Math Grade 5 Preschool and Elementary School...grade mathematics. The course will incorporate many activities that promote critical thinking, problem solving, and math practices endorsed

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CITY OF BURLINGTON PUBLIC SCHOOL DISTRICT CURRICULUM

Math – Grade 5

Revision Date: July 2017

Submitted by: Antoinette Margaretta

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Table of Contents:

Page #

Course Overview 3

Pacing Chart 4

Unit #1 Understanding the Place Value System - Overview At-a-Glance 5

Unit #1 Understanding the Place Value System Targeted Instructional Planning to Address Central Unit Standards 10

Unit #2 Understanding Volume and Operations on Fractions - Overview At-a-Glance 13

Unit #2 Understanding Volume and Operation on Fractions Targeted Instructional Planning to Address Central Unit Standards 18

Unit #3 More Operations and Fractions - Overview At-a-Glance 23

Unit #3 More Operations and Fractions - Targeted Instructional Planning to Address Central Unit Standards 27

Unit #4 Coordinate Geometry and Classifying Figures - Overview At-a-Glance 31

Unit #4 Coordinate Geometry and Classifying Figures - Targeted Instructional Planning to Address Central Unit Standards 36

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Course Overview In this course, students will focus on four units that that develop skills involving place value, fractions, mixed numbers, volume, and

coordinate geometry. These units are based on the NJ Student Learning Standards (NJSLS) and the Curricular Framework for fifth

grade mathematics. The course will incorporate many activities that promote critical thinking, problem solving, and math practices

endorsed by the NJSLS. PARCC preparation is an essential component of the activities and students will utilize the many resources

provided by the NJ Department of Education, PARCC practice assessments and released items, and the performance tasks provided by

the curricular framework.

Primary Resource(s)

Textbooks

Title: Envision Math 2.0

Publisher: Pearson Education, Inc. Copyright: 2016

Supplemental Materials and Resources

Title: Mathematics Common Core Performance Coach

Publisher: Triumph Learning Copyright: 2015

Dept. of Education Curricular Frameworks: http://www.state.nj.us/education/cccs/frameworks/math/

NJ Center for Teaching and Learning: https://njctl.org/courses/math/5th-grade-math/

PARCC Online: http://parcc-assessment.org/

NJ Common Core Standards for Mathematics, 5th Grade: http://www.corestandards.org/Math/Content/5/introduction/

Teacher Generated materials

http://www.state.nj.us/education/cccs/frameworks/math/

https://njctl.org/courses/math/5th-grade-math/

http://parcc-assessment.org/

http://www.corestandards.org/Math/Content/5/introduction/

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Pacing Chart Unit # & Title Pacing

(must equal 165 days for full-year or 83 days for

half-year course)

Unit 1: Understanding the Place Value System 40 days

Unit 2: Understanding Volume and Operations on Fractions 60 days

Unit 3: More Operations on Fractions 30 days

Unit 4: Coordinate Geometry and Classifying Figures 35 days

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Unit 1 Overview At-a-Glance Unit #1 – Understanding the Place Value System

Unit Description:

In this unit, students will write and interpret numerical expressions; understand the place value system; and perform operations with

multi-digit whole numbers and with decimals to hundredths. This unit will cover topics 1 through 6 from Envision Math 2.0, which

include:

Topic 1: Understand Place Value

Topic 2: Add and Subtract Decimals to Hundredths

Topic 3: Fluently Multiply Multi-Digit Whole Numbers

Topic 4: Use Models and Strategies to Multiply Decimals

Topic 5: Use Models and Strategies to Divide Whole Numbers

Topic 6: Use Models and Strategies to Divide Decimals.

Essential Skills:

Explain that a digit in one place represents 1/10 of what I would represent in the place to its left and ten times what it would

represent in the place to its right

Explain patterns in the number of zeros in the product when a whole number is multiplied by a power of 10; represent powers of

10 using whole-number exponents

Use the standard algorithm to multiply a whole number of up to four digits by a whole number of up to two digits

Calculate whole number quotients of whole numbers with 4-digit dividends and 2-digit divisors; explain and represent

calculations with equations, rectangular arrays, and area modules

Compare two decimals to thousandths using >, =, and < for numbers presented as base ten numerals, number names, and/ or in

expanded form

Round decimals to any place value

Standards Addressed within Unit 1 – Understanding the Place Value System

Central Unit Standards- This unit will focus primarily on

learning goals aligned with the following standards:

NJSLS 5.NBT.A.1

NJSLS 5.NBT.A.2

NJSLS 5.NBT.A.3

NJSLS 5.NBT.A.4

Supporting Unit Standards- This unit will also include activities

aligned with the following standards:

NJSLS 5.OA.A.1

NJSLS 5.OA.A.2

NJSLS SA.R1

NJSLS RI.5.1

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NJSLS 5.NBT.B.5

NJSLS 5.NBT.B.6

NJSLS 5.NBT.B.7

NJSLS RI.5.7

NJSLSSA.W1

NJSLSA.W2

NJSLSA.SL1

NJSLSA.SL2

NJSLSA.SL4

Unit 1 Details - Understanding the Place Value System

Modifications for Special Education Students,

English Language Learners, Students at Risk

of Failure, and Gifted Students- Modify

instructional approach and/or assignments and

evaluations as needed based for students with

IEPs, 504s, ELLs and gifted and talented

students including but not limited to:

Envision 2.0 online personalized practice

Envision 2.0 Visual Learning Bridge

activities

Envision ELL Toolkit Supporting

English Language Learners

Alternate responses (drawings with

captions, spoken responses, etc.)

Advance/guided notes

Extended time

Teacher modeling (non-verbal teacher

communication in addition to spoken

instructions)

Simplified written and verbal instructions

ELL support materials (eDictionaries,

native language prompts, etc.)

Integration of 21st century skills through NJSLS 9 and Career Education:

The 5th grade math curriculum emphasizes collaboration, communication,

problem solving, and critical thinking. We have supported and stressed the

21st century skills by incorporating the following activities into our lessons:

o Group Relay Races

o Scavenger Hunts

o Menu Math

o GRAPHiti

o Study Island PARCC like questions

Lessons, where appropriate, incorporate multiple perspectives to infuse

cultural and global awareness.

Learning incorporates skills focusing on financial, economic, business, and

entrepreneurial literacy.

Lessons integrate a focus on civic literacy so that students can better

understand the rights and obligations of citizenship.

Learning advocates for health literacy as a critical component of a healthy

lifestyle and the ability to make good health-related decisions.

Students explore areas that support environmental literacy, including

society’s impact on the environment and what can be done to support

environmental solutions.

Lessons, activities, and assessments require creativity and innovation on the

part of the students. They are required to create projects and products as

examples of mastery in each unit.

