Mathematics
Grades K-5
Curriculum Contributors:
Kimberly Zengewald
Sharon Greenblatt
Kristy Weaver
Ana Amaral
Jessica Russo
Isabel Silva
Jennifer Gentile
Vanessa Hamilton
Azure Diggs
Johanna Williams
Cathy Crisanaz
Nancy DaSilva
Jeannet Revollar
Sandy Duque
Lorie Tschoepe
Jennifer Wilson-Pinho
Maryam Muhammad
Deborah Parsons
Superintendent
Dr. Thomas Kane
Directors
Grace Conway, Elementary Ed.
Supervisor
Nicholas Sansone, Academic
Board of Education Approved:
August 18, 2011
Hillside Township School District
Table of Contents
Section
Page
Mission Statement
3
Academic Overview
3
Affirmative Action Compliance Statement
3
Interdisciplinary Units
Grade K
4
Grade 1
12
Grade 2
25
Grade 3
47
Grade 4
74
Grade 5
110
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Hillside Township School District
District Mission Statement
The mission of the Hillside Public Schools is to ensure that all students at all grade levels achieve the Common Core Curriculum
Content Standards and make connections to real-world success. We are committed to strong parent-community school partnerships,
providing a safe, engaging, and effective learning environment, and supporting a comprehensive system of academic and
developmental support that meets the unique needs of each individual.
Academic Area Overview
The Hillside Township School District is committed to excellence. We believe that all children are entitled to an education that will equip
them to become productive citizens of the twenty-first century. We believe that an education grounded in the fundamental principles of
science will provide students with the skills and content necessary to become our future leaders.
Mathematics is an excellent forum for students to develop the thinking and problem-solving skills necessary to be life-long learners.
The math curriculum was designed to foster students' natural curiosity by encouraging all students, regardless of gender, economic
status, or cultural heritage, to develop the ability, confidence, and motivation to succeed academically. Everyday Math is utilized in
grades K-5 and the program is aligned with the Common Core Curriculum Content Standards. The program is committed to providing
integrated learning experiences that will engage children and empower them to feel a sense of control over their own lives. Once
enabled to problem solve, communicate, and access information, these students will be prepared to be contributing members of
society. The ultimate goal of mathematics curriculum reform is to achieve mathematical literacy for all students.
Equality and Equity in Curriculum
The Hillside Township School District ensures that the district’s curriculum and instruction are aligned to the State’s Core Curriculum
Content Standards and addresses the elimination of discrimination and the achievement gap, as identified by underperforming schoollevel AYP reports for State assessment, by providing equity in educational programs and by providing opportunities for students to
interact positively with others regardless of race, creed, color, national origin, ancestry, age, marital status, affectional or sexual
orientation, gender, religion, disability or socioeconomic status.
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Hillside Township School District
N.J.A.C. 6A:7-1.7(b): Section 504, Rehabilitation Act of 1973; N.J.S.A. 10:5; Title IX, Education Amendments of 1972
KINDERGARTEN
CONTENT STRAND: Counting and Cardinality
ENDURING UNDERSTANDINGS
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There are many ways to represent a number.
Number sense develops through experience.
CCS
K.CC.1
K.CC.2
K.CC.3
K.CC.4
K.CC.4a
K.CC.4b
K.CC.4c
K.CC.5
K.CC.6
K.CC.7
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ESSENTIAL QUESTIONS
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KNOWLEDGE
Students will know:
Counting and one-to-one correspondence
through multisensory activities
Numbers 0-20
Counting to 100
Number sense and counting skills
Oral counting skills
The meaning of numbers
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Key Terms: number, tricky teens, zero, total,
count, count back, count on, forward, how many,
number line, first, second, third…, pattern
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ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Read numbers 0-20
Count using one-to-one correspondence
Music-Sing “This Old Man”; Dance to “Cha Cha
Slide”
Physical Ed-Play Simon Says using numbers
Literature Link: Arlene Alda’s 1 2 3 by Arlene
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How do I determine the best numerical representation
(pictorial, symbolic, objects) for a given situation?
What kinds of experiences help develop number sense?
SKILLS
Students will be able to:
Count objects, sounds, and taps
Use one-to-one correspondence to count objects
Recognize and represent numbers with groups of
objects
Count numbers and ordinal numbers in sequence
Compare and order whole numbers up to 20
Represent numbers with claps or taps
Orally count forward by ones to 100
Recognize a visual pattern of numbers
INTERNET AND OTHER RESOURCES
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Five Little Monkeys Jumping on the Bed by Eileen
Christelow
Emily’s First 100 Days of School by Rosemary Wells
The Button Box by Margarette S. Reid
Bat Jamboree by Kathi Appelt
Monster Squeeze Game
Hillside Township School District
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Alda
Math Masters pg 11
Counting with Sports Smart Exchange Lesson
Counting with Beads Smart Exchange Lesson
SheppardSoftware Early Math Games
PBSKids Counting Games
TIMEFRAME Section 1: September-October
Section 2: October- November
Section 3:November-December
Section 4: December-January
Section 5: January-February
Section 6: February-March
Section 7: March-April
Section 8: May-June
KINDERGARTEN
CONTENT STRAND: Operations and Algebraic Thinking
ENDURING UNDERSTANDINGS
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ESSENTIAL QUESTIONS
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Operations create relationships between numbers.
The relationships among the operations and their properties
promote computational fluency.
CCS
K.OA.1
K.OA.2
K.OA.3
K.OA.4
K.OA.5
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KNOWLEDGE
Students will know:
Addition and subtraction number stories
Addition and subtraction terminology and
symbols
Skip counting by 5s and 10s
Key Terms: add, all together, digit, equal, left,
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Why do I need mathematical operations?
How do mathematical operations relate to each other?
How do I know which mathematical operations (+,-) to
use?
SKILLS
Students will be able to:
• Distinguish between joining and take-away stories
• Use concrete materials and pictures to represent
and solve addition and subtraction stories
• Read and write expressions and number
sentences using the symbols +, -, =
• Demonstrate appropriate fluency with addition and
Hillside Township School District
less, more, same, subtract, take away, skip count
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ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
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Use +, -, and = symbols in a number sentence
and distinguish addition and subtraction
situations
Add small numbers
Science-Collect recyclables and group by 5s
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TIMEFRAME
Section 1: September-October
Section 2: October- November
Section 3:November-December
Section 4: December-January
Section 5: January-February
Section 6: February-March
Section 7: March-April
Section 8: May-June
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subtraction facts within 5
Skip count by 5s and 10s
Represent groups of 5 through counting and
patterns
INTERNET AND OTHER RESOURCES
12 Ways to Get to 11 by Eve Merriam
I Went Walking by Sue Williams
One Is a Snail, Ten Is a Crab by April Pulley Sayre and
Jeff Sayre
More, Fewer, Less by Tana Hoban
Chugga-Chugga Choo-Choo by Kevin Lewis
Train Games
LadyBug Addition Smart Exchange Lesson
Understanding Subtraction for Primary Grades Smart
Exchange Lesson
Gumball Math Smart Exchange Lesson
Starfall Addition Game
Adding and Subtracting Song
Hillside Township School District
KINDERGARTEN
CONTENT STRAND: Number and Operations in Base Ten
ENDURING UNDERSTANDINGS
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ESSENTIAL QUESTIONS
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There are many ways to represent a number.
Our number system is based on groups of ten.
Number sense develops through experience.
CCS
K.NBT.1
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KNOWLEDGE
Students will know:
Teen numbers represent “10 and some more”
How to read and enter numbers on a calculator
How to represent place value of tens and ones
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Key Terms: teen, count, ten, more, less, same,
equal, calculator, display, clear, exchange,
bundle, tens, ones
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
SKILLS
Students will be able to:
Identify numbers 0-19
Use concrete materials to represent numbers 0-19
Recognize each teen number as 10 + a digit
Read and display numbers on a calculator
Count by 10s and 1s
Represent numbers with manipulatives as 10s and
1s
INTERNET AND OTHER RESOURCES
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TIMEFRAME
How do I determine the best numerical representation
(pictorial, symbolic, objects) for a given situation?
What kinds of experiences help develop number sense?
Use manipulatives to model numbers and to
make exchanges
• Art-Create Paper Chains
• Art-Create Teen Numbers Class Book
• Science-Investigating the Solar Cell
Section 1: September-October
Section 2: October- November
Section 3:November-December
Section 4: December-January
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Teen Frame Game
Math Masters pg 137
My First Math Book pg 18
Butterfly Teen Math Smart Exchange Lesson
Online Calculator
Hillside Township School District
Section 5: January-February
Section 6: February-March
Section 7: March-April
Section 8: May-June
KINDERGARTEN
CONTENT STRAND: Measurement and Data
ENDURING UNDERSTANDINGS
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ESSENTIAL QUESTIONS
Measurement describes the attributes of objects and events.
Standard units of measure enable people to interpret results or
data.
All measurements have some degree of uncertainty.
CCS
K.MD.1
K.MD.2
K.MD.3
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KNOWLEDGE
Students will know:
How to describe measurable attributes of
objects
How to classify and sort objects into given
categories
How to directly compare measurable attributes
such as length and weight of two objects
How to measure time periods relative to a day
and week
The need for standard measurement units
Coin attributes
How to make and analyze a bar graph
How to conduct surveys and graph their results
Apply basic concepts of probability
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Why do I measure?
Why do I need standardized units of measurement?
How exact does a measurement have to be?
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SKILLS
Students will be able to:
Identify attributes
Find ways to sort objects using a variety of
attributes
Compare heights and weights of objects using
“more” or “less”
Tell time to the hour and half hour
Identify and measure with standard and nonstandard units/ tools
Sort coins according to various attributes
Construct a bar graph
Discuss information presented in a bar graph and
answer questions
Use survey information to make a graph
Describe events using certain, possible,
Hillside Township School District
Key Terms: bigger, smaller, longer, shorter,
compare, data, graph, bar graph, survey, heavier,
lighter, measure, pan balance, weight, weigh,
certain, possible, impossible, penny, nickel, dime,
quarter, dollar bill
impossible, and other basic probability terms
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
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TIMEFRAME
INTERNET AND OTHER RESOURCES
Use nonstandard measuring tools and units to
measure length
Compare lengths of 2 objects
Use attribute rules to find an object
Answer questions based on bar graphs
Science-Sort and classify objects found in
nature
Section 1: September-October
Section 2: October- November
Section 3:November-December
Section 4: December-January
Section 5: January-February
Section 6: February-March
Section 7: March-April
Section 8: May-June
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Attribute Spinner Game
Math Master pg 118
Weight and Measure 100th Day projects
Measuring Madness Smart Exchange Game
Making Graphs Smart Exchange Game
How Tall? Game
Measuring with feet Video
Coin Song
Hillside Township School District
KINDERGARTEN
CONTENT STRAND: Geometry
ENDURING UNDERSTANDINGS
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Geometry and spatial sense offer ways to interpret and reflect
on our physical environment.
Analyzing geometric relationships develops reasoning skills.
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CCS
K.G.1
K.G.2
K.G.3
K.G.4
K.G.5
K.G.6
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KNOWLEDGE
Students will know:
Basic geometric shapes and be able to identify
them
Describe an object’s location using relative
position
2-dimensional and 3-dimensional shapes
Analyze and compare the attributes of 2dimensional and 3-dimensional shapes
Shapes using the sense of touch
Construct shapes using given manipulatives
Combine simple shapes to make bigger
shapes
Geometric and spatial vocabulary and
concepts
Identify shapes on the Pattern-Block Template
Key Terms: shape, hexagon, length, rhombus,
trapezoid, square, triangle, circle, rectangle,
corner, side, round, curve, 2-dimensional, 3dimensional, attributes, cone, cube, cylinder,
sphere, top, below, next to, between, behind, in
front of, around, over, under, inside, outside,
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ESSENTIAL QUESTIONS
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How do geometric models describe spatial
relationships?
How are geometric shapes and objects classified?
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SKILLS
Students will be able to:
Identify circles, triangles, squares, and rectangles
Construct and compare 2-dimensional shapes and
3-dimensional shapes
Explore, recognize, and identify shapes by feel
Describe attributes of shapes
Use spatial vocabulary and concepts in everyday
situations
Use the names of pattern-block shapes and record
patterns
Hillside Township School District
above, beside, up, down, left, right
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
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TIMEFRAME
INTERNET AND OTHER RESOURCES
Identify and name triangle and circle
Physical Ed-Play Over, Under Relay Races
Physical Ed-Play Twister
Music-Dance “Hokey Pokey” including spatial
vocabulary
Section 1: September-October
Section 2: October- November
Section 3:November-December
Section 4: December-January
Section 5: January-February
Section 6: February-March
Section 7: March-April
Section 8: May-June
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Going on a Bear Hunt by Michael Rosen
Attribute Spinner Game
Shapes Smart Exchange Lesson
Kindergarten Shapes Smart Exchange Lesson
3D Shapes Song Video
We’re Going on a Bear Hunt: spatial vocab video
Hillside Township School District
GRADE 1
CONTENT STRAND: OPERATIONS AND ALGEBRAIC THINKING
ENDURING UNDERSTANDINGS
ESSENTIAL QUESTIONS
 Operations create relationships between numbers.
 The relationships between operations and their properties
promote computational fluency.
 Real world situations can be represented symbolically and
graphically.
 Algebraic expressions and equations generalize
relationships from specific cases.
CCS
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1.OA.1
1.OA.2
1.OA.3
1.OA.4
1.OA.5
1.OA.6
1.OA.7
1.OA.8
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KNOWLEDGE
Students will know:
How to find numbers that are one more
and one less
How to count nickels pennies, dimes and
quarters
How to use the number line for addition
and subtraction
To identify and continue number patterns
Create and solve a variety of number
stories for addition, subtraction, and
finding the difference
Basic addition facts
Dollars and cents notation
Identify individual value and count
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What is meant by equality?
Why do I need mathematical operations?
How do I know which operation to use?
How do mathematical operations relate to each other?
SKILLS
Students will be able to:
Count objects by 1(1.5, 5.1, 5.7, 8.3)
Locate numbers on a number line (1.5)
Name numbers that are one more and one less than a given
number (1.5)
Use a number line to solve number stories (1.5)
Find numbers that are larger than and smaller than a given
number (1.2)
Describe numbers using comparison vocabulary such a
smaller than, smaller than, bigger than, less than (1.2)
Count up from smaller number to a larger number (1.2)
Represent numbers using tally marks (1.10)
Compare pairs of 2 digit numbers (1.10, 3.13, 5.6)
Hillside Township School District
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combinations of pennies, nickels, dimes
and quarters
How to exchange pennies, nickels, dimes
and quarters
That data can be collected and interpreted
through charts and graphs (line plots, bar
graphs)
Count beyond 100
Solve and recite basic addition facts
(sums of 10, doubles, +1, +0)
Measure and compare lengths using nonstandard units of measure
Measure in inches and centimeters
The cumulative property of addition (turnaround facts)
To count up and back on the calculator
To use addition and subtraction facts table
Count up on the number line
Represent and solve problems involving
addition and subtraction
Understand and apply properties of
operations and the relationship between
addition and subtraction
Add and subtract within 20
Work with addition and subtraction
equations
Identify place value on a calculator
To identify place value and digit patterns
Use relation symbols < and >
Create and solve more than and less than
number stories
Create number models for greater than
and less than number stories
Generate sums
Find equivalent names for numbers (ex: 5
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Solve 1-digit by 1-digit change-to-less stories (2.12)
Write addition and subtraction number sentences using +, and = symbols (2.12)
Exchange pennies for nickels (2.13)
Show amounts of money using pennies and nickels (2.13)
Count forward and backwards by 1’s from a given number
(2.13, 2.12, 3.6, 4.2, 4.10, 5.13, 6.6)
Model and solve 1 digit by 1 digit number stories (2.13, 3.6)
Write addition and subtraction number sentences and
models using +, - and = symbols (2.12, 3.9, 8.1)
Count forwards and backwards by 1’s, 2’s, & 5’s from a
given number (3.10, 5.12, 6.8)
Identify and continue the pattern when given a set of
numbers (3.9, 5.12, 6.8)
Create number patterns (3.9)
Show amounts of money with the fewest amount of coins
possible (8.1)
Organize, create and interpret line plots and tally charts
(3.13, 5.9, 6.7)
Estimate and compare quantities in relation to 10 (more
than, less than, equal to) (3.14)
Identify and sort even and odd numbers (3.14, 6.7)
Order numbers from smallest to greatest (3.14, 5.8)
Estimate sums (3.14)
Find sums by taking apart and putting together numbers
(3.14, 5.10)
Compare heights (4.2)
Measure length in non-standard units (4.2)
Choose and label measurement units (4.2)
Subtract on a number grid (4.2)
Compare groups of objects (5.7)
Find sums (4.11, 5.10)
Identify and discuss patterns of sums for easy facts (3.14,
5.10)
Read numbers and symbols on a calculator (3.10)
Hillside Township School District
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= 4+1 or 7-2)
Understand the associative property of
addition
Understand fact families
To sort attribute blocks according to rules
Understand characteristics of plane
shapes (pattern block template)
The value of a dollar
Understand place value for ones, tens,
and hundreds
Understand factional parts of a whole
Understand relationship between multiples
and fractions
Understand fraction notation
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Key Terms: penny, nickel, dime, quarter,
more, less, add, subtract, number stories,
number models, exchange, equal to, plus,
minus, number line, dollars and cents
notation, line plot, tally chart, sum, measure,
unit, length, digit, decimal point, tape
measure, inch, centimeter, timeline,
difference, turn-around fact, doubles, digital
clock, analog clock, program, typical, bar
graph, scroll, fact power, flat, hundreds,
metric system, attribute, triangle, circle,
square, hexagon, rectangle, square, tens,
ones, hundreds place, tens place, ones place,
fraction, fractional part, near doubles
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Recite simple addition facts (+1, +0 and doubles) (4.12,
5.11)
Find sums of addition facts with and without a calculator
(5.11)
Use manipulatives to solve addition problems (4.11, 4.12)
Use addition and subtraction facts table for addition and
subtraction (6.1, 6.5)
Use +, - and = to count forward and backwards on a
calculator by 1s and 10s (3.10, 5.2)
Find and compare sums of whole numbers (4.12, 6.1, 6.7)
Identify describe and continue numerical patterns (5.13, 6.1)
Use manipulatives to model equivalent names for numbers
(6.2)
Write number sentences to express equivalencies (6.2)
Count and record the number of flats, longs and cubes
(base-10 blocks) (4.7)
Find a typical value in a set of data (4.7)
Create line plot and bar graph to analyze data (4.7)
Estimate and measure height to the nearest inch (4.7)
Create plane shapes and designs on geo-boards (4.7)
Use number scrolls (4.10)
Order numbers through 100 or more (4.10)
Name, read and write whole numbers modeled by base-10
blocks (5.1, 8.3)
Model numbers using base-10 blocks (5.1, 5.2)
Exchange base-10 blocks to show different representations
of the same number (5.1, 5.2)
Recognize patterns on a number grid (4.10, 5.2)
Compare whole numbers using < > and = (5.3)
Calculate and compare money amounts using < > and =
(5.3)
Use base-10 blocks to model and solve addition problems
(5.6)
Write number models using < and > (5.6)
Count up from larger number to solve addition problems
Hillside Township School District
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(5.9)
Draw conclusions about the probability of dice rolls (5.9)
Find different sets of 2 or more addends with the same sum
(6.2)
Identify and explain turn-around facts (5.11)
Use addition to check answers for subtraction (and vice
versa) (6.5)
Estimate, measure, and draw line segments to the nearest
inch and centimeter (6.6)
Identify and describe plane shapes (7.1, 7.3)
Sort plane shapes by size, shape and color (7.1)
Create designs using plane shapes (7.2)
Identify and apply rules to extend patterns (7.2)
Identify rules in which plane shapes are sorted (7.2)
Count sides and corners on plane shapes (7.3)
Compare plane shapes (7.3)
Calculate the value of combinations of coins (8.1)
Show amounts of money with the fewest amount of coins
(8.1)
Identify a dollar and know its value (8.2)
Make exchanges between coins (8.2)
Count equal parts of a whole (8.7)
Identify shapes divided into halves, thirds, and fourths (8.7)
Record the number of equal parts in a whole and label each
part with a corresponding fraction (8.7, 8.9)
Use fractions to relate smaller shapes to larger shapes (8.9)
Recognize and sort near doubles facts (8.9)
Generate and record number models to match solution
strategies for addition and subtraction (3.6, 5.7, 5.8)
Tell, write and solve number stories (5.8, 8.4)
Express amounts of money using dollars and cents notation
(8.4)
Create, solve and record money number stories and discuss
solution strategies (8.4)
Show amounts of money with the fewest amount of coins
Hillside Township School District
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ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Everyday Math Games
 Monster Squeeze (1.2)
 Penny Dice (1.3)
 Bunny Hop (1.5)
 Nickel Penny Grab (2.11)
 High Roller (2.12)
 Coin Top-It (2.13)
 Coin Dice (3.12)
 Dime, Nickel Penny Grab (3.13)
 Domino Top-It (3.14)
 Time Match (4.4)
 Shaker Addition Top-It (4.12)
 Two-Fisted Penny Addition (5.2)
 Base-10 Exchange (5.3)
 The Difference Game (5.7)
 Beat the Calculator (5.11)
 Penny, Nickel, Dime Exchange
(5.13)
 Addition Top-It (6.1)
 Fact Power Game (6.7)
 Tric-Trac (6.8)
 Coin Exchange (6.10)
 Make My Design (7.1)
 Attribute Train (7.2)
 Dollar Exchange (8.2)
Assessments
(8.1, 8.4)
Write number sentences to match solution strategies (8.4)
INTERNET AND OTHER RESOURCES
Chika, Chika 1, 2, 3
By: Bill Martin Jr.
http://bkflix.grolier.com/p/node-32750/bk0025pr
If You Made a Million
By: David M. Schwartz
http://bkflix.grolier.com/p/node-32750/bk0033pr
Addition Game:
http://www.abcya.com/addition.htm
Comparing Numbers:
http://www.brainpopjr.com/math/numbersense/comparingnumbers/
Rounding:
http://www.brainpopjr.com/math/numbersense/rounding/
Money:
http://www.brainpopjr.com/math/money/
Fractions:
http://www.brainpopjr.com/math/fractions/
Collecting & Interpreting Data:
http://www.brainpopjr.com/math/data/
Addition & Subtraction:
16
Hillside Township School District
http://www.brainpopjr.com/math/additionandsubtraction/
Math Journal
 25-26 (2.13)
 37-38 (3.6)
 43-44 (3.9)
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45 (3.10)
50 (3.13)
51-52 (3.14)
56-59 (4.2)
69-70 (4.7)
76 (4.10)
77-78 (4.11)
79 (4.12)
82-83 (5.1)
85(5.2)
89-90 (5.6)
92-93 (5.7)
94-95 (5.8)
96 (5.9)
98-99(5.10)
100-101(5.11)
103-104 (5.12)
105 (5.13)
110 (6.1)
11-112(6.2)
118-119(6.5)
120-122(6.6)
124-125(6.8)
138 (7.1)
139(7.2)
140-142 (7.3)
151 & 153(8.1)
154-155 (8.2)
156 (8.3)
Smart Exchange File: Unit 1 Lessons
http://exchange.smarttech.com/details.html?id=e3461bec-bd93413d-b16a-9413a5ecc0ed
Smart Exchange File: Unit 2 Lessons
http://exchange.smarttech.com/details.html?id=fa2af349-f954-44ff8564-859ee8c8ff9c
Smart Exchange File: Unit 6
http://exchange.smarttech.com/details.html?id=57009f0c-16f14e7a-9bf5-239fa0ed9a31
Counting Backwards from 10 (Kdg review)
http://more2.starfall.com/m/math-k/song-index-demo/load.htm?f
More Starfall (addition and subtraction)
http://more2.starfall.com/m/math/add-subtract-demo/load.htm?f
Addition Video:
http://www.youtube.com/watch?v=O_ccOKla2DA
Counting by 2’s, 5’s,10’s:
http://www.youtube.com/watch?v=GTYxfltyPgg
Addition/Subtraction:
http://player.discoveryeducation.com/index.cfm?guidAssetId=F63D
5CD5-0C3E-40B8-B56B29AC8330B0DA&blnFromSearch=1&productcode=US
Math Investigations ( Addition, Subtraction, Counting by 10’s, Place
Value and Fractions):
17
Hillside Township School District
 160(8.4)
 168-169(8.7)
 174(8.9)
http://player.discoveryeducation.com/index.cfm?guidAssetId=7726
C3D7-4A56-4A34-AAD6CA74ABF7D989&blnFromSearch=1&productcode=US
Interdisciplinary Connections
Social Studies – Create simple bar graphs
Science – Compare tree sizes
GRADE 1
CONTENT STRAND: NUMBER AND OPERATIONS IN BASE-TEN
ENDURING UNDERSTANDINGS
ESSENTIAL QUESTIONS
 There are many ways to represent a number.
 Number sense develops through experience.
 Operations create relationships between numbers.
CCS
1.NBT.1
1.NBT.2
1.NBT.2A
1.NBT.2B
1.NBT.2C
1.NBT.3
1.NBT.4
1.NBT.5
1.NBT.6
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 How do I determine the best numerical representation
(pictorial, symbolic, objects) for a given situation?
 Why do I need mathematical operations?
