CURRICULUM FOR MATHEMATICS - rahway.net · place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. 4.NBT.A.2. Read and write

CURRICULUM

FOR

MATHEMATICS

GRADE 4

This curriculum is part of the Educational Program of Studies of the Rahway Public Schools.

ACKNOWLEDGMENTS

Dr. Kevin K. Robinson, Program Supervisor of STEM

The Board acknowledges the following who contributed to the preparation of this curriculum.

Jaclyn Basso

Cynthia Zatorski

Christine H. Salcito, Assistant Superintendent

Subject/Course Title: Date of Board Adoptions:

Mathematics October 16, 2012

Grade 4 Revised – August 26, 2014

Revised – August 22, 2017

RAHWAY PUBLIC SCHOOLS CURRICULUM

UNIT OVERVIEW

Content Area: Mathematics

Unit Title: Unit 1- Place Value & Operations with Whole Numbers

Target Course/Grade Level: Grade 4

Unit Summary: Students will gain familiarity with factors and multiples as well as generate and analyze patterns. In addition,

students will solve problems involving measurement and the conversion of measurements. Students will use the

four operations with whole numbers to solve problems in addition to generalizing place value understanding for multi-digit

whole numbers.

Approximate Length of Unit: 4-5 weeks (September-mid October)

Primary interdisciplinary connections: Language Arts Literacy, Science, Social Studies, 21st Century Life and Career

Standards, Technology

LEARNING TARGETS

Content Strands: Operations and Algebraic Thinking & Numbers and Operations in Base Ten

Standards:

4.OA.B.4. Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of

each of its factors. Determine whether a given whole number in the range 1– 100 is a multiple of a given one-

digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

4.OA.C.5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were

not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in

the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain

informally why the numbers will continue to alternate in this way.

4.MD.A.1. Know relative sizes of measurement units within one system of units including km, m, cm. mm; kg, g; lb, oz.; l,

ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a

smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as

long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing

the number pairs (1, 12), (2, 24), (3, 36), ...

4.OA.A.1. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as

many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication

equations.

4.OA.A.2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and

equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative

comparison from additive comparison.

4.NBT.A.1.Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the

place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

4.NBT.A.2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.

Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to

record the results of comparisons.

4.NBT.A.3. Use place value understanding to round multi-digit whole numbers to any place.

21st Century Learning Standards:

CRP2. Apply appropriate academic and technical skills. Career-ready individuals readily access and use the knowledge

and skills acquired through experience and education to be more productive. They make connections between

abstract concepts with real-world applications, and they make correct insights about when it is appropriate to

apply the use of an academic skill in a workplace situation

CRP4. Communicate clearly and effectively and with reason. Career-ready individuals communicate thoughts, ideas,

and action plans with clarity, whether using written, verbal, and/or visual methods. They communicate in the

workplace with clarity and purpose to make maximum use of their own and others’ time. They are excellent

writers; they master conventions, word choice, and organization, and use effective tone and presentation skills to

articulate ideas. They are skilled at interacting with others; they are active listeners and speak clearly and with

purpose. Career-ready individuals think about the audience for their communication and prepare accordingly to

ensure the desired outcome.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. Career-ready individuals

readily recognize problems in the workplace, understand the nature of the problem, and devise effective plans to

solve the problem. They are aware of problems when they occur and take action quickly to address the problem;

they thoughtfully investigate the root cause of the problem prior to introducing solutions. They carefully consider

the options to solve the problem. Once a solution is agreed upon, they follow through to ensure the problem is

solved, whether through their own actions or the actions of others.

CRP11. Use technology to enhance productivity. Career-ready individuals find and maximize the productive value of

existing and new technology to accomplish workplace tasks and solve workplace problems. They are flexible

and adaptive in acquiring new technology. They are proficient with ubiquitous technology applications. They

understand the inherent risks-personal and organizational-of technology applications, and they take actions to

prevent or mitigate these risks.

CRP12. Work productively in teams while using cultural global competence. Career-ready individuals positively

contribute to every team, whether formal or informal. They apply an awareness of cultural difference to avoid

barriers to productive and positive interaction. They find ways to increase the engagement and contribution of

all team members. They plan and facilitate effective team meetings.

Unit Understandings

Students will understand that…

Whole numbers are a multiple of each of its factors

Prime numbers do not have factors other than 1 and the number itself

Patterns contain features that are not explicitly stated in the rule defining the numerical pattern

Relative sizes of measurements

Multiplication equations represent comparisons

A quantitative relationship exists between the digits in place value positions of a multi-digit number

Multiple representations of whole numbers exist

Multiplication and division word problems involve multiplicative comparison

Numbers can be estimated

Unit Essential Questions

How is place value related to comparing numbers (greater than and less than)?