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Differentiated instruction to meet varied

needs and levels of all students (task

cards, centers, labs)

Multi-sensory instruction

Heterogeneous and homogeneous

grouping

One-on-one instruction in small groups

for remediation

Increased integration of higher order

thinking processes, creative and critical

thinking activities, problem-solving, and

open-ended tasks

Self-regulated group interaction

Advanced pacing levels

Greater opportunities for freedom of

choice and independent study that

encourage independent and intrinsic

learning

Inquiry-based projects and assignments

Critical thinking and problem solving skills are a core component of learning

and assessment throughout this curriculum. Students are required, in each

unit, to advance their learning through all levels of Bloom’s Taxonomy to

address the evaluation, synthesis, and creation of products using learning at

the highest levels. Problem-solving is a recurring theme in the curriculum as

students must seek ways to creatively apply the concepts to solve problems

rather than simply remember the material.

Communication and collaboration is crucial for student success as learners.

Throughout this curriculum, students must be able to communicate deep

understanding through open ended responses (both orally and in writing). In

addition, students are often required to work collaboratively with their peers

which promotes the ability to succeed in the area of social cooperative work,

increases communication skills, and promotes leadership and responsibility.

Students must be information literate, i.e. they must be able to find and use

information effectively, in order to succeed in class as learning activities

require independent research of relevant information outside of the provided

textbook and/or resources.

In order to succeed in this course, students must be able to use technology as

a tool in order to research, organize, evaluate, and communicate information.

Activities in the curriculum help develop life and career skills in all students

by promoting flexibility and adaptability, requiring initiative and self-

direction in the learning process, supporting social and cross-cultural skills in

both content and teamwork efforts, and measuring productivity and

accountability through independent and group assignment completion.

Assessments- including benchmarks,

formative, summative, and alternative

assessments

Fall NWEA

Curricular Framework Illustrated Math

resources

Mid-topic assessments

Topic performance tasks

Suggested Interdisciplinary Activities for this Unit

Career Education: Research a math career and make a poster that illustrates the

career responsibilities and skills.

Health/PE: Have students calculate the cost of materials used to engage in various

PE activities. Have students estimate the cost of materials, and eventually have them

calculate to find an exact answer.

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Exit tickets

Lesson quizzes

Weekly math journal

PARCC released questions

Pearson cumulative topic assessments

Unit 1 test

Unit 1 performance tasks

English Language Arts/Literacy: Using “Problem Solving Reading Mat” before

each new topic, read about: Oceans of the Past; Nature’s Survivors; Company of

Wolves; Bats; Migrants and Residents; and Clouds of All Kinds. In math journal, list

any terms that are unfamiliar; write a questions you may have about the real-world

math topic; write a word problem based on the information provided in the “Problem

Solving Reading Mat”; or work with a partner to add an additional fact about the

topic as it relates to your community.

Science: Research Envision topics in the math and science projects pages regarding

producers and consumers. Write and solve decimal addition and subtraction problems

for the amounts of food the consumers need; estimate weekly water usage for various

household activities and organize data in a table.

Social Studies: Research populations in various towns in NJ or in different states.

Write these population numbers in expanded form.

Technical Subjects: Use a “Data Grapher” to illustrate data gather in the classroom

or school – number of students who buy lunch over a period of a week; number of

students who 1, 2, 3, etc. siblings; populations in different states. Make a visual

display for the classroom.

https://illuminations.nctm.org/Activity.aspx?id=4098

World Languages: Count to 10 (or more) in a different language (Spanish). Make

visual vocabulary cards to illustrate the word and its meaning.

Arts: Have students work in teams to put on short skits. Student will be digits, and

roles will be based on their place value. The higher their place values, the “older”

their character should act. The smallest place value should be the baby of the number

family. (Assign the “older” place values small digits, and the “younger” place values,

larger digits. This could spark the conversation that says a digit is only as valuable as

the place he resides!)

https://illuminations.nctm.org/Activity.aspx?id=4098

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Unit Resources

Teachers should utilize school resources available in our Media Center to infuse alternate sources, perspectives, and approaches.

Resources should include textual support but also span multimedia options to engage multiple modalities. In addition, to support

struggling readers and increase rigor for advanced readers, the coursework may also draw on additional developmentally appropriate

resources to facilitate challenging levels of work for all students.

Leveled Supplemental Materials and

Media/School Library Resources

Including but not limited to:

Scholastic Math magazine

Dan Meyer’s 3-Act problems

Online Resources:

http://www.commoncoresheets.com

http://www.pearsonrealize.com

http://www.ixl.com

http://www.brainpop.com

http://www.scholasticmath.com

http://www.studyisland.com

http://www.kahnacademy.com

http://thinkmath.edc.org/resources-5th-

grade

https://whenmathhappens.com/3-act-math/

Integration of the Technology Standard

NJSLS 8.1.8.A.4, NJSLS 8.1.8.A.5

Presentations, posters, and visual vocabulary definitions generated on Microsoft software

programs, such as Word and Publisher.

Pics for Learning for a free gallery of photos and clipart for visual vocabulary

(http://www.pics4learning.com/)

Books created on the Cloud on various topics to publish and share using MyEbookMaker

(https://myebookmaker.com/)

Utilize various websites, including but not limited to:

Pearson Realize: www.pearsonrealize.com

Front Row Ed

Pearson Realize Math Games

PBS Math Club

Illustrative Mathematics

Math Antics

National Library of Virtual Manipulatives

Study Island

Khan Academy

Brain Pop

AAA Study

Mathisfun.com


Coolmath.com

www.nctm.org

Smartech.com

http://www.commoncoresheets.com/

http://www.pearsonrealize.com/

http://www.ixl.com/

http://www.brainpop.com/

http://www.scholasticmath.com/

http://www.studyisland.com/

http://www.kahnacademy.com/

http://thinkmath.edc.org/resources-5th-grade

http://thinkmath.edc.org/resources-5th-grade


http://www.pics4learning.com/

https://myebookmaker.com/



http://www.nctm.org/

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Unit #1 Targeted Instructional Planning to Address Central Unit Standards: Central Unit Standard

and Student Learning

Objective

Suggested Instructional Activities Suggested Student

Output

Formative Assessments

(Portfolios, Projects, Tasks,

Evaluations, & Rubrics)

NJSLS 5.NBT.A.1

NJSLS 5.NBT.A.2

NJSLS 5.NBT.A.3

NJSLS 5.NBT.A.4 Number and Operation in

Base Ten – Understand

the place value system

NJSLS 5.NBT.B.5

NJSLS 5.NBT.B.6

NJSLS 5.NBT.B.7

Number and Operations

in Base Ten – Perform

operations with multi-

digit whole numbers and

with decimals to

hundredths.

Facilitate guided, group, and independent

practice using tasks from the NJ DOE

Curricular Framework for Mathematics:

5.NBT.A.1 Which number is it?

The purpose of this task is to help students

understand the fact that the value of a digit

in one place is ten times the value of the

same digit in the place to the right.

5.NBT.A.1 Millions and Billions of People

The purpose of this task is to help students

understand the multiplicative relationship

between commonly used large numbers

(millions and billions) by using their

understanding of place value.