KNOWLEDGE
Students will know:
Extend the counting sequence
Understand place value
Use place value understanding and
properties of operations to add and
subtract
That the two digits of a two-digit number
represent amounts of tens and ones
10 can be thought of as a bundle of onescalled a “ten”
Numbers 11 through 19 are composed of
a ten and one, two, three, four, five, six,
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18
SKILLS
Students will be able to:
Count to 120 starting at any number less than 120 (number
of the day routine)
Order 1 and 2 digit whole numbers (5.8)
Solve numbers stories (5.8)
Generate and record number models to match solution
strategies (5.8)
Extend place value concepts to 100
Count collections of objects (8.3)
Read and write whole numbers modeled with base-10
blocks (8.3)
Express amounts of money using dollars and cents notation
Hillside Township School District
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seven, eight or nine ones
The numbers 10, 20, 30, 40, 50, 60, 70,
80, and 90 refer to one, two, three, four,
five, six, seven, eight, or nine tens (and
zero ones)
How to compare two digit numbers based
on meanings of the tens and ones digits
Compare groups of tens and ones using
< , > , and =
Create and solve a variety of number
stories
Show amounts of money with coins
Solving number stories with 2 digit
numbers
Solve comparison number stories and
calculate amounts of change from
purchases
Add and subtract two 2 digit numbers
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Key Terms: hundreds, tens, ones, hundreds
place, tens place, ones place
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ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Everyday Math Games
 The Digit Game (5.1)
 $1, $10, $100 Exchange
(10.4)
(8.4)
Create, solve and record money number stories and discuss
solution strategies (8.4)
Show amounts of money with the fewest amount of coins
(8.1, 8.4, 10.3)
Write number sentences to match solution strategies (8.4)
Count forward by 25’s, 10’s and 5’s (10.3, 10.4)
Tell, write and solve number stories (5.8, 10.3)
Write addition and subtraction number sentences and
models using +, - and = symbols (2.12, 3.9, 8.1, 10.3)
Compare quantities and heights (4.2, 10.4)
Solve comparison number stories (10.4)
Identify money equivalencies (10.4)
Project 9
Use base-10 blocks to model numbers less than 100, name
whole numbers less than 100
Use base-10 blocks to model 2 and 3 digit whole numbers
Exchange base-10 longs and cubes to show different
representations of the same number
Use base-10 blocks to find sums of 2 and 3 digit numbers
Model Parts-and-total diagrams for addition number stories
Explain strategies use to solve problems involving the
addition and subtraction of 2 digit by 2 digit numbers
INTERNET AND OTHER RESOURCES
Place Value:
http://www.brainpopjr.com/math/numbersense/placevalue/
http://www.brainpopjr.com/math/numbersense/onehundred/
Everyday Math Unit 5 Lessons
Assessment
19
Hillside Township School District
Math Journal Pages
 82-83 (5.1)
 88 (5.5)
 94-95(5.8)
 156 (8.3)
 160(8.4)
 182-183(9.4)
 198-199(10.3)
 200 (10.4)
http://exchange.smarttech.com/details.html?id=5b65c70c-25f34c8d-8c27-89735a81bd5d
Interdisciplinary Connections
Social Studies – Compare continent sizes
Science – Order animal lengths
GRADE 1
CONTENT STRAND: MEASUREMENT AND DATA
ENDURING UNDERSTANDINGS
ESSENTIAL QUESTIONS
 Measurement describes the attributes of objects and
events.
 Standard units of measure enable people to interpret
results or data
 All measurements have some degree of uncertainty.
 The way data is collected, organized and displayed
influences interpretation.
CCS
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KNOWLEDGE
Students will know:
Why do I measure?
Why do I need standardized units of measure?
How does what I measure influence how we measure?
How exact does a measurement have to be?
Why is data collected and analyzed?
How do people use data to influence others?
How can predictions be made based on data?
SKILLS
Students will be able to:
20
Hillside Township School District
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1.MD.1
1.MD.2
1.MD.3
1.MD.4
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Measure lengths indirectly and iterating
length units
How to tell and write time
Represent and interpret data
Measure and compare lengths using nonstandard units
The inch and the centimeter are standard
units of length
Measurements can be made to the
nearest inch
How to estimate and measure the lengths
of objects in inches
The centimeter is a unit of measure in the
metric system
The length measurement of an object is
the number of same size length units that
span it with no gaps or overlaps
Time can be written to the half hour and
hour in analog and digital form
Data can be collected, organized,
represented and interpreted
How to add and subtract tens
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Count forward and backwards by 1s & 10s (4.2, 4.4, 6.6,
9.2)
Use the number grid to add and subtract 1’s and 10’s from 2
digit numbers (9.2)
Compare heights (4.2)
Measure length in non-standard units (4.2)
Choose and label measurement units (4.2)
Use language of approximation while measuring (4.4)
Estimate and measure length to the nearest inch or
centimeter (4.4, 6.6)
Compare standards units of measure (4.4)
Use reference objects to estimate length (4.5)
Measure and draw line segments to the nearest inch and
centimeter (4.5, 6.6)
Solve addition and subtraction problems with and without
manipulatives and tools (9.2)
Use number grid patterns to solve addition and subtraction
problems (9.2)
Key Terms: data, chart, inch, in., centimeter,
cm., analog, digital, unit, measure, length,
digit, yard, estimate, metric system
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Everyday Math Games
 Time Match (4.4)
 Number Grid Game (9.2)

Assessments
INTERNET AND OTHER RESOURCES
Time:
http://www.brainpopjr.com/math/time/
Measurement:
http://www.brainpopjr.com/math/measurement/inchesandfeet/
21
Hillside Township School District
Math Journal Pages
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http://www.brainpopjr.com/math/measurement/centimetersmeterskil
ometers/
56-58(4.2)
62-63(4.4)
64-65 (4.5)
120-122 (6.6)
179 (9.2)
Everyday Math Unit 3 Lessons
http://exchange.smarttech.com/details.html?id=05a09f42-3bd7421f-b2e1-b459a81426d6
Interdisciplinary Connections
LAL - Inch by Inch by, Leo Leoni
http://bkflix.grolier.com/p/node-32750/bk0024pr
Social Studies– Create personal time lines using
proportional inch spacing
Measurement :
http://player.discoveryeducation.com/index.cfm?guidAssetId=BDCF
2266-974A-4669-BC7A87D504E96822&blnFromSearch=1&productcode=US
GRADE 1
CONTENT STRAND: GEOMETRY
ENDURING UNDERSTANDINGS
 Geometry and special sense offer ways to interpret
and reflect on our physical environment.
 Analyzing geometric relationships develops reasoning
and justification skills.
CCS
•
1.G.1
1.G.2
1.G.3
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KNOWLEDGE
Students will know:
Polygons have defining characteristics (they
are closed, do not overlap, have all straight
sides, have corners where two sides meet)
The basic 3-dimensional shapes have names
and attributes (cylinder, cube, sphere,
rectangular prism, cone, pyramid)
ESSENTIAL QUESTIONS
 How do geometric models describe spatial relationships?
 How are geometric shapes and objects classified?
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SKILLS
Students will be able to:
Name, model and describe plane shapes using straws and twistties (10.5)
Name and describe solid figures (10.5)
Identify and describe attributes of plane shapes and solid figures
(7.5, 7.6, 10.5)
Count the numbers of sides, faces and corners on plane
Hillside Township School District
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Shapes have different attributes
Fractional parts of a whole have many
names
Key Terms: geometry, shapes, polygon, sphere,
cylinder, rectangular prism, surface, face,
pyramid, cone, cube
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Everyday Math Games
 Make My Design (7.1)
 Attribute Train (7.2)
Assessments
Math Journal Pages
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144 (7.4)
145 (7.5)
147-148 (7.6)
190-192(9.8)
201-203(10.5)
Interdisciplinary Connections
LAL
When a Line Bends…A Shape Begins
By: Rhonda Gowler Greene
Art – Create a drawing using only polygons and
circles
Science- Identify shapes found in nature
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shapes(7.4, 7.5, 7.6)
Model polygons (7.4)
Compare and contrast polygons and solid figures (7.4, 7.6)
Project 10
Use manipulatives to model equivalent names for numbers (6.2,
9.8)
Use “=” to describe the relationship between fractions (9.8)
INTERNET AND OTHER RESOURCES
Geometry:
http://www.brainpopjr.com/math/geometry/
Identifying 2-dimensional shapes:
http://www.ixl.com/math/grade-1/identify-2-dimensional-shapes
Identifying 3-dimensional figures:
http://www.ixl.com/math/grade-1/identify-3-dimensional-figures
Halves, Thirds, Fourths:
http://www.ixl.com/math/grade-1/halves-thirds-fourths
Equal Parts:
http://www.ixl.com/math/grade-1/equal-parts
Naming Fractions:
http://www.ixl.com/math/grade-1/what-fraction-does-the-shape-show
http://www.ixl.com/math/grade-1/which-shape-matches-the-fraction
Attribute Trains:
http://nlvm.usu.edu/en/nav/frames_asid_271_g_1_t_3.html?open=instr
uctions&from=topic_t_3.html
Various Geometry Games:
http://nlvm.usu.edu/en/nav/topic_t_3.html
23
Hillside Township School District
Building with Shapes:
http://www.abcya.com/shapes_geometry_game.htm
Geometry of everyday objects:
HTTP://WWW.IXL.COM/MATH/GRADE-1/GEOMETRY-OFEVERYDAY-OBJECTS
GRADE 1
TIMEFRAME
Unit
Pacing Guide
1
September
2
Late September - Mid October
3
Late October - Mid November
4
Late November - Mid December
5
Late December - Mid January
6
Late January - Mid February
7
Late February - Mid March
8
Late March - Mid April
9
Late April - Mid May
24
Hillside Township School District
10
Late May - June
GRADE 2
CONTENT STRAND: Operations and Algebraic Thinking
Represent and solve problems involving addition and subtraction
ENDURING UNDERSTANDINGS
 Counting finds out the answer to “how many” in object/sets.
 Flexible methods of computation involve grouping numbers in
strategic ways.
 Real world situations can be represented symbolically using
numbers and operations.
CCS
2.OA.1
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KNOWLEDGE
Students will know how:
To make up, represent, and solve addition
number stories
+0 and +1 addition facts; and addition facts in
which one of the addends is 0, 1, 2 or 3
To use -0 and -1 shortcuts; and identify the
subtraction facts related to given addition facts
To identify missing numbers in number pairs
that are generated by a rule and determine the
rule used to generate such number pairs
To solve frames-and-arrows problems having
two rules
To make change with assistance by counting
up from the cost of an item to the amount
tendered
25
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ESSENTIAL QUESTIONS
What are different ways to count?
What do numbers convey?
How do I know which mathematical operation to use?
How do I determine the best numerical representation
for a given situation?
SKILLS
Students will be able to:
Solve number stories involving addition that involve
parts-and-total and change situations
Write number models to summarize number stories
Discuss +0 and +1 facts shortcuts
Identify patterns in addition facts
Practice subtraction facts
Use symbols to write number sentences for fact families
Find missing numbers and rules for “What’s My Rule?”
problems
Identify and use rules for a function involving addition
and subtraction
Make change by counting up
Show coin combinations for an amount
Calculate money amounts
Hillside Township School District
• To solve multistep problems with assistance
for amounts under $1.00 and make change
using nickels, dimes and quarters
• To solve change-to-more number stories
• To solve parts-and-total number stories
• To read and illustrate temperature and to solve
number stories about temperature changes
• To develop strategies for adding two digit
numbers mentally; to calculate the total cost of
two items; and to demonstrate making change
for whole-dollar amounts up to $100.
• To identify comparison number stories and use
comparison diagrams
• To select and complete an appropriate
diagram to help solve an addition or
subtraction problem
• To enter money amounts into a calculator and
interpret calculator displays
• To compare prices and solve problems about
price differences
• To make change by counting up and estimate
totals by rounding to the nearest ten cents
• To understand the use of parentheses in
number models
Key Terms: addition number story, label, unit
box, number model, addition fact, +0 facts, +1
facts, fact power, subtraction number story, -0
facts, -1 facts, “What’s My Rule?”, function
machine, change-to-more number story, mental
arithmetic, parts-and-total diagram, comparison
number story, difference, parentheses
26
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Create and solve change-to-more number stories
Solve parts-and-total number stories
Solve problems involving addition and subtraction of 2digit whole numbers
Use parts-and-total diagrams to solve multi-digit addition
problems
Describe and solve comparison number stories
Identify change, parts-and-total, and comparison
number stories
Make and solve difference and comparison problems
Estimate and share solution strategies for finding
change
Solve problems involving three or more addends
Hillside Township School District
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
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INTERNET AND OTHER RESOURCES
LAL – Make a number story book (2.1)
Play Beat the Calculator (2.2)
Exit Slip: Write two addition and two
subtraction facts for a domino (2.6)
Create “What’s My Rule?” Tables (2.11)
Math Message (3.6)
Play Digit Game (3.7)
Calculating the Value of a Name (3.8)
LAL-Make a Change-to-More Story book (4.1)
Play Addition Spin (4.2)
My Reference Book pg. 116-118 (4.4)
Play Customer and Clerk: Shopping
Activity(4.6)
Penny Grab Activity(6.2)
LAL: Using Different Diagrams to Write
Number Stories(6.4)
Play Pick a Coin (10.3 & 10.4)
Math Message (10.6)
Play Soccer Spin (10.11)
EM Games
EM Facts Workshop Game
Fact Dash Game
Algorithm Animations
http://www.brainpopjr.com/math/additionandsubtraction/basica
dding/
http://www.brainpopjr.com/math/additionandsubtraction/basics
ubtraction/
http://www.brainpopjr.com/math/numbersense/placevalue/
http://www.ixl.com/math/grade-2
http://www.eduplace.com/kids/mw/swfs/mathlingo_grade2.html
(end of the year math vocabulary game)
GRADE 2
CONTENT STRAND: Operations and Algebraic Thinking
Add and subtract within 20
ENDURING UNDERSTANDINGS
ESSENTIAL QUESTIONS
27
Hillside Township School District
 Counting finds out the answer to “how many” in
objects/sets.
 Flexible methods of computation involve grouping numbers
in strategic ways.
 The relationships among the operations and their
properties promote computational fluency.
CCS
2.OA.2
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 What are different ways to count?
 How do I know which mathematical operation to use?
KNOWLEDGE
Students will know how:
To establish partnership principles
between number facts
To identify place-value patterns on number
grids
To utilize doubles facts to compute sums
To utilize the turn-around shortcut for
addition; and to discover a shortcut for
addition facts that have 9 as an addend
To utilize the doubles-plus-one and
doubles-plus-two facts
To demonstrate the inverse relationship
between addition and subtraction; and to
add and subtract facts for sums up to and
including 10
To review, develop, and provide practice
for subtraction strategies
To utilize shortcuts for subtracting the
number 9 or 8 from any numbers
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SKILLS
Students will be able to:
Write number sentences
Use place-value skills to complete number-grid puzzles
Solve facts involving doubles
Identify and use patterns to solve +9 facts
Explore the turn-around rule for facts
Develop and practice strategies for addition that use doubles
facts
Use symbols to write number sentences for fact families
Use counting-up and counting-back strategies for
subtraction
Solve -8 and -9 subtraction facts
Key Terms: doubles facts, sum, Facts Table,
row, column, diagonal, turn-around facts,
subtraction number story, Fact Triangle, fact
family, difference
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
INTERNET AND OTHER RESOURCES
28
Hillside Township School District
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EM Games
EM Facts Workshop Game
Fact Dash Game
Algorithm Animations
Two of Everything: A Chinese Folktale by: Lily Toy Hong (2.3)
http://www.brainpopjr.com/math/additionandsubtraction/countingon/
http://www.ixl.com/math/grade-2
Play Addition Top-It (1.4)
Play Penny Plate (1.6)
Play Number Grid Game (1.8)
Addition/Subtraction Facts Table (2.3)
Minute Math(2.4)
Math Message (2.5)
Fact Family Chain (2.7)
Writing/Reasoning(2.12)
GRADE 2
CONTENT STRAND: Operations and Algebraic Thinking
Work with equal groups of objects to gain foundations for multiplication.
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ENDURING UNDERSTANDINGS
Operations create relationships between numbers.
Flexible methods of computation involve grouping
numbers in strategic ways.
The relationships among the operations and their
properties promote computational fluency.
Multiplication is repeated addition.
CCS
2.OA.3
2.OA.4
KNOWLEDGE
Students will know how:
• To count and look for patterns on the
calculator
• To combine values of ones, tens, and
hundreds using base-ten blocks; and
explore addition facts on dominoes
• To utilize doubles facts
• To utilize the turn-around shortcut for
addition; and to discover a shortcut
for addition facts that have 9 as an
addend
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ESSENTIAL QUESTIONS
What are different ways to count?
How do I know which mathematical operation to use?
How is multiplication related to addition?
What are the different models and algorithms for multiplication?
SKILLS
Students will be able to:
Identify odd and even numbers on the number grid
Use the number grid to find 1 more, 1 less, 10 more or 10 less.
Identify patterns in counts and use the patterns to answer
questions
Count by 1s, 10s, and 100s with base-10 blocks
Practice addition facts
Solve facts involving doubles
Identify and use patterns to solve +9 facts
Explore the turn-around rule for facts
Develop and practice strategies for addition that use doubles
Hillside Township School District
• To explore and utilize doubles-plusone and doubles-plus-two strategies
to compute sums
• To demonstrate the inverse
relationship between addition and
subtraction
• Addition and subtraction facts for
sums up to and including 10
• To find the total number of objects in
equal groups
• To develop readiness for
multiplication
• To use multiplication as a way to find
the total number of things in several
equal groups
• To create and use rectangular arrays
to solve multiplication problems
• To find the total number of items in
several equal groups by multiplying.
• To master multiplication facts where
one of the factors is 2, 5 or10
• Utilize the identity property of
multiplication and the multiplication
property of zero
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Key Terms: number scroll, even number,
odd number, base-10 blocks, cube, long,
flat, doubles facts, sum, facts table, row,
column, diagonal, turn-around facts,
subtraction number story, fact triangle,
fact family, equal groups, multiplication,
times, multiply by, multiplication
diagram, x-by-y array, product,
multiplication fact
30
facts
Use symbols to write number sentences for fact families
Use repeated addition to solve problems
Use arrays to model multiplication
Count objects in an array
Create equal-size groupings
Count the total number of objects in several groups
Make arrays to represent equal groups
Use various strategies to solve number stories that involve
equivalent groups.
Create and solve multiplication number stories using rectangular
arrays
Use repeated addition, arrays, and skip counting to model
multiplication
Use skip counting to model multiplication
Find number patterns
Hillside Township School District
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
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Class Number Scroll (1.7)
Math Message (1.10)
Sorting Dominoes (1.12)
Addition/Subtraction Facts Table
(2.3)
Minute Math(2.4)
Math Message (2.5)
Fact Family Chain (2.7)
Egg Nests (2.8)
Cube Arrays (5.4)
Geoboard Arrays (6.6)
Solving Equal-Groups Riddles (6.7)
Playing Simon Says (6.8)
Building Arrays (6.9)
Making Arrays with Geoboard fences
(8.2)
Array Bingo (11.4)
Creating Arrays (11.6)
Square Numbers (11.7)
INTERNET AND OTHER RESOURCES
EM Games
EM Facts Workshop Game
Fact Dash Game
Algorithm Animations
Amanda Bean’s Amazing Dream by Cindy Neuschwander (6.7)
Each Orange Had 8 Slices: A Counting Book by Paul Gigante, Jr. (6.7)
http://www.brainpopjr.com/math/additionandsubtraction/doubles/
http://www.brainpopjr.com/math/multiplicationanddivision/
http://www.ixl.com/math/grade-2
GRADE 2
CONTENT STRAND: Numbers and Operations in Base Ten
Understand Place Value
ENDURING UNDERSTANDINGS
 Grouping is a way to count, measure and estimate.
 Our place value system is based on groups of ten.
CCS
ESSENTIAL QUESTIONS
 How does the position of a digit in a number affect its value?
 In what ways can numbers be composed and decomposed?
 How are place value patterns repeated in numbers?
KNOWLEDGE
SKILLS
31
Hillside Township School District
2.NBT.1
2.NBT.1a
2.NBT.1b
2.NBT.2
2.NBT.3
2.NBT.4
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Students will know how:
To relate number sequences and use
number lines
To group by tens and to exchange $1,
$10, and $100 bills
To identify the relationship between
months, weeks, and days
To identify place value in 2-digit and 3digit numbers
To make change by counting up from the
cost of an item to the amount tendered
To utilize the partial-sums addition
algorithm
To utilize place value concepts and
connect place value in money to place
value in base-10 blocks
To develop place value concepts by
using place
value tools
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To identify place value to ten-thousands
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To use and apply the trade-first
subtraction algorithm
To find the values of coin combinations
To identify and describe number patterns
and sequences
To explore place value patterns on
numbers grids
To give equivalent names for numbers
To use a calculator to look for patterns
To utilize counting by 2s, 5s, and 10s
concepts; to count by any number n; and
to describe patterns that result from
counting
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Students will be able to:
Read and write numbers to 10s, 100s, and 1000s
Count up and back by 1s, 2s, 5s, 10s, 25s, 100s and 1000s
Name days in a week
Describe calendar patterns and use them to solve problems
Count by 1s, 10s, and 100s with base-10 blocks
Explore place value concepts with base-10 blocks; read and
write 2- and 3- digit numbers
Identify the value of digits in multi-digit numbers
Use base-10 blocks and fact extensions to add two 2-digit
whole numbers
Model and write 3-digit and 4-digit numbers using base-10
blocks and money
Read, write, and model numbers to the ten-thousands using
place value tools
Identify the values of digits in numbers
Make equivalent numbers using base-10 blocks
Use a counting-up strategy to calculate the total value of coin
combinations
Use the number grid to find 1 more, 1 less, 10 more, or 10
less
Use place value skills to complete number-grid puzzles
Identify the ones digit in numbers
Compare numbers using the relation symbols
Use patterns to find rules for Frames-and-Arrows problems
Find missing numbers and rules for Frames-and-Arrows
problems
Hillside Township School District
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To combine values of 1s, 10s, and 100s
using base-10 blocks
To compare numbers using the relation
symbols <, >, =
To use a given addition or subtraction
rule to generate a number sequence, and
to identify the rule for a given number
sequence
Key Terms: algorithm, flat, long, cube, place
value, big cube, ones, tens, hundreds,
thousands, ten-thousands, trade-first,
multiple on 10, greater than, less than, equal
to, frame, arrow, arrow rule
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
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Writing Numbers on a Number Line (1.1)
Sorting and Counting Coins (1.2)
Building a Calendar for the Month (1.3)
Play Money Exchange Game(1.5)
Exploring Counting Patterns on the
Number-Grid Poster (1.7)
Play the Number-Grid Game (1.8)
Solving Hundreds-Tens-and-Ones
Problems (1.9)
Counting with a Calculator (1.10)
MJ pg. 17 (1.11)
Base-10 Structures (1.12)
Ongoing Assessment: Recognizing
Student Achievement (2.10)
Play The Digit Game (3.1)
Ongoing Assessment: Exit Slip (3.7)
Play the Fact Extension Game (4.9)
INTERNET AND OTHER RESOURCES
EM Games
EM Facts Workshop Game
Fact Dash Game
Algorithm Animations
Lot’s of Lady Bugs! Counting by Fives by Michael Dahl (1.2)
http://www.brainpopjr.com/math/numbersense/placevalue/
http://www.brainpopjr.com/math/numbersense/placevalue/
http://bkflix.grolier.com/b/node-32750/bk0025pr
http://pbskids.org/cyberchase/games/numbersense/
http://www.ixl.com/math/grade-2
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Hillside Township School District
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Music & Movement Link: Counting by 2s,
5s, and 10s (7.1)
Ongoing Assessment: Informing
Instruction (10.8)
Doing Digit Discovery (10.9)
S.S. Ordering 5-digit numbers (10.10)
Ongoing Assessment: Mental Math
(11.3)
GRADE 2
CONTENT STRAND: Numbers and Operations in Base Ten
Use place value understanding and properties to add and subtract
ENDURING UNDERSTANDINGS
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 Our place value system is based on groups of ten.
 Strategies based on place value can be used to solve addition and
subtraction problems.
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CCS
2.NBT.5
2.NBT.6
2.NBT.7
2.NBT.8
2.NBT.9
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KNOWLEDGE
Students will know how:
To add 2-digit numbers mentally
To calculate the total cost of two items
To develop paper-and-pencil strategies for
adding 2-digit and 3-digit numbers; and to use
estimation to check the reasonableness of
answers
To use the partial-sums addition algorithm
To solve addition problems, with emphasis on
problems having three addends
To identify and use solution strategies for
subtraction of 2-digit numbers
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ESSENTIAL QUESTIONS
How does the position of a digit in a number affect its
value?
In what ways can numbers be composed and
decomposed?
What are some algorithms for addition and subtraction
of 2 or more digit numbers?
How can understanding place value help to subtract?
SKILLS
Students will be able to:
Identify the place value in two-digit numbers
Use base-10 blocks to add two 2-digit numbers
Estimate sums by changing the addends to “close but
easier” numbers
Identify the value of digits in multi-digit numbers
Use base-10 blocks and fact extensions to add two 2digit whole numbers
Use and explain strategies for adding three or more
numbers
Count up and back 1s, 10s, 100s, and 1000s
Model 2-digit numbers using base-10 blocks
Hillside Township School District
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To use the trade-first subtraction algorithm
To select and complete an appropriate diagram
to help solve an addition or subtraction problem
To explore situations that require equal sharing
or making equal groups of things
To build mental arithmetic skills for adding three
or more 1- and 2- digit numbers
To identify complements of ten and compute the
differences between 2-digit numbers and higher
multiples of ten.
To provide experiences with place value
concepts to ten-thousands
To identify the subtraction facts related to given
addition facts.
To demonstrate the inverse relationship between
addition and subtraction
Key Terms: ballpark estimate, algorithm, addend,
trade, division, equal sharing, remainder, equal
grouping, flat, long, cube, place value, big cube,
ones, tens, hundreds, thousands, ten-thousands,
fact family
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
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Domino Facts MJ pg. 35 (2.6)
Ongoing Assessment: Recognizing Student
Achievement (2.7)
Play the Number-Grid Difference Game (2.12)
Mental Math (4.6)
Ongoing Assessment: Recognizing Student
Achievement (4.8)
Reviewing Place Value Concepts (4.9)
Algorithm Project 1, A1 (4.9)
Play Three Addends (6.1)
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Make equivalent numbers using base-10 blocks
Solving 2-digit addition and subtraction problems within
number stories
Explore the concept of equal sharing and equal
grouping using concrete objects
Solve addition problems with 3 or more numbers
Use a number grid and calculator to find differences
between 2-digit numbers and multiples of ten.
Find the complements of multiples of ten.
Model and write 3-and 4- digit numbers using base-10
blocks and money
Make exchanges with base-10 blocks and relate that to
exchanges with money
Use dominoes to model related addition and
subtraction facts
Practice basic facts in the context of Fact Triangles
Use addition and subtraction facts to solve subtraction
problems
INTERNET AND OTHER RESOURCES
EM Games
EM Facts Workshop Game
Fact Dash Game
Algorithm Animations
http://www.brainpopjr.com/math/additionandsubtraction/addin
gandsubtractingtens/
http://www.brainpopjr.com/math/additionandsubtraction/addin
gwithregrouping/
http://www.brainpopjr.com/math/numbersense/evenandodd/
http://www.ixl.com/math/grade-2
http://www.eduplace.com/kids/mw/swfs/rockhopper_grade2.ht
Hillside Township School District
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Solving a Partner’s Number Story (6.4)
Play Base-10 Trading (6.5)
Sharing Cookies Equally (6.10)
Play Hit the Target (7.2)
Play Basketball Addition (7.3)
Play the Money Exchange Game(10.8)
Making a Place-Value tool (10.9)
Social Studies Link: Ordering 5-digit Numbers
(10.10)
Modeling Subtraction with Base-10 Blocks (11.3)
Algorithm Project 2, A6 (11.3)
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http://www.eduplace.com/kids/mw/swfs/faf_grade2.html
GRADE 2
CONTENT STRAND: Measurement and Data
Measure and Estimate Lengths in Standard Units
ENDURING UNDERSTANDINGS
 Standard units provide common language for communication
measurements.
 In certain situations, an estimate is as useful an exact answer.