Out of the three ways a number can be expressed, which way is the most useful in the real world and why?

Define and explain the similarities and difference between factors and multiples.

How is knowing your multiplication facts related to determining whether a number is prime or composite?

How do you create number and shape patterns that follow a given rule?

What are everyday situations where rounding would be helpful?

Knowledge and Skills

Students will know…

Vocabulary: ten thousand, hundred thousand, word form, standard form, word form, expanded form, greater than, less

than, more than, greatest, least, order, round, estimate, product, regroup, quotient, remainder, factor, common factor,

greatest common factor, composite number, prime number, multiple, common multiple, least common multiple

Three ways to express a number

Rules for number patterns

Multiplication facts to find factors and multiples

Divisibility rules to find factors and multiples

Rules or checkpoints for determining whether a number is prime or composite

Conversion rules

Students will be able to…

find all factor pairs for any whole number (between 1 and 100)

determine whether a given whole number (between 1 and 100) is a multiple of a one digit number given that one digit

number

determine whether a given whole number (between 1 and 100) is prime or composite

produce number patterns from a given rule

produce shape patterns from a given rule

analyze a sequence of numbers in order to identify features that are not explicitly stated in the rule

express measurements of a larger unit in terms of a smaller unit (within a single measurement system) (e.g. convert

hours to minute, kilometers to centimeters, etc).

generate a two-column table to record measurement equivalents

explain multiplication equations as comparisons

write multiplication equations given word problems indicating multiplicative comparison

multiply to solve word problems involving multiplicative comparison

divide to solve word problems involving multiplicative comparison

represent problems with drawings and equations, using a symbol for an unknown number

distinguish word problems involving multiplicative comparison from those involving additive comparison

explain that a digit in one place represents ten times what it would represent in the place to its right

read and write multi-digit whole numbers using base-ten numerals

read and write multi-digit whole numbers using number names

read and write multi-digit whole numbers using expanded form

compare two multi-digit numbers using >,=, and < symbols

round whole numbers to any place

EVIDENCE OF LEARNING

Assessment

What evidence will be collected and deemed acceptable to show that students truly “understand”?

Teacher observations

Oral assessments

Exit slips or do now assignments

Written quizzes

Math in Focus Chapter Assessments and Cumulative Assessments

Math In Focus Online Chapter Assessments

Technology Enhanced Assignments and/or assessments

Project Based Learning

Learning Activities

What differentiated learning experiences and instruction will enable all students to achieve the desired results?

Math In Focus Program Activities:

Enrichment, Extra Practice, or ReTeach Worksheets

Student Workbook

Problem of the Lesson

Hands On Activity

Let’s Explore

Reading and Writing Math Journal

Put On Your Thinking Cap!

Cross- Curricular Connections at the beginning of each chapter

Differentiated Learning Experiences

Real Life Connection Activities and Discussion

Choice Boards


Tiered Online Math Practice Activities

Story Based Learning

Instruction

Note taking

Graphic organizers

Challenging students to explain their math; Provide sentence starters

Real life connections

Diagrams

Model how to explain thinking behind a concept

Manipulatives

Tiered assignments based on pretest results or daily assignment results

Differentiated grouping/pairs based on pretest or assignment results

RESOURCES

Teacher Resources:

Math in Focus Teacher Resource Blackline Masters

Math in Focus Teacher Edition

Math in Focus Big Book

Math in Focus Enrichment, Re-Teach, Critical Thinking, and Extra Practice Worksheets

Math in Focus Student hard cover textbook and workbook

Teacher’s guide to transition

Calendar Math

Equipment Needed:

Place-value chips or blocks

Place-value charts

Place-value mat

Prime numbers chart

Number cards

Rulers

Measurement conversion chart

White boards and markers

Laptops or computers

Smart-Board, White-Board, or Chalk Board

Technology Resources for Students

Illustrative Mathematics for 4.OA Domain: https://www.illustrativemathematics.org/4.OA

Illustrative Mathematics for 4.NBT Domain: https://www.illustrativemathematics.org/content-standards/4/NBT