5.NBT.A.3 Placing Thousandths on the

Number Line

Though this task primarily deals with

comparing decimal numbers on a number

line, it also requires students to draw upon

what they know about the base ten system.

They must recognize that the distance from

0 to 0.1 is partitioned into ten equal pieces

and that one tenth of one tenth is 0.01.

5.NBT.A.4 Rounding to Tenths and

Hundredths

Journals using pertinent

math vocabulary such as

tenths, hundredths, tens,

hundreds, base ten, and

place value

Constructed arguments of

topics to explain correct

reasoning in performing

multi-digit operations

Modeling of place value

and multi-digit operations

using pictures, equations,

or manipulatives

Solutions to various

practice problems

Explain that a digit’s

value based on its place in

a number

Explain patterns in the

number of zeros when

multiplied by powers of

ten

Performance Assessment

Fall NWEA

Curricular Framework

Illustrated Math

resources performance

tasks

Mid Topic Assessments

Topic Performance Tasks

Topic Tests

Exit Tickets

Lesson Quizzes

Weekly Math Journal

based on math

vocabulary; error

analysis; real-world

connection; lesson

reflections

PARCC Released

Questions

Pearson Cumulative

Topic Assessments

Unit 1Test

https://www.illustrativemathematics.org/content-standards/5/NBT/A/1/tasks/1799






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The purpose of this task is for students to

use the position of a number on the number

line to round the number without knowing

its exact value.

5.NBT.B.5 Elmer's Multiplication Error

This task has students explore a very

common multiplication error that occurs

when using the standard algorithm.

Pose the Solve-and- Share Problem for

topics

Ask guiding questions as needed

5.OA.A.1 Using Operations and

Parentheses (supporting)

The purpose of this task is to give students a

chance to work creatively with three of the

four fundamental arithmetic operations

(addition, subtraction, and multiplication).

5.OA.A.1 Watch out for Parentheses 1

(supporting)

This problem asks the student to evaluate

six numerical expressions that contain the

same integers and operations yet have

differing results due to placement of

parentheses.

Share and discuss solutions of example

problems

Provide guided practice of concepts and

skills using Envision 2.0 presentation tools

Multiply a whole number

of up to four digits by a

whole number of up to

two digits

Calculate whole number

quotients of whole

numbers with 4-digit

dividends and 2-digit

divisors

Explain and represent

calculations with

equations, rectangular

arrays, and area modules.

Compare two decimals to

thousandths using >, =,

and < for numbers

presented as base ten

numerals, number names,

and/ or in expanded form.

Round decimals to any

place value.

Use of Envision rubrics –

Listen and Look for

Lesson Videos (teacher

observations)

Unit Journal Prompt:

A centurion was an officer in

the Roman army. Each

centurion led a unit of 100

men. At the height of the

Roman Empire, the army

consisted of 175 legions. The

number of men in a legion

could vary from 4,000 to

6,000 men. What is the

highest number of men in the

175 legions? Research how

the U.S. government

determines how many troops

are needed to build a military.

https://www.illustrativemathematics.org/content-standards/5/NBT/B/5/tasks/1812

https://www.illustrativemathematics.org/content-standards/5/OA/A/1/tasks/1596



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Practice the use of math vocabulary in

topics (My Word Cards) by completing

definitions and recreating visual

representations for notes and classroom

word wall.

Write explanations for understanding

concepts and procedural execution of math

topics using unit Envision 2.0 features, such

as Solve and Share, Convince Me!, and

Math Practice and Problem Solving

Utilize online tools for instruction, practice,

and remediation

Content videos

Practice Buddy for skills

Gaming for reinforcing lesson content

Thinking games and Fluency games to

reinforce concepts, procedural skills,

and fluency

Adapted Assignments for differentiated

instruction

Envision Centers kit for independent

learning

Another Look Homework Videos),

Envision 2.0 Problem-Solving Reading

Mats (real-world literacy activities)

Discuss skills in Math Practice posters to

explain strategies in problem solving

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Unit 2 Overview At-a-Glance Unit #2 – Understanding Volume and Operations on Fractions

Unit Description:

In this unit, students will use equivalent fractions as a strategy to add and subtract fractions, and apply and extend previous

understandings of multiplication and division to multiply and divide fractions. They will use geometric measurement by understanding

concepts of volume and relate volume to multiplication and to addition. This unit will cover Envision topics 7, 8, and 10 which include:

Topic 7: Equivalent fractions to add and subtract fractions

Topic 8: Apply understanding of multiplication and divisions to multiply and divide fractions

Topic 10: Understand volume concepts

Essential Skills:

Add and subtract fractions (including mixed numbers) with unlike denominators by replacing the given fractions with equivalent

fractions having like denominators

Fluently multiply multi-digit whole numbers with accuracy and efficiency

Solve word problems involving adding or subtracting fractions with unlike denominators, and determine if the answer to the

word problem is reasonable, using estimations with benchmark fractions

Interpret a fraction as a division of the numerator by the denominator; solve word problems in which division of whole numbers

leads to fractions or mixed numbers as solutions

For whole number or fraction q, interpret the product (a/b) x q as a parts of a whole partitioned into b equal parts added q times

(e.g. using a visual fraction model)

Tile a rectangle with unit fraction squares to find the area and multiply side lengths to find the area of the rectangle, showing that

the areas are the same

Measure volume by counting the total number cubic units required to fill a figure without gaps or overlaps

Show that the volume of a right rectangular prism found by counting all the unit cubes is the same as the formulas V = l × w × h

or V = B × h

Apply formulas to solve real world and mathematical problems involving volumes of right rectangular prisms that have whole

number edge lengths

Find the volume of a composite solid figure composed of two non-overlapping right rectangular prisms, applying this strategy to

solve real-world problems.

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Standards Addressed within Unit 2 - Understanding Volume and Operations on Fractions



5.NF.A.1

5.NF.A.2

5.NF B.3

5 .NF.B.4

5.NF.B.5

5.MD.C.3

5.MD.C.4

5.MD.C.5



NJSLS SA.R1

NJSLS RI.5.1

NJSLS RI.5.7

NJSLSSA.W1

NJSLSA.W2

NJSLSA.SL1

NJSLSA.SL2

NJSLSA.SL4

Unit 2 Details - Understanding Volume and Operations on Fractions

Modifications for Special Education

Students, English Language Learners,

Students at Risk of Failure, and Gifted

Students- Modify instructional approach and/or

assignments and evaluations as needed based

for students with IEPs, 504s, ELLs and gifted

and talented students including but not limited

to:

Envision 2.0 online personalized

practice


activities






Extended time





o Group Relay Races

o Scavenger Hunts

o Menu Math

o GRAPHiti










Students explore areas that support environmental literacy, including society’s

impact on the environment and what can be done to support environmental

solutions.

