volume is 40 cubic units.

additive

decomposing

2 R Solve real world problems by decomposing a solid figure into two non-overlapping right rectangular prisms and adding their volumes

I can decompose a 3D shape into 2 separate right rectangular prisms and add their volumes together.

This means I can take a shape apart, find the volume of each piece and then add the volumes together to get a total.

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reasoning.


9 Weeks Grade.Content.Standard Overall Standard Type 1st 2nd 3rd 4th 5.MD.2 K R S P

Domain Standard Measurement and Data Make a line plot to display a data set of measurements in fractions of a unit (1/2. 1/4. 1/8). Use operations

of fractions for this grade to solve problems involving information presented in line plots For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Cluster Represent and Interpret Data


# Target Type



Printed Resources


1 K Identify benchmark fractions (1/2, 1/4, 1,8).

I can identify benchmark fractions (1/2, 1/4, 1,8).

line plot

benchmark

fractions (0, ½, 1)

identify

2 K Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4 , 1/8).

I can make a line plot between 0 and 1 using benchmark fractions.

3 R Solve problems involving information presented in line plots which use fractions of a unit (1/2, 1/4 , 1/8) by adding, subtracting, multiplying, and dividing fractions.

I can solve computational problems using fractions on a line plot.

This means I can read a line plot and correctly use addition, subtraction, multiplication, and/or division with fractions and/or whole numbers.

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quantitatively.



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strategically.


structure.



reasoning.



1st 2

nd 3

rd 4

th 5.G.1 K R S P

Domain Standard

Geometry Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of

the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by

using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far

to travel from the origin in the direction of one axis, and the second number indicates how far to travel in

the direction of the second axis, with the convention that the names of the two axes and the coordinates

correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate.

Cluster

Graph points on the coordinate plane to solve real-world and mathematical problems.


Target

#

Target

Type


(If Appropriate)



Printed

Resources


1 K Define the coordinate

system.

I can define the coordinate

system.

perpendicular

number lines

axis

coordinate system

intersection

origin

locate

coordinates (ordered

pairs)

x-axis

y-axis

corresponding

coordinates

given point in a plane

(exact location)

2 K Identify the x- and y- axis. I can identify the x and y

axis.

3 K Locate the origin on the

coordinate system.

I can identify and locate

the origin as (0,0) on the

coordinate plane.

4 K Identify coordinates of a

point on a coordinate

system.

I can identify the ordered

pairs of numbers for a

point on a coordinate

plane.

5 K Recognize and describe the

connection between the

ordered pair and the x- and

y- axis (from the origin).

I can find a point on a

coordinate plane and

correctly go left/right then

up/down.

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quantitatively.



of others.


strategically.


structure.



reasoning.



1st 2

nd 3

rd 4

th 5.G.2 K R S P

Domain Standard

Geometry Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate

plane, and interpret coordinate values of points in the context of the situation. Cluster

Graph points on the coordinate plane to solve real-world and mathematical problems.


Target

#

Target

Type


(If Appropriate)


introduced

Printed Resources


1 K Gap Skill I can locate the first

quadrant.

ordered pairs

graph

first quadrant

coordinate values

exact location

scale

coordinate grid

2 K Graph points in the first

quadrant.

I can graph points in the

first quadrant.

3 R Represent real world and

mathematical problems by

graphing points in the first

quadrant.

I can graph an ordered pair

in the first quadrant to

show real world

mathematical situations.

4 R Interpret coordinate values

of points in real world

context and mathematical

problems.

I can find distances from

one location to another on

a map or other real world

examples.

5 R I can find distances

between two locations

when given the coordinate

values on a map or other

real world.

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reasoning.


9 Weeks Grade.Content.Standard Overall Standard Type 1st 2nd 3rd 4th 5.G.3 K R S P

Domain Standard Geometry Understand that attributes belonging to a category of two-dimensional figures also belong to all

subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

Cluster Classify 2-dimensional figures into categories based on their properties.


# Target Type



Printed Resources


1 K Recognize that some 2-dimensional shapes can be classified into more than one category based on their attributes.

I can identify 2D shapes based on their attributes.

2 – dimensional (2-D) plane figure Polygons:

triangle square pentagon hexagon heptagon octagon nonagon decagon circle

center point classify categories subcategories attributes angles parallel lines right angles degrees Quadrilateral:

parallelogram rhombus rectangle square trapezoid kite

2 K Recognize if a 2-dimensional shape is classified into a category, that it belongs to all subcategories of that category.

I can classify 2D shapes in all categories and subcategories. For example: a square is a quadrilateral, rhombus, parallelogram, and a rectangle.

This means I can identify all categories that a shape could be grouped in.

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quantitatively.



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strategically.


structure.



reasoning.



1st 2

nd 3

rd 4

th 5.G.4 K R S P

Domain Standard

Geometry Classify two-dimensional figures in a hierarchy based on properties.

Cluster

Classify two-dimensional figures into categories based on their properties.


Target

#

Target

Type


(If Appropriate)


introduced

Printed Resources


1 K Recognize the hierarchy of

2-dimensional shapes

based on their attributes.

I can identify the

*hierarchy of two-

dimensional shapes based

on attributes. (the more

categories a shape fits in ,

the higher up on the

hierarchy, the shape will

be)

This means I can place

shapes into categories and

subcategories based on

their attributes.

hierarchy

attributes/propert

ies

describe

Triangles:

scalene

isosceles

equilateral

Angles:

acute

obtuse

right

2 R Analyze properties of two-

dimensional figures in

order to place in to a

hierarchy.

I can analyze (compare) a

shape’s attributes (angles,

sides, etc.) to determine

where a shape fits in the

hierarchy of two-

dimensional shapes.

This means that I can tell

how shapes are alike based

on their traits (attributes).

3 R Classify two-dimensional

figures into categories

based on attributes.

I can classify shapes into

categories and/or sub-

categories based on

attributes and provide

support as why they are in

each category.

This means I can give at

least one reason why I

classified the shape in a

category.

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5th grade mathematics pacing guide and curriculum map

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