Prodigy: https://prodigygame.com/play/

Tenmarks: https://www.tenmarks.com/

Moby Max: https://www.mobymax.com/

Khan Academy: https://www.khanacademy.org/math/cc-fourth-grade-math

Game- Identify factors

https://www.ixl.com/math/grade-4/identify-factors

Game-Factors

http://www.mathnook.com/math/skill/factorgames.php

Game-Greatest Common Factor

http://www.sheppardsoftware.com/mathgames/fractions/GreatestCommonFactor.htm

Game-Multiples

http://www.abcya.com/number_ninja_multiples.htm

Game-Multiples

https://www.turtlediary.com/game/finding-factors.html

Game-Comparing Numbers

http://www.sheppardsoftware.com/mathgames/placevalue/FSCompareNumbers.htm

MIF Virtual Manipulatives https://www-

k6.thinkcentral.com/content/hsp/math/mathinfocus/common/itools_int_9780547673844_/main.html

MIF- Student interactivities

http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/na/gr4/reteach_and_enrich_9780547671819_/index.html?g

JumptoPage=S&gPageId=N

https://www.illustrativemathematics.org/4.OA

https://www.illustrativemathematics.org/content-standards/4/NBT

https://prodigygame.com/play/

https://www.tenmarks.com/

https://www.mobymax.com/

https://www.khanacademy.org/math/cc-fourth-grade-math

https://www.ixl.com/math/grade-4/identify-factors

http://www.mathnook.com/math/skill/factorgames.php

http://www.sheppardsoftware.com/mathgames/fractions/GreatestCommonFactor.htm

http://www.abcya.com/number_ninja_multiples.htm

https://www.turtlediary.com/game/finding-factors.html

http://www.sheppardsoftware.com/mathgames/placevalue/FSCompareNumbers.htm

https://www-k6.thinkcentral.com/content/hsp/math/mathinfocus/common/itools_int_9780547673844_/main.html


http://www-k6.thinkcentral.com/content/hsp/math/mathinfocus/common/itools_int_9780547673844_/main.html

http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/na/gr4/reteach_and_enrich_9780547671819_/index.html?gJumptoPage=S&gPageId=N


Technology Resources for Parents/Teachers

MIF - Video- Estimation and Number Theory http://www-

k6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760278_te/chapter/chapter2.html

MIF - Video- Place Value of Whole Numbers http://www-


MIF - Video- Whole Number Multiplication and Division http://www-


MIF Interactive Whiteboard http://www-

k6.thinkcentral.com/content/hsp/math/mathinfocus/common/iwb_dl_v2/contents/Main4.html

MIF Transition Resource Map http://www-

k6.thinkcentral.com/content/hsp/math/hspmath/na/gr4/math_in_focus_transition_planner_9780547608655_/launch.ht

ml

Khan Academy Videos: https://www.khanacademy.org/math/cc-fourth-grade-math

Useful websites for teachers to explore:

○ Prodigy: https://prodigygame.com/play/

○ Illustrative Mathematics for 4.OA Domain: https://www.illustrativemathematics.org/4.OA

○ Illustrative Mathematics for 4.NBT Domain: https://www.illustrativemathematics.org/content-

standards/4/NBT

○ Tenmarks: https://www.tenmarks.com/

○ Moby Max: https://www.mobymax.com/

○ Khan Academy: https://www.khanacademy.org/math/cc-fourth-grade-math

○ IXL: https://www.ixl.com/math/grade-4

○ https://www-k6.thinkcentral.com/ePC/start.do

○ http://illuminations.nctm.org

○ http://www.k-5mathteachingresources.com

○ https://sites.google.com/site/emilou2010

○ http://www.onlinemathlearning.com

○ http://www.internet4classrooms.com

http://www-k6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760278_te/chapter/chapter2.html






http://www-k6.thinkcentral.com/content/hsp/math/mathinfocus/common/iwb_dl_v2/contents/Main4.html


http://www-k6.thinkcentral.com/content/hsp/math/hspmath/na/gr4/math_in_focus_transition_planner_9780547608655_/launch.html











https://www.ixl.com/math/grade-4

https://www-k6.thinkcentral.com/ePC/start.do


http://www.k-5mathteachingresources.com/

https://sites.google.com/site/emilou2010




UNIT OVERVIEW


Unit Title: Unit 2- Multi-digit Arithmetic & Fraction Equivalence


Unit Summary: Students will use place value understanding and properties of operations to perform multi-digit arithmetic.

Students will use the four operations with whole numbers to solve problems. Students will solve problems involving

measurement and conversion of measurements. Students will build fractions from unit fractions and extend their understanding

of fraction equivalence and ordering.

Approximate Length of Unit: 5 weeks (mid-October, mid-November)



LEARNING TARGETS

Content Strand: Number and Operations in Base Ten & Number and Operations-Fractions

Standards:

4.NBT.B.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.

4.NBT.B.5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers,

using strategies based on place value and the properties of operations. Illustrate and explain the calculation by

using equations, rectangular arrays, and/or area models.