15



instructions)

Simplified written and verbal

instructions








grouping


for remediation




open-ended tasks






learning






and assessment throughout this curriculum. Students are required, in each unit,

to advance their learning through all levels of Bloom’s Taxonomy to address

the evaluation, synthesis, and creation of products using learning at the highest

levels. Problem-solving is a recurring theme in the curriculum as students must

seek ways to creatively apply the concepts to solve problems rather than

simply remember the material.











In order to succeed in this course, students must be able to use technology as a

tool in order to research, organize, evaluate, and communicate information.


by promoting flexibility and adaptability, requiring initiative and self-direction

in the learning process, supporting social and cross-cultural skills in both

content and teamwork efforts, and measuring productivity and accountability

through independent and group assignment completion.



assessments


resources


Career Education: What careers or professions use terms that are rooted in Latin?

16



Exit tickets

Lesson quizzes

Weekly math journal



Unit 1 test


Health/PE: Poll students in class as to which sport they prefer. Limit choices to

basketball and football. Write survey results as a fraction of the total (such as 3/5 of

class or 7/10). Compare the fractions to each other.

English Language Arts/Literacy: Read and analyze data found in Problem-Solving

Reading Mats: Roots of Music; Fruit; and Site and Monuments. In math journal, list

any terms that are unfamiliar; write a questions you may have about the real-world

math topic; write a word problem based on the information provided in the “Problem

Solving Reading Mat”; or work with a partner to add an additional fact about the topic

as it relates to their community.

Science: The human cells use division (mitosis) in order to multiply. Discuss what it

means for a cell to “divide.”

Social Studies: Research what countries or people spoke Latin. Why is it a root

language of so many technical words?

Technical Subjects: Take a picture of 2 individuals similar in height and

juxtaposition them so that in the picture one person is half or ¼ the size of the other

person. Compare the measurements to the actual height of the individuals. Construct

shapes on paper using the scale of 1/2:1.

World Languages: Solidus is a Latin word for the slash that is sometimes used with

fractions instead of a horizontal bar. Solidus in Latin means solid. Why do people

prefer the horizontal bar rather than the solidus?

Arts: You can play music by filling glass tumblers with water and tapping the edge

with a spoon. By using these measures, you can play “Mary Had a Little Lamb”.

Here’s how:

Arrange the tumblers in a line and fill them up with the following amounts of water

Tumbler A: 1 3/4 cups

Tumbler B: 1 1/2 cups

Tumbler C: 1 1/4 cups

How much water will you need?

17

Unit Resources










Online Resources:



http://www.ixl.com






NJSLS 8.1.8.A.4, NJSLS 8.1.8.A.5

Presentations, posters, and visual vocabulary definitions generated on Microsoft

software programs, such as Word and Publisher.



Books created on the Cloud on various topics to publish and share using

MyEbookMaker (https://myebookmaker.com/)



Front Row Ed


PBS Math Club


Math Antics


Study Island

Khan Academy

Brain Pop

AAA Study

Math.com

Mathisfun.com

Coolmath.com

www.nctm.org

Smartech.com



http://www.ixl.com/









18

Unit #2 Targeted Instructional Planning to Address Central Unit Standards: Central Unit Standard

and Student Learning

Objective

Suggested Instructional Activities Suggested Student

Output


(Portfolios, Projects,

Tasks, Evaluations, &

Rubrics)

5.NF.A.1

5.NF.A.2

Number and

Operations—Fractions

A. Use equivalent

fractions as a strategy to

add and subtract

fractions.

5.NF B.3

5.NF.B.4

5.NF.B.5

5.NF.B.6

Number and

Operations—Fractions

B. Apply and extend

previous understandings

of multiplication and

division to multiply and

divide fractions.




5.NF.A.1 Making S'Mores

The purpose of this instructional task is to

motivate a discussion about adding fractions

and the meaning of the common denominator.

5.NF.A.2 Do These Add Up?

This task addresses common errors that students

make when adding fractions.

5.NF.A Measuring Cups

This task could form part of a classroom

activity where students are encouraged to find

as many different ways as possible to make

different fractions such as 112 and then share

their methods.

5.NF.B.3 How Much Pie?

The purpose of this task is to help students see

the connection between a÷b and ab in a

particular concrete example.

5.NF.B.4b Chavone's Bathroom Tiles


math vocabulary

regarding fractions, their

parts, and how to operate

with fractions


topics to explain

reasoning on topics

regarding equivalent

fraction and operations

with fractions

Modeling of fraction

equivalence using

pictures, equations, or

manipulatives


practice problems

Estimate sums and

difference of fractions and

mixed numbers with

common denominators

and unlike denominators

Curricular

Framework

Illustrated Math

resources

performance

tasks

Mid Topic

Assessments

Topic

Performance

Tasks

Topic Tests

Exit Tickets

Lesson Quizzes

Weekly Math

Journal based on

math vocabulary;

error analysis;

real-world

connections;

lesson reflections

PARCC Released

Questions

Pearson

Cumulative

Topic

Assessments

Unit 2 Test

https://www.illustrativemathematics.org/content-standards/5/NF/A/1/tasks/861

https://www.illustrativemathematics.org/content-standards/5/NF/A/2/tasks/481

https://www.illustrativemathematics.org/content-standards/5/NF/A/tasks/1518

https://www.illustrativemathematics.org/content-standards/5/NF/B/3/tasks/858


19

This task helps students link the concepts of

multiplication and area.

Three-Act Problem – What fraction is the

average guy of Paul Sturgess?

https://whenmathhappens.com/2014/04/17/paul-

sturgess/

Math Modeling and Reasoning of multiplication

and divisions of fractions

Pose the Solve-and- Share Problem for topics

on multiplication and division of fractions


Share and discuss solutions of example

problems

Provide guided practice of concepts and skills

using Envision 2.0 presentation tools

Practice the use of math vocabulary in topics

(My Word Cards) by completing definitions

and recreating visual representations for notes

and classroom word wall.

Write explanations for understanding concepts

and procedural execution of math topics using

unit Envision 2.0 features, such as Solve and

Share, Convince Me!, and Math Practice and

Problem Solving


and remediation

Find common

denominators

Use models to add and

subtract mixed numbers

Use models to multiply a

whole number by a

fraction and to model to

multiply a fraction by a

whole number

Use models to multiply

two fractions and to use a

standard algorithm to

multiply two fractions

Use multiplication to find

the area of a rectangle

Interpret multiplication as

scaling (or resizing) by

comparing the size of a

product to the size of one

factor on the basis of

another factor without

performing the

multiplication

Use of Envision

rubrics – Listen

and Look for

Lesson Videos

Journal prompt: The

word fraction is derived

from the Latin word

fractus, which means to

break. The words

numerator and

denominator also come

from Latin words.