 Graphs convey data in a concise way.
CCS
2.MD.1
2.MD.2
2.MD.3
2.MD.4
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KNOWLEDGE
Students will know how:
To measure lengths and distances to the
nearest inch and centimeter
To measure length to the nearest centimeter
and to the nearest inch
To utilize the concept of nonstandard units of
measure; and to understand what is meant by a
yard and meter
To measure using inches, feet, centimeters and
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ESSENTIAL QUESTIONS
 What are tools of measurement and how are they used?
 What is the purpose of standard units of measurement?
 How can information be gathered, recorded, and
organized?
 What kinds of questions can and cannot be answered
from a graph?
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SKILLS
Students will be able to:
Distinguish between centimeter and inch
Compare lengths in centimeters and inches
Measure to the nearest inch, centimeter, foot, and
decimeter
Estimate and measure using nonstandard measurement
units
Develop an understanding of the importance of standard
units
Hillside Township School District
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decimeters; and to guide children as they begin
a table of equivalent linear measures
To measure to the nearest half-inch and halfcentimeter
To determine perimeters by measuring to the
nearest centimeter or inch
To identify the mile and kilometer as standard
units for longer distances and solve problems
about road-map distances
To understand the relationships among units of
capacity and identify equivalent measures of
capacity
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Measure using a yardstick.
Find the fractional part (1/2) of an inch and centimeter
Measure and estimate to the nearest ½ inch and ½
centimeter
Use addition to find the perimeter of polygons
Estimate measures
Develop an understanding of units of capacity
Key Terms: inch, centimeter, arm span, standard
unit, yard, meter, foot, decimeter, perimeter, mile,
kilometer, capacity, cup, pint, quart, gallon, liter
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
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INTERNET AND OTHER RESOURCES
Measuring Lengths with a Tape Measure (4.7)
Ongoing Assessment: Recognizing Student
Achievement (7.6)
Math Message (9.1)
Ongoing Assessment: Recognizing Student
Achievement (9.2)
MJ # 4 p. 215 (9.3)
Measuring Perimeter in Paces (9.4)
Choosing the Best Unit of Measure (9.5)
Ongoing Assessment: Informing Instruction
(9.8)
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EM Games
EM Facts Workshop Game
Fact Dash Game
Algorithm Animations
Inch by Inch by Leo Leonni (4.7)
How Big is a Foot? by Rolf Myller (9.1)
Twelve Snails to One Lizard by Susan Hightower (9.2)
Measuring Penny by Loreen Leedy (9.2)
Inchworm and a Half by Elinor J. Pinczes (9.3)
Millions to Measure by David Schwartz (9.6)
Spaghetti and Meatballs for All by Marilyn Burns (9.8)
http://www.brainpopjr.com/math/measurement/
http://bkflix.grolier.com/b/node-32750/bk0085pr
http://bkflix.grolier.com/p/node-32750/bk0024pr
http://www.ixl.com/math/grade-2
Hillside Township School District
GRADE 2
CONTENT STRAND: Measurement and Data
Relate Addition and Subtraction to Length
ENDURING UNDERSTANDINGS
 Standard units provide common language for communication
measurements.
 Measurement describes the attributes of objects and events.
CCS
2.MD.5
2.MD.6
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KNOWLEDGE
Students will know how:
To create comparison number stories by using
comparison diagrams.
To identify number sequences and use number
lines.
To discover a shortcut for addition facts that
has 9 as an addend.
To read and display temperatures and solve
number stories involving temperature changes.
To measure and interpret events on a timeline.
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ESSENTIAL QUESTIONS
What are tools of measurement and how are they
used?
What is the purpose of standard units of measurement?
How does what I measure influence how I measure?
What information can I gather about events using a
timeline?
SKILLS
Students will be able to:
Describe and solve comparison number stories.
Compare and order numbers on a number line.
Compare the distances between two numbers on a
number grid.
Identify and use patterns on a number grid to solve +9
facts.
Demonstrate, explain and solve temperature change
stories.
Order numbers in the context of timelines.
Hillside Township School District
Key Terms: number line, time line
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ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Comparing Number Stories (6.2)
MJ pg. 1 (1.1)
MJ pg. 25 (2.2)
Use a number grid to show +9 shortcuts (2.4)
MJ pgs. 90-91 (4.4)
Project: Make a timeline of your day (12.3)
INTERNET AND OTHER RESOURCES
EM Games
EM Facts Workshop Game
Fact Dash Game
Algorithm Animations
http://www.mathplayground.com/gsmbegin.html
http://www.mathplayground.com/katiebegin.html
http://www.ixl.com/math/grade-2
GRADE 2
CONTENT STRAND: Measurement and Data
Work with Time and Money
ENDURING UNDERSTANDINGS
 Standard units provide common language for
communication measurements.
 Measurement describes the attributes of objects and
events.
CCS
2.MD.7
2.MD.8
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KNOWLEDGE
Students will know how:
To relate and convert between months, weeks
To demonstrate telling time using digital and
analog notation
To describe time equivalencies and use a
calendar
To read times in different ways, to show time
to the nearest five minutes on a clock face,
and calculate times relative to the given time
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ESSENTIAL QUESTIONS
What are tools of measurement and how are they used?
How does the position of number affect its value?
When do I need to estimate?
What value do numbers convey?
How do units within a system relate to each other?
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SKILLS
Students will be able to:
Tell and show time to the nearest half hour.
Name days in a week
Distinguish between analog and digital clocks
Tell and write times
Match the time on a clock face with the digital notation
Describe relationships among units of time
Write and tell time to the nearest five-minute interval
Hillside Township School District
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To group by tens to exchange and convert
between$1, $10, and $100 bills
To identify coin values and make exchanges
among coins; and to determine coin
combinations needed to pay for items
To make change by counting up from the cost
of an item to the amount tendered
To solve multistep problems for amounts
under $1.00 and make change using nickels,
dimes, and quarters
To calculate the total value of a group of coins
To use estimation to solve problems for which
an exact answer is not necessary
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Make exchanges among coins and bills
Read and write money amounts in dollar-and-cents notation
Calculate money amounts
Making change by counting up
Show coin combinations for an amount
Compare money amounts
Estimate money amounts to solve problems
Share strategies for calculating exact money amounts and
estimating total money amounts
Find equivalent names for money amounts
Solve money number stories using a calculator
Solve and record solution strategies for equal sharing
problems in the context of money
To calculate the total cost of two items; and to
demonstrate making change for whole dollar
amounts up to $100
To determine coin combinations equivalent to
$1.00
To enter money amounts into a calculator and
interpret monetary displays on a calculator
To compare prices and solve problems
involving price differences
To estimate costs and calculate exact costs
To develop readiness for division
Key Terms: minute hand, hour hand, clock face,
analog clock, digital clock, nickel, penny, dime,
quarter, dollar bill, change
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
INTERNET AND OTHER RESOURCES
40
Hillside Township School District
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Ongoing Assessing: MJ #s 1,2, 4, 5, pg. 4
(1.3)
Play Penny-Nickel Exchange (1.5)
Play Spinning for Money (3.2)
Calculating Elapsed Time (3.3)
Solving a Coin Puzzle (3.7)
Practice Making Change (3.8)
Ongoing Assessment: Recognizing Student
Achievement (4.3)
MJ #s 1-3, pg. 93 (4.5)
Solving Shopping Problems (4.6)
Making Cards and Doing a Clock
Concentration Activity (5.1)
Ongoing Assessment: Recognizing Student
Achievement (6.6)
Solving Dollar Riddles (6.6)
Sharing Money (7.5)
Plan a Picnic (10.1)
Play Pick-a-Coin (10.3)
Ongoing Assessment: Recognizing Student
Achievement(10.4)
MJ pg. 243 (10.5)
Math Message (10.6)
Ongoing Assessment: Recognizing Student
Achievement (11.1)
Make Up and Solve Money Number Stories
(11.2)
Math Message (12.1)
Telling Time to Five Minutes (12.2)
EM Games
EM Facts Workshop Game
Fact Dash Game
Algorithm Animations
Pigs on a Blanket by Amy Axelrod (3.3)
26 Letters and 99 Cents by Tana Hoban (3.2)
The Big Buck Adventure by Shelley Gill and Deborah Tobola(3.2)
Pigs Will Be Pigs:Fun with Math and Money by Amy Axelrod (3.8)
Betcha! by Stuart J. Murphy (4.5)
The $1.00 Word Riddle Book by Marilyn Burns (4.6)
Sold! by Nathan Zimelman (10.1)
Alexander Who Used to Be Rich Last Sunday by Judith Viorst
(10.6)
Follow the Money by Loreen Leedy (10.6)
http://www.brainpopjr.com/math/time/
http://www.brainpopjr.com/math/money/
http://bkflix.grolier.com/p/node-32750/bk0033pr
http://www.ixl.com/math/grade-2
GRADE 2
CONTENT STRAND: Measurement and Data
Represent and Interpret Data
41
Hillside Township School District
ENDURING UNDERSTANDINGS
 Standard units provide common language for communication
measurements.
 Graphs convey data in a concise way.
CCS
2.MD.9
2.MD.10
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KNOWLEDGE
Students will know how:
To measure length to the nearest centimeter
and to the nearest inch
To sort numerical data and arrange data in an
ascending and descending order, and as they
find the middle value (median) for a set of
numerical data
To create a frequency table, line plot, and bar
graph for a set of data; and find the median of
a set of data
To gather and organize a set of data with a line
plot and frequency table
To display a set of data with a bar graph, and
identify its median and mode.
Key Terms: data, median, middle number, sort,
line plot, bar graph, frequency table, mode, range,
tally chart, predict
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
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Math Message (3.5)
Ongoing Assessment: Informing Instruction
(6.3)
Collecting and Recording Standing Long Jump
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ESSENTIAL QUESTIONS
 What are tools of measurement and how are they used?
 How can information be gathered, recorded, and
organized?
 What kinds of questions can and cannot be answered
from a graph?
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SKILLS
Students will be able to:
Collect, record, and organize data
Find the median, mode, and range of a data set using
concrete materials
Create tally charts, frequency tables, line plots, and bar
graphs
Use graphs to answer questions and draw conclusions
Discuss data in a tally chart and bar graph
INTERNET AND OTHER RESOURCES
EM Games
EM Facts Workshop Game
Fact Dash Game
Algorithm Animations
Probably Pistachio by Stuart J. Murphy (7.8)
Hillside Township School District
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Data and Arm Span Data (7.6)
Finding the Median (7.7)
Graphing Data Side by Side (7.8)
Ongoing Assessment: Recognizing Student
Achievement (12.6)
Landmarks of a Data Set (12.7)
The Tortoise and the Hare by Aesop (12.6)
http://www.brainpopjr.com/math/data/
http://www.ixl.com/math/grade-2
GRADE 2
CONTENT STRAND: Geometry
Reason with shapes and their attributes
ENDURING UNDERSTANDINGS
 Objects can be described and compared using their geometric
attributes.
 Points, lines, and planes are the foundation of geometry.
CCS
2.G.1
2.G.2
2.G.3
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KNOWLEDGE
Students will know how:
To make, describe, and compare geoboard
shapes
To develop readiness for classifying geometric
shapes
To demonstrate rules used to classify shapes
To define, name, and draw line segments
To understand and relate the concepts of
parallel and parallel segments
To name and classify polygons and describe
their similarities and differences using attribute
blocks
To identify the names and characteristics of
various quadrangles and explore the
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ESSENTIAL QUESTIONS
 How can plane and solid shapes be described?
 How are geometric figures constructed?
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SKILLS
Students will be able to:
Model, describe, and compare shapes on a geoboard
Sort attribute blocks by three different attributes
Describe rules for a group of sorted attribute blocks
Connect points in a sequence to draw line segments
Use a straightedge to draw a line segment
Identify parallel line segments
Draw a quadrangle
Name, compare and construct polygons
Create shapes out of triangles and rectangles
Identify characteristics of quadrangles
Compare quadrangles
Identify, describe, and compare cones, pyramids,
prisms, cubes and cylinders.
Hillside Township School District
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similarities and differences among
quadrangles
To compare and contrast the characteristics of
3-dimensional shapes
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To construct pyramids and explore the
relationships among the number of faces,
edges, and vertices in pyramids
To calculate area by tiling surfaces
To calculate the areas of shapes by using inch
and centimeter grids
To distinguishing between area and perimeter
To calculate the area of rectangular figures by
counting squares
To identify basic fraction concepts
To link a fraction amount to the size of the
ONE, or a whole
To use fractions to name parts of collections
To identify equivalent fractions using
manipulatives.
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Model 2-dimensional shapes and pyramids using straws
and twist ties
Divide shapes into equal parts
Find area by tiling with pattern blocks and counting
shapes
Count unit squares to find the area
Divide shapes into equal parts
Use manipulatives to model ½, ¼, and 1/8.
Compare fractional parts using pattern blocks
Use manipulatives to model fractions as equal parts of a
collection of things
Label fractional parts of a circle
Make up and solve fraction number stories
Forming fractions on a geoboard
Key Terms: point, straightedge, line segment,
endpoint, parallel, quadrangle, trapezoid,
rhombus, polygon, triangle, quadrangle,
pentagon, hexagon, heptagon, octagon, side,
vertex, vertices, angle, square corner, square,
rectangle, parallelogram, kite, cylinder, cone,
sphere, curved surface, rectangular prism, cube,
pyramid, flat surface, face, edge, base, apex,
tiling, area, square inch, square centimeter,
surface, fraction, denominator, numerator, one
(the whole)
ASSESSMENTS/PERFORMANCE TASKS/
INTERNET AND OTHER RESOURCES
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Hillside Township School District
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INTERDISCIPLINARY CONNECTIONS
Making and Comparing Geoboard Shapes
(3.4)
Sorting Attribute Blocks (4.3)
Tiling Surfaces with Different Shapes (4.7)
Math Message (5.1)
Ongoing Assessment: Recognizing Student
Achievement (5.2)
Drawing Line Segments (5.3)
Finding Shapes Around the Room (5.4)
Exploring Tangrams (5.5)
Math Message (5.6)
Constructing a Pyramid out of Straws (5.7)
Math Message (8.1)
Comparing Pairs of Shapes When One Shape
Represents ONE (8.2)
MJ #s 1-6, pg. 192 (8.3)
MJ pg. 196-197 (8.4)
MJ # 4 pg. 201(8.5)
Play Fraction-Top It (8.6)
LAL: Fraction Number Stories Book (8.7)
Estimating Area (9.6)
Finding the Areas of Geoboard Rectangles
(9.7)
Forming Fractions on the Geoboard (10.7)
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EM Games
EM Facts Workshop Game
Fact Dash Game
Algorithm Animations
The Greedy Triangle by Marilyn Burns (5.4)
Shapes, Shapes, Shapes by Tana Hoban (5.4)
A Cloak for the Dreamer by Aileen Friedman (5.4)
Grandfather Tang’s Story by Ann Tompert (5.5)
Three Pigs, One Wolf, and Seven Magic Shapes by Grace
Maccarone (5.5)
Give Me Half! by Stuart Murphy (8.1)
Apple Fractions by Jerry Pallotta (8.3)
Fraction Action by Loreen Leedy (8.7)
http://www.brainpopjr.com/math/geometry/
http://www.brainpopjr.com/math/fractions/
http://www.ixl.com/math/grade-2
Hillside Township School District
GRADE 2
TIMEFRAME
Units
Time Frame
1
17 blocks September-October
2
20 blocks October-November
3
15 blocks November-December
4
14 blocks November-December
5
15 blocks December-January
6
15 blocks January-February
7
12 blocks February
8
9 blocks February-March
9
13 blocks March
46
Hillside Township School District
10
19 blocks March-April
11
13 blocks April-May
12
11 blocks May-June
GRADE 3
CONTENT STRAND: Number and Operation in Base Ten
UNIT 1: Number Sense
ENDURING UNDERSTANDINGS
ESSENTIAL QUESTIONS
 Graphs convey data in a concise way.
 Flexible methods of computation involve taking apart
and combining numbers using a variety of approaches
and tools.
CCS





How can I identify different kinds of numbers?
How will place value help me understand numbers?
How are numbers used?
How can I use a number grid to solve problems?
How do I use the Student Reference Book, number grid
and other math tools?
 How do I analyze data represented on a graph?
 How do I count bills and coins and write the total using
dollar and cents notation?
 How do I know when to use an exact number or
estimation?
KNOWLEDGE
Students will know:
SKILLS
Students will be able to:
47
Hillside Township School District
3.OA.9
3.NBT.1
3.NBT.2
3.MD.1
3.MD.3
•
•
•
•
•
•
•
Students will know various uses for
different types of numbers.
Students will know data can convey
information and help draw
conclusions.
Students will know different names
used to identify numbers.
Students will know the place value
structure of the base ten number
system.
Students will know how the patterns
on a number grid will help to identify
differences.
Students will know whether an exact
answer or estimate is appropriate in
situations involving money.
•
•
•
•
•
•
•
Read, write, compare and order whole numbers using
math tools.
Describe patterns in number grids and solve problems.
Understand that there are many names for numbers.
Use a calculator to review place value.
Review data concepts using graphs to draw conclusions.
Write, compare, and solve problems using dollars- and
cents notation.
Practice estimation skills with money amounts.
Review telling time and calculating elapsed time.
Key Terms: arrow rule, bar graph,
calculate, centimeter, Data Bank,
decimal, decimal point, difference,
elapsed time, equivalent, essay estimate,
estimation, event, frame, Frames-andArrows diagram, inch index, line plot,
make change, mathematical tools,
maximum, median, minimum, mode,
museum, name-collection box, number
grid, number-grid puzzle, range, regular
price, sale price, tally chart, tool kit,
units.
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
INTERNET AND OTHER RESOURCES
48
Hillside Township School District
Formative Assessment
• Use math journal page 3, Problems
8-9 Students will complete number
grid puzzles to practice extended
math problems
• Use math journal page 5, Problems
1-3 Students will practice clock skills
using math tool kit.
• Use math journal p. 8, problem 1
Students will practice Writing
Numbers using standard base-10
notations
• Use math journal Page 9, problems 3
and 4 Students will practice writing
equivalent names for numbers
• Use exit slip 1-8 to answer the
question “Explain how you found the
difference between 71 and 92?”
• Use journal page 15, problem 7,
Students will solve addition and
subtraction problems.
• Use journal page 17 Students will
compare coin and bill combinations.
• Use journal page 23, problems 5-6,
Students will solve number pattern
problems
• Progress Check 1
Games
• Number line sequence
• Less Than You
• Addition Top-It
• Name That Number
• Number Grid Difference Game
• Beat the Calculator
• Coin Top-It
• Spinning for Money
Internet Resources
Making Change
http://mathplayground.com/making_change.html
Time Clock
http://www.primarygames.com/math/timeclock/start.htm
How many under the shell (addition and subtraction)
http://illuminations.nctm.org/ActivityDetail.aspx?ID=198
Time What Time Will it Be?
http://nlvm.usu.edu/en/nav/frames_asid_318_g_1_t_4.html?from=
category_g_1_t_4.html
Math Clock
http://nlvm.usu.edu/en/nav/frames_asid_317_g_1_t_4.html?from=
category_g_1_t_4.html
Literacy Connections:
• A Million Fish…More or Less,
McKissack, Patricia C.
• I Hate Mathematics! Book, Burns,
Marilyn
• Pigs Will be Pigs: Fun with Math and
49
Hillside Township School District
Money, Axelrod, Amy
TIMEFRAME
Beginning September through Mid
September
GRADE 3
CONTENT STRAND: Number and Operations in Base Ten
UNIT 2: Adding and Subtracting Whole Numbers
ENDURING UNDERSTANDINGS
 Computation involves taking apart and combining numbers
using a variety of approaches.
 Flexible methods of computation involve grouping numbers in
strategic ways.







CCS
KNOWLEDGE
Students will know:
ESSENTIAL QUESTIONS
What strategies can I use to complete addition and
subtraction computations with multi-digit numbers?
What strategies can I use to solve addition or
subtraction problems?
How do I determine number patterns?
How can I use parts-and-total diagrams to help solve
parts-and-total number stories?
How can I use the partial-sums algorithm to add 2- and
3- digit numbers?
How do I use the trade-first algorithm to subtract 2- and
3- digit numbers?
How do I solve addition number stories involving three
or more addends?
SKILLS
Students will be able to:
50
Hillside Township School District
3.NBT.1
3.NBT.2
3.NBT.3
•
•
•
•
Students will know addition and subtraction facts
have an inverse relationship.
Students will know basic addition and
subtraction facts can be extended to solve
problems with larger numbers.
Students will know various diagrams can be
used to help solve addition and subtraction
number stories.
Students will know key strategies for solving
number stories involving three or more addends.
Key Terms: addend, ballpark estimate, change
diagram, change-to-less number story, change-tomore number story, comparison diagram,
comparison number story, complement, countingup method, deposit, fact extension, fact family,
function machine, higher-decade facts, input, label,
measurement unit, number family, number model,
output, partial-sums algorithm, partial-sums
method, parts-and-total diagram, parts-and-total
number story, rule, trade-first algorithm, trade-first
method, turn-around rule, unit box, “What’s My
Rule?”
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Formative Assessment
• Use math journal page 31, problem 3 Students
practice writing whole numbers.
• Use math journal page 34, problems 1 and 2
Students write and use rules for functions
involving addition and subtraction
• Use Exit Slip 2-4 to assess students’ ability to
write number models.
51
•
•
•
•
•
•
•
•
•
•
•
•
Use Fact Triangles and fact families to develop
automaticity with addition and subtraction facts.
Use basic addition and subtraction facts to solve
problems with multiples of 10 and extended fact
problems.
Use basic facts to compute and solve extended
facts problems.
Describe rules for patterns and use them to solve
problems.
Solve multi-digit addition and subtraction number
stories using parts-and-total diagrams.
Model multi-digit numbers with base-10 blocks.
Use basic facts to solve extended fact problems
with the partial-sums algorithm.
Use base-10 blocks to extend the partial-sums
algorithm to 3-digit addends.
Use basic facts to solve extended fact problems
involved in trade-first subtraction.
Use base-10 blocks to model and solve
subtraction problems.
Solve addition number stories with three or more
addends.
Use a parts-and-total diagram to solve addition
number stories involving three or more addends.
INTERNET AND OTHER RESOURCES
Games
• Roll to 100
• Name That Number
• Beat the Calculator
• Number-Grid Difference
• Target 50
• Base-10 Trading Game
Hillside Township School District
•
•
•
•
Use math journal page 2-5, problem 3, Students
will express the value of digits in a given number
Use math journal page 45, problems 1 and 2,
Students will solve multidigit addition problems
Use math journal page 50, problems 1 and 2,
Students will solve multidigit subtraction
problems.
Progress Check 2
Literacy Connection:
• Math-terpieces by Tang, Gregory
• The Grapes of Math by Tang, Gregory
Internet Resources
Skater Math
http://www.primarygames.com/math/skatermath/start.htm
Okta’s Rescue
http://illuminations.nctm.org/ActivityDetail.aspx?ID=219
Base Blocks Addition
http://nlvm.usu.edu/en/nav/category_g_2_t_1.html
Base Blocks
http://nlvm.usu.edu/en/nav/category_g_2_t_1.html
Base Blocks Subtraction
http://nlvm.usu.edu/en/nav/category_g_2_t_1.html
Number Puzzles
http://nlvm.usu.edu/en/nav/category_g_2_t_1.html
TIMEFRAME Mid September through Mid October
GRADE 3
CONTENT STRAND: Measurement and Data
UNIT 3: Linear Measures and Area
ENDURING UNDERSTANDINGS
ESSENTIAL QUESTIONS
52
Hillside Township School District
 Objects have distinct attributes that can be measured.
 Standard units provide common language for
communication of measurements.
CCS
3.MD.1
3.MD.2
3.MD.5.A
3.MD.6
3.MD.7.A
3.MD.7.B
3.MD.7.C
3.MD.7.D
3.MD.8
•
•
•
•
•
 How can I make linear measures?
 Why do I need to use standard units of measure?
 How do I estimate and measure lengths to the nearest
½ inch, ¼ inch and nearest centimeter, ½ centimeters
and millimeter?
 How can I measure sides of polygons and find
perimeters?
 What is the significance of collecting, analyzing, and
interpreting experimental data?
 How can I construct triangles using given lengths and
then find the perimeters?
 How does counting squares relate to area?
 How do I measure diameters and circumferences of
circular objects?
KNOWLEDGE
Students will know:
Students will know length of objects can
be measured with or without tools.
Students will know a relationship exists
among various units of measurement.
Students will know the perimeter and
area of polygons can be measured using
different strategies.
Students will know strategies to calculate
area using tiles or counting squares.
Students will know circular objects have a
diameter and a circumference that can be
calculated to the nearest cm.
•
•
•
•
•
•
•
•
•
•
Key Terms: about 3 times circle rule, area,
center, centi-, centimeter (cm),
circumference, deci-, diameter, foot, inch
(in), length, line segment, meter, metric
system, milli-, millimeter (mm),
parallelogram, perimeter, personal
•
•
53
SKILLS
Students will be able to:
Use nonstandard units to measure the lengths of objects.
Estimate the length of and measure objects using the
nonstandard units of measurement.
Select measuring tools and appropriate units for
particular measuring tasks.
Measure to the nearest inch, ½ inch, ¼ inch, centimeter,
½ centimeter, and millimeter.
Change units of length within the U.S. customary and
metric systems.
Measure sides of polygons to the nearest inch.
Add side lengths to find perimeter.
Create triangles and rectangles with a given perimeter.
Tile equal areas with different size pattern blocks
Find the area of a rectangular region divided into square
units.
Count the unit squares to determine the areas of
rectangles.
Measure the circumference and the diameter of circular
Hillside Township School District
references, polygon, rectangle, rhombus,
square, square feet, square yards, standard
unit, tiling, trapezoid, triangle, U.S.
customary system, yard
objects to the nearest cm.
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
INTERNET AND OTHER RESOURCES
Formative Assessment
• Use Math Journal page 58, Problem 1, to
assess students’ progress with
measuring line segments to the nearest
½ inch.
• Use math journal page 65, problem 2,
Students will measure line segments to
the nearest centimeter.
• Use math journal page 66, problem 5,
Students will apply and describe the
commutative and associative properties
of addition.
• Use math journal page 74, problems 1-3,
to assess students’ progress with using
strategies to calculate the area of
rectangular shapes.
• Use math journal page 77, problem 2,
students’ will complete an Exit slip to
explain “What did you do to find the areas
of rectangular shapes.”