4.NBT.B.6. Find whole-number quotients and remainders with up to four-digit dividends and one-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.

4.OA.A.3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four

operations, including problems in which remainders must be interpreted. Represent these problems using

equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental

computation and estimation strategies including rounding.

4.MD.A.3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find

the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a

multiplication equation with an unknown factor.

4.NF.A.1. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention

to how the number and size of the parts differ even though the two fractions themselves are the same size. Use

this principle to recognize and generate equivalent fractions.

4.NF.A.2. Compare two fractions with different numerators and different denominators, e.g., by creating common

denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons

are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >,

=, or <, and justify the conclusions, e.g., by using a visual fraction model.

4.NF.B.3a `Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

4.NF.B.3b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each

decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8

+ 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

Unit Understandings


there is a proper and improper use of an equal sign

adding and subtracting multi-digit whole numbers use a standard algorithm

there is a relationship between multiplication and division

multiplying and dividing whole numbers can be represented with equations, rectangular arrays, and area models

multiplying and dividing multi-digit whole numbers use a standard algorithm

area and perimeter real world and mathematical problems can be solved by using formulas

equivalent fractions are the same size while the number and size of the parts differ

fractions may only be compared when the two fractions refer to the same whole

some fractions can be decomposed

the addition and subtraction of fractions is joining/separating parts referring to the same whole




abstract concepts with real-world applications, and they make correct insights about when it is appropriate to

apply the use of an academic skill in a workplace situation

CRP4. Communicate clearly and effectively and with reason. Career-ready individuals communicate thoughts, ideas, and

action plans with clarity, whether using written, verbal, and/or visual methods. They communicate in the






CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. Career-ready individuals

readily recognize problems in the workplace, understand the nature of the problem, and devise effective plans to

solve the problem. They are aware of problems when they occur and take action quickly to address the problem;

they thoughtfully investigate the root cause of the problem prior to introducing solutions. They carefully consider

the options to solve the problem. Once a solution is agreed upon, they follow through to ensure the problem is

solved, whether through their own actions or the actions of others.


existing and new technology to accomplish workplace tasks and solve workplace problems. They are flexible and

adaptive in acquiring new technology. They are proficient with ubiquitous technology applications. They



CRP12. Work productively in teams while using cultural global competence. Career-ready individuals positively

contribute to every team, whether formal or informal. They apply an awareness of cultural difference to avoid

barriers to productive and positive interaction. They find ways to increase the engagement and contribution of all

team members. They plan and facilitate effective team meetings.


What can happen if you choose the wrong operations to solve real world problems?

How is an equal sign in mathematics similar to a period in language arts?

How does understanding place value help you to solve multi-digit addition and subtraction problems?

What is a standard procedure for multiplying multi-digit numbers? What is a standard procedure for dividing multi-

digit numbers?

Can a remainder in a division word problem affect its meaning? What does this tell you?

Do you need to know equivalent fractions in order to compare fractions? Argue your opinion with reasoning.

Why does the numerator change but the denominator stay the same when adding or subtracting like fractions?

If you are baking, will the recipe still be executed successfully if you use equivalent fraction measurements that are

different than what the recipe calls for? Prove justification for your answer.

Distinguish the difference between area and perimeter and their uses.

How can patterns be used to determine standard formulas for area and perimeter?



Vocabulary: sum, difference, product, quotient, remainder, regroup, area, perimeter, length, width, round, estimate,

bar models, numerator, denominator, equivalent fractions, like fractions, unlike fractions, parts, whole

multiplication and division facts

strategies for solving multi-digit multiplication problems (equations, arrays, area models)

properties of multiplication and division

proper and improper use of equal signs

strategies for solving multi-step word problems

key words for addition, subtraction, multiplication, and division

area and perimeter formulas

equivalent fractions

what a fraction is and its different parts

comparison symbols and how to use them properly

addition and subtraction facts


add multi-digit whole numbers using the standard algorithm with accuracy and efficiency

subtract multi-digit whole numbers using the standard algorithm with accuracy and efficiency

multiply a whole number of up to four digits by a one-digit whole number using strategies based on place value

multiply two two-digit numbers using strategies based on place value

represent these operations with equations, rectangular arrays, and area models

explain the calculation by referring to the model (equation, array, or area model)

find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors using strategies

based on place value, the properties of operations, and the relationship between multiplication and division

solve multi-step word problems involving any of the four operations

solve multi-step word problems involving interpretation (in context) of a remainder

write equations to represent multi-step word problems, using a letter to represent the unknown quantity

explain why an answer is reasonable

use mental computation and estimation strategies to determine whether an answer is reasonable