Numerator comes from

numeros, meaning

number, and

denominator comes from

denominare, meaning

name. Discuss how these

terms may have come

about to describe a

“fraction.”

https://whenmathhappens.com/2014/04/17/paul-sturgess/

https://whenmathhappens.com/2014/04/17/paul-sturgess/

20

Content videos




reinforce concepts, procedural skills, and

fluency


instruction


learning


Problem-Solving Reading Mats (real-world

literacy activities)



5.MD.C.3

5.MD.C.4

5.MD.C.5 Measurement and Data

C. Geometric

measurement:

understand concepts of

volume and relate

volume to multiplication

and to addition.




5.MD.C.5 Breaking Apart Composite Solids

The purpose of this task is to help students see

different ways of breaking a solid into right

rectangular prisms and to relate volume to the

operations of multiplication and division.

5.MD.C.5a using Volume to Understand the

Associative Property of Multiplication

The purpose of this task is for students to use

the volume of a rectangular prism to understand

the associative property of multiplication.


math vocabulary about

volume of various objects


topics to explain

reasoning behind volume

calculations/ formulas

Modeling of volume using

pictures, equations, or

manipulatives


practice problems

Curricular

Framework

Illustrated Math

resources

performance

tasks

Mid Topic

Assessments

Topic

Performance

Tasks

Topic Tests

Exit Tickets

Lesson Quizzes

https://www.illustrativemathematics.org/content-standards/5/MD/C/5/tasks/1971



21

5.MD.C.5b Cari's Aquarium

This task supports the standard 5.MD.5.b in that

it asks students to use the volume formula and

conceptual understanding to solve real-world

problems. The standard calls for students to find

the volume, but not necessarily a missing

length. This task also supports students thinking

about what is appropriate in a real-life context.

5.MD.C Box of Clay

This task provides an opportunity to compare

the relative volumes of boxes in order to

calculate the mass of clay required to fill them.

These relative volumes can be calculated

geometrically, filling the larger box with

smaller boxes, or arithmetically using the given

dimensions.

Three-Act problem – Using measurement

Sam Houston:

https://whenmathhappens.com/2014/02/14/sam-

houston/

Pose the Solve-and- Share Problem for topics in

measurement and data


Share and discuss solutions

Provide guided practice of concepts and skills

Practice the use of math vocabulary in topics of

measurement and data (My Word Cards) by

regarding fractions and

geometric measurement

Find volume of solid

figures

Find volume of

rectangular prisms using a

formula

Find volume of prisms

using different ways, such

as unit cubes

Find the volume of a solid

figure that is a

combination of two or

more rectangular prisms

Weekly Math

Journal based on

math vocabulary;

error analysis;

real-world

connections;

lesson reflections

PARCC Released

Questions

Pearson

Cumulative

Topic

Assessments

Unit 1 Test

Use of Envision

rubrics – Listen

and Look for

Lesson Videos

(teacher

observations


Certain species of fish

need specific size

aquariums in order to

live. The character Dory

is a Pacific Blue Tang

fish and should not be

kept in an aquarium

because they are only

born in the ocean and can

be aggressive towards

other fish. The best fish

for an unheated tank is a


https://www.illustrativemathematics.org/content-standards/5/MD/C/tasks/1031

https://whenmathhappens.com/2014/02/14/sam-houston/

https://whenmathhappens.com/2014/02/14/sam-houston/

22

completing definitions and recreating visual

representations for notes and classroom word

wall.

Write explanations for understanding concepts

and procedural execution of math topics


and remediation

Content videos




reinforce concepts, procedural skills,

and fluency


instruction


learning


Envision 2.0 Problem-Solving Reading Mats

(real-world literacy activities)



goldfish. If you have

goldfish that need 240

cubic feet of water to

live, what are some

possible dimensions of

the tank (rectangular

prism)?

23

Unit 3 Overview At-a-Glance Unit #3 – More Operations and Fractions

Unit Description:

In this unit, students will apply and extend previous understanding of multiplication and division; further understand the place value

system; perform operations with multi-digit whole numbers and with decimals to hundredths; and convert like measurement units within

a given measurement system. This unit will cover Envision topics 9 and 11 which include:

Topic 9: Apply Understanding of Division to Divide Fractions

Topic 11: Convert Measurements

Essential Skills:

Multiply fractions by whole numbers and fractions by fractions, drawing visual models to represent products, showing (a/b) x

(c/d) = ab(1/bd), and creating story contexts

Explain how a product is related to the magnitude of the factors, including cases in which one factor is a fraction greater than 1

and cases in which one factor is a fraction less than 1

Solve real-world problems involving multiplication of fractions (including mixed numbers), using visual fraction models or

equations to represent the problem

Divide a unit fraction by a non-zero whole number and interpret by creating a story context or visual fraction model

Divide a whole number by a unit fraction and interpret by creating a story context or visual fraction model

Solve real-world problems involving division of unit fractions by whole numbers or whole numbers by unit fractions

Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10; represent

powers of 10 using whole-number exponents

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; explain the reasoning used, relating the

strategy to the written method

Convert standard measurement units within the same system (e.g., centimeters to meters) in order to solve multi-step problems

Standards Addressed within Unit 3 – More Operations and Fractions



5.NF.B.4b

5.NF.B.5



5.MD.A.1

NJSLS SA.R1

24

5.NF.B.6

5.NF.B.7

5.NBT.A.2

5.NBT.B.5

NJSLS RI.5.1, 7

NJSLSSA.W1

NJSLSA.W2

NJSLSA.SL1, 2, 4

Unit 3 Details – More Operations and Fractions

Modifications for Special Education

Students, English Language Learners,

Students at Risk of Failure, and Gifted

Students- Modify instructional approach

and/or assignments and evaluations as

needed based for students with IEPs, 504s,

ELLs and gifted and talented students

including but not limited to:

Envision 2.0 online personalized

practice

Envision 2.0 Visual Learning

Bridge activities






Extended time

Teacher modeling (non-verbal

teacher communication in addition

to spoken instructions)

Simplified written and verbal

instructions

ELL support materials

(eDictionaries, native language

prompts, etc.)


The 5th grade math curriculum emphasizes collaboration, communication, problem

solving, and critical thinking. We have supported and stressed the 21st century

skills by incorporating the following activities into our lessons:

o Group Relay Races

o Scavenger Hunts

o Menu Math

o GRAPHiti


Lessons, where appropriate, incorporate multiple perspectives to infuse cultural and

global awareness.



Lessons integrate a focus on civic literacy so that students can better understand the

rights and obligations of citizenship.

Learning advocates for health literacy as a critical component of a healthy lifestyle

and the ability to make good health-related decisions.

Students explore areas that support environmental literacy, including society’s

impact on the environment and what can be done to support environmental

solutions.

Lessons, activities, and assessments require creativity and innovation on the part of

the students. They are required to create projects and products as examples of

mastery in each unit.

