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1
CITY OF BURLINGTON PUBLIC SCHOOL DISTRICT CURRICULUM
Math – Grade 5
Revision Date: July 2017
Submitted by: Antoinette Margaretta
2
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
3
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
4
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
5
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
6
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.
7
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.
8
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!)
9
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
https://whenmathhappens.com/3-act-math/
Coolmath.com
www.nctm.org
Smartech.com
10
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
11
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.
12
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
13
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.
14
Standards Addressed within Unit 2 - Understanding Volume and Operations on Fractions
Central Unit Standards- This unit will focus primarily on
learning goals aligned with the following standards:
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
Supporting Unit Standards- This unit will also include activities
aligned with the following standards:
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
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
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.
15
Teacher modeling (non-verbal teacher
communication in addition to spoken
instructions)
Simplified written and verbal
instructions
ELL support materials (eDictionaries,
native language prompts, etc.)
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
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 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
Curricular Framework Illustrated Math
resources
Suggested Interdisciplinary Activities for this Unit
Career Education: What careers or professions use terms that are rooted in Latin?
16
Mid-topic assessments
Topic performance tasks
Exit tickets
Lesson quizzes
Weekly math journal
PARCC released questions
Pearson cumulative topic assessments
Unit 1 test
Unit 1 performance tasks
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
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
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
Math.com
Mathisfun.com
Coolmath.com
www.nctm.org
Smartech.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
Formative Assessments
(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.
Facilitate guided, group, and independent
practice using tasks from the NJ DOE
Curricular Framework for Mathematics:
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
Journals using pertinent
math vocabulary
regarding fractions, their
parts, and how to operate
with fractions
Constructed arguments of
topics to explain
reasoning on topics
regarding equivalent
fraction and operations
with fractions
Modeling of fraction
equivalence using
pictures, equations, or
manipulatives
Solutions to various
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
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
Ask guiding questions as needed
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
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.”
20
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),
Problem-Solving Reading Mats (real-world
literacy activities)
Discuss skills in Math Practice posters to
explain strategies in problem solving
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.
Facilitate guided, group, and independent
practice using tasks from the NJ DOE
Curricular Framework for Mathematics:
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.
Journals using pertinent
math vocabulary about
volume of various objects
Constructed arguments of
topics to explain
reasoning behind volume
calculations/ formulas
Modeling of volume using
pictures, equations, or
manipulatives
Solutions to various
practice problems
Curricular
Framework
Illustrated Math
resources
performance
tasks
Mid Topic
Assessments
Topic
Performance
Tasks
Topic Tests
Exit Tickets
Lesson Quizzes
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
Ask guiding questions as needed
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
Unit Journal Prompt:
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
22
completing definitions and recreating visual
representations for notes and classroom word
wall.
Write explanations for understanding concepts
and procedural execution of math topics
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
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
Central Unit Standards- This unit will focus primarily on
learning goals aligned with the following standards:
5.NF.B.4b
5.NF.B.5
Supporting Unit Standards- This unit will also include activities
aligned with the following standards:
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
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.
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)
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
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
Curricular Framework Illustrated
Math resources
Mid-topic assessments
Topic performance tasks
Exit tickets
Lesson quizzes
Weekly math journal
PARCC released questions
Suggested Interdisciplinary Activities for this Unit
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.
English Language Arts/Literacy: Read and analyze data found in Problem-Solving
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
Unit 1 performance tasks
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
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
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.
27
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
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
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
Formative Assessments
(Portfolios, Projects,
Tasks, Evaluations, &
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
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.
Pose the Solve-and- Share Problem for topics
Ask guiding questions as needed
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
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
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
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
Central Unit Standards- This unit will focus primarily on
learning goals aligned with the following standards:
5.G.A.1
5.G.A.2
5.OA.B.3
5.G.B.3
Supporting Unit Standards- This unit will also include activities
aligned with the following standards:
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
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.
33
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
Spring NWEA
Curricular Framework Illustrated Math
resources
Mid-topic assessments
Topic performance tasks
Suggested Interdisciplinary Activities for this Unit
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
PARCC released questions
Pearson cumulative topic assessments
Unit 1 test
Unit 1 performance tasks
English Language Arts/Literacy: Read and analyze data found in Problem-Solving
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.
35
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
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
Math.com
Mathisfun.com
Coolmath.com
www.nctm.org
Smartech.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
Formative Assessments
(Portfolios, Projects,
Tasks, Evaluations, &
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
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 1Test
Use of Envision
rubrics – Listen and
Look for Lesson
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
Ask guiding questions as needed
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
Practice Buddy for skills
Gaming for reinforcing lesson content
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
38
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
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
Curricular Framework
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.
Pose the Solve-and- Share Problem for topics
Ask guiding questions as needed
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
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
Problem-Solving Reading Mats (real-world literacy activities)
Discuss skills in Math Practice posters
vocabulary; error
analysis; real-world
connections; lesson
reflections
PARCC Released
Questions
Pearson Cumulative
Topic Assessments
Unit 1Test
Use of Envision rubrics –
Listen and Look for
Lesson Videos (teacher
observations)
Unit 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.