• Progress Check 3
Games
• Addition Top-It
• Subtraction Top-It
Internet Resources
Fun brain Measure It
http://www.funbrain.com/measure/
Johnnies Math Page (Math Games)
http://jmathpage.com/JIMSMeasurementlengthmassvolume.html
The Ruler Game
http://www.rickyspears.com/rulergame/
Sleuths on the Loose (Informal Measurement)
http://pbskids.org/cyberchase/games/bodymath/
Literacy Connections:
• How Big is a Foot, Myller, Rolf
• Probably Pistachio, Murphy, Stuart
• Counting on Frank, Clement, Rod
• Sir Cumference and the First Round
54
Hillside Township School District
•
Table, Neuschwander, Cindy
Measuring Penny, Leedy, Loreen
TIMEFRAME Mid October through Mid November
GRADE 3
CONTENT STRAND: Operations and Algebraic Thinking
UNIT 4: Multiples of Equal Groups
ENDURING UNDERSTANDINGS
 A variety of numerical representations can be
used to describe quantitative relationships.
 Numbers and their properties can be used to
compute flexibly and fluently, and to
reasonably estimate measures and quantities.
CCS
ESSENTIAL QUESTIONS
 How will memorizing multiplication and division facts help
improve my mathematical skill?
 How can I solve and write number stories involving equal groups?
 How do I use models to solve multiplication number stories?
 How can I use equal sharing and equal grouping to complete
division problems?
 How can I solve division number stories using models?
 How can I use multiplication facts power and fact shortcuts?
 How can I practice the multiplication and division facts using the
Facts Table and fact families?
 How can I estimate the number of dots in a large array?
 How do I solve a problem involving factors of whole numbers?
 How do I use a map scale to estimate distances?
 How can I represent the likelihood of outcomes with visual
models?
KNOWLEDGE
SKILLS
55
Hillside Township School District
3.OA.1
3.OA.2
3.OA.3
3.OA.4
3.OA.5
3.OA.6
3.OA.7
3.OA.8
3.OA.9
•
•
•
•
Students will know:
Students will know how to
identify patterns in
multiplication facts using
concrete objects, models,
diagrams, and technology.
Students will know the basic
facts to solve multiplication
and division number stories.
Students will know that map
scales used as a tool will help
to estimate real distances
Students will know that data
can be organized into a display
Key Terms: array, as the crow flies,
dividend, divisor, equally likely,
fact power, factor, fair, heads, map
scale, multiples of equal groups,
multiplication,
multiplication/division diagram,
multiplication/division facts Table,
product, quotient, remainder, scale
factor, square numbers, tails, turnaround shortcut
•
•
•
•
•
•
•
•
•
•
•
Students will be able to:
Use facts to solve multiplication stories
Use strategies (counters, pictures, or arrays) to compute facts up
to 10x10.
Use multiplication diagrams to model number stories involving
equal groups.
Use basic facts to solve multiplication number stories.
Create arrays to model multiplication facts.
Use basic facts to solve division problems.
Use arrays and diagrams to model equal-sharing and equalgrouping number stories.
Identify the quotient, dividend, divisor, and remainder.
Use fact triangles and the fact tables to generate multiplication and
division fact families.
Use multiplication strategies to solve map-scale problems.
Analyze and record the results of a coin toss experiment in a table.
ASSESSMENTS/PERFORMANCE
TASKS/ INTERDISCIPLINARY
CONNECTIONS
INTERNET AND OTHER RESOURCES
56
Hillside Township School District
Formative Assessment
• Use math journal page 81 to
assess students’ ability to draw
arrays to solve problems.
• Use math journal page 84 to
assess students’ ability to tell
time to the nearest minute and
writing time in digital notation.
• Use math journal page 89,
problem 6 to assess students’
ability to find the area of
rectangular shapes.
• Use math journal page 98,
problem 1 to assess student’s
ability to collect and organize
data.
• Progress Check 4
Literacy Connections:
• Each Orange Had 8 Slices: A
Counting Book, Giganti, Paul
• The Doorbell Rang, Hutchins,
Pat
TIMEFRAME
Games
• Division Arrays
• Beat the Calculator
• Baseball Multiplication
Interactive Websites
Multiplication Tunnel Blaster
http://www.playkidsgames.com/games/Tunnel/MULTIPLY.HTM#
Math Fact Practice
http://www.playkidsgames.com/games/mathfact/default.htm
Save the Math Apples
http://www.playkidsgames.com/games/apples/savetheApples.htm
Skater Math
http://www.primarygames.com/math/skatermath/start.htm
Product Game
http://illuminations.nctm.org/ActivityDetail.aspx?ID=29
Factor Dazzle
http://calculationnation.nctm.org/Games/Game.aspx?GameId=A0537FC63B08-4AFC-9AD6-0CC5E3BC9B86
Times Square
http://calculationnation.nctm.org/Games/
Mid November through Beginning
December
GRADE 3
CONTENT STRAND: Number and Operations in Base Ten
UNIT 5: Place Value in Whole Numbers and Decimals
57
Hillside Township School District
ENDURING UNDERSTANDINGS
ESSENTIAL QUESTIONS
 Numbers can represent quantity, location, position and
relationships.
 Our system of place value is based on groups of ten.
 Graphs can be used to convey data in a concise way.
CCS
•
3.NBT1
3.NBT2
3.NBT3
3.MD2
•
•
•
 How do I read, write, compare, and order whole
numbers and decimals?
 How do I read and write numbers through ten-thousands
correctly?
 How Do I read, write, compare, and order numbers less
than 100,000?
 How do I compute large numbers?
 How do I compare perimeters and areas?
 How can I model decimals with base-10 blocks?
 How do I read, write, order, and compare decimals to
thousandths?
KNOWLEDGE
Students will know:
To model decimals with base-10 blocks and to
review decimals with money
To model tenths and hundredths with base-10
blocks and to model exchanges between
tenths and hundredths
To develop a sense of very large numbers
To provide practice for reading, writing,
comparing and ordering numbers less than
100,000
Key Terms: big cube, census, cube, decimeter,
flat, hundred-thousands, hundredths, >(is greater
than), <(is less than), line graph, long, maximum,
median, millimeter, millions, pie graph,
population, precipitation, ten-thousands, tenths,
thousands, thousandths
•
•
•
•
•
•
•
•
•
•
58
SKILLS
Students will be able to:
Read and write numbers up to 100,000
Compare and order whole numbers less than
100,000
Read and write 6-and 7-digit whole numbers
Use multiples of 10 to count a large quantity of
base-10 blocks
Read and write decimal numbers through
hundredths
Use base-10 blocks and a meter stick to represent,
compare, and order decimals through hundredths
Compare and order decimals using a
centimeter/millimeter scale.
Estimate answers to decimals number stories
involving difference and ratio comparisons
Use Place-Value Book routines to read, identify,
write, and order decimals
Identify digits and express their values
Hillside Township School District
•
•
•
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Find the maximum, minimum, and range using data
from the Sunrise and Sunset
Record
Draw line segments, conclusions from a line graph
INTERNET AND OTHER RESOURCES
Formative Assessment
• Use Math Masters, page 119 to assess
students’ ability to write whole numbers up to
five digits.
• Use Math Journal p. 104/Problem 2 to assess
students’ progress toward finding the
maximum, minimum, and range of a data set.
• Use Math Journal p. 109/Problem 1 to assess
students’ progress toward using basic facts to
compute extended facts.
• Use Math Journal p. 110/Problem 11 to assess
students’ progress toward using multiples of 10
to count base-10 blocks.
• Use Math Journal p. 118/Problem 5 to assess
students’ progress in describing relationships
between units of time.
• Use Math Journal p. 119/Problems 2-4 to
assess students’ progress in comparing
decimals.
• Use the half sheets from Number Top-It
(Decimals) to assess students’ progress in
comparing decimals.
• Use Math Journal p. 123/Problems 1 and 2 to
assess students’ progress toward identifying
values of digits in decimals.
• Use Exit Slip (Math Masters, p. 398) to assess
students’ progress toward demonstrating
59
GAMES
• Baseball Multiplication
• Number Top-It through Millions
• Number Top-It Decimals
• Beat the Calculator
• Base-10 Decimal Exchange
• Decimal Solitaire
Internet Resources
Decimals of the Caribbean
www.mrnussbaum.com
Death to Decimals
www.mrnussbaum.com
Place Value Puzzler
www.funbrain.com
Decimal Ducks
http://www.free-training-tutorial.com/decimal/placevalue-decimal-ducks.htm
Hillside Township School District
•
automaticity with multiplication facts through
10x10.
Progress Check 5
Football Math-Decimals Place Value
http://www.math-play.com/football-math-decimalsplace-value/football-math-decimals-placevalue.html
Literacy Connections
• How Much is a Million? By David M.
Schwartz
• A Million Fish…More or Less by Patricia
C. McKissack
• If You Made a Million by David M.
Schwartz
• On Beyond a Million: An Amazing Math
Journey by David M. Schwartz
TIMEFRAME
December
GRADE 3
CONTENT STRAND: Geometry
UNIT 6: Geometry
ENDURING UNDERSTANDINGS
 Objects can be described and compared using their
geometric attributes.
 Points, lines and planes are the foundation of geometry.
ESSENTIAL QUESTIONS
 How are geometric properties used to solve problems in
everyday life?
 How can plane and solid shapes be described?
 How are geometric figures constructed?
 What strategies can be used to verify symmetry and
congruency?
 How will a shape look when rotated, reflected, and/or
translated?
 How is the location of a point on a grid described?
60
Hillside Township School District
CCS
3.G.1
3.G.2
3.MD.4
•
•
•
•
•
•
KNOWLEDGE
Students will know:
Identify, draw, and name line segments,
lines, and rays.
Draw parallel and intersecting line
segments, lines, and rays.
Draw angles as records of rotations.
Identify right angles.
Identify and name 2-D and 3-D shapes.
Identify symmetric figures and draw
lines of symmetry.
•
•
•
•
•
•
•
•
•
Key Terms: 2-dimensional, 3-dimensional,
adjacent sides, angle, apex, arrowhead,
base of a prism, bases of a pyramid,
clockwise, cone, congruent,
counterclockwise, cylinder, degree, edge,
endpoint, equilateral triangle, face, full turn,
half-turn, hexagonal prism, intersect, kite,
line, line of symmetry, mirror image,
parallel, parallelogram, plane figures,
polygon, polyhedron, pyramid, quadrangle,
quarter-turn, ray, rectangle, rectangular
prism, regular polygon, rhombus, right
angle, right triangle, rotation, side, sphere,
square, symmetric, symmetry, trapezoid,
triangle, triangular prism, vertex, vertices
•
•
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
SKILLS
Students will be able to:
Problem solve in context
Understand properties of polygons
Identify quadrilaterals
Relate 3-dimensional objects to 2-dimensional
counterparts
Classify angles as right, acute and obtuse
Compare polyhedrons by edges, vertices, and shapes of
faces
Identify and label the vertex of an angle
Practice slides, flips, and turns with variety of objects
Predict the results of transforming two-dimensional
shapes
Find and record coordinates on grid
Develop mapping skills
INTERNET AND OTHER RESOURCES
61
Hillside Township School District
Formative Assessment
• Use Math Journal page 128, Problem 3
to assess students’ progress toward
drawing line segments.
• Use Math Journal page 130 to assess
students’ progress in identifying parallel
and intersecting lines and segments.
• Use Math Journal page 135, Problem 5
to assess students’ progress in drawing
line segments, rays, and lines.
• Use Math Journal page 136, Part One
to assess students’ progress toward
identifying points and drawing line
segments to form a quadrangle.
• Use Math Journal page 144 to assess
students’ ability to recognize a right
angle.
• Use Math Journal page 146, Problems
1-4 to assess students’ ability to
complete symmetric shapes.
• Progress Check 6
•
•
•
•
•
Games
• Number Top-It (Decimals)
• Robot Game
• Name That Number
• Touch-and-Match Quadrangles
• Shading Shapes
• Angle Race
Internet Resources
Geometric Figures Game
http://www.math-play.com/geometric-figures-game/geometricfigures-game.html
Types of Polygons
http://www.math-play.com/types-of-poligons.html
Angles Jeopardy Game
http://www.math-play.com/Angles-Jeopardy/AnglesJeopardy.html
Pick a Polygon
http://illuminations.nctm.org/webresourcelist.aspx?ref=2&std=2&
grd=0
Literacy Connection
A Cloak For The Dreamer (Brainy Day
Books) by Aileen Friedman
Grandfather Tang's Story (Dragonfly
Books) by Ann Tompert
Spaghetti And Meatballs For All
(Marilyn Burns Brainy Day Books) by
Marilyn Burns
The Greedy Triangle (Brainy Day
Books) by Marilyn Burns
Arrow to the Sun: A Pueblo Indian
Tale by Gerald McDermott
62
Hillside Township School District
•
•
TIMEFRAME
Jumanji by Chris Van Allsburg
Mummy Math: An Adventure in
Geometry by Cindy Neuschwander
• Sir Cumference and the Dragon of Pi (A
Math Adventure) by Cindy
Neuschwander
• Sir Cumference: And the First Round
Table (A Math Adventure) by Cindy
Neuschwander
• Sir Cumference and the Great Knight of
Angleland (A Math Adventure) by Cindy
Neuschwander
• What's Your Angle, Pythagoras? A
Math Adventure by Julie Ellis
• When a Line Bends . . . A Shape
Begins by Rhonda Gowler Greene
January
GRADE 3
CONTENT STRAND: Operations and Algebraic Thinking
UNIT 7: Multiplication and Division
ENDURING UNDERSTANDINGS
ESSENTIAL QUESTIONS
 Multiplication and division are inverse operations of one
another and are used to create fact families.
 How will multiplication and division improve my math
skills?
 How do I determine multiplication, division and square
number patterns?
 How do I use parentheses in number models?
 How do I determine when an estimate is appropriate?
 How do I multiply by multiples of 10, 100 and 1,000?
 How do I divide such multiples by 1-digit numbers?
63
Hillside Township School District
CCS
3.OA.1
3.OA.2
3.OA.3
3.OA.4
3.OA.5
3.OA.6
3.OA.7
3.OA.8
3.OA.9
3.NBT.3
•
•
•
•
KNOWLEDGE
Students will know:
Know and recognize square products, multiplication and
division patterns.
Express numbers as sums of products using number
models that contain parentheses.
Multiply 1-digit numbers by multiples of 10, 100 and 1,000
and divide such multiples by 1-digit numbers.
Determine when an estimate is appropriate and make
estimates.
•
•
•
•
•
•
SKILLS
Students will be able to:
Compute multiplication facts.
Use arrays to model multiplication.
Find and use rules to solve
multiplication and division problems.
Recognize that parentheses affect the
order of operations.
Explain how an estimate was obtained.
Multiply 2-digit numbers by a 1-digit
number.
Key Terms: estimate, extended facts, factor, parentheses,
product, similar figures, square number, square product
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Formative Assessments
• Use Math Journal page 157/Part A to assess students’
progress toward learning multiplication facts.
• Use Math Message 7.3 to assess students’ progress
toward finding and using rules to solve multiplication and
division problems.
• Use Math Journal page 164/Problems 4 and 5 to assess
students’ progress toward recognizing that parentheses
affect the order of operations.
• Use Exit Slip 7.7 (Math Masters, p. 398) to assess
students’ knowledge of estimation. Have students answer
the following: When you are shopping, why might you
make an estimate? Explain how you would make the
estimate.
• Use Math Journal page 173/Problems 7 and 8 to assess
students’ ability to multiply 2-digit numbers by a 1-digit
number.
• Progress Check 7
64
INTERNET AND OTHER RESOURCES
Games
• Multiplication BINGO
• Name That Number
• Beat the Calculator
• Baseball Multiplication with 10’s
Internet Resources
Interactive Multiplication Table
http://www.aplusmath.com/cgibin/Homework_Helper/mtable
Math Baseball
http://www.funbrain.com/math/index.html
Hillside Township School District
Math Car Racing Game
Literacy Connections
• Africa Counts: Number and Pattern in African Cultures
Zaslavsky, Claudia
•
Alice in Pastaland: A Math Adventure
•
Amanda Bean's Amazing Dream (Brainy Day Books) Cindy
Neuschwander/Marilyn Burns
•
Anno's Magic Seeds Anno, Masaichiro & Mitsumasa –
•
Arctic Fives Arrive Pinczes, Elinor J
•
Bats on Parade Appelt, Kathi
•
Bean Thirteen McElligot, Matthew
•
Building Tables on Tables: A Book about Multiplication
(Young Math) Trivett, John V.
•
Bunches and Bunches of Bunnies Mathews, Louise
•
Cheetah Math: Learning About Division from Baby
Cheetahs Nagda, Ann Whitehead
•
Division (Question of Math) Cato, Sheila; Sweeten, Sami
•
Each Orange Had 8 Slices Paul Giganti, Jr
•
Elsie Times Eight Babbitt, Natalie
•
Minnie's Diner: A Multiplying Menu Dodds, Dayle Ann
•
My Full Moon is Square Pinczes, Elinor J.
•
Now for My Next Number!: Songs for Multiplying Fun
Park, Margaret
TIMEFRAME February
65
http://www.funbrain.com/osa/index.html
Hillside Township School District
GRADE 3
CONTENT STRAND: Number and Operations - Fractions
UNIT 8: Fractions
ENDURING UNDERSTANDINGS
 A fraction is a way of representing part of a whole.
ESSENTIAL QUESTIONS





What do the parts of a fraction represent?
How is a fraction an equal part of a whole?
How do I find equivalent fractions?
How do I compare fractions?
Can I name quantities greater than 1 with fractions and mixed
numbers?
 How do I solve number stories involving fractions?
CCS
3.NF.1
3.NF.2.A
3.NF.2.B
3.NF.3.A
3.NF.3.B
3.NF.3.C
3.NF.3.D
•
•
•
•
•
KNOWLEDGE
Students will know:
As the number of pieces of a whole increases, the
size of the single piece decreases.
The denominator tells the number of equal parts into
which a whole is divided
The numerator tells the how many equal parts are
described in the fraction.
Models for decimals can be real-life examples that
represent decimals as part of a whole, ten-frames,
grid paper, and base-10 blocks.
Understand that a decimal can be written in
standard form and/or written form.
Key Terms: denominator, equal, equivalent fractions,
mixed number, numerator, random draw, unit fraction,
whole (the ONE)
ASSESSMENTS/PERFORMANCE TASKS/
66
•
•
•
•
•
•
•
•
•
SKILLS
Students will be able to:
Identify and write fractions that name regions.
Read and write fractions.
Use fraction cards to find equivalent fractions.
Identify fractions on a number line.
Shade fractional parts of regions to represent
fractions greater than 1.
Model and name mixed numbers and
fractions.
Use lines of symmetry to divide figures into
equal parts.
Solve problems involving fractional parts of a
collection.
Describe solution strategies for solving fraction
number stories.
INTERNET AND OTHER RESOURCES
Hillside Township School District
INTERDISCIPLINARY CONNECTIONS
Formative Assessment
• Use the Fractions Equivalent Game to assess
students’ ability to find equivalent fractions using the
Fraction Cards (Activity Sheets 5-8).
• Use Math Journal page 180, Problems 6-9 to
assess students’ ability to identify and write fractions
that name regions.
• Use Math Masters p. 250 to assess students’ ability
to identify fractions on a number-line.
• Use Math Journal page 201, Problems 10-13 to
assess students’ progress toward solving problems
involving fractional parts of a collection.
• Progress Check 8
Literacy Connections
• Fraction Action Leedy, Loreen
• Fraction Fun Adler, David A.
• Apple Fractions Pallotta, Jerry
• The Hershey's Milk Chocolate Bar Fractions Book
Pallotta, Jerry
• Twizzlers Percentages Book Pallotta, Jerry
Games
• The Block Drawing Game
• Multiplication BINGO
• Fraction Top-It
• The Equivalent Fractions Game
Internet Resources
Fresh Baked Fractions
http://www.funbrain.com/fract/index.html
Fraction Frenzy
http://www.learningplanet.com/sam/ff/index.asp
Fraction Models
http://illuminations.nctm.org/ActivityDetail.aspx?ID=11
TIMEFRAME End of February through Mid March
GRADE 3
CONTENT STRAND: Operations and Algebraic Thinking
UNIT 9: Multiplication and Division
67
Hillside Township School District
ENDURING UNDERSTANDING
ESSENTIAL QUESTIONS
 Multiplication and division are inverse operations of one
another and are used to create fact families.
CCS
3.OA.1
3.OA.2
3.OA.3
3.OA.4
3.OA.5
3.OA.6
3.OA.7
3.OA.8
3.OA.9
3.NBT.1
3.NBT.2
3.NBT.3
•
 How will I use multiplication and division concepts and skills?
 How do I multiply and divide using multiples of 10, 100, and
1,000?
 How can I use mental math to multiply 1-digit numbers by
multi-digit numbers using partial products and lattice
multiplication?
 How do I identify and find factors of a number?
 How do I share whole dollar amounts equally?
 How do I compare and order positive and negative numbers?
KNOWLEDGE
Students will know:
Demonstrate the ability to compute
problems involving the multiplication of 2and 3- digit whole numbers by 1- digit
whole numbers using mental math, lattice
multiplication, and the partial products
algorithm.
•
•
•
•
•
•
•
•
Key Terms: algorithm, Celsius scale, degrees
Celsius, degrees Fahrenheit, equilateral
triangle, factors, Fahrenheit scale, lattice
multiplication, partial-products algorithm
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
SKILLS
Students will be able to:
Find multiples of 10, 100, and 1,000.
Compare and order numbers.
Use multiplication facts to solve problems.
Use the partial products algorithm to solve problems.
Make reasonable estimates.
Use equal sharing to solve division number stories.
Compare and order positive and negative numbers.
Solve number stories involving the addition and
subtraction of positive and negative numbers.
INTERNET AND OTHER RESOURCES
GAMES
Formative Assessments
• Use Math Journal, p.206/Problems 1 and
2 to assess students’ progress toward
solving problems involving multiples of
•
•
•
68
Name That Number
Factor Bingo
Array Bingo
Hillside Township School District
•
•
•
•
•
10, 100, and 1,000.
Use Math Journal, p. 208/Problem 1 to
assess students’ progress toward using
strategies to solve problems involving
multiplication of 2-digit numbers by a 1digit number.
Use Math Journal, p.214/Problem 1 to
assess students’ progress toward using
strategies to solve multiplication
problems.
Use Math Journal, p. 225/Problem 2 to
assess students’ progress toward
understanding that parentheses affect the
order of operations.
Use Math Journal, p. 238/Problem 1 to
assess students’ progress toward finding
the areas of rectangular shapes.
Progress Check 9
Literacy Connections
• Anno’s Magic Seeds Mitsumasa Anno,
Philomel
• Less Than Zero Murphy, Stuart J.
• A Remainder of One Pinczes, Elinor
• The Great Divide: A Mathematical
Marathon Dodds, Dayle A.
• Minnies Diner Dodds, Dayle
• Amanda’s Beans Amazing Dream,
Neuschwander, Cindy
• The Best of Times, Tang, Gregg
• The Visit, Chapman, Helen
• One Hundred Hungry Ants, Pinczes
• The Doorbell Rang, Hutchins, Pat
TIMEFRAME
•
•
•
Finding Factors
Money Trading Game
Roll to 100
Internet Resources
Multiplication Dart Board
http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_re
sources/852/multipletables.swf
Hit the Button
http://www.wmnet.org.uk/resources/gordon/Hit%20the%20button%2
0v9.swf
Number Monster
http://www.coolmath4kids.com/times-tables/number-monster-timestables-multiplication.htm
Basic Operations
http://www.sheppardsoftware.com/math.htm
Learn about Positive and Negative Numbers
http://math.pppst.com/negatives.html
Line Jumper
http://www.funbrain.com/linejump/index.html
Multiplication Bingo
http://www.abcya.com/math_bingo.htm
Mid March through Mid April
69
Hillside Township School District
GRADE 3
CONTENT STRAND: Measurement and Data
UNIT 10: Measurement and Reference Frames
ENDURING UNDERSTANDINGS
ESSENTIAL QUESTIONS
 Measurement describes the attributes of objects and events.
 Standard units of measure enable people to interpret results
or data.
 All measurements have some degree of uncertainty.
KNOWLEDGE
Students will know:
CCS
3.MD.2
3.MD.3
3.MD.4
 How can I use measuring tools to make measurements?
 How are statistical measures (mean, median and mode)
used to analyze measurement data?
 What units and tools are used to measure length?
 How do I determine the volume of rectangular prisms?
 How do I read weights on different kinds of scales?
 How do I find the median and mean of a set of data?
 How can I make a frequency table?
 How do I plot a point on a coordinate grid?
•
•
•
•
•
•
Solve problems involving measurement and
estimation of intervals of time, liquid volumes,
and masses of objects.
To provide review of units, tools, and
measuring length in U.S. customary and
metric systems.
To explore the volume of rectangular prisms.
To provide experiences ordering objects by
volume, building rectangular prisms having
the same volume but different dimensions,
and measuring weight using various kinds of
scales.
To introduce the mean of a set of data; and to
70
•
•
•
•
•
•
•
•
•
SKILLS
Students will be able to:
Measure line segments to the nearest ½ inch and ½
centimeter.
Label on a ruler.
Describe relationships among units of length.
Predict the weight of objects.
Measure area as square units.
Identify bases of a rectangular prism.
Order objects by weight.
Check predictions of weight of objects to the actual
weight of objects.
Use multiplication facts to find the area of the base
of a rectangular prism.
Predict the volume of objects and test the
predictions.
Hillside Township School District
•
•
•
•
•
•
review the median of a set of data.
To calculate the mean of a set of data; and
review the median of a set of data.
To introduce the memory keys on a
calculator.
To guide students as they make frequency
tables, and as they find the median, mean,
and mode of data sets.
To introduce plotting coordinates on
coordinate grids.
•
•
•
Find the median and mean of data sets.
Collect and organize data to create a frequency
table.
Find the median and mode a data set.
Order numbers on a number line.
Draw line segments to connect plotted on a
coordinate grid.
Key Terms: average, capacity of a container,
capacity of a scale, coordinate, coordinate grid,
cubic centimeter, frequency table, height of a
prism, mean, median, memory, memory keys,
mode, ordered pair, plotting the point, precision,
square centimeter, square inch, volume, weight
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
INTERNET AND OTHER RESOURCES
Formative Assessment
• Use Math Journal, p.240/Problem1 and 2 to
assess students’ progress toward measuring
to the nearest ½ inch and ½ cm.
• Use an Exit Slip (Math Masters, p. 398) to
assess students’ progress toward drawing
conclusions about data representations.
• Use Math Journal, p. 254 to assess students’
ability to complete a bar graph.
• Use Exit Slip (Math Masters, p. 398) to
assess students’ progress toward explaining
what median means.
• Use Math Journal, p. 265/Problem 5 to
assess students’ ability to find the median of a
71
Games
• Fraction Top-It
• Factor BINGO
• Beat the Calculator (Multiplication)
• Multiplication Top-It
Internet Websites
Measure It!
http://www.funbrain.com/measure/index.html
Math Data Games for Kids
http://www.kidsmathgamesonline.com/numbers.html
Mean, Median, and Mode Game
http://www.kidsmathgamesonline.com/numbers.html
Hillside Township School District
•
data set.