Critical thinking and problem solving skills are a core component of learning and

assessment throughout this curriculum. Students are required, in each unit, to

advance their learning through all levels of Bloom’s Taxonomy to address the

25

Differentiated instruction to meet

varied needs and levels of all

students (task cards, centers, labs)



grouping

One-on-one instruction in small

groups for remediation

Increased integration of higher

order thinking processes, creative

and critical thinking activities,

problem-solving, and open-ended

tasks



Greater opportunities for freedom

of choice and independent study

that encourage independent and

intrinsic learning

Inquiry-based projects and

assignments

evaluation, synthesis, and creation of products using learning at the highest levels.

Problem-solving is a recurring theme in the curriculum as students must seek ways

to creatively apply the concepts to solve problems rather than simply remember the

material.




addition, students are often required to work collaboratively with their peers which

promotes the ability to succeed in the area of social cooperative work, increases

communication skills, and promotes leadership and responsibility.


information effectively, in order to succeed in class as learning activities require

independent research of relevant information outside of the provided textbook

and/or resources.

In order to succeed in this course, students must be able to use technology as a tool

in order to research, organize, evaluate, and communicate information.

Activities in the curriculum help develop life and career skills in all students by

promoting flexibility and adaptability, requiring initiative and self-direction in the

learning process, supporting social and cross-cultural skills in both content and

teamwork efforts, and measuring productivity and accountability through

independent and group assignment completion.



assessments

Curricular Framework Illustrated

Math resources



Exit tickets

Lesson quizzes

Weekly math journal



Career Education: Choose a recipe a chef might use for a school cafeteria. Calculate the

amount of each ingredient that will be needed for 10 people, 50 people, and 100 people.

Health/PE: Record various times to run a race in PE class and record times as decimals,

fractions, and mixed numbers. Which recording method is easiest to understand and easiest

to compare? Explain your reasoning.


Reading Mats: Jewels and Jade and Animal Records. In math journal, list any terms that

are unfamiliar; write a questions you may have about the real-world math topic; write a

26

Pearson cumulative topic

assessments

Unit 1 test


word problem based on the information provided in the “Problem Solving Reading Mat”;

or work with a partner to add an additional fact about the topic as it relates to your

community.

Science: Investigate what environmental elements will affect the growth of seedlings.

Design and conduct an experiment and chart daily growth.

Social Studies: Research the Eiffel Tower in Paris or the Burj Khalifa in Dubai and make

a presentation (poster, slide show, brochure, etc.) to inform the viewer of important facts

that involve measurements (height, number of windows, stairs, etc.)

Technical Subjects: Using the PARCC online tools, type a solution and explanation for a

problem that requires fractions.

World Languages: The word multiplication comes from the Latin words mult and plicare.

Multi means “many” and plicare means “fold.” Discuss how “fold” applies to the process

use for multiplying numbers, fractions, or mixed numbers.

Arts: Make a poster containing pertinent information regarding measurement of a

particular location in Wilbur Watts Intermediate School. Include customary and metric

measurements.

Unit Resources










NJSLS 8.1.8.A.4

NJSLS 8.1.8.A.5

Presentations, posters, and visual vocabulary definitions generated on Microsoft software

programs, such as Word and Publisher.

27


Online Resources:



http://www.ixl.com







Books created on the Cloud on various topics to publish and share using MyEbookMaker

(https://myebookmaker.com/)



Front Row Ed


PBS Math Club


Math Antics


Study Island

Khan Academy

Brain Pop

AAA Study

Math.com

Mathisfun.com

Coolmath.com

www.nctm.org

Smartech.com

Unit #3 Targeted Instructional Planning to Address Central Unit Standards: Central Unit

Standard and

Student Learning

Objective

Suggested Instructional Activities Suggested

Student Output




Rubrics)

5.NF.B.4b

5.NF.B.5

5.NF.B.6

Facilitate guided, group, and independent practice using

tasks from the NJ DOE Curricular Framework for

Mathematics:

Journals using

pertinent math

vocabulary

Curricular

Framework

Illustrated Math



http://www.ixl.com/









28

5.NF.B.7

Number and

Operations -

Fractions

Apply and extend

previous

understandings of

multiplication and

division to multiply

and divide

fractions.

5.NBT.A.2

Numbers and

Operations in Base

10

A. Understand the

place value system.

5.NBT.B.5

B. Perform

operations with

multi-digit whole

numbers and with

decimals to

hundredths.

5.NF.B.4b New Park

Part 1 of this task is designed to elicit student thinking

about multiplication of fractions and the commutative

property. Part 2 of the task uses the area of a rectangle to

help students understand why the commutative property

always holds.

5.NF.B.5 Comparing Heights of Buildings

The goal of this task is to compare three quantities using

the notion of multiplication as scaling.

5.NF.B.5 Grass Seedlings

Student must compare the size of each of two products

(112×R, and 34×R) to one factor (R) on the basis of the other

factor without performing any computations. They will

explain their reasoning.

5.NF.B.5b Mrs. Gray's Homework Assignment

This problem assesses students’ ability to explain 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)

5.NF.B.6 To Multiply or not to multiply?

This problem illustrates how many real world problems appear

similar. Even when students might know what operation to

choose when the problem only involves whole numbers, they

often are confused with fractions. It is also important for

students to know that 18×25 is equal to 25×18

5.NF.B.7 Banana Pudding

regarding

multiplying and

dividing fractions

Constructed

arguments of

topics to explain

reasoning of

operations with

fractions and

decimals

Modeling of

fractions,

division, and

conversion using

pictures,

equations, or

manipulatives

Solutions to

various practice

problems for

multiplying and

dividing fractions,

decimals, and

place value

Relate fractions to

division

Implement

division of

fractions to show

resources

performance tasks

Mid Topic

Assessments

Topic Performance

Tasks

Topic Tests

Exit Tickets

Lesson Quizzes

Weekly Math

Journal based on

math vocabulary;

error analysis; real-

world connections;

lesson reflections

PARCC Released

Questions

Pearson Cumulative

Topic Assessments

Unit 3 Test

Use of Envision

rubrics – Listen and

Look for Lesson

Videos (teacher

observations)

Unit Journal Prompt: The

phrase Divide and Conquer

is derived from the Latin

saying Divide et impera.

Discuss how the process of

dividing compares to this

phrase.







29

The purpose of this task is to provide students with a concrete

situation they can model by dividing a whole number by a unit

fraction.

5.NBT.A.2 Multiplying Decimals by 10

The purpose of this task is to help students understand and

explain why multiplying a decimal number by 10 shifts all the

digits one place to the left.

5.NBT.A.2 Marta's Multiplication Error

This task highlights a common misconception among students

deriving the rules for multiplying a number by a power of 10.

5.NBT.B.7 The Value of Education

The purpose of this task is for students to add, subtract,

multiply, and divide decimal numbers in a real-world context.

