EAST ALLEN COUNTY SCHOOLS
Bundle 3
Grade 3
Math
Solving Problems with Patterns
and Inverse Relationships
Big Idea: Relationships
Enduring Understandings
Essential Questions
Growing and repeating patterns can be identified, described, and extended with
words and symbols.
When are patterns used in our daily lives?
Patterns are used to predict outcomes.
Where in the real world do we see things multiply?
Multiplication and division are based on properties, patterns, and number
relationships.
Where in the real world do we see things divide?
What strategies do you use to identify, extend, or create a pattern?
How do mathematicians communicate their thinking about math on paper?
Real-world math problems can be translated into mathematical equations.
Mathematical situations can be represented using variables, expressions, and
equations.
CC/Learning Targets
*3.2.2
*3.2.3
*3.2.4
*3.2.5
3.2.7.
3.OA.1
3.OA.2
*3.3.1
*3.3.2
*3.3.4
*3.3.5
3.OA.3
3.OA.5
*3.3.6
*3.6.1-3.6.9
3.OA.4
3.OA.6
3.OA.7
3.OA.8
3.OA.9
Core Vocabulary
division
multiplication
Links to Technology
-Third Grade IXL website for all skills
-My Math Flashcards (app)
-Conundra Math (app) (all operations- challenging)
-Educreation Interactive Whiteboard app
-Division!! App
-Fun Brain website for all skills
Bundle Performance Task(s)
You really want to go on a field trip to Cedar Point, and you have to earn money so that you can attend. In your small group, you need to make a choice between
two jobs to make your money: walking dogs and mowing yards. You will earn $3 per walk. If you choose to mow, you will make $6 each time, and you will be
expected to mow only four times. You are a true animal lover and really want to walk the dogs. So you have to determine how many times you need to walk the
dogs in order to make the same amount as you would if you chose to mow lawns. Write an equation to determine the number of times you would need to walk the
dogs. Check your solution by using the inverse relationship. Finally, use manipulatives or draw an illustration to communicate your thinking about solving the
problem and share your reasoning with another group on why your solution is reasonable.
As an extension, ask students to present their mathematical thinking to the class using the “Poster Method” described in Balanced Math.
Grade 3
Math Bundle 3
Quarter 2
Oct.-Dec.
Recommended Read-Alouds
G3 - Bundle 3
Big Idea: Relationships
Title
Relates to…
Author
A Remainder of One
Elinor J. Pinczes
Division
Cheetah Math Learning About Division from Baby Cheetahs
Ann Whitehead Nagda
Division
Divide and Ride
Stuart J. Murphy
Division
Great Divide
Pat Hutchins
Division
One Hundred Hungry Ants
Elinor J. Pinczes
Division
One of Each
Mary Ann Hoberman
Division
The Best Vacation Ever
Stuart J. Murphy
Division
The Doorbell Rang
Pat Hutchins
Division
The Rainbow Fish
Marcus Pfister
Division
The Great Tak e-Away
Louise Mathews
Equations
Twelve Ways to Get to Eleven
Eve Merriam
Equations