Progress Check 10
Perimeter: Find the Missing Side Length
http://www.ixl.com/math/grade-3
Area
http://www.ixl.com/math/grade-3
Literacy Connections
• Millions to Measure Schwartz, David M.
•
A Fly on the Ceiling: A Math Myth
Glass, Julie
•
Who Sank the Boat? Allen, Pamela
TIMEFRAME April
GRADE 3
CONTENT STRAND: Measurement and Data
UNIT 11: Probability
ENDURING UNDERSTANDINGS
ESSENTIAL QUESTIONS
 The way that data is collected, organized and displayed
influences interpretation.
 The probability of an event’s occurrence can be
predicted with varying degrees of confidence.
CCS
3.NF.1
3.NF.3.A
3.NF.3.B
3.NF.3.C
3.NF.3.D
3.MD.1
3.MD.3
•
•
 How is data collected and analyzed?
 How do I collect, tabulate, and interpret experimental data?
 How can predictions be made based on data?
KNOWLEDGE
Students will know:
Understand and use the language of
probability.
Use fractions to record probabilities of
events.
•
•
•
•
•
Key Terms: autumnal equinox, summer
solstice, vernal equinox, winter solstice
72
SKILLS
Students will be able to:
Use addition and subtraction to solve problems involving
units of time.
Use graphs to draw conclusions.
Find the difference between high and low temperatures.
Use data to create a frequency table and bar graph.
Shade fractional parts of a circle.
Hillside Township School District
•
3.MD.4
3.G.2
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Apply equivalent fractions to shade fractional parts of a
circle.
INTERNET AND OTHER RESOURCES
Formative Assessment
• Use an Exit Slip, Math Masters, p. 398 to
assess students’ ability to recall
multiplication facts.
• Use Math Journal, p. 268, Problem 1 to
assess students’ progress toward telling
and writing time to the nearest minute on
an analog clock.
• Use Math Journal, p. 269, Problems 4
and 6 to assess students’ ability to
collect and organize data.
• Use Math Journal, p. 272, Problem 1 to
assess students’ ability to understand
basic probability terms.
• Use an Exit Slip, Math Masters, p. 398 to
assess students’ progress toward
drawing conclusions based on data
representations.
• Progress Check 11
Games
• Beat the Calculator (Multiplication)
• Soccer Spin
• The Block Drawing Game
• Spinning to Win
Internet Resources
Probability Fair
www.mrnussbaum.com
Card Sharks
www.mrnussbaum.com
Probability-Dice, Spinners, Coins, and More
http://jmathpage.com/JIMSProbabilitypage.html
Probability Game
http://www.kidsmathgamesonline.com/numbers/probability.html
Literacy Connections
• Do You Wanna Bet? Your Chance to
Find Out about Probability Cushman,
Jean
• Probably Pistachio Murphy, Stuart J.
• Betcha! Murphy, Stuart J.
• It's Probably Penny Leedy, Loreen
73
Hillside Township School District
•
•
A Very Improbable Story: A Math
Adventure Einhorn, Edwar
Tally O'Malley Murphy, Stuart J.
TIMEFRAME Mid May through June
GRADE 4
CONTENT STRAND: GEOMETRY
UNIT 1: Name and Constructing Geometric Figures
74
Hillside Township School District
ENDURING UNDERSTANDINGS
•
•
•
•
ESSENTIAL QUESTIONS
•
•
•
•
Geometric shapes are identified by their characteristics and
properties.
Geometric language is used to describe special
relationships.
The world is filled with geometry; angles, lines, curves and
patterns exist in everyday phenomena.
Basic concepts of geometry and spatial relationships are
used to construct, draw, describe and compare geometric
models and their transformations to solve problems.
CCS
•
4.G.1
4.G.2
•
•
•
•
•
•
•
KNOWLEDGE
Students will know:
Use a compass and straightedge to
construct geometric figures
Identify properties of polygons
Classify quadrangles according to side
and angle properties.
Name, draw, and label line segments,
lines, and rays.
Name, draw, and label angles, triangles,
and quadrangles.
Identify and describe right angles, parallel
lines, and line segments
•
•
•
•
•
•
•
•
Key Terms: point, line segment, end point,
line, ray, angle, vertex, right angle, triangle,
quadrangle, quadrilateral, square, rhombus,
rectangle, parallelogram, trapezoid, kite,
parallel lines, intersect, parallel line
segments, parallel rays, side, angle,
pentagon, polygon, vertex (vertices), convex,
concave, hexagon, heptagon, octagon,
75
How do the ways lines intersect identify shapes?
What properties are used to classify shapes?
What geometric features are present in our surroundings?
How do geometric patterns and relationships affect our
everyday lives?
What role do geometric shapes and patterns play in your life?
How do you sort, classify and construct different geometric
shapes and patterns?
SKILLS
Students will be able to:
Identify and describe characteristics of lines, rays and line
segments.
Name, construct, describe and identify quadrangles.
Develop definitions for parallel, perpendicular and
intersecting line segments, lines and rays.
Classify quadrangles based on side and angle properties.
Construct and describe convex and concave polygons.
Use a compass to draw circles and construct inscribed
squares.
Copy a line segment with a compass and straightedge
Construct a regular hexagon inscribed in a circle
Hillside Township School District
nonagon,
n-gon, interior, regular polygon, equilateral
triangle, compass, circle, center (of a circle),
inscribed square, circle, radius, concentric
circles, intersect, compass, slate, straight
edge
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Assessments
Lesson 1.2
• Exit Slip: Describe a line segment and a
line
Lesson 1.3
• Exit Slip: Compare/contrast plane figures
Lesson 1.4
• MJ pg 10 #s 2 and 3 (parallel line
segments)
Lesson 1.5
• MJ pg 12 #1 (properties of polygons)
Lesson 1.6
• MJ pg 16 #3 (right angles)
Lesson 1.7
• MJ pg 17 #1 (construct circle with a
compass)
INTERNET AND OTHER RESOURCES
Internet Resources
Triangle Webquest
AAAKnow: Classifying triangles (sides)
AAAKnow: Classifying Triangles (angles)
AAAKnow: Naming Polygons
Triangle lesson and sorting activity
Interactive Geoboard
Identifying angles game
Geometry Concepts
Smart Exchange: Geometry Smartboard Lessons
Everyday Mathematics Online
BrainPop Geometry and Measurement
Discovery Education ~ Geometry
BrainPop: Polygons
Games
1.2 Sprouts SRB p. 313
1.4 Sz’kwa SRB p. 310, Masters 505
1.6 Polygon Pair Up SRB p. 258 Masters 496-497
1.7 Polygon Pair Up SRB p. 258 Masters 496-497
Assessment Handbook pg 154, self-assessment
Teacher’s Edition pg 63 oral & slate
assessments
Assessment Handbook – Unit 1 Assessment
pgs 155 – 157
76
Hillside Township School District
Interdisciplinary Connections:
Literacy Connection
Lesson 1-5: The Greedy Triangle, by Marilyn
Burns, Scholastic Inc., 1995
Lesson 1-6: Ed Emberley’s Picture Pie: A
Cut and Paste Drawing Book, by Ed Emberley,
Little Brown, 2006
Lesson 1.6 Art Link – Creating Circle Designs
“Ed Emberley’s Picture Pie: A Cut and Paste
Drawing Book” (Little Brown, 2006)
Lesson 1.8 Art Link – Creating 6-Point Designs
MM p. 32 Inscribed hexagons in circles
TIMEFRAME
September
30 periods
GRADE 4
CONTENT STRAND: Number and Operations in Base Ten
UNIT 2: Using Numbers and Organizing Data
ENDURING UNDERSTANDINGS
•
•
ESSENTIAL QUESTIONS
•
•
Reading, understanding, interpreting and communicating
data are critical in modeling a variety of real-world situations,
drawing appropriate inferences, making informed decisions
and justifying those decisions.
Operations with numbers are used to solve problems at all
levels of mathematics.
•
•
•
77
What meaning do numbers have?
How do mathematical ideas interconnect and build on one
another to produce a whole?
How can we compare and contrast numbers?
How can counting, measuring and labeling make sense of the
world around us?
How do we use numbers to convey information and problem
solve?
Hillside Township School District
•
•
•
CCS
4.NBT.1
4.NBT.2
4.NBT.3
4.NBT.4
4.NBT.5
4.NBT.6
•
•
•
•
•
•
•
KNOWLEDGE
Students will know:
Display data with a line plot, bar graph, or
tally chart
Use the statistical landmarks median, mode,
and range
Use the statistical landmarks maximum and
minimum
Subtract multi-digit numbers
Add multi-digit numbers
Read and write numerals to hundredmillions; give the value of the digits in
numerals to hundred-millions
Find equivalent names for numbers
•
•
•
•
•
•
•
•
•
•
•
•
Key Terms: whole numbers, counting
numbers, digits, place, guess, estimate, tally
chart, landmark, maximum, minimum, range,
mode, line plot, partial-sums method,
column-addition method, bar graph, trade
first, partial differences
•
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Assessments
Lesson 2.2
• RSA MJ pg 30 # 6
Equivalent names for whole numbers
How can organizing, interpreting and displaying data be used
to answer questions?
How do we organize data so that we can draw conclusions?
How many different ways are there to represent numbers?
SKILLS
Students will be able to:
Use numbers written in number-word notation
Compare uses of estimate and exact counts
Locate points on a coordinate map
Give equivalent mathematical expressions for whole numbers
Make true number sentences by inserting grouping symbols
Read and write numbers (in expanded notation) and identify
the value of their digits
Use and describe patterns to find sums
Add and subtract multi-digit numbers
Solve open sentences
Find landmarks for a set of data; use the landmarks and
representations to make predictions
Create a tally chart, line plot and a bar graph
Use partial-sums and column-addition algorithms to solve
multi-digit addition problems
Apply extended subtraction facts; use trade-first and partial
differences algorithms to solve multi-digit subtraction problems
INTERNET AND OTHER RESOURCES
Internet Resources
Smart Exchange: Intel Skool - Methods of Addition
IXL Names for Numbers
AAAMath: Place Value Game
Shodor: Interactive Bar Graphs
78
Hillside Township School District
Lesson 2.3
• RSA MJ pg 33 # 1-4 values of digits and
whole numbers
Lesson 2.4
• exit slip master 389 identify places in
whole numbers and value of the digits
Lesson 2.5
• RSA-Master pg 506 Addition Top It Game
Lesson 2.6
• RSA MJ page 40 # 3 understanding data
landmarks
Lesson 2.7
• RSA MJ page 42 # 4-6 solving multi-digit
addition problems
Lesson 2.8
• RSA MJ pg 46 # 4 using landmarks and a
bar graph to draw conclusions about data
Lesson 2.9
• RSA MJ page 49 # 4-6 multi digit
subtraction
IXL: Mean, Median and Mode
BBC: Snakes and Ladders Addition Game
Interactive Math Websites
Smart Exchange: Mean and Median
BrainPop: Landmarks
Games
2.2 Name That Number SRB p 284, Masters 489
2.4 Fishing for Digits SRB 242, Masters 472
2.5 Addition Top It SRB 263, Masters 506
2.6 Subtraction Top It SRB 263-264, Masters 506
2.7 High Number Toss SRB 252 Master 487
2.9 Subtraction Target Practice SRB 262 Master 504
Assessment Handbook pg 159, self-assessment
Teacher’s Edition pg 139 oral & slate
assessments
Assessment Handbook – Unit 2 Assessment
pgs 160-163
Interdisciplinary Connections
Literacy Connection
12 Ways to Get to 11, by Eve Merriam, Aladdin
Paperbacks, 1996
If You Made a Million, by David M. Schwartz,
HarperCollins, 1994
How Tall, How Short, How Far Away?, by
David A. Adler, Holiday House, 2000
79
Hillside Township School District
The History of Counting, by Denise SchmandtBesserat, HarperCollins, 1999
Lesson 2.8 Consumer Link – Determining the
Validity of the “One Size Fits All” Claim
MJ pp. 46-47
MM p. 63
TIMEFRAME
October
20 periods
GRADE 4
CONTENT STRAND: Operations and Algebraic Thinking
UNIT 3: Multiplication and Division: Number Sentences and Algebra
ENDURING UNDERSTANDINGS
•
•
•
•
ESSENTIAL QUESTIONS
•
A quantity can be represented numerically in various ways.
There are multiple algorithms for finding mathematical
solutions.
Multiple representations of a number can give a fuller
understanding of a problem.
Operations with numbers are used to solve problems at all
levels of mathematics.
•
•
•
•
•
CCS
KNOWLEDGE
Students will know:
How do mathematical ideas interconnect and build on
one another to produce a coherent whole?
How can we compare and contrast numbers?
How can counting, measuring or labeling help to make
sense of the world around us?
What makes a computational strategy both effective and
efficient?
How do operations affect numbers?
How do you create number sentences to solve everyday
number story?
SKILLS
Students will be able to:
80
Hillside Township School District
4.0A.1.
4.0A.2.
4.0A.3.
4.0A.4
4.0A.5.
•
•
•
•
•
•
•
Words and symbols can be used to describe
functions
Factors and multiples, square numbers and
patterns in Multiplication/Division fact table
Line graphs can be used to describe data
Number models can be used to represent
addition/subtraction number stories
Conventional notation can be used to write
number sentences
Evaluate expressions containing parentheses
and determine whether expressions are true or
false
Use a “guess and check” strategy to make
reasonable estimates for open sentences.
•
•
•
•
•
•
•
•
Solve open number sentences
Understand the function and placement of parentheses
in number sentences
Determine whether number sentences are true or false
Solve addition and subtraction number stories
Use a map scale to estimate distances
Know division facts
Know multiplication facts
Understand the relationship between multiplication and
division
Key Terms: dividend, divisor, fact family, factor
pair, factors, false number sentences, function
machine, input, multiples, multiplication facts,
number sentences, open sentences, output,
parentheses, percent, products, quotient,
remainder, rule, solution, solve, square numbers,
true number sentences, turn-around facts,
variable, “What’s My Rule?”
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
INTERNET AND OTHER RESOURCES
81
Hillside Township School District
Assessments
Lesson 3-1
• RSA: MJ page 53, Problems 1 and 2 (correctly
complete “What’s My Rule?” tables
Lesson 3-2
• RSA: MM page 489 (numerical expressions
involving one or more of the basic four
arithmetic operations)
Lesson 3-3
• RSA: MJ page 59 (estimate reasonable
solutions for whole number
addition/subtraction)
Lesson 3-4
• RSA: 50-facts test (MM pg 411)
Lesson 3-5
• RSA: MJ pg. 61, problem 1 (use conventional
notation to write multiplication and division
number sentences)
Lesson 3-6
• RSA: MJ pg. 63, problem 4 (multi-digit
addition/subtraction problems)
Lesson 3-7
• RSA: MJ pg. 64, problem 4 (using map scale
to estimate distances)
Lesson 3-8
• RSA: Exit Slip MM pg. 389 (use and explain a
strategy for solving addition number story)
Lesson 3-9
• RSA: MJ pg. 69, problem 9 (determine
whether a number sentence is true or false)
Lesson 3-10
• RSA: Mental Math/Reflexes (proficiency with
basic division facts)
Lesson 3-11
82
Internet Resources
Illuminations: Resources for Teaching Math
Mathwire: Standards Based Math Activities
Multiplication.com: Interactive games for kids
BrainPop: Multiplication
BrainPop: Order of operations
Everyday Math Games
3-2, 3-10: Name that Number (SRB pg. 254;
MM pg. 489)
3-2: Buzz and Bizz-Buzz (SRB pg. 234)
3-3: Baseball Multiplication (SRB pgs 231-2; Masters pg. 460)
3-3, 3-6: Multiplication Top-It (SRB pg. 264; Masters pg. 506)
3-5: Beat the Calculator (SRB pg. 233; Masters pg. 461)
3-5: Division Arrays (SRB pg. 240; Masters pg. 470)
3-6: Seega (SRB pg. 309; Masters pg. 503)
3-8: High-Number Toss (SRB pg. 252; Masters pg. 487)
Hillside Township School District
• RSA: Exit Slip MM pg. 389 (use and explain a
strategy for solving open number sentences)
Self Assessment: Assessment Handbook pg. 164
Oral and Slate Assessment: TE pg. 221
Written Assessment: Assessment Handbook pgs.
165-168
Interdisciplinary Connections
Literacy Connection
Each Orange Had 8 Slices: A Counting Book, by
Paul Giganti, Jr., Greenwillow Books, 1999
My Full Moon Is Square, by Elinor J. Pinczes,
Houghton Mifflin, 2002
Sea Squares, by Joy N. Hulme, Hyperion Books for
Children, 1999
Lesson 3-6: Nine O’Clock Lullaby, by Marilyn
Singer, HarperCollins, 1993
Safari Park, by Stuart J. Murphy, HarperCollins
Publishers, 2002
Lesson 3.6 Social Studies Link – Examine a list of
countries and regions in the World Tour
SRB pp. 279-281
Lesson 3.6 Social Studies Link – Read a short
essay, then solve and write a number story
MM p. 93
Lesson 3.11 Social Studies Link – Using a Map
scale to measure distances
MJ p. 75
TIMEFRAME
October - November
22 class periods
83
Hillside Township School District
GRADE 4
CONTENT STRAND: Number Operations -Fractions
UNIT 4: Decimals and Their Uses
ENDURING UNDERSTANDINGS
•
•
•
•
•
•
ESSENTIAL QUESTIONS
A quantity can be represented numerically in various ways.
There are multiple algorithms for finding mathematical solutions.
Multiple representations of a number can give a fuller
understanding of a problem.
Fractions, decimals and percents express a relationship
between two numbers.
Estimating, approximating and judging the reasonableness of
answers are useful tools in everyday life.
Customary, metric and nonstandard units are used to
approximate and compute measurements and communicate
their validity.
•
•
•
•
•
•
•
•
CCS
4.NF.6
4.NF.7
•
•
•
•
•
•
KNOWLEDGE
Students will know:
Express metric measures with decimals.
Convert between metric measures
Compare and order decimals.
Draw and measure line segments to the nearest
millimeter.
Use personal references to estimate lengths in
metric units.
Solve 1- and 2-place decimal addition and
subtraction problems and number stories
84
•
•
•
•
•
•
How do mathematical ideas interconnect and build on
one another to produce a coherent whole?
How can we compare and contrast numbers?
How can counting, measuring or labeling help to make
sense of the world around us?
What makes a computational strategy both effective and
efficient?
How do operations affect numbers?
How are common fractions, decimals and percents alike
and different?
What connections can be made between decimals and
fractions?
What is the relationship between the metric system and
decimals?
SKILLS
Students will be able to:
Identify the values of digits in decimals.
Order decimals through the thousandths on a number
line.
Model decimals through hundredths with base 10 blocks.
Name the fractional part of the ONE represented by
based 10 blocks.
Rename fractions with 100 in the denominator as
decimals.
Compare and order decimals through hundredths.
Hillside Township School District
•
•
Draw and measure line segments to the nearest
centimeter.
Use dollars-and-cents notation.
Key Terms: ONE, whole, unit, tenth, hundredth,
odometer, trip meter, speedometer, deposit,
withdrawal, balance, interest, thousandth,
centimeter (cm), millimeter (mm), meter (m),
decimeter (dm), personal measurement reference
•
•
•
•
•
•
•
•
•
•
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Compare whole numbers and decimals.
Estimate sums and differences of decimals.
Express values of digits in decimals.
Add and subtract decimals to the hundredths place.
Estimate reasonable solutions for decimal addition and
subtraction problems.
Name the fractional part of ONE represented by each
base 10 block.
Read and write decimals through hundredths
Measure objects of distances to the nearest centimeter
Identify personal references for metric units of length
Measure the length of objects or distances in
centimeters, decimeters and meters.
INTERNET AND OTHER RESOURCES
Assessments
Lesson 4.1
• RSA Math Boxes #3a-3d, identify digits in
whole numbers
Lesson 4.3
• RSA Pg 83 # 1 compare decimals through the
hundredths place
Lesson 4.4
• MJ pg 85 # 4&5 estimate sums and explain
estimation
Lesson 4.5
• RSA Math Message understanding decimal
digits
Lesson 4.6
• RSA Math Boxes #4 understanding of
landmarks
Lesson 4.7
85
Internet Resources
• AAAmath: Place value
• Place Value Games
• Math-Play: Addition of Decimals Interactive Game
• Addition and Subtraction of decimals
• Smart Exchange: Smartboard Lessons and Games for
Decimals
• Smart Exchange: Measuring Lessons
• Math Playground: Making Change for Money Game
• Smart Exchange: Smartboard Lessons for Money
• BrainPop: Estimating
Everyday Math Games
4.2 Baseball Multiplication SRB 231-232 Masters 460
4.3 Product Pile Up SRB 259
4.4 Number Top It Decimals-SRB 256 Masters 490 and 506
4.6 Name That Number SRB 254 Masters 489
4.8 Fishing for Digits SRB 242 Masters 472
Hillside Township School District
•
RSA Mental Math and Reflexes writing
decimals through hundredths
Lesson 4.8
• RSA pg 96 # 2 measure line segments to the
nearest centimeter
Lesson 4.9
• RSA Number Top-It record sheet Masters pg
506
Lesson 4.10
• RSA Mental Math and Reflexes multiplying
automatically
Assessment Handbook pg 169, self-assessment
Teacher’s Edition pg 295 oral & slate assessments
Assessment Handbook – Unit 2 Assessment pgs 170173
Interdisciplinary Connections
Literacy Connection
Lesson 4-3: The Everything Kids’ Joke Book:
Side-Splitting, Rib-Tickling Fun, by Michael Dahl,
Adams Media Corporation, 2002
Lesson 4-3: Kids’ Funniest Jokes, edited by Shelia
Anne Barry, Sterling Publishing Co., 1994
Lesson 4-10: If You Hopped Like a Frog, by David
M. Schwartz, Scholastic Inc., 1999
Millions to Measure, by David M. Schwartz,
HarperCollins, 2006
Lesson 4.7 Social Studies Link – World Tour
Visiting Africa
MJ pp. 171-173, 176 and 177
SRB pp. 276 – 277, 279, 282, 283, and 296306
MM pp. 419-421
Lesson 4.10 Science Link – Measuring Land
Invertebrates MJ pp. 101-103
86
4.9 Number Top It Decimals-SRB 256 Masters 490 and 506
Hillside Township School District
November
24 periods
TIMEFRAME
GRADE 4
CONTENT STRAND: Number and Operations In Base Ten_
UNIT 5: Big Numbers, Estimation and Computation
ENDURING UNDERSTANDINGS
•
•
•
•
•
ESSENTIAL QUESTIONS
•
Physical models can be used to clarify mathematical
relationships.
Mathematical models can be used to describe and quantify
physical relationships.
There are multiple algorithms for finding a mathematical
solution.
Computational fluency includes understanding the meaning
and appropriate use of numerical operations.
A quantity can be represented numerically in many ways.
CCS
4.NBT.1
4.NBT.2
4.NBT.3
4.NBT.4
•
•
•
•
•
•
•
•
•
•
KNOWLEDGE
Students will know:
Extend basic multiplication facts to products of
ones and tens and products of tens and tens
Extend multiplication facts to multiplication of
multi-digit numbers
Estimate sums
Estimate products in tens, hundreds, and
thousands
Utilize the partial-products algorithm for 1-digit
and 2-digit multipliers
Utilize the lattice method for multiplication for 1
and 2-digit multipliers
87
•
•
•
•
•
•
•
•
How do mathematical ideas interconnect and build on
one another to produce a coherent whole?
How can we compare and contrast numbers?
What makes a computational strategy both effective and
efficient?
How do operations affect numbers?
What role does place value have in solving larger
multiplication and division problems?
SKILLS
Students will be able to:
Use exponential notation to represent powers of 10.
Know extended multiplication facts.
Make magnitude estimates for products of multi-digit
numbers.
Solve multi-digit multiplication problems.
Round whole numbers to a given place.
Read and write numbers to billions; name the values of
digits in numerals to billions.
Compare large numbers.
Estimate sums.
Hillside Township School District
•
•
•
•
Read, write and compare large numbers using
patterns in the base-ten value system
Use exponential notation for powers of 10 to
name values of places in the base-ten placevalue system.
Compare numerical data and develop the
meaning of percent as per 100
Identify the difference between estimates and
exact counts
Key Terms: extended multiplication facts,
estimation, rough estimate, partial-products
method, partial product, lattice method (for
multiplication), lattice, million, billion, trillion,
quadrillion, quintillion, sextillion, powers of 10,
exponent, rounding
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
INTERNET AND OTHER RESOURCES
Assessments
Internet Resources
Lesson 5.1
• Gamequarium: Multiplication Games
• MJ p.107 Explanation of how to use basic facts
• Smart Exchange: Multiplication Smartboard Lessons
to compute fact extensions
• Partial Product Examples
Lesson 5.2
• Interactive Partial Product Game
• MJ p. 109 Interpreting Chart Data
• aaamath: Rounding Numbers
• MJ p.110 #3 True/False Number Sentences
• BrainPop: Exponents
Lesson 5.3
• Multiplication.com: Multiplication Games
• MJ p.111 Using Estimation to solve problems
• Multiplication Games
Lesson 5.4
• SRB p.253;MM p.488 Multiplication Wrestling
Everyday Math Games
Lesson 5.5
Multiplication Top-It : SRB p.264; MM p.506
• MJ p. 118 Problems 1 & 2 Partial-products
Multiplication Wrestling: SRB p. 253; MM p. 488
Lesson 5.6
Product Pile-Up: SRB p. 259
• TE p.344 Mental Math & Reflexes Estimate
Name That Number: SRB p. 254; MM p. 489
88
Hillside Township School District
multiplication
Lesson 5.7
• MM p.506 Multiplication Top-It
Lesson 5.8
• Exit Slip MM p.388 or 389 Extended
Multiplication Facts
Lesson 5.9
• Exit Slip MM p. 388-389 Describe numeric
patterns
Lesson 5.10
• 50 Facts Test MM pp. 410,414, 416
Lesson 5.11
• MJ p.135 Problems 2a-2d
Self Assessment : Assessment Handbook p.174
Oral & Slate Assessments: TE p.379
Unit 5 Test: Assessment Handbook p.175-177
Interdisciplinary Connections
Literacy Connection
Ten Times Better, by Richard Michelson, Marshall
Cavendish Children’s Books, 2000
Moira’s Birthday, by Robert Munsch, Annick Press,
1992
Lesson 5.2 Social Studies Link – Interpreting a data
table on Presidents
MJ p. 109
Lesson 5.3 Social Studies Link – Examine a travel
map
MJ p. 112
Lesson 5.8 Social Studies Link – Analyzing a data
table on Internet
Users
MJ p. 128
Lesson 5.11 Social Studies Link – Comparing
Height data of the Tallest
89
High Number Toss: SRB p. 252; MM p. 487
Number Top-It: SRB p. 255; MM pp. 492,493,506
Hillside Township School District
Mountains
SRB pp. 294 and 304
Lesson 5.11 Social Studies Link – World Tour Data
for Europe
MJ p. 134
SRB pp. 279-281, 297, and 301
MM p. 426
Lesson 5.11 Social Studies Link – World Tour
Update of Route Map
MJ pp. 171-173, 178-179
SRB pp. 276, 277, 279-281,297, and 302-306
MM pp. 419 – 421
TIMEFRAME
November-December
24 periods
GRADE 4
CONTENT STRAND: Number and Operations-Base Ten
UNIT 6: Division, Map Reference Frames, Measures of Angles
ENDURING UNDERSTANDINGS
•
•
ESSENTIAL QUESTIONS
Reading, understanding, interpreting and communicating data
are critical in modeling a variety of real-world situations, drawing
appropriate inferences, making informed decisions and justifying
those decisions.