5.MD.A.1, 5.NF.B.3 Converting Fractions of a Unit into a

Smaller Unit

In these problems students are given a set of a specified size

and a specified number of subsets into which it is to be

divided. They are expected to realize that they need that

information rather than giving it to them upfront. Students

identify what information they need to have to solve the

problem and knowing where to go to find it allows them to

engage in Standard for Mathematical Practice 5- Use

appropriate tools strategically.



quotients as

fractions

Use multiplication

to divide a whole

number by a

fraction

Use models such

as pictorial model

or a number line

to show dividing

whole number by

a unit fraction

Use models to

divide unit

fractions by non-

zero whole

numbers

Use models to

divide whole

numbers and unit

fractions and then

check using

multiplication

Explain patterns

in the number of

zeros when

multiplied by

powers of ten




https://www.illustrativemathematics.org/content-standards/5/MD/A/1/tasks/293

https://www.illustrativemathematics.org/content-standards/5/MD/A/1/tasks/293

30

Share and discuss solutions of example problems

Provide guided practice of concepts and skills using

Envision 2.0 presentation tools

Practice the use of math vocabulary in topics (My Word

Cards) by completing definitions and recreating visual

representations for notes and classroom word wall.

Write explanations for understanding concepts and

procedural execution of math topics using unit Envision

2.0 features, such as Solve and Share, Convince Me!, and

Math Practice and Problem Solving

Utilize online tools for instruction, practice, and remediation

Content videos



Thinking games and Fluency games to reinforce concepts,

procedural skills, and fluency

Adapted Assignments for differentiated instruction

Envision Centers kit for independent learning

Another Look Homework Videos

Envision 2.0 Problem-Solving Reading Mats (real-world


Discuss skills in Math Practice posters to explain

strategies in problem solving

Fluently multiply

multi-digit whole

numbers using the

standard

algorithm

31

Unit 4 Overview At-a-Glance

Unit #4 – Coordinate Geometry and Classifying Figures

Unit Description:

In this unit, student will graph points on the coordinate plane to solve real-world and mathematical problems; Analyze patterns and

relationships; classify two dimensional figures into categories based on their properties; Represent and interpret data; perform operations

with multi-digit whole numbers and with decimals to hundredths; and apply and extend previous understanding of multiplication and

division. This unit will cover Envision topics 12, 13, 14, 15, and 16 which include:

Topic 12: Represent and Interpret Data

Topic 13: Write and Interpret Numerical Expressions

Topic 14: Graph Points on the Coordinate Plane

Topic 15: Algebra – Analyze Patterns and Relationship

Topic 16: Geometric Measurement – Classify Two-Dimensional Figures

Essential Skills:

Represent real world and mathematical problems by graphing points defined by whole number coordinates in the first quadrant of

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

Generate two numerical patterns from two given rules, identify the relationship between corresponding terms, create ordered

pairs and graph the ordered pairs

Classify two- dimensional figures in a hierarchy based on properties

Fluently multiply multi-digit whole numbers with accuracy and efficiency

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; explain the reasoning used, relating the

strategy to the written method

Solve real world problems involving division of unit fractions by whole numbers or whole numbers by unit fractions

Standards Addressed within Unit 4 – Coordinate Geometry and Classifying Figures



5.G.A.1

5.G.A.2

5.OA.B.3

5.G.B.3



NJSLS SA.R1

NJSLS RI.5.1

NJSLS RI.5.7

NJSLSSA.W1

32

5.G.B 4

5.NBT.B.5

5.NBT.B.7

5.NF.B.7

NJSLSA.W2

NJSLSA.SL1

NJSLSA.SL2

NJSLSA.SL4

Unit 4 Details - Coordinate Geometry and Classifying Figures

Modifications for Special Education Students,

English Language Learners, Students at Risk

of Failure, and Gifted Students- Modify

instructional approach and/or assignments and

evaluations as needed based for students with

IEPs, 504s, ELLs and gifted and talented

students including but not limited to:

Envision 2.0 online personalized practice


activities






Extended time



instructions)

Simplified written and verbal instructions







o Group Relay Races

o Scavenger Hunts

o Menu Math

o GRAPHiti










Students explore areas that support environmental literacy, including

society’s impact on the environment and what can be done to support

environmental solutions.




33






grouping


for remediation




open-ended tasks






learning



and assessment throughout this curriculum. Students are required, in each

unit, to advance their learning through all levels of Bloom’s Taxonomy to

address the evaluation, synthesis, and creation of products using learning at

the highest levels. Problem-solving is a recurring theme in the curriculum as

students must seek ways to creatively apply the concepts to solve problems

rather than simply remember the material.











In order to succeed in this course, students must be able to use technology as

a tool in order to research, organize, evaluate, and communicate information.


by promoting flexibility and adaptability, requiring initiative and self-

direction in the learning process, supporting social and cross-cultural skills in

both content and teamwork efforts, and measuring productivity and

accountability through independent and group assignment completion.



assessments

Spring NWEA


resources




Career Education: Research how a video game developer uses coordinate geometry

to program a game. Write an entry in math journal as to how coordinate geometry

may be used in your favorite video game

Health/PE: Students physically play coordinate grid “Battleship!”

34

Exit tickets

Lesson quizzes

Weekly math journal



Unit 1 test



Reading Mats: Sedimentary Rocks; Sporting Life; Where and Why?; Life in the

Oceans; and the Age of Sail. In math journal, list any terms that are unfamiliar; write

a questions you may have about the real-world math topic; write a word problem

based on the information provided in the “Problem Solving Reading Mat”; or work

with a partner to add an additional fact about the topic as it relates to your

community.

Science: Research and create a line graph of the age and height of a human from age

0 to 12 years; x-axis being age, y-axis being height. Write the points on the graph as

ordered pairs. (This activity is preparation for the Meerkat Performance Task)

Social Studies: Overlay a transparent coordinate plane on a map of a foreign country

and ask students to locate various cities.

Technical Subjects: Play “Hour of Code” to learn programming and the code used

to move an avatar. (https://hourofcode.com/us )

World Languages: Read about the Great Pyramids of Giza. Classify the triangle(s)

used and make a 3-D drawing of a pyramid; label the measurements.

Arts: Discuss the shapes and patterns that can be found in African decorations,

baskets, and art. Create a pattern of your own to display in the classroom. Include an

African country as a reference for the “new” pattern.

https://hourofcode.com/us

35

Unit Resources










Online Resources:



http://www.ixl.com






NJSLS 8.1.8.A.4, NJSLS 8.1.8.A.5

Presentations, posters, and visual vocabulary definitions generated on Microsoft

software programs, such as Word and Publisher.



Books created on the Cloud on various topics to publish and share using

MyEbookMaker (https://myebookmaker.com/)



Front Row Ed


PBS Math Club


Math Antics


Study Island

Khan Academy

Brain Pop

AAA Study

Math.com

Mathisfun.com

Coolmath.com

www.nctm.org

Smartech.com



http://www.ixl.com/









36

Unit #4 Targeted Instructional Planning to Address Central Unit Standards: Central Unit

Standard and

Student Learning

Objective

Suggested Instructional Activities Suggested

Student Output




Rubrics)

5.G.A.1

5.G.A.2

Graph points on the

coordinate plane to

solve real-world

and mathematical

problems.