solve real world and mathematical problems by finding the area of rectangles using a formula

solve real world and mathematical problems by finding the perimeter of rectangles using a formula

explain, using visual fraction models, why two fractions are equivalent

generate equivalent fractions, using fraction a/b as equivalent to (nxa)/(nxb)

create common denominators in order to compare two fractions

create common numerators in order to compare two fractions

compare two fractions with different numerators and different denominators by comparing to a benchmark fraction

record the results of comparisons with the symbols >,=,or <, and justify the conclusions, e.g., by using a visual

fraction model

decompose a fraction into a sum of fractions with the same denominator in more than one way

write decompositions of fractions as an equation

develop visual fraction models that represent decomposed fractions and uses them to justify decompositions


Assessment



Oral assessments


Written quizzes





Learning Activities



Enrichment, Extra Practice, or Re-Teach Worksheets

Student Workbook


Hands On Activity

Let’s Explore






Choice Boards




Instruction

Note taking

Graphic organizers



Diagrams


Manipulatives



RESOURCES

Teacher Resources:




Math in Focus Enrichment, ReTeach, Critical Thinking, and Extra Practice Worksheets



Calendar Math

Equipment Needed:

Place-value chips or blocks

Place-value charts

Place-value mat

Base ten blocks

Number cards

Rulers

Multiplication and Division Strategies Charts

Multiplication Chart

Equivalent Fraction Charts

Fraction Strips or Circles

Area and Perimeter Formulas Table





Illustrative Mathematics for 4.OA Domain: https://www.illustrativemathematics.org/4.OA


Illustrative Mathematics for 4.NF Domain: https://www.illustrativemathematics.org/content-standards/4/NF





Game- 2 digit multiplication

http://www.softschools.com/math/multiplication/2_digit_multiplication/2_digit_by_2_digit_multiplication/

Open Ed Games: https://www.opened.com/search?resource_type=game&standard=4.NBT.5__4.NBT.4__4.NBT.6

Mr. Nussbaum Games by Standard: http://mrnussbaum.com/grade_4_standards/







MIF - Video- Whole Number Multiplication and Division http://www-



https://www.illustrativemathematics.org/content-standards/4/NF





http://www.softschools.com/math/multiplication/2_digit_multiplication/2_digit_by_2_digit_multiplication/

https://www.opened.com/search?resource_type=game&standard=4.NBT.5__4.NBT.4__4.NBT.6

https://www.opened.com/search?resource_type=game&standard=4.NBT.5__4.NBT.4__4.NBT.6

http://mrnussbaum.com/grade_4_standards/








MIF Video Compilation Based on Chapter https://www-

k6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760278_te/index.html





ml






standards/4/NBT

○ Illustrative Mathematics for 4.NF Domain: https://www.illustrativemathematics.org/content-

standards/4/NF












https://www-k6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760278_te/index.html

https://www-k6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760278_te/index.html
























UNIT OVERVIEW


Unit Title: Unit 3- Building Fractions & Decimal Notation


Unit Summary: Students will build fractions from unit fractions. Students will represent and interpret data. Students will

understanding decimal notation for fractions and compare decimal fractions. Students will solve problems involving

measurement and conversion of measurements. Students will use place value understanding and properties of operations to add

and subtract.

Approximate Length of Unit: 14 weeks (mid-November - beginning of March)



LEARNING TARGETS

Content Strands: Operations and Algebraic Thinking & Numbers and Operations in Base Ten

Standards

4.NF.B.3.c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent

fraction, and/or by using properties of operations and the relationship between addition and subtraction.

4.NF.B.3.d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like

denominators, e.g., by using visual fraction models and equations to represent the problem.

4.NF.B.4.a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the

product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

4.NF.B.4.c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction

models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of

roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what

two whole numbers does your answer lie?

4.NF.C.5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to

add two fractions with respective denominators 10 and 100.4 For example, express 3/10 as 30/100, and add 3/10 +

4/100 = 34/100.

4.NF.C.6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a

length as 0.62 meters; locate 0.62 on a number line diagram.

4.NF.C.7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only

when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and

justify the conclusions, e.g., by using a visual model.

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.

4.MD.A.2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of

objects, and money, including problems involving simple fractions or decimals, and problems that require

expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using

diagrams such as number line diagrams that feature a measurement scale.

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

involving addition and subtraction of fractions by using information presented in line plots. For example, from a

line plot find and interpret the difference in length between the longest and shortest specimens in an insect

collection.




abstract concepts with real-world applications, and they make correct insights about when it is appropriate to apply

the use of an academic skill in a workplace situation.








CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. Career-ready individuals readily

recognize problems in the workplace, understand the nature of the problem, and devise effective plans to solve the

problem. They are aware of problems when they occur and take action quickly to address the problem; they

thoughtfully investigate the root cause of the problem prior to introducing solutions. They carefully consider the

options to solve the problem. Once a solution is agreed upon, they follow through to ensure the problem is solved,

whether through their own actions or the actions of others.






CRP12. Work productively in teams while using cultural global competence. Career-ready individuals positively contribute

to every team, whether formal or informal. They apply an awareness of cultural difference to avoid barriers to

productive and positive interaction. They find ways to increase the engagement and contribution of all team

members. They plan and facilitate effective team meetings.

Unit Understandings


some fractions can be decomposed

addition/subtraction of fractions is joining/separating parts referring to the same whole

line plots can be used to display a data set of measurements involving fractions

any fraction a/b as a multiple of fraction 1/b

any multiple of fraction a/b is also a multiple of fraction 1/b

fractions can become equivalent fractions

like fractions can be added or subtracted

unlike fractions can be added or subtracted if made into like fractions

there is a relationship between place value and fractions

decimals can be compared

decimals can be represented using models

all four operations can be used to solve multi-step word problems that involve time, measurement, and real world

applications

diagrams can be used to represent measurement quantities

standard algorithms can be utilized to add and subtract accurately and efficiently


What is the relationship between the numerator and the denominator in a fraction?

When can fractions and decimals be compared?

Explain situations in everyday life where you would see and use decimals.

Are decimals and fractions important? Why or why not?

How do adding and subtracting fractions compare to adding and subtracting whole numbers?

What is the best strategy to find equivalent fractions?

What are some way fractions can be combined or separated?



Vocabulary: numerator, denominator, equivalent, fraction, part, whole, sum, difference, product, whole number,

improper fraction, simplest form, like fraction, unlike fraction, decimal form, tenth, hundredth, decimal point,

expanded form, placeholder zero, more than, less than, greater than, greatest, least, order, round

addition and subtraction

multiplication and division

place value

fraction a/b is equivalent to a fraction (nxa)/(nxb)

Fractions a/b with a>1 is the sum of fractions 1/b

Fraction a/b is a multiple of 1/b

the steps to to take to find an equivalent fraction

how to represent a fraction in decimal notation

how to compare and order fractions or decimals based on their size and provide reasoning

using line plot to display measurement data sets

represent word problems using diagrams, equations, and visual models

steps for converting mixed number to improper fraction or improper fraction to mixed number

the difference between like and unlike fractions

multiplying fractions by whole numbers

creating like fractions


add and subtract fractions having like denominators in order to solve real world problems

develop visual fraction models and write equations to represent real world problems involving addition and subtraction

of fractions

add and subtract mixed numbers with like denominators

create a line plot given a data set consisting of measurements in fractions of a unit

add and subtract fractions with like denominators in order to solve problems using measurement information presented

in line plots

represent a/b as ax(1/b) using a visual fraction model

represent nx(a/b) as (nxa)/b in a visual fraction model

multiply a fraction by a whole number

solve real world problems by multiplying a fraction by a whole number, using visual fraction models and equations to

represent the problem

add two fractions with respective denominators of 10 and 100 by writing each fraction with denominator 100

write a decimal as a fraction that has a denominator of 10 or 100

represent a decimal using a model

compare two decimals to hundredths by reasoning about their size

explain that comparisons are valid when the two decimals refer to the same whole

record the results of comparison with the symbols >,=,or <, and justify the conclusions

solve word problems involving distances, intervals of time, measurement, and money involving simple fractions,

decimals, or conversions using the four operations

construct diagrams to represent measurement quantities

add and subtracting the standard algorithm with accuracy and efficiency


Assessment



Oral assessments


Written quizzes





Learning Activities



Enrichment, Extra Practice, or ReTeach Worksheets

Student Workbook


Hands On Activity

Let’s Explore






Choice Boards




Instruction

Note taking

Graphic organizers



Diagrams


Manipulatives



RESOURCES

Teacher Resources:







Calendar Math

Equipment Needed:

Fraction strips

Fraction circles or cubes

Square and rectangular colored paper

Scissors

Fraction bar models

Number cubes

Equivalent Fraction Chart

Place Value Chart





Illustrative Mathematics for 4.NF Domain: https://www.illustrativemathematics.org/content-standards/4/NF

Illustrative Mathematics for 4.MD Domain: https://www.illustrativemathematics.org/content-standards/4/MD