Statistics are used together to collect, organize, display, and
analyze data, simulate events and test hypothesis.
•
•
•
•
•
•
90
What meaning do numbers have?
How do mathematical ideas interconnect and build on
one another to produce a whole?
How can we compare and contrast numbers?
How can counting, measuring and labeling make sense
of the world around us?
How do we use numbers to convey information and
problem solve?
How can organizing, interpreting and displaying data be
used to answer questions?
Hillside Township School District
•
CCS
4.NBT.1
4.NBT.2
4.NBT.3
4.NBT.4
4.NBT.5
4.NBT.6
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•
•
•
KNOWLEDGE
Students will know:
Solve whole-number division problems.
Express the remainder of a whole-number
division problem as a fraction and the answer as
a mixed number.
Interpret the remainder in division problems.
Solve multiplication and division number stories.
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•
•
•
Key Terms: equal-groups notation, quotient,
remainder, dividend, divisor, partial quotient,
quotient, remainder, Multiplication/Division
Diagram
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
How do we organize data so that we can draw
conclusions?
SKILLS
Students will be able to:
Solve multiplication and division stories
Use repeated addition, skip counting, and arrays to
model multiplication
Identify the use of multiples
Solve equal grouping division number stories
Apply extended multiplication facts to long-division
situations
Solve division number stories and interpret remainders
Write number models to represent stories
INTERNET AND OTHER RESOURCES
Assessments
Lesson 6.1
• RSA MJ pgs 138-139 #1-4 write number models
to represent number stories
Lesson 6.2
• RSA: Math Boxes 2a-2c solve open ended
sentences
Lesson 6.3
• RSA MJ 144-145 #1,2,5 ability to solve division
problems and number stories with 1 digit divisors
and 2 digit dividends
Lesson 6.4
• RSA Math Boxes #3 ability to solve decimal
additions and subtraction problems
91
Internet Resources
• KidNumbers: Division Games
• Funbrain: Baseball Math
• Smart Exchange: Division Smartboard Lessons
• Smart Exchange: Smartboard games and lessons
• BrainPop: Division
• BrainPop Angles
EM Games
6.1 Division Arrays SRB 240, Masters 470
6.2 High Number Toss SRB 252, Masters 487
6.3 Beat the Calculator SRB 233, Masters 461
6.4 Division Dash SRB 241, Masters 471
Hillside Township School District
Assessment Handbook pg 179, self-assessment
Teacher’s Edition pg 461oral & slate assessments
Assessment Handbook – Unit 2 Assessment pgs 180183
Interdisciplinary Connections
Literacy Connection
Lesson 6-4: A Remainder of One, by Elinor J.
Pinczes, Houghton Mifflin Harcourt, 2002
Lesson 6-7: Sir Cumference and the Great Knight
of Angleland, by Cindy Neuschwander,
Charlesbridge Publishing, 2001
Lesson 6-9: Sea Clocks: The Story of Longitude,
by Louise Borden, Margaret K. McElderry Books,
2004
Lesson 6.5 Social Studies Link – Making a bar
graph on population
MJ p. 154
SRB p. 301
Lesson 6.7 Social Studies Link – World Tour Visits
Europe
MJ pp. 171-173, 180-181
SRB pp. 276, 277, 280, 284, 285, 297, and
302-305
MM pp. 419-421
Lesson 6.9 Social Studies Link – Locating Places
on a globe TE pp. 451-452
TIMEFRAME
December
10 periods
GRADE 4
92
Hillside Township School District
CONTENT STRAND: Number and Operations-Fractions
UNIT 7: Fractions and Their Uses; Chance and Probability
ENDURING UNDERSTANDINGS
•
•
•
•
ESSENTIAL QUESTIONS
A quantity can be represented numerically in various ways.
Numeric fluency includes both the understanding of and the ability to
appropriately use numbers.
The magnitude of numbers affects the outcome of operations on them.
One representation may sometimes be more helpful than another and,
used together, multiple representations give a fuller understanding of a
problem.
•
How do mathematical ideas interconnect and build on
one another to produce a coherent whole?
How can we compare and contrast numbers?
How can counting, measuring, or labeling help to
make sense of the world around us?
What makes a computational strategy both effective
and efficient?
How do operations affect numbers?
How do mathematical representations reflect the
needs of society across cultures?
What is the relationship between whole numbers and
fractions?
•
•
•
•
•
•
CCS
4.NF.1
4.NF.2
4.NF.3A
4.NF.3B
4.NF.3C
4.NF.3D
•
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•
•
•
•
•
•
KNOWLEDGE
Students will know:
Fractions are equal parts of a whole or the ONE
Fractions can be renamed as decimals and/or
percents
Equivalent fractions can be created by increasing or
decreasing the fractional parts of a set or polygonal
region
Fractions and mixed numbers have places on a
number line between whole numbers
Words and/or numbers can be used to identify the
probability or chance of an event occurring.
Fraction addition and subtraction can be modeled with
pattern blocks
Fractions with 10 or 100 in the denominator can be
easily renamed as a decimal.
Patterns can be developed to compare and order
93
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•
•
•
•
•
•
•
SKILLS
Students will be able to:
Add and subtract fractions
Rename fractions with denominators of 10 and 100
as decimals
Apply basic vocabulary and concepts associated
with chance events
Compare and order fractions
Find equivalent fractions for given fractions
Identify the whole for fractions
Identify fractional parts of a collection of objects
Identify fractional parts of regions
Hillside Township School District
fractions
Key Terms: denominator, equal chance, equally (more,
less) likely, equivalent fractions, Equivalent Fractions Rule,
event, expect, fair (die or spinner), favorable outcome,
mixed number, numerator, outcome, probability, “whole”
box, whole (or ONE or unit)
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
INTERNET AND OTHER RESOURCES
Assessments/Performance Tasks
Lesson 7-1
• RSA: Journal page 186, Problem 8 (understanding of
fractions as equal parts of a whole)
Lesson 7-2
• RSA: Journal page 190, Problems 4a-8a (solving
“fraction-of” problems)
Lesson 7-3
• RSA: Journal page 192, Problem 4 (use a basic
probability term to describe the likelihood of an event)
Lesson 7-4
• RSA: Exit Slip, MM pg. 389 (relationship between the
whole and its fractional parts)
Lesson 7-5
• RSA: Journal page 198, problem 1 (use pattern
blocks to solve fraction addition problems)
Lesson 7-6
• RSA: Journal page 200, problem 4 (estimate the
measure of an angle)
Lesson 7-7
• RSA: Math Masters, page 225 (understanding of
equivalent fractions)
Lesson 7-8
• RSA: Journal page 203, problems 1-4, 7 and 8
(rename tenths and hundredths as decimals with the
94
Internet Resources
• National Library of Virtual Manipulatives
• Gamequarium: Math Games with Fractions
• Visual Fractions Games
• Cool Math 4 Kids: Amusement park of math
• Math Playground
• The Decifractor: Changes fractions to decimals
• Smart Exchange: Fractions for the Smartboard
• BBC Bitesize: SmartBoard interactive videos/games
• BrainPop: Probability
Everyday Math Games
7-1: Product Pile-Up (SRB pg. 259)
7-2, 7-3: Fraction Of (SRB pg. 244-5, MM pgs.
477-480)
7-3, 7-6: Grab Bag (SRB pg. 249, MM pgs. 483485)
7-6, 7-7: Fraction Match (SRB pg. 243, MM pgs.
473-476)
7-9, 7-10: Fraction Top-It (SRB pg. 247, Masters
pg. 506)
7-10: Getting to One (SRB pg. 248)
Hillside Township School District
assistance of a visual model)
Lesson 7-9
• RSA: Journal page 206, problem 6 (compare fractions
and explain strategies)
Lesson 7-10
• RSA: Masters pg. 506 (comparing fractions)
Lesson 7-11
• RSA: Mental Math and Reflexes (express the
probability of an event as a fraction)
Lesson 7-12
• RSA: Exit Slip, MM pg. 389 (predict the outcomes of
an experiment and test the predictions using
manipulatives)
Self Assessment: Assessment Handbook pg. 184
Oral and Slate Assessments: TE pg. 639-640
Written Assessment: Assessment Handbook pgs. 186-188
Interdisciplinary Connections
Literacy
Lesson 7-5 Full House: An Invitation to Fractions, by
Dayle Ann Dodds, Candlewick Press, 2009
Lesson 7-11 Do You Wanna Bet? Your Chance to Find Out
About Probability, by Jean Cushman, Houghton Mifflin,
2007
Art Connection: Lesson 7-1
Naming Fractional Parts of a Region
TE pg. 575 (use pattern blocks to draw and color a
design and identify fractional parts)
Social Studies Connection: Lesson 7-2
World Tour: Update Route Map, locate facts and fill in
Country Notes
MJ pgs 329-333; SRB pgs 276, 277, 280, 286, 287,
297, and 302-5;
MM pgs 419-21
Technology Connection: Lesson 7-11
http://illuminations.nctm.org/ActivityDetail.aspx?id=79
95
7-11: Chances Are (SRB pgs. 236-7, MM pgs. 4626)
Hillside Township School District
MJ pg. 211: Create spinners and compare expected
results for a specified number of spins to the actual
results
TIMEFRAME
January-February
26 Class Periods
GRADE 4
CONTENT STRAND: Measurement and Data
UNIT 8: Perimeter and Area
ENDURING UNDERSTANDINGS
•
•
•
Everyday objects have a variety of attributes, each of which can
be measured in many ways.
What we measure affects how we measure it.
Measurements can be used to describe, compare, and make
sense of phenomena.
CCS
4.MD.1
4.MD.2
4.MD.3
•
•
•
•
KNOWLEDGE
Students will know:
Make and interpret scale drawings
Use formulas to find areas of rectangles,
parallelograms, and triangles
Find the perimeter of a polygon.
Find the area of a figure by counting unit squares
and fractions of unit squares inside the figure.
Key Terms: time-and-motion study, work triangle,
perimeter, rough floor plan, scale drawing, scale,
96
ESSENTIAL QUESTIONS
•
•
How can measurements be used to solve problems?
How do we use measurements to describe and compare
phenomena?
Can the area of all shapes be measured in the same way?
What is the relationship between area and perimeter?
•
•
•
•
•
•
•
•
SKILLS
Students will be able to:
Describe properties of and types of triangles
Use division to compare two quantities
Create a tally chart; Find the minimum, maximum, mode
and median of a data set
Calculate the perimeter of a triangle
Convert between feet and inches
Find the area of polygons by counting squares; identify
polygons
Hillside Township School District
•
•
•
•
•
area, square units, base, width, length, height,
area, formula, variable, base, height,
perpendicular, equilateral triangle, isosceles
triangle, base, height
•
•
•
Use an estimate; estimate area
Convert between square inches and square feet
Rename fractions as decimals
Find the area of a rectangles and parallelograms
Apply the Distributive Property of Multiplication over
Addition
Calculate the area of a parallelogram; describe its
properties
Identify perpendicular line segments and right angles
Estimate and compare area measurements
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
INTERNET AND OTHER RESOURCES
Assessments
Lesson 8-1
• RSA: Mental Math and Reflexes (rename
fractions as decimals and percents)
Lesson 8-2
• RSA: MM, page 414 (use data to create a line
graph)
Lesson 8-3
• RSA: MJ page 227, Problems 1-4 (find the area
of a polygon)
Lesson 8-4
• RSA: Exit Slip, MM, page 389 (count unit
squares and fractions of unit squares to estimate
the area of an irregular figure)
Lesson 8-5
• RSA: MJ page 235, Problem 2 (find the perimeter
of a figure)
Lesson 8-6
• RSA: MJ page 239, Problem 4 (solve fraction
addition and subtraction problems)
Lesson 8-7
Internet Resources
Map Scale Explanations of using scale and exercise
practicing using scales on maps
Bird's Eye View Use geometry to find buildings on a map
Area of Triangles Calculate areas of triangles with
formulas; drill
Rectangle Area Compute the area; multiple choice
Area of Parallelograms Drill on figuring the area of
parallelograms
Perimeter Explorer Find the perimeter of shapes
Fence the Dog Lesson on perimeter with problems to
solve
Area Explorer Change the perimeter setting to make
irregular shapes within a grid
BrainPop: Area
BrainPop: Distributive Property
97
Rugs and Fences: SRB p.260-261; MM 498-502
Perimeters on a Geoboard: MM pp. 248 and 437
Pattern-Block Perimeters: MM p. 249
Hillside Township School District
•
RSA: MJ page 242, Problem 8 (describe a
strategy for finding and comparing the areas of a
square and a polygon)
Lesson 8-8
• RSA: MM, page 485 (calculate the probability of
an event)
Self Assessment: Assessment Handbook, page 189
Oral and Slate Assessment: TE pgs. 705-6
Written Assessment: Assessment Handbook, pgs.
190-4
Interdisciplinary Connections
Literacy
Actual Size, by Steve Jenkins, Houghton Mifflin, 2004
Castle, by David Macaulay, Houghton Mifflin, 1982
TIMEFRAME
Industrial Arts Connection: Lesson 8-1
TE pg. 660 (Sketch kitchen work triangles to
show distances between pairs of appliances)
Science Connection: Lesson 8-8
MM pg. 271 (Calculating Gravitational Pull)
Determine the gravitational pull of each planet
relative to Earth
Social Studies Connection: Lesson 8-4
MJ pgs 329-331, 334-5; SRB pgs. 276, 277,
280, 287, 297, and 302-305; MM pgs 419 and
420
Visit a second country in South America on the
World Tour
Social Studies Connection: Lesson 8-8
MJ pg. 245; SRB pgs 286-7
Compare areas of countries in South America
February - March
20 periods
98
Hillside Township School District
GRADE 4
CONTENT STRAND: Numbers and Operations-Fractions
UNIT 9: Fractions, Decimals and Percents
ENDURING UNDERSTANDINGS
•
•
•
•
A quantity can be represented numerically in various ways.
There are multiple algorithms for finding mathematical solutions.
Multiple representations of a number can give a fuller
understanding of a problem.
Fractions, decimals and percents express a relationship
between two numbers.
ESSENTIAL QUESTIONS
•
•
•
•
•
•
CCS
•
4.NF.2
4.NF.4A
4.NF.4B
4.NF.4C
4.NF.5
4.NF.6
•
•
•
•
•
KNOWLEDGE
Students will know:
Use an estimation strategy to divide decimals by
whole numbers.
Use an estimation strategy to multiply decimals
by whole numbers.
Find a percent or a fraction of a number.
Convert between “easy” fractions (fourths, fifths,
and tenths), decimals, and percents
Convert between hundredths-fractions, decimals,
and percents.
Use a calculator to rename any fraction as a
decimal or percent.
Key Terms: 100% box, percent, regular price or
list price, discount, percent or fraction of
99
•
•
•
•
•
•
•
•
•
•
•
•
How do mathematical ideas interconnect and build on
one another to produce a coherent whole?
How can we compare and contrast numbers?
How can counting, measuring or labeling help to make
sense of the world around us?
What makes a computational strategy both effective and
efficient?
How do operations affect numbers?
How are common fractions, decimals and percents alike
and different?
SKILLS
Students will be able to:
Solve “percent-of” problems
Rename fractions as decimals
Find equivalent names for percents
Use a calculator to rename fractions as decimals
Find patterns in decimals
Solve number stories involving discounts
Use a calculator to rename fractions as percents
Rename decimals as percents
Use a data table
Compare fractions with unlike denominators
Create a table and a tally chart
Order and interpret data; Create a table, chart, and map
to display data
Hillside Township School District
discount, sale price, urban, rural, life expectancy,
rank, literate and illiterate, percent of literacy
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
•
•
•
•
•
•
•
Identify place value in decimals
Multiply decimals
Round decimals and estimate products
Use a formula to calculate the area of a rectangle
Identify place value in decimals
Divide decimals by whole numbers
Round decimals and estimate quotients
INTERNET AND OTHER RESOURCES
Assessments
Lesson 9-1
• RSA: MM, page 278, Problems 1 and 2 (finding
equivalent fractions)
Lesson 9-2
• RSA: MJ, page 253 (rename fourths, fifths,
tenths and hundredths as decimals and percents)
Lesson 9-3
• RSA: Mental Math and Reflexes (rename fourths,
fifths, tenths and hundredths as decimals and
percents)
Lesson 9-4
• RSA: MJ, page 259, Problem 4 (solve “fractionof” problems)
Lesson 9-5
• RSA: MJ, page 260, Problem 4 (divide a multidigit whole number by a 1-digit divisor)
Lesson 9-6
• RSA: MJ, page 262, Problem 4 (interpret a map
scale)
Lesson 9-7
• RSA: MJ, page 265, Problem 6 (draw
conclusions from a data representation)
100
Internet Resources
Rounding Decimals Lesson with sports problems on
estimating with decimals
Saloon Snap Find equivalent fractions, percents, and
decimals; timed
Fraction Decimal Converter Activities on finding the decimal
and fraction equivalents
Percent Estimation What percent of the bar is shaded?
Decimal Challenge Estimate the location of a spot on a
number line; challenging
Penguin Waiter Calculate the percentage of a restaurant bill
as a tip
BrainPop: Fractions to decimals
BrainPop: Percents
Games
Fraction Match: SRB p.243; MM pp. 473-476
Fraction/Percent Concentration: SRB p. 246; MM pp. 481 and
482
Fraction Top-It: SRB p. 247; MM p.506
Fraction Of: SRB pp. 244-245; MM pp. 477-480
Hillside Township School District
Lesson 9-8
• RSA: MJ, page 268, Problem 4 (estimate the
product of a whole number and a decimal)
Lesson 9-9
• RSA: MJ, page 270, Problems 5-7 (estimate the
quotient of a decimal divided by a whole number)
Self Assessment: Assessment Handbook, page 195
Oral and Slate Assessments: TE pgs. 775-6
Written Assessment: Assessment Handbook, pgs.
196-9
Interdisciplinary Connections
Literacy
Count Your Way through China, by Jim Haskins,
Lerner Publishing Group, 1988
Piece = Part = Portion: Fractions = Decimals =
Percents, by Scott Gifford, Tricycle Press, 2008
Consumer Connection: Lesson 9-4
MJ pgs 256-7
Use calculators and mental arithmetic to solve
discount number stories (discount and sale
price)
Social Studies Connection: Lesson 9-5
MJ pgs 329-311, 336-7; SRB pgs 276, 277,
281, 288, 289, 297 and 302-305; MM pgs 419420
Update World Tour Country Notes page and
Route Log
Social Studies Connection: Lesson 9-7
SRB pg. 301: World Tour Population Data
TIMEFRAME
March
22 periods
101
Hillside Township School District
GRADE 4
CONTENT STRAND: Geometry
UNIT 10: Reflections and Symmetry
ENDURING UNDERSTANDINGS
•
•
•
•
Geometric shapes are identified by their characteristics and
properties.
Geometric language is used to describe special relationships.
The world is filled with geometry; angles, lines, curves and
patterns exist in everyday phenomena.
Basic concepts of geometry and spatial relationships are used to
construct, draw, describe and compare geometric models and
their transformations to solve problems.
CCS
4.G.1
4.G.2
4.G.3
•
•
•
•
•
KNOWLEDGE
Students will know:
Add integers.
Rotate figures.
Translate figures.
Use a transparent mirror to draw the reflection of a
figure.
Identify lines of symmetry, lines of reflection,
reflected figures, and figures with line symmetry.
Key Terms: transparent mirror, recessed, image,
reflection, line of reflection, line of reflection,
image, line of symmetry, symmetric, turn
symmetry, frieze pattern, reflection (flip),
translation (slide), rotation (turn), opposite (of a
number), credit, debit
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
102
ESSENTIAL QUESTIONS
•
•
•
•
•
•
•
•
•
•
•
•
•
How do the ways lines intersect identify shapes?
What properties are used to classify shapes?
What geometric features are present in our
surroundings?
How do geometric patterns and relationships affect our
everyday lives?
What is the connection between reflections and
symmetry?
SKILLS
Students will be able to:
Draw and describe properties of congruent figures, right
angles and perpendicular lines
Identify, describe and sketch reflections of twodimensional figures
Measure length
Identify polygons and describe properties of regular
polygons
Identify and draw lines of symmetry
Identify and draw congruent figures
Identify, describe and sketch reflections, rotations and
translations
Extend, describe and create geometric patterns
INTERNET AND OTHER RESOURCES
Hillside Township School District
Assessments
Lesson 10-1
• RSA: MM, page 494 (plot points in the first
quadrant of a coordinate grid)
Lesson 10-2
• RSA: Mental Math and Reflexes, TE page 800
(compare fractions)
Lesson 10-3
• RSA: MM, page 309, Problems 1 and 2 (sketch
and describe a reflection)
Lesson 10-4
• RSA: Exit Slip, MM page 389 (describe a pattern
and use it to solve problems)
Lesson 10-5
• RSA: MJ page 281, Problem 1 (identify and
sketch an example of a reflection and identify
examples of translations and rotations)
Lesson 10-6
• RSA: MJ page 284, Problem 1 (express the
probability of an event as a fraction)
Internet Resources
BrainPop: Exponents
Discovery Education: Geometry
Signed Numbers Lesson and practice on using signed
numbers
Line Jumper Use the number line to practice adding
positive and negative numbers
Wrapping Paper Lesson on slides, rotations, and flips
Bathroom Tiles Practice rotation, translation & reflection
Build a Mandala Use the tool to build your own mandala
(symmetry)
World Symmetry Interesting website for exploring with
many examples of symmetry; no activities
Symmetry Video Video explanation of symmetry with
interaction
Make a Symmetrical Figure Choose the type of
symmetry & make a figure; good for exploration; teacher
involvement
Make a Snowflake Work with rotation or reflection to
make a snowflake; can print
Self Assessment: Assessment Handbook, page 200
Oral and Slate Assessment, TE pages 829-830
Written Assessment: Assessment Handbook, pgs.
201-4
EM Games
Dart Game: MJ p. 276; Activity Sheet 7
Pocket-Billiards Game: MJ p. 276; Activity Sheet 8
Polygon Pair-Up: SRB p. 258; MM pp. 496
Interdisciplinary Connections
Literacy
Shadows and Reflections, by Tana Hoban,
Greenwillow, 1990
Count Your Way through Japan, by Jim Haskins,
Carolrhoda Books, 1987
Count Your way through Russia, by Jim Haskins,
Carolrhoda Books, 1987
How the Second Grade Got $8,205.50 to Visit the
103
Hillside Township School District
Statue of Liberty, by Nathan Zimelman, Albert
Whitman & Company, 1987
Reflections, by Ann Jonas, Greenwillow, 1987
Art Connection: Lesson 10-2
MM pg. 389; TE pg 803: Creating a Paint
Reflection
Technology Connection: Lesson 10-2
Investigate the use of a mirror as a virtual
manipulative (reflections and lines of reflection)
http://nlvm.usu.edu/en/nav/frames_asid_297_g
_2_t_3.html?open=activities
Social Studies Connection: Lesson 10-3
MJ pg. 329-331, 338 and 339; SRB pgs 276,
277, 281, 288-291, 297 and 302-305; MM pg.
419-421
World Tour Option: Visiting a Second Country
in Region 4 (Route Log, Route Map and
Country Notes)
Art Connection: Lesson 10-5
MJ pg 281: Sketch designs for frieze patterns
on cm grid paper
MM pg 389: Explore geometric patterns using
pattern blocks (identify slides, flips and turns)
Technology Connection: Lesson 10-5
Explore tessellations (identify and describe
reflections, rotations and translations)
http://nlvm.usu.edu/en/nav/frames_asid_163_g_2_t_3.
html?open=activities
TIMEFRAME
March-April
18 periods
104
Hillside Township School District
GRADE 4
CONTENT STRAND: Measurement and Data
UNIT 11: 3-D shapes, Weight, Volume and Capacity
ENDURING UNDERSTANDINGS
•
•
•
•
ESSENTIAL QUESTIONS
Everyday objects have a variety of attributes, each of which can be
measured in many ways.
What we measure affects how we measure it.
Measurements can be used to describe, compare and make sense
of phenomena.
Customary, metric and non-standard units are used to approximate
and compute measurements and communicate their validity.
CCS
•
4.MD.1
4.MD.2
4.MD.3
4.MD.4
•
•
•
•
•
KNOWLEDGE
Students will know:
Use a formula to calculate volumes of rectangular
prisms.
Subtract positive and negative integers.
Add positive and negative integers.
Estimate the weight of objects in ounces or
grams; weight objects in ounces or grams.
Solve cube-stacking volume problems
Describe properties of geometric solids.
Key Terms: gram, rectangular prism, triangular
prism, square pyramid, cylinder, cone, sphere,
geometric solid, curved surface, cube, edge, face,
flat surface, vertex (vertices), 3-dimensional,
polyhedron, triangular pyramid (tetrahedron),
dodecahedron, cubic units, volume, dimensions,
rectangular prism, formula, capacity
105
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
How can measurements be used to solve problems?
How do we use measurements to describe and compare
phenomena?
What properties are associated with customary and
metric units of weight and capacity?