5.G.B.3

5.G.B 4

Classify two-

dimensional figures

into categories

based on their

properties.

5.OA.B.3 Analyze patterns

and relationships.

Facilitate guided, group, and independent practice using tasks

from the NJ DOE Curricular Framework for Mathematics:

5.G.A.1 Battle Ship Using Grid Paper

The purpose of this task is to give students practice plotting

points in the first quadrant of the coordinate plane and naming

coordinates of points.

5.G.A.2 Meerkat Coordinate Plane Task

The purpose of this task is for students to answer questions about

a problem situation by drawing and interpreting the meaning of

points that are in the first quadrant of the coordinate plane.

5.G.B.3 Always, Sometimes, Never

The purpose of this task is to have students reason about different

kinds of shapes based on their defining attributes and to

understand the relationship between different categories of shapes

that share some defining attributes.

5.G.B.4 What is a Trapezoid? (Part 2)

The purpose of this task is for students to compare different

definitions for trapezoids. Some people define trapezoids to have

one and only one pair of opposite sides parallel, while some

people define trapezoids to have at least one pair of opposite

sides parallel.

5.OA.B.3 Sidewalk Patterns

This purpose of this task is to help students articulate

mathematical descriptions of number patterns.

Journals using

pertinent math

vocabulary

regarding

coordinate

geometry and 2-

dimensional

figures

Constructed

arguments of

topics to explain

reasoning for

number patterns

and classifying

figures

Modeling of math

concepts of

figures graphed on

a coordinate plane

using pictures,

equations, or

manipulatives

Solutions to

various practice

problems

Performance

Assessment


Illustrated Math

resources performance

tasks

Mid Topic

Assessments

Topic Performance

Tasks

Topic Tests

Exit Tickets

Lesson Quizzes

Weekly Math Journal

based on math

vocabulary; error


connections; lesson

reflections

PARCC Released

Questions

Pearson Cumulative

Topic Assessments

Unit 1Test

Use of Envision

rubrics – Listen and

Look for Lesson

https://www.illustrativemathematics.org/content-standards/5/G/A/1/tasks/489

https://www.illustrativemathematics.org/content-standards/5/G/A/2/tasks/1516

https://www.illustrativemathematics.org/content-standards/5/G/B/3/tasks/1941

https://www.illustrativemathematics.org/content-standards/5/G/B/4/tasks/1505

https://www.illustrativemathematics.org/content-standards/5/OA/B/3/tasks/1895

37

Prior to Fractions on a Line Plot, create surveys to gather

and record data on line plots.

5.MD.B.2 5.NF.A.1 Fractions on a Line Plot

The purpose of this task is for students to add unit fractions with

unlike denominators and solve addition and subtraction problems

involving fractions that have more than one possible solution

(5.NF.1). Students are asked to record their results on a line plot

so that they have a way to systematically record their sums and to

help them reason about the possible sums they can make with the

cards.

Pose the Solve-and- Share Problem for topics classifying 2-

dimensional figures and patterns and relationships in expressions









procedural execution of math topics using unit Envision 2.0

features, such as Solve and Share, Convince Me!, and Math

Practice and Problem Solving


Content videos



Locate points on a

coordinate plane

Solve real-world

problems by

graphing points

Use reasoning to

solve problems

making sense of

quantities and

relationships

Use order of

operations

Evaluate

expressions with

parenthesis,

brackets, and

braces

Write simple

expressions that

show calculations

with numbers

Interpret

numerical

expressions

without evaluating

them

Videos (teacher

observations)

Unit Journal Prompt: Read

the story “Daisy’s Decimal

Disaster” online. Write 3

ways decimals are applied in

real-life.

http://www.storyjumper.com/

book/index/3329232/Daisy-

s-Decimal-Disaster

https://www.illustrativemathematics.org/content-standards/5/MD/B/2/tasks/1563

http://www.storyjumper.com/%20book/index/3329232/Daisy-s-Decimal-Disaster



38

Thinking games and Fluency games to reinforce

concepts, procedural skills, and fluency




Envision 2.0 Problem-Solving Reading Mats (real-world


Discuss skills in Math Practice posters to explain strategies

in problem solving

Journal Prompt:

Write an expression a person might use in everyday life , such as

“Oh, my gosh!” or “That’s awesome.” Many of these expressions

have abbreviations when texting (OMG, LOL, BTW). How can

these expressions be similar to algebraic expressions? (example:

These expressions can apply to many different scenarios. So can

algebraic expressions. 10x can mean $10 per hour or 10 feet per

second.) Students may write various expressions in words and in

algebra.

5.NBT.B.5

5.NBT.B.7

Numbers and

Operations in Base

Ten

B. Perform

operations with

multi-digit whole

numbers and with

decimals to

hundredths.

Facilitate guided, group, and independent practice using tasks

from the NJ DOE Curricular Framework for Mathematics:

5.NBT.B.7, 5.NF.B.3 What is 23 divided by 5? The purpose of this problem is to illustrate that when a division

problem involving whole numbers does not result in a whole

number quotient, it is important for students to be able to decide

whether the context requires the result to be reported as a whole

number with remainder or a mixed number/decimal.

5.NF.B.7c Salad Dressing

The purpose of this task is to have students add fractions with

unlike denominators and divide a unit fraction by a whole

Performance

Assessment


performance tasks

Mid Topic

Assessments

Performance Tasks

Topic Tests

Exit Tickets

Lesson Quizzes

Weekly Math Journal

based on math



39

5.NF.B.7

Numbers and

Operations -

Fractions

B. Apply and

extend previous

understandings of

multiplication and

division to multiply

and divide

fractions.

number. This accessible real-life context provides students with

an opportunity to apply their understanding of addition as joining

two separate quantities.










procedural execution of math topics using unit Envision 2.0

features, such as Solve and Share, Convince Me!, and Math

Practice and Problem Solving


Content videos



Thinking games and Fluency games to reinforce

concepts, procedural skills, and fluency




Problem-Solving Reading Mats (real-world literacy activities)

Discuss skills in Math Practice posters

vocabulary; error


connections; lesson

reflections

PARCC Released

Questions

Pearson Cumulative

Topic Assessments

Unit 1Test

Use of Envision rubrics –

Listen and Look for

Lesson Videos (teacher

observations)


Write an expression a person

might use in everyday life ,

such as “Oh, my gosh!” or

“That’s awesome.” Many of

these expressions have

abbreviations when texting

(OMG, LOL, BTW). How

can these expressions be

similar to algebraic

expressions? (example:

These expressions can apply

to many different scenarios.

So can algebraic expressions.

10x can mean $10 per hour

or 10 feet per second.)

Students may write various

expressions in words and in

algebra.

Documents

Math Grade 5 Preschool and Elementary School...grade mathematics. The course will incorporate many activities that promote critical thinking, problem solving, and math practices endorsed