Game- Fractions https://www.opened.com/search?resource_type=game&standard=4.NF.3

Game- Mixed Fractions https://www.turtlediary.com/common-core/CCSS.Math.Content.4.NF.B.3/games.html

Game- Decomposing Fractions

http://www.internet4classrooms.com/common_core/understand_fraction_ab_1_sum_number_operations_fractions_fo

urth_4th_grade_math_mathematics.htm

Game-Line Plot with Fractions http://www.learningfarm.com/web/practicePassThrough.cfm?TopicID=490

Game-Equivalent Fractions https://www.turtlediary.com/quiz/equivalent-fractions-with-denominators-of-10-100-and-

1000.html

Games-Decimals http://www.sheppardsoftware.com/mathgames/decimals.htm







https://www.illustrativemathematics.org/content-standards/4/MD






https://www.opened.com/search?resource_type=game&standard=4.NF.3

https://www.turtlediary.com/common-core/CCSS.Math.Content.4.NF.B.3/games.html

http://www.internet4classrooms.com/common_core/understand_fraction_ab_1_sum_number_operations_fractions_fourth_4th_grade_math_mathematics.htm

http://www.internet4classrooms.com/common_core/understand_fraction_ab_1_sum_number_operations_fractions_fourth_4th_grade_math_mathematics.htm

http://www.learningfarm.com/web/practicePassThrough.cfm?TopicID=490

https://www.turtlediary.com/quiz/equivalent-fractions-with-denominators-of-10-100-and-1000.html


http://www.sheppardsoftware.com/mathgames/decimals.htm







MIF - Video- Fractions and Mixed Numbers (Top Tips)

http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760278_te/chapter/chapter6.

html





ml






standards/4/NBT

○ Illustrative Mathematics for 4.NF Domain: https://www.illustrativemathematics.org/content-

standards/4/NF


○ Turtle Diary: https://www.turtlediary.com/games/fourth-grade/math.html










http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760278_te/chapter/chapter6.html















https://www.turtlediary.com/games/fourth-grade/math.html











UNIT OVERVIEW


Unit Title: Unit 4- Geometry and Measurement


Unit Summary: Students will draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Students will understand concepts of angles and the measurement of angles. Students will use the four operations with whole

numbers to solve problems. Students will use place value understanding and properties of operations to perform multi-digit

arithmetic.

Approximate Length of Unit: 8 weeks (March-June)



LEARNING TARGETS

Content Strands: Geometry, Measurement and Data, Operations and Algebraic Thinking, Number in Base Ten

Standards

4.G.A.1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and

parallel lines. Identify these in two-dimensional figures.

4.G.A.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the

presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right

triangles.

4.G.A.3. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can

be folded along the line into matching parts. Identify line-symmetric figures and

draw lines of symmetry.

4.MD.C.5a An angle is measured with reference to a circle with its center at the common endpoint of the rays, by

considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle

that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

4.MD.C.5b An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

4.MD.C.6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

4.MD.C.7. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle

measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to

find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a

symbol for the unknown angle measure.

4.OA.A.3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four

operations, including problems in which remainders must be interpreted. Represent these problems using equations

with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation

and estimation strategies including rounding.

4.NBT.B.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.




abstract concepts with real-world applications, and they make correct insights about when it is appropriate to apply

the use of an academic skill in a workplace situation.








CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. Career-ready individuals readily

recognize problems in the workplace, understand the nature of the problem, and devise effective plans to solve the

problem. They are aware of problems when they occur and take action quickly to address the problem; they

thoughtfully investigate the root cause of the problem prior to introducing solutions. They carefully consider the

options to solve the problem. Once a solution is agreed upon, they follow through to ensure the problem is solved,

whether through their own actions or the actions of others.






CRP12. Work productively in teams while using cultural global competence. Career-ready individuals positively contribute

to every team, whether formal or informal. They apply an awareness of cultural difference to avoid barriers to

productive and positive interaction. They find ways to increase the engagement and contribution of all team

members. They plan and facilitate effective team meetings.

Unit Understandings


a trapezoid is a quadrilateral with at least one pair of parallel sides

lines of symmetry can be drawn

figures can have lines of symmetry which are lines across the figure such that the figure can be folded along the line

into matching parts

angles are formed by two rays sharing a common endpoint and result from the rotation of one ray around the endpoint

an angle that turns through n one-degree angles is said to have an angle measure of n degrees

angles are measured in the unit of degrees

angle measures may be added; when an angle is decomposed into non overlapping parts, the angle measure of the

whole (original angle) is the sum of the angle measures of the parts

the equal sign has a proper and improper use

addition and subtraction can be done using a standard algorithm


How do lines of symmetry and reflection relate to nature?

How are angles present in our environment?

How does geometry depend on measurement in order to describe shapes?

Where could you find a picture that shows either symmetry, congruency, or reflections?

How are angles classified and measured?

How can you use only a right angle to classify all angles?

Compare and contrast the similarities and differences between two-dimensional figures.



Vocabulary: ray, vertex, protractor, degree, inner scale, outer scale, acute angle, obtuse angles, straight angle, turn,

line of symmetry, symmetric figure, rotation, rotational symmetry, center of rotation, clockwise, counter-clockwise,

perpendicular line segments, drawing triangle, parallel line segments, base, horizontal lines, vertical lines

the difference between parallel and perpendicular lines

how to identify two-dimensional figures based on parallel and perpendicular lines

recognize and draw a line of symmetry for a two-dimensional figure

define an angle as a geometric shape that forms when two rays share a common endpoint

angles can be identified into three different types based on their angle measurement

protractors are important tools in measuring angles

addition and subtraction can be used to find unknown angles

how to solve multi-step word problems that involve the four operations

how to interpret a remainder

how to assess the reasonableness of answers using mental computation and estimation strategies


draw points, lines, line segments and rays

draw angles (right, acute, obtuse)

draw perpendicular and parallel lines

distinguish between lines, line segments, and rays

identify points, lines, line segment, rays, right angles, acute angles, obtuse angles, perpendicular lines, and

parallel lines in two-dimensional figures

classify triangles based on the presence or absence of perpendicular lines and based on the presence or

absence of angles of a particular size

classify quadrilaterals based on the presence or absence of parallel or perpendicular lines and based on the

presence or absence of angles of a particular size

fold a figure along a line of in order to create matching parts

identify lines of symmetry as a line across the figure such that the figure can be folded along the line into

matching parts

identify figures having line symmetry

draw lines of symmetry

describe an angle as measured with reference to a circle with the center of the circle being the common

endpoint of the rays

explain a ‘one-degree angle’ and its relation to a circle; a “degree” is defined as 1/360 (one degree angle)

of the entire circle

measure angles in whole-number degrees

sketch an angle given an angle’s measure

add and subtract to find unknown angles on a diagram in real world and mathematical problems

write an equation with a symbol for the unknown angle measure

solve multi-step problems involving any of the four operations as well as the interpretation of a remainder

write equations to represent multi-step word problems, using a letter to represent the unknown quantity

explain why an answer is reasonable

use mental computation and estimation strategies to determine whether an answer is reasonable

add and subtract using the standard algorithm with accuracy and efficiency


Assessment



Oral assessments


Written quizzes





Learning Activities



Enrichment, Extra Practice, or Re-Teach Worksheets

Student Workbook


Hands On Activity

Let’s Explore






Choice Boards




Instruction

Note taking

Graphic organizers



Diagrams


Manipulatives



RESOURCES

Teacher Resources:







Calendar Math

Equipment Needed:

Protractors

Angle strips

Two dimensional shape charts

Two dimensional shape models or cut outs

Geoboard





Illustrative Mathematics for 4.G Domain: https://www.illustrativemathematics.org/content-standards/4/G

Illustrative Mathematics for 4.MD Domain: https://www.illustrativemathematics.org/content-standards/4/MD






Game-Angles http://www.mathplayground.com/alienangles.html.

Game-Types of Angles https://www.mathgames.com/skill/4.1-acute-right-obtuse-and-straight-angles

Game-Lines of Symmetry

http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/SymmetryLinesShapesShoot.htm

Games-Lines http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/line_shoot.htm







MIF - Video- Perpendicular and Parallel Line Segments

http://wwwk6.thinkcentral.com/content/hsp/math/hspmath/common/mif_pd_vid/9780547760278_te/chapter/chapter1

0.html

MIF - Video- Squares and Rectangles


1.html

https://www.illustrativemathematics.org/content-standards/4/G

https://www.illustrativemathematics.org/content-standards/4/MD







https://www.mathgames.com/skill/4.1-acute-right-obtuse-and-straight-angles

http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/SymmetryLinesShapesShoot.htm

http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/line_shoot.htm










MIF- Video- Symmetry


3.html





ml






standards/4/NBT

○ Illustrative Mathematics for 4.G Domain: https://www.illustrativemathematics.org/content-standards/4/G


○ Turtle Diary: https://www.turtlediary.com/games/fourth-grade/math.html






















https://www.illustrativemathematics.org/content-standards/4/G


https://www.turtlediary.com/games/fourth-grade/math.html










Documents

CURRICULUM FOR MATHEMATICS - rahway.net · place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. 4.NBT.A.2. Read and write