SKILLS
Students will be able to:
Estimate tools
Convert between metric and customary units of weight
Extend numeric patterns
Identify parallel and intersecting line segments and
parallel planes
Identify congruent faces
Construct a rectangular prism
Construct polyhedrons
Solve volume problems
Find the area of the base of a rectangular prism
Calculate the surface area of a rectangular prism
Write number models with parentheses
Find the area of the base and the surface area of a
rectangular prism
Compare integers
Add and subtract signed numbers
Hillside Township School District
•
•
•
Use division to solve conversion problems
Round to the nearest whole number
Estimate weight
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
INTERNET AND OTHER RESOURCES
Assessments
Lesson 11-1
• RSA: MJ page 288, Problem 1a (describe a
translation)
Lesson 11-2
• RSA: MJ page 290, Problem 8 (describe a
rectangular prism)
Lesson 11-3
• RSA: MJ page 296, Problem 3a (find multiples of
whole numbers less than 10)
Lesson 11-4
• RSA: Mental Math and Reflexes: TE page 867
(multiplication and division facts)
Lesson 11-5
• RSA: MJ page 302, Problems 1, 2 and 5 (find the
volume of stacks of centimeter cubes)
Lesson 11-6
• RSA: MJ page 304, Problem 2 (identify an
example of a rotation)
Lesson 11-7
• RSA: MJ page 307, Problem 4 (describe the
relationship among U.S. customary units of length
and among metric units of length)
Internet Resources
Volume E-Lab E-Lab constructs a prism; calculate the
volume
Color Chips Subtraction Subtract positive & negative
numbers with the help of this interactive tool
Number Line Integers Choose two numbers and the
operation; applet demonstrates the answer; teacher
involvement
Line Jumper Use the number line to practice adding positive
and negative numbers
Space Coupe to the Rescue Use positive & negative
numbers to shoot the pods
Signed Numbers Lesson and practice on using signed
numbers
Platform Scale Weigh Greg in metric units on a doctor's scale
Balance the Scale E-Lab Activity on measuring in metric
Animal Weigh-In Balance the scales in metric
Factory Choose the nets that match the solid figures
Solid Geometry E-Lab Activity on measuring in metric
BrainPop: Volume of prisms
Self Assessment: Assessment Handbook, page 206
Oral and Slate Assessment: TE pages 891-2
Written Assessment: Assessment Handbook pages
106
EM Games
Ordering Weights: MM p. 389
Comparing Geometric Solids: MM p. 390
Cube Nets: MM p. 389 and p. 444
Rectangular Prisms: MM p. 389
Hillside Township School District
207-210
Interdisciplinary Connections
Literacy
A Grain of Rice, by Helena Clare Pittman, Scholastic
Inc., 1997
Mummy Math: An Adventure in Geometry, by
Cindy Neuschwander, Square Fish, 2009
Is a Blue Whale the Biggest Thing There Is?, by
Robert E. Wells, Albert Whitman, 1993
Fannie in the Kitchen: The Whole Story from Soup
to Nuts of How Fannie Farmer Invented Recipes
with Precise Measurements, by Deborah Hopkinson,
Aladdin, 2004
Social Studies Connection: Lesson 11-1
MJ pg. 329-331, 340 and 341; SRB pgs 276,
277, 281, 292, 293, 297 and 302-305; MM pg.
419-421
World Tour Option: Update Route Log, Route
Map and Country Notes
Technology Connection: Lesson 11-2
Describe solid figures and explore relationships
among vertices, edges and faces of
polyhedrons
http://nlvm.usu.edu/en/nav/frames_asid_g_2_t_
3.html?open=instructions
Technology Connection: Lesson 11-4
Create boxes of varying dimensions and
manipulate and count unit cubes, rows of unit
cubes or layers of unit cubes
http://illuminations.nctm.org/ActivityDetail.aspx?ID=
6
TIMEFRAME
April - May
22 periods
107
Hillside Township School District
GRADE 4
CONTENT STRAND: Measurement and Data
UNIT 12: Rates
ENDURING UNDERSTANDINGS
•
•
•
•
ESSENTIAL QUESTIONS
Everyday objects have a variety of attributes, each of which can
be measured in many ways.
What we measure affects how we measure it.
Measurements can be used to describe, compare, and make
sense of phenomena.
Patterns enable us to discover, analyze, describe, extend and
formulate concrete understandings of mathematical and real
world phenomena.
CCS
4.MD.1
4.MD.2
4.MD.3
4.MD.4
•
•
•
•
•
KNOWLEDGE
Students will know:
Find unit rates.
Calculate unit prices to determine which
product is the “better buy”.
Evaluate reasonableness of rate data.
Collect and compare rate data.
Use rate tables, if necessary, to solve rate
problems.
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Key Terms: rate, per, rate table, unit rate, unit
price label, consumer, products services,
comparison shopping unit price
108
How can measurements be used to solve problems?
How do we use measurements to describe and compare
phenomena?
How can converting rates help us in our everyday living?
How can collecting, organizing and displaying data help us
analyze information and make reasonable and informed
decisions?
SKILLS
Students will be able to:
Collect and organize data to create a table
Find the median and mean of a data set
Write number sentences with parentheses
Find multiples
Solve multiplication and division facts
Multiply and divide decimals
Use patterns and rules to solve rate problems
Find multiples
Divide whole numbers
Round decimals and whole numbers
Convert between rates
Analyze and interpret data
Compare and round decimals
Solve problems involving division of multidigit whole
numbers; interpret the remainder
Hillside Township School District
•
•
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Use data to create a line graph
Use the median, mean, and a line graph to draw
conclusions about a data set
INERNET AND OTHER RESOURCES
Assessments
Lesson 12-1
• RSA: MJ page 311, Problems 4a-4c (compare
integers between 100 and -100)
Lesson 12-2
• RSA: Exit Slip, MM pg. 389 (describe a rule for
a pattern and use the rule to solve problems)
Lesson 12-3
• RSA: MJ page 318, Problem 1 (use given data
to create a line graph)
Lesson 12-4
• RSA: MM page 489 (insert grouping symbols to
make true number sentences)
Lesson 12-5
• RSA: MJ page 322, Problem 4 (use scaling to
model multiplication and division)
Lesson 12-6
• RSA: MM pages 412, 414 and 416 (use the
50-fact test to assess automaticity with
multiplication facts through 10*10)
Self Assessment: Assessment Handbook, page
211
Oral and Slate Assessment: TE pages 942-3
Written Assessment: Assessment Handbook,
pages 212-215
109
Internet Resources
Rates Lesson Lesson on rates and ratios with practice quiz
Farm Stand Calculate prices when given unit price and quantity
Grocery Store Blues Solve problems for irate customers
concerning unit prices
BrainPop- Comparing Prices Movie about comparing prices
Calculators Calculators to determine MPG, loan payments, etc
EM Games
Mammal Speeds: MM pp. 343-344
Comparison Shopping: MM pp. 348 and 428
Credits/Debits (Advanced Version): SRB p. 239; MM p. 469
Name That Number: SRB p. 254; MM p. 489
Hillside Township School District
Interdisciplinary Connections
Literacy
Each Orange Had 8 Slices: A Counting Book,
by Paul Giganti, Greenwillow Books, 1999
If Dogs Were Dinosaurs, by David M. Schwartz,
Scholastic Inc., 2005
If You Hopped Like a Frog, by David M. Schwartz,
Scholastic Inc., 1999
The Grapes of Math, by Greg Tang, Scholastic
Paperbacks, 2004
Social Studies Connection: Lesson 12-1
Create a “Rates All Around Museum”
Record examples of rates from pgs 271 and
299 of SRB
Consumer Connection: Lesson 12-4
TIMEFRAME
May-June
18 periods
110
Hillside Township School District
GRADE 5
CONTENT STRAND: Number and Operations in Base Ten
UNIT 1: Number Theory
ENDURING UNDERSTANDINGS
•
•
•
Number patterns and relationships can be represented using
variables.
Numbers can represent quantity, position, location, and
relationships.
Our system of place value is based on groups of ten.
•
•
•
•
•
•
KNOWLEDGE
Students will know:
CCS
5.NBT.1
5.NBT.3.A
5.NBT.3.B
5.NBT.5
5.NBT.6
ESSENTIAL QUESTIONS
•
•
•
•
•
•
•
Identify factor pairs of a number and list all
factors
Understand square numbers and exponential
notation
How to multiply multi-digit whole numbers
How to read, write and compare decimals to
millionths
Build arrays and identify factors to describe
them
Understand multi-digit numbers based upon
divisibility rules
Identify the factors of a number
Key Terms: even number, factor, product, factor
pair, factor (of a number), odd number,
remainder, divisibility, square array, square
number, exponential notation, exponent key (on
111
How do I determine all factor pairs for a number?
How are factors and divisibility related?
What is meant by the square root of a square number?
How do arrays represent multiplication number models?
How can I test for divisibility?
How can numbers be represented as products of factors
and prime factors?
SKILLS
Students will be able to:
•
•
•
•
•
•
•
•
•
•
Find factors of a number using divisibility rules
Apply multiplication/division relationships to divisibility and
factors
Use exponential notation to name square numbers and explore
the relationship between square numbers and square roots
Fluently use all basic multiplication facts to fluently multiply
multi-digit numbers
Identify places in whole numbers and decimals and
express value of digits in those places
Compare two decimals using >, <, and =
Find factors of a number
Use divisibility rules to solve problems
Use exponents to rename numbers
Apply problem solving and critical thinking skills
Hillside Township School District
a calculator), exponent, “unsquaring” a number,
square root, square root key (on a calculator),
rectangular array, number model, turn-around
rule (for multiplication), perpetual calendar,
factor rainbow, divisible, quotient, divisibility
test, name-collection box, factor string, prime
factorization exponent
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
INTERNET AND OTHER RESOURCES
Summative Assessments
Unit 1 Progress Check
Slate/Oral Assessment
Interdisciplinary/Cross Curricular
1.1 LAL, 1.6 & 1.9 S.S.
Ongoing Assessment
1.1 MJ p.4 Math Boxes Problems 2 and 5 – Place
Value
1.2 MJ p.5 Build Arrays and Identify Factors
1.3 MJ p.10 Problem 2 – Factor Pairs
1.4 TE p.35 Exit Slip - Factor Captor Strategies
1.5 MJ p.15 Math Boxes Problem 4 – Place Value
1.6 TE p.43 Math Message - Factor Numbers in
Arrays
1.7 TE p.50 Exit Slip – Square Numbers
1.9 MJ p.25 Finding Factors of a Number
Portfolio
Assessment Handbook p.157
Divisibility Test
Literature
Math Talk, by Theoni Pappas
112
http://exchange.smarttech.com/#tab=0
(Interactive Smartboard Lessons)
http://www.mrnussbaum.com/mathgames.htm (Multiplication &
Division Games)
http://www.factmonster.com/math/flashcards.html (Multiplication
& Division Facts)
http://www.mathisfun.com/ (Notes & Try) Multiplication &
Division
http://www.softschools.com/grades/5thgrade.jsp (Multiplication &
Division)
http://illuminations.nctm.org/ActivityDetail.aspx?ID=64
(Factorize) 1.3
http://www.mathsisfun.com/divisibility-rules.html (Divisibility
Rules & Try) 1.5
http://www.aaastudy.com/fra63ax2.htm (Prime & Composite)
1.6
http://www.math-play.com/Prime/prime-and-compositenumbers.html (Prime & Composite) 1.6
http://www.oswego.org/ocsdweb/games/spookyseq/spookysqno.html (Square Numbers) 1.7
http://exchange.smarttech.com/#tab=0 (Interactive Smartboard
Lessons)
http://www.mathsisfun.com/prime-factorization.html (Prime
Factorizations) 1.9
http://www.mrnussbaum.com/factorization_forest.htm (Prime
Hillside Township School District
12 Ways to Get to 11, by Eve Merriam
Speed Mathematics, by Bill Handley
Factorization Game) 1.9
http://www.softschools.com/math/factors/factor_tree/ (Factor
Trees) 1.9
www.everydaymathonline.com
www.emgames.com
1.3 Beat the Calculator
Multiplication Wrestling
Multiplication Top It
1.4 Factor Captor
1.6 Baseball Multiplication
1.7 Factor Top It
1.9 Name That Number
Factor Bingo
TIMEFRAME
September
GRADE 5
CONTENT STRAND: Number and Operations in Base Ten
UNIT 2: Estimation and Computation
ENDURING UNDERSTANDINGS
•
•
•
ESSENTIAL QUESTIONS
Numbers can be used to represent quantity, position, location,
and relationships.
In certain situations, an estimate is as useful as an exact
answer.
Our system of place value is based on groups of ten.
•
•
•
•
KNOWLEDGE
Students will know:
CCS
5.NBT.4
5.NBT.7
•
•
What algorithms can be used to add and subtract whole
numbers and decimals?
How can I multiply whole numbers using various
algorithms?
When is it appropriate to use estimation?
What numerical values are represented by decimals?
How are decimals useful and needed?
SKILLS
Students will be able to:
•
•
Add/subtract/multiply whole numbers using
various algorithms
113
Solve multi-digit addition/subtraction problems.
Understand the relationship between addition and
Hillside Township School District
•
•
•
•
•
•
Add/subtract/multiply decimals using various to
thousandths using given algorithms
Make magnitude estimates
Estimate products
Place value up to trillions
Use place value understanding to round
decimals to any place
Solve real life word problems involving addition
and subtraction of whole numbers and
decimals
Key Terms: value, digit, place, place value,
algorithm, partial-sums method, column-addition
method, trade-first method, partial-differences
method, magnitude, estimate, partial-products
method, lattice method, lattice
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Summative Assessments
Unit 2 Progress Check
Slate/ Oral Assessment
Interdisciplinary/Cross Curricular
2.1 S.S., 2.2 LAL, 2.5 Science
Portfolio
Assessment Handbook p.163
Fund Raising
Ongoing Assessment
2.2 MJ p.33 Problems 1 and 2 – Addition Algorithms
2.3 MJ p.35 Problems 1 and 2 – Subtraction
Algorithms
2.4 MJ pp.37-38 Problems 1,3, and 4 Open Number
Sentences
114
•
•
•
•
subtraction
Use estimation to evaluate sums and differences
Use estimation to evaluate and place the decimal in
products
Apply multiplication facts
Apply problem solving and critical thinking skills
INTERNET AND OTHER RESOURCES
http://exchange.smarttech.com/#tab=0 (Interactive Smartboard
Lessons)
http://www.gamequarium.com/estimation.html (Estimation) 2.1
http://www.mrnussbaum.com/hotel.htm (Adding & Subtracting
with Decimals) 2.2 & 2.3
http://www.mathplayground.com/WordProblemsWithKatie1.html
(Addition & Subtraction Number Stories) 2.4
http://www.mathplayground.com/WordProblemsWithKatie2.html
(Multiplication & Division Number Stories) 2.4
http://www.math-play.com/multiplying-decimals-game.html
(Multiplication of Decimals) 2.8
www.coolmath4kids.com (Notes) Lattice Multiplication 2.9
http://www.gamequarium.com/placevalue.html (Place Value)
2.10
http://www.funbrain.com/tens/index.html (Place Value) 2.10
www.everydaymathonline.com
Hillside Township School District
2.7 MJ p.49 Math Boxes Problems 3 and 4
2.8 MJ p.50 Problems 1-6 Magnitude Estimates
2.9 TE p.130 Exit Slip – Multiplication Algorithms
Literature
Counting on Frank, by Rod Clement
How Much is a Million?, by David M. Schwartz
Anno’s Magic Seed, by Mitsumasa Anno
Math Curse, by Jon Scieska
www.emgames.com
2.3 Subtraction Target Practice
Addition Top It
2.4 Name That Number
2.5 High Number Toss- Decimal Version
2.7 Multiplication Bulls-eye
2.8 Multiplication Wrestling
2.9 Factor Bingo
2.10 Number Top It
High Number Toss
TIMEFRAME
September and October
115
Hillside Township School District
GRADE 5
CONTENT STRAND: Geometry
UNIT 3: Geometry Explorations
ENDURING UNDERSTANDINGS
•
•
•
•
•
•
Points, lines, and planes are the foundation of geometry.
Objects can be described and compared using their
geometric attributes.
KNOWLEDGE
Students will know:
CCS
5.G.3
5.G.4
ESSENTIAL QUESTIONS
•
•
•
•
•
How do geometric models describe spatial relationships?
How can I measure and construct angles?
How can I classify and sort geometric shapes?
How do I determine which polygons tessellate and which do
not?
SKILLS
Students will be able to:
•
•
•
•
Understand ½ circle and full circle
protractors
Recognize relationships between sides and
angles in polygons
Understand that attributes that belong to a
category of two-dimensional figures also
belong to all subcategories of those
geometric figures
Construct angles
Estimate and measure angles
•
•
•
Key Terms: acute angle, obtuse angle, right
angle, straight angle, reflex angle, Geometry
Template, regular polygon, tessellation, regular
tessellation, tessellate
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
116
Define and classify angles according to their measures
Use angle relationships to determine angle measurements
Describe properties of regular polygons
Classify two-dimensional figures in a hierarchy based on
attributes
Use geometric tools (protractor, ruler, compass)
Identify, describe, and create tessellations
Apply problem solving and critical thinking skills
INTERNET AND OTHER RESOURCES
Hillside Township School District
Summative Assessments
Unit 3 Progress Check
Slate/Oral Assessment
Interdisciplinary/Cross Curricular
3.1 S.S., 3.5 Art, 3.8 Art
Portfolio
Assessment Handbook p.169
Adding Angles
Ongoing Assessment
3.3 MJ p.66 Identify Angle Measures
3.4 TE p.175 Exit Slip - Angle Measures Full and
½ Circle Protractor
3.7 MJ p.80 Identify Polygons
3.9 TE p.203 Angles Measures
Literature
A Cloak for the Dreamer, by Aileen Friedman
The Greedy Triangle, by Marilyn Burns
Grandfather Tang’s Story, by Ann Tompert
What’s Your Angle, Pythagoras?, by Julie Ellis
http://exchange.smarttech.com/#tab=0 (Interactive Smartboard
Lessons)
http://www.ezschool.com/Games/Angles.html (Exploring Angle
Measures) 3.3
http://www.mrnussbaum.com/antihomework.htm
(Estimating Angle Measures)
http://www.mathleague.com/help/geometry/angles.htm (Angle
Notes)
http://www.mathplayground.com/measuringangles.html (Using A
Protractor) 3.4
http://www.mathplayground.com/alienangles.html (Using A
Protractor) 3.4
http://www.mathsisfun.com/geometry/construct-ruler-compass1.html (Tutorial) 3.5
http://www.math-play.com/Polygon-Game.html (Polygons) 3.7
http://www.coolmath4kids.com/tesspag1.html
(Tessellations Notes ) 3.8
http://www.math-play.com/Angles-Jeopardy/Angles-Jeopardy.html
(Review Game on Angles)
http://www.mrnussbaum.com/airmadillos.htm (Angle Game)
http://www.mrnussbaum.com/shapeinvaders.htm (Polygon and
Shapes Games)
www.everydaymathonline.com
www.emgames.com
3.3 Multiplication Top It
3.6 Triangle Sort
Angle Tangle
3.7 Polygon Capture
TIMEFRAME
Mid/October and Mid/November
117
Hillside Township School District
GRADE 5
CONTENT STRAND: Number and Operations in Base Ten
UNIT 4: Division
ENDURING UNDERSTANDINGS
•
•
ESSENTIAL QUESTIONS
•
Computation involves taking apart and combining
numbers using a variety of approaches.
Operations create relationships between numbers.
•
•
•
KNOWLEDGE
Students will know:
CCS
5.NBT.6
•
•
•
•
How do I use mental math divide 2-digit numbers by 1-digit
numbers?
What algorithms can be used for dividing whole numbers and
decimals by whole numbers?
How are multiplication and division related?
How is the remainder in division used and interpreted?
SKILLS
Students will be able to:
•
Apply various algorithms to solving
division problems with up to four digit
dividends and two or more digit divisors
(partial-quotient, column division, friendly
numbers)
Understand the inverse relationship
between multiplication and division
Express a remainder as a fraction or
decimals
Understand what a remainder represents
and how to interpret the remainder
•
•
•
•
Key Terms: dividend, divisor, partial
quotient, quotient, remainder, magnitude
estimate
118
Use friendly numbers to divide 2-digit numbers by a 1-digit
number
Use the partial-quotients algorithm for quotients
Use divisibility to identify multiples
Interpret the remainder in number story solutions
Apply problem solving and critical thinking skills
Hillside Township School District
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Summative Assessments
Unit 4 Progress Check
Slate/Oral Assessment
Interdisciplinary/Cross Curricular
4.3 & 4.7 S.S
Portfolio
Assessment Handbook p.174
Missing Digits
Ongoing Assessment
4.1 MJ p.99 Problems 1-4 Division Facts
4.2 MJ p.101 Division Algorithms
4.4 MJ p.107 Problem 10 Division Number
Story
4.5 MJ p.109 Magnitude Estimate for Division
4.6 MJ p.111-112 Problems 1-3 Interpreting
Remainders
Literature
A Remainder of One, by Elinor J. Pinczes
One Hundred Hungry Ants, by Elinor J. Pinczes
INTERNET AND OTHER RESOURCES
http://exchange.smarttech.com/#tab=0 (Interactive Smartboard
Lessons)
http://www.coolmath4kids.com/long-division/index.html (Long
Division Notes)
http://www.harcourtschool.com/activity/thats_a_fact/english_K_3.html
(Division Facts) 4.1
http://www.gamequarium.com/division.html (Division Games)
http://www.mathsisfun.com/numbers/division.html (Division Notes &
Try)
http://www.mathsisfun.com/long_division.html (Long Division Notes &
Try)
http://www.softschools.com/math/games/division_practice.jsp
(Division Game)
http://www.softschools.com/math/division/long_division/ Division
Game)
http://www.funbrain.com/football/ (Decimal Division Game)
http://www.mathplayground.com/division02.html (Division with
Remainders)
http://www.mathsisfun.com/long_division2.html (Notes & Try)
http://www.kidsnumbers.com/long-division.php (Division Practice
Games)
www.everydaymathonline.com
www.emgames.com
4.1 Name That Number
4.2 Division Dash
4.4 Divisibility Dash
4.5 Division Top It
4.6 First to 100
4.7 Division Dash
Algebra Election
119
Hillside Township School District
TIMEFRAME
Mid/November and Mid/December
GRADE 5
CONTENT STRAND: Number and Operation - Fractions
UNIT 5: Fractions, Decimals, and Percents
ENDURING UNDERSTANDINGS
•
•
ESSENTIAL QUESTIONS
•
Fractions, decimals, and percents express a relationship
between two numbers.
Fractions are used to represent a part of a whole.
KNOWLEDGE
Students will know:
CCS
5.NF.3
•
•
•
•
•
•
•
•
•
•
Explain the relationship between the
numerator and denominator
Interpret a fraction as division of the
numerator by the denominator (a/b = a ÷ b)
Convert between equivalent number forms
Compare fractions
Understand fraction and decimal relationships
Recognize percent equivalents for fractions
Key Terms: whole (or ONE or unit), denominator,
numerator, unit fraction, equivalent fractions,
fraction stick, round down, round up, round to
the nearest…, repeating decimal, percent
120
•
•
•
•
•
•
•
How are common fractions, decimals, and percents alike
and different?
How can I find fractional parts of large whole numbers?
How do I compare and order fractions?
How can I rename simple fractions as decimals?
How do I use a calculator to convert fractions to decimals,
decimals to percent, and find decimal equivalents for
percents?
SKILLS
Students will be able to:
Find equivalent names for a fraction of a set
Compare fractions to 0, ½, and 1
Order fractions from least to greatest
Rename fractions and mixed numbers as decimals
Convert between fractions, decimals, and percents
Use visual fraction models or equations to represent a
problem
Apply problem solving and critical thinking skills
Hillside Township School District
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
INTERNET AND OTHER RESOURCES
Summative Assessments
Unit 5 Progress Check
Slate/Oral Assessment
Interdisciplinary/Cross Curricular
5.1 & 5.8 LAL, 5.12 S.S. , 5.10 Science
Portfolio
Assessment Handbook p.179
Finding Fraction
Ongoing Assessment
5.1 MJ p.122 Problem 2 Exit Slip - Unit Fraction
5.2 MJ p.125 Problem 5 Calculate Unit Fraction
5.3 MJ p.129 Problem 5 Comparing Fractions
5.4 TE p.312 Exit Slip - Equivalent Fractions
5.6 MJ p.144 Math Boxes Problem 5 Ordering
Fractions
5.7 MJ p.145 Problem 1 Converting Fractions to
Decimals
5.10 MJ p.154 Estimate Circle Graph Sectors
Literature
Fourscore and 7: Investigating in American History,
by Besty Franco
Tiger Math, by Ann Whitehead Nagda
www.emgames.com
5.1 Fraction Top It
5.4 Multiplication Bulls-Eye
Factor Captor
5.5 Estimation Squeeze
5.6 Number Top it
5.7 Frac-Tac-Toe
5.8 Fraction/Percent Concentration
121
http://exchange.smarttech.com/#tab=0 (Interactive Smartboard
Lessons)
http://www.coolmath4kids.com/fractions/index.html (Fraction
Review) 5.1
http://www.mathsisfun.com/fractions-menu.html (Notes & Try for
Fractions)
http://www.aaamath.com/fra43ax2.htm (Comparing Fractions
with Like Denominators) 5.4
http://www.aaamath.com/fra43bx2.htm (Comparing
Fractions with Unlike Denominators) 5.4
http://www.aaamath.com/fra43cx2.htm (Comparing Unlike
Fractions) 5.4
http://www.aaamath.com/dec42bx2.htm (Fractions and
Decimals) 5.5-5.7
http://www.toonuniversity.com/flash.asp?err=198 (Fractions and
Decimals) 5.5-5.7
http://www.mrnussbaum.com/deathdecimals.htm (Converting
Fractions to Decimals Game) 5.5-5.7
http://www.aaamath.com/rat61cx2.htm (Fractions to Percents)
5.8
http://www.gamequarium.com/fractions.html (Fraction Games)
http://www.mrnussbaum.com/icgraphing.htm (Bar Graphs and
Pie Charts Game) 5.9
http://nlvm.usu.edu/en/nav/category_g_2_t_1.html
www.everydaymathonline.com
Hillside Township School District
5.11 Fraction Of
5.12 Name That Number
TIMEFRAME
Mid/December and Mid/January
GRADE 5
CONTENT STRAND: Number and Operation - Fractions
UNIT 6A: Addition and Subtraction of Fractions
ENDURING UNDERSTANDINGS
•
•
ESSENTIAL QUESTIONS
•
Fractions, decimals, and percents express a relationship
between two numbers.
Equivalent fractions represent the same part of a whole.
KNOWLEDGE
Students will know:
CCS
5.NF.1
5.NF.2
•
•
•
•
•
Use an algorithm to add/subtract fractions and
mixed numbers with unlike denominators and
common denominators
Write equivalent fractions
Solve word problems involving the addition and
subtraction of fractions with like and unlike
denominators
•
•
•
•
•
•
Key Terms: common denominator, unlike
denominators, quick common denominator,
simplest form
•
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
How is computation with rational numbers similar and
different to whole number computation?
How can I find common denominators quickly?
How can I add/subtract fractions using various
algorithms?
SKILLS
Students will be able to:
Convert between fractions and mixed numbers for sums
and differences
Add fractions and mixed numbers with like
denominators
Find common denominators
Rename pairs of fractions using a common denominator
Use visual fraction models or equations to represent a
problem
Estimate fractional numbers mentally to assess the
reasonableness of an answer
Apply problem solving and critical thinking skills
INTERNET AND OTHER RESOURCES
122
Hillside Township School District
Summative Assessments
Unit 6 Progress Check
Slate/Oral Assessment
http://exchange.smarttech.com/#tab=0 (Interactive
Smartboard Lessons)
http://www.kidsnumbers.com/fractions.php (Fraction Games)
http://www.math-play.com/adding-and-subtracting-fractionsgame.html (Adding and Subtracting Fraction Game)
http://www.funbrain.com/fract/index.html (Equivalent Fraction
Game)
http://www.mrnussbaum.com/tonyfraction.htm (Equivalent
Fractions Game)
http://www.mrnussbaum.com/fractiondolphins.htm (Equivalent
Fractions Game)
Interdisciplinary/Cross Curricular
6.3 LAL, 6.2 & 6.6 S.S., 6.7 Science
Portfolio
Assessment Handbook p.184
Mean Age
Ongoing Assessment
6.8 MJ p.191-192 Problems 3-6 Add/Subtract
Fractions
6.9 MJ p.194 Problems 16-24 Add/Subtract Fractions
6.10 TE p.432 Exit Slip - Finding Common
Denominators
Literature
Jim and the Beanstalk, by Jean Cushman
Esio Trot, by Roald Dahl
Fraction Action, by Loreen Leedy
www.emgames.com
6.8 Divisibility Dash
6.9 Fraction Capture
TIMEFRAME
Mid/January and Mid/February
123
http://nlvm.usu.edu/en/nav/category_g_2_t_1.html
www.everydaymathonline.com
Hillside Township School District
GRADE 5
CONTENT STRAND: Measurement and Data
UNIT 6B: Using Data
ENDURING UNDERSTANDINGS
•
ESSENTIAL QUESTIONS
Standard units of measure enable people to interpret results
or data.
•
•
•
•
KNOWLEDGE
Students will know:
CCS
5.MD.1
5.MD.2
•
•
•
•
•
•
•
•
Why is data collected and analyzed?
How would I describe the prominent features of a data
set?
How do I interpret data in line plots and stem-and-leaf
plots?
How can I interpret the relationship between sample size
and reliability of predictions?
SKILLS
Students will be able to:
•
•
Display data on line plot
Create a line plot to display a data set of
measurements
Identify and use customary measures of
length
Discuss data’s organization
Understand structure of stem-and-leaf plots
Interpret data display in line plots
Construct stem-and-leaf plots
Identify and use data landmarks
•
•
•
•
•
Key Terms: organizing data, landmark,
minimum, maximum, range, mode, median,
mean (average), line plot, span, normal span,
great span, stem, leaf, stem-and-leaf plot, angle
of separation, sample
124
Organize data using a picture, graphs, table or list
Identify data landmarks for data sets (mean, mode,
median)
Convert between inches, feet, yards and miles
Collect, organize, and interpret class data
Interpret line plots and stem-and-leaf plots
Use landmarks to identify and draw conclusions about
data sets
Apply problem solving and critical thinking skills
Hillside Township School District
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
INTERNET AND OTHER RESOURCES
Summative Assessments
Mid-Year Assessment
Ongoing Assessment
6.1 MJ p.165 Organizing Data & Identify Landmarks
6.3 TE p.393 Exit Slip - Stem-and-Leaf
6.4 MJ p.176 Problems 5 and 6 Line Plots
6.5 TE p.401 Math Message - Sample Size
www.emgames.com
6.2-6.6 First to 100
6.6 Frac-Tac-Toe
http://exchange.smarttech.com/#tab=0 (Interactive Smartboard
Lessons)
http://www.mrnussbaum.com/coolgraphing.htm (Several graphs
to practice organizing data) 6.1
http://www.gamequarium.com/data.html (Landmarks Games:
Range, Mode, median, etc.)
http://www.mathplayground.com/howto_stemleaf.html
(Interactive Tutorial on Stem –and-Leaf Plot) 6.3
http://www.shodor.org/interactivate/activities/StemAndLeafPlotter/
(Stem-and- Leaf) 6.3
www.everydaymathonline.com
TIMEFRAME
Mid/January and Mid/February
GRADE 5
CONTENT STRAND: Operations and Algebraic Thinking
UNIT 7: Exponents and Negative Numbers
ENDURING UNDERSTANDINGS
•
•
•
•
•
ESSENTIAL QUESTIONS
Patterns can grow and repeat.
Patterns can be generalized.
Numbers can represent quantity, position, location, and
relationships.
Grouping is a way to count, measure, and estimate.
Flexible methods of computation involve grouping numbers in
strategic ways.
125
•
•
•
•
•
How can I rename numbers using exponential notation,
scientific notation, powers of 10, and standard form?
How can I use parenthesis in number sentences to make
the expression correct?
What are the rules for using order of operations?
How can I compare and order positive and negative
numbers?
How are positive and negative numbers added and
subtracted?
Hillside Township School District
KNOWLEDGE
Students will know:
CCS
5.OA.1
5.OA.2
5.OA.3
5.NBT.2
•
•
•
•
•
•
•
•
•
SKILLS
Students will be able to:
Write equivalent names using powers of ten
Explain patterns in the number of zeros of the
product obtained by multiplying by a power of
ten
Translate numbers from standard notation to
expanded notation
Use the order of operations to write number
sentences that demonstrate accuracy and
flexibility
Generate 2 numerical patterns using 2 given
rules
Identify and extend number patterns
How to model problems by pairing positive
counters with negative counters to find answer
How to use a number line to solve positive
and negative number problems
How to develop and apply rules for adding
and subtracting positive and negative
numbers
Key Terms: exponential notation, exponent,
base, factor, standard notation, powers key,
power, number-and-word notation, power of 10,
scientific notation, ambiguous, nested
parentheses, brackets, order of operations,
negative number, opposite, account balance, in
the black, debt, in the red, change-of-sign or OPP
key
126
•
•
•
•
•
•
•
•
•
•
Describe the number patterns inherent to exponential
notation and powers of 10
Translate numbers from scientific notation to number and
word notation
Insert and use parentheses and brackets in order to
make true number sentences
Write simple expressions that record calculations with
numbers
Evaluate numerical expressions using order of
operations
Model sums and differences of positive and negative
numbers with manipulative
Use concrete models to add/subtract signed numbers
Use signed number addition patterns to describe rules for
adding signed numbers
Use a calculator to add/subtract signed numbers
Apply problem solving and critical thinking skills
Hillside Township School District
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
INTERNET AND OTHER RESOURCES
Unit 7 Progress Check
Slate/Oral Assessment
Interdisciplinary/Cross Curricular
7.1 S.S., 7.3 Science
Portfolio
Assessment Handbook p.189
Operations in the Klasies Caves
Ongoing Assessment
7.1 MJ p.210 Problems 4-6 Exponential Notation
7.2 TE p.548 Math Message - Powers of 10
7.3 MJ p.217 Problems 1-5 Expanded Notation
7.4 TE p.559 Exit Slip - Using Parenthesis
7.8 MJ p.233 Problems 1-3 Addition of Positive and
Negative Numbers
7.10 MJ p.243 Problems 3 and 4 Number Patterns
Literature
Less Than Nothing is Really Something, by Robert
Froman
The King’s Chessboard, by David Birch
Anno’s Mysterious Multiplying Jar, by Mitsumasa
Anno
www.emgames.com
7.1 Exponent Ball
7.2 First to 100
7.3 High Number Toss
7.7 Top It (Positive/Negative Numbers)
7.8 Credits/Debits
7.9 High Number Toss – Decimal
127
http://exchange.smarttech.com/#tab=0 (Interactive Smartboard
Lessons)
http://www.softschools.com/math/games/exponents_practice.jsp
7.1 (Exponential Notation)
http://www.gamequarium.com/exponents.html 7.1 (Exponential
Notation)
http://www.ezschool.com/Games/Exponents.html 7.1
(Exponential Notation)
http://www.mrnussbaum.com/orderops.html
7.3 (Scientific
Notation)
http://www.math-play.com/Order-of-OperationsMillionaire/order-of-operations-millionaire.html 7.5 (Order of
Operations)
http://themathgames.com/our-games/arithmetic-games/orderpositive-negative-integers (Ordering Negative and Positive
Numbers)
http://exchange.smarttech.com/#tab=0 (Interactive Smartboard
Lessons)
http://nlvm.usu.edu/en/nav/frames_asid_161_g_2_t_1.html 7.8
(Addition of Positive and Negative Numbers)
http://nlvm.usu.edu/en/nav/frames_asid_162_g_2_t_1.html 7.9
Subtraction of Positive and Negative Numbers)
http://www.ixl.com/math/grade-3/line-plots
7.10 (Line Plots)
www.everydaymathonline.com
Hillside Township School District
7.11 Broken Calculator
7.12 Top It (Positive/Negative Numbers)
TIMEFRAME
February
GRADE 5
CONTENT STRAND: Number and Operation - Fractions
UNIT 8: Fractions and Ratios
ENDURING UNDERSTANDINGS
•
Fractions, decimals, and percents express a relationship
between two numbers.
ESSENTIAL QUESTIONS
•
•
•
KNOWLEDGE
Students will know:
CCS
5.NF.4
5.NF.4A
5.NF.4B
5.NF.5
5.NF.5A
5.NF.5B
5.NF.6
5.NF.7
5.NF.7A
5.NF.7B
5.NF.7C
•
•
•
•
•
Add and subtract mixed numbers
Apply and extend previous understandings of
multiplication to multiply a fraction or mixed
number by a fraction
Multiply mixed numbers and fractions and
describe the algorithm used (a/b x c/d =
ac/bd)
Explain why multiplying a given number by a
fraction greater than one results in a product
that is greater than the given number
Explain why multiplying a given number by a
128
How is computation with rational numbers similar and
different to whole number computation?
How do I add/subtract fractions and mixed numbers with
like denominators?
What multiplication algorithms can be used to find the
product of whole numbers and mixed numbers?
SKILLS
Students will be able to:
•
•
•
•
•
•
•
Find equivalent fractions in simplest form
Rename fractions to have common denominators and
reduce to simplest form
Compare and order fractions and mixed numbers
Add/subtract fractions and mixed numbers
Convert between improper fractions and mixed numbers
Solve real world problems involving multiplication and
division of unit fractions, fractions and/or mixed numbers
Apply problem solving and critical thinking skills
Hillside Township School District
•
•
•
•
fraction less than one results in a product that
is less than the given number
Rename mixed numbers as a fraction
Recognize common denominators in a
problem and divide numerators to find an
answer.
Divide unit fractions by whole numbers and
whole numbers by unit fractions
Divide fractions and mixed numbers
Key Terms: Quick Common Denominator (QCD),
area model
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Summative Assessments
Unit 8 Progress Check
Slates/Oral Assessment
Interdisciplinary/Cross Curricular
8.4 Science, 8.11 S.S.
Portfolio
Assessment Handbook p.193
Writing Egyptian Fractions
Ongoing Assessment
8.2 MJ p.252 Exit Slip - Adding Mixed Numbers
8.4 TE p.637 Math Message - Order Fractions
8.5 MJ p.259 Problems 1-6 Fractional Parts on a
Number Line
8.6 MJ p.265 Area Model for Fraction Multiplication
8.7 MJ p.271 Math Boxes Problem 1 Convert
Fractions to
Decimals and Percents
129
INTERNET AND OTHER RESOURCES
http://exchange.smarttech.com/#tab=0 (Interactive Smartboard
Lessons)
http://www.aaamath.com/fra66dx2.htm 8.2 (Adding Mixed
Numbers)
http://www.aaamath.com/fra66ex2.htm 8.3 (Subtracting Mixed
Numbers) 8.4-8.8
http://www.mathplayground.com/fractions_mult.html (Multiplying
Fractions)
http://www.math-play.com/soccer-math-multiplying-fractionsgame/multiplying-fractions-game.html (Multiplying Fractions)
http://www.mathplayground.com/percent_shopping.html 8.9
(Finding the Percent of a Number)
http://www.mrnussbaum.com/tipster.htm 8.9 (Finding the
Percent of a Number)
http://www.funbrain.com/fractop/index.html 8.12 (Fraction
Division)
http://www.xpmath.com/forums/arcade.php?do=play&gameid=28
8.12 (Fraction Division)
http://nlvm.usu.edu/en/nav/category_g_2_t_1.html
www.everydaymathonline.com
Hillside Township School District
8.8 TE p.662 Exit Slip - Mixed Numbers
8.9 TE p.665 Mental Math and Reflexes - Convert
Fractions to
Decimals and Percents
8.10 MJ p.280 Unit Fractions & Unit Percents
8.12 MJ p.289 Problem 1and 2 Division of Fractions
Literature
Fraction Action, by Loreen Leedy
Gator Pie, by Louise Matthews
Eating Fractions, by Bruce McMillian
Only One, by Marc Harshmanm
www.emgames.com
8.1 Build-It
8.2 Fraction Capture
8.3 Mixed Number Spin
8.4 Fraction Action/Fraction Friction
8.5 Fraction Spin
8.7 Fraction Top It
8.8 Frac-Tac-Toe
8.10 Factor Captor
TIMEFRAME
March
130
Hillside Township School District
GRADE 5
CONTENT STRAND: Measurement and Data
UNIT 9A: Area, Volume, and Capacity
ENDURING UNDERSTANDINGS
•
•
ESSENTIAL QUESTIONS
Standard units of measure enable people to interpret results or
data.
Analyzing geometric relationships develops reasoning and
justification skills.
•
•
KNOWLEDGE
Students will know:
CCS
5.MD.3
5.MD.3A
5.MD.3B
5.MD.4
5.MD.5
5.MD.5A
5.MD.5B
5.MD.5C
•
•
•
•
•
•
•
•
•
•
How can I identify and apply the formula for the area of a
rectangle/triangle?
How do I develop and use a formula to find the volume of
a rectangle prism?
How can I calculate the volume of any prism?
SKILLS
Students will be able to:
Calculate the area of rectangles,
parallelograms and triangles
Recognize volume as an attribute of solid
figures
Understand the meaning of a cubic unit and the
concepts of volume measurement
Relate the magnitude of a cubic centimeter
Measure volume by counting unit cubes
Calculate the volume of prisms using the given
formula (V= l x w x h and V = b x h)
Calculate the volume of a rectangular and right
prism
Understand that volume is additive
Solve real world and mathematical problems
involving area and volume
Key Terms: area, square units, base, height,
formula, variable, volume, cubic unit, rectangular
131
•
•
•
•
•
•
•
Use a formula to calculate area
Compare inch and centimeter measures of length.
Measure and compare using customary and metric units
of capacity
Use and apply formulas
Use formulas to calculate volume of rectangular prisms
Write number sentences with variables to model volume
problems
Apply problem solving and critical thinking skills
Hillside Township School District
prism, face, base (of a rectangular prism), height
(of a rectangular prism), prism, face
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
INTERNET AND OTHER RESOURCES
Summative Assessments
Unit 9 Progress Check
Slates/Oral Assessment
http://exchange.smarttech.com/#tab=0 (Interactive Smartboard
Lessons)
http://www.aaamath.com/geo78_x3.htm 9.4 (Area of a
Rectangle)
http://www.aaamath.com/geo79_x7.htm 9.8 (Area of
Rectangular Prisms)
http://www.mathsisfun.com/geometry/prisms.html 9.9 (Volume
of Right Prisms) Notes and Practice
http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/math
s/measures/index.htm 9.10 Capacity: Liter, Milliliter, & Cubic
centimeter
www.everydaymathonline.com
Interdisciplinary/Cross Curricular
9.2 S.S, 9.5 & 9.10 Literature
Portfolio
Assessment Handbook p.198
Countertop Tiles
Ongoing Assessment
9.4 TE p.726 Exit Slip - Calculate Area
9.6 MJ p.314 Problem 2 and 3 Area Formula
9.10 TE p.763 Exit Slip - Volume and Capacity
Literature
Room for Ripley, by Stuart J. Murphy
G is for Googol, by David M. Schwartz
Spaghetti and Meatballs for All, by Marilyn Burns
Mr. Archimedes’ Bath, by Pamela Allen
www.emgames.com
9.5 Frac-Tac-Toe
9.6 Fraction Action/Fraction Friction
9.9 Polygon Capture
TIMEFRAME
Mid/March and Mid/April
132
Hillside Township School District
GRADE 5
CONTENT STRAND: Geometry
UNIT 9B: Coordinates
ENDURING UNDERSTANDINGS
•
ESSENTIAL QUESTIONS
Geometry and spatial sense offer ways to interpret and reflect
on our physical environment.
•
•
•
•
KNOWLEDGE
Students will know:
CCS
5.G.1
5.G.2
•
SKILLS
Students will be able to:
Understand the meaning and relationship of
the origin in a coordinate system to other
points within the coordinate plane
Write and plot ordered number pairs
Graph points on a coordinate plane
•
•
How can I locate ordered number pairs and coordinates
on a coordinate grid?
How can I plot number pairs to form a given figure?
How can a geometric shape be translated and
transformed?
What are the uses of a coordinate system?
Key Terms: coordinate grid, ordered number
pair, coordinate, axis, quadrant, transformation
•
•
•
•
•
•
•
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Understand and use positive and negative integers
Use ordered pairs of numbers to name, locate, and plot
points in the first quadrant of a coordinate grid
Represent real world and mathematical problems by
graphing points in a coordinate plane
Use geometric tools (rulers, protractor, compass)
Construct congruent figures on a coordinate grid
Describe translations and reflections of plane figures on a
coordinate grid
Apply problem solving and critical thinking skills
INTERNET AND OTHER RESOURCES
Summative Assessments
Unit 9 Progress Check
Slates/Oral Assessment
http://exchange.smarttech.com/#tab=0 (Interactive Smartboard
Lessons)
http://www.mathplayground.com/locate_aliens.html 9.1-9.3
(Coordinates)
133
Hillside Township School District
Ongoing Assessment
9.2 MJ p.298 Problems 2 and 3 Plot Ordered
Numbers
9.3 MJ p.301 Plot Points on a Coordinate Grid
http://www.mrnussbaum.com/stockshelves.htm 9.1- 9.3
(Coordinates)
http://www.oswego.org/ocsd-web/games/BillyBug2/bug2.html
9.1- 9.3 (Coordinates)
www.everydaymathonline.com
www.emgames.com
9.1 Hidden Treasure
9.3 Advance Hidden Treasure
TIMEFRAME
Mid/March and Mid/April
GRADE 5
CONTENT STRAND: Operations and Algebraic Thinking
UNIT 10: Using Data: Algebra Concepts Skills
ENDURING UNDERSTANDINGS
•
ESSENTIAL QUESTIONS
•
•
Real world situations can be represented symbolically and
graphically.
•
•
•
CCS
KNOWLEDGE
Students will know:
134
How do I represent rates with formulas, tables, and graphs?
How can I use a table and graph to solve and interpret a
problem based on a real-world situation?
How can I interpret line graphs?
How can I solve pan-balance problems that model sets of
two equations in two unknowns?
How do I translate word descriptions into algebraic
expressions?
SKILLS
Students will be able to:
Hillside Township School District
5.OA.1
5.OA.2
5.OA.3
•
•
•
•
•
•
•
Use table data to plot points on a graph
Read and interpret graphs
Extend graphed lines to see increase in
time and distance
Interpret mystery line plots and graphs
Solve one and two-step pan-balance
problems
Write algebraic expressions to represent
situations
Calculate the area and circumference of a
circle
•
•
•
•
•
•
•
•
•
•
Use table data and create line graphs
Represent functions with tables, graphs, and formulas
Extend patterns and graphs and tables to solve problems
Construct line graphs that repeat two sets of data
Read and analyze line graphs and answer questions based
on the data
Use all operations to solve pan-balance problems
Identify and use patterns to solve problems
Write algebraic expressions to model rules
Use variables to write number models that describe
situations
Apply problem solving and critical thinking skills
Key Terms: rate, rate of speed, formula,
variable, line graph, ordered number pairs,
coordinates, mystery graph, algebraic
expression
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Summative Assessments
Unit 10 Progress Check
Slates/Oral Assessment
INTERNET AND OTHER RESOURCES
http://exchange.smarttech.com/#tab=0 (Interactive Smartboard
Lessons)
http://www.gamequarium.com/data.html 10.4 (Rules, Tables and
Graphs)
Interdisciplinary/Cross Curricular
http://www.worldplenty.com/g59_cix1.htm 10.8 (Circumference of
10.1 S.S., 10.5 Science, 10.8 Literature
a Circle)
http://www.worldplenty.com/g5_612x1.htm 10.9 (Area of a Circle)
Portfolio
http://exchange.smarttech.com/#tab=0 (Interactive Smartboard
Assessment Handbook p.204
Lessons)
An Age Puzzle
http://illuminations.nctm.org/activitydetail.aspx?id=33 10.1 (Pan
Balance)
Ongoing Assessment
http://www.mathplayground.com/algebraic_reasoning.html 10.1
10.4 MJ p.348-349 Plotting Points on a Graph
(Pan Balance)
10.6 TE p.818 Exit Slip - Interpret Graphs
http://teams.lacoe.edu/documentation/classrooms/linda/algebra/ac
10.7 MJ p.356 Math Message - Interpret Line
tivities/balance/balance.html 10.1 (Pan Balance)
135
Hillside Township School District
Graphs
10.2 TE p.792 Math Message - Pan-Balance
Models
10.3 MJ p.341 Algebraic Expressions
http://www.math-play.com/Algebraic-ExpressionsMillionaire/algebraic-expressions-millionaire.html
10.3 (Algebraic Expressions)
www.everydaymathonline.com
Literature
The Librarian Who Measured the Earth, by
Kathryn Lasky
Sir Cumference and the First Round Table, by
Cindy Neuschwander
Sir Cumference and the Dragon of Pi: A Math
Adventure, by Cindy Neuschwander
www.emgames.com
10.1 First to 100
10.3 Name That Number
10.6 Mixed Number Spin
TIMEFRAME
Mid/April and Mid/May
GRADE 5
CONTENT STRAND: Measurement and Data
UNIT 11: Volume
ENDURING UNDERSTANDINGS
•
•
ESSENTIAL QUESTIONS
Standard units of measure enable people to interpret results or
data.
Analyzing geometric relationships develops reasoning and
justification skills.
CCS
KNOWLEDGE
Students will know:
136
•
•
•
How do I solve volume problems for prisms and
cylinders?
How do I determine the volume of an irregular object?
How can I convert and compare measurements units of
weight, capacity, and volume?
SKILLS
Students will be able to:
Hillside Township School District
5.MD.1
5.MD.3
5.MD.4
5.MD.5
5.G.3
5.G.4
•
•
•
•
•
Identify the attributes of geometric solids
Identify customary and metric units of capacity and weight
Explain differences and similarities between finding
volumes of cylinders and prisms
Use formulas to find volume of prisms and cylinders
Calculate the surface area of pyramids and prisms
•
•
•
•
•
Key Terms: geometric solid, prism, pyramid, cylinder, cone,
sphere, edge, vertex (vertices or vertexes), flat surface,
curved surface, face, polyhedron, cube
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
Summative Assessments
Unit 11 Progress Check
Slates/Oral Assessment
•
Use tables to collect and record data
Convert between inches, feet, and yards;
mm, cm. m, and km
Apply formulas to calculate volume of
prisms and cylinders
Use various methods to find volume of
irregular solids
Convert between standard units of capacity
and weight.
Apply problem solving and critical thinking
skills
INTERNET AND OTHER RESOURCES
http://exchange.smarttech.com/#tab=0 (Interactive
Smartboard Lessons)
http://gamequarium.org/geometry.html 11.1 – 11.2
(Geometry Games)
http://www.mrnussbaum.com/soda.htm 11.6
(Capacity and Weight)
www.everydaymathonline.com
Interdisciplinary/Cross Curricular
11.1 S.S., 11.5 Science, 11.2, 11.5 Literature
Portfolio
Assessment Handbook p.209
A Treasure Hunt
Ongoing Assessment
11.1 MJ p.369 Properties of Geometric Solids
11.2 MJ p.373 Properties of Prisms, Cylinders, and Cones
11.3 TE p.869 Exit Slip - Volume of Cylinders and Prisms
11.7 MJ p.389 Surface Area
MJ p.390 Measuring to the nearest ¼ in and 0.1 cm
Literature
137
Hillside Township School District
Flatland, by Edwin Abbott
Who Sank the Boat?, by Pamela Allen
The Boy Who Reserved Himself, by William Sleator
Sir Cumference and the Sword in the Cone, by Cindy
Neuschwander
www.emgames.com
11.2 3-D Shape Sort
11.4 Rugs and Fences
11.6 Name That Number
TIMEFRAME
May
GRADE 5
CONTENT STRAND: Number Operations - Fractions
UNIT 12: Probability, Ratios, and Rates
ENDURING UNDERSTANDINGS
•
ESSENTIAL QUESTIONS
Proportional relationships express how quantities change in
relationship to each other.
•
•
•
•
CCS
KNOWLEDGE
Students will know:
When and why do I use proportional comparisons?
How do I use and express ratios?
How can I solve problems involving ratios of part of a set to
the whole set?
How can I write and solve number models for ratio number
stories?
SKILLS
Students will be able to:
138
Hillside Township School District
5.NF.1
5.NF.2
5.NF.3
•
•
•
•
•
•
Determine the probability of a given event
Convert between fractions, decimals, and
percents
Solve ratio problems
Solve ratio and rate number stories
•
•
•
Write ratios in equivalent forms
Use equivalent fractions and ratio models to solve fractions
of problems
Model and solve ratio problems
Graph and interpret data
Apply problem solving and critical thinking skills
Key Terms: ratio, ratio comparison, magnitude
ASSESSMENTS/PERFORMANCE TASKS/
INTERDISCIPLINARY CONNECTIONS
INTERNET AND OTHER RESOURCES
Summative Assessments
Unit 12 Progress Check
Slates/Oral Assessment
http://exchange.smarttech.com/#tab=0 (Interactive Smartboard
Lessons)
http://nlvm.usu.edu/en/nav/frames_asid_202_g_2_t_1.html?from=c
ategory_g_2_t_1.html 12.1 (Factor Trees)
http://www.mathplayground.com/factortrees.html 12.1 (Factor
Trees)
http://www.mrnussbaum.com/cardsharks.htm 12.2 (Probability)
www.everydaymathonline.com
Interdisciplinary/Cross Curricular
12.3 LAL, 12.2, 12.8 Literature, 12.3 S.S., 12.6,
12.7 Health, 12.8 Science
Portfolio
Assessment Handbook p.215
Counting Cars
Ongoing Assessment
12.1 MJ p.394 Problem 4 Factor Tree and Prime
Factorization
12.2 MJ p.398 Math Message - Probability
12.4 MJ p.408 Ratio Problems
Literature
Jumanji, by Chris Van Allsburg
If You Hopped Like a Frog, by David M. Schwartz
Do You Wanna Bet? Your Chance to Find Out
About Probability, by Martha Wetson
139
Hillside Township School District
www.emgames.com
12.1 Factor Captor
12.3 First to 100
12.6 Spoon Scramble
12.8 Coordinate Search
TIMEFRAME
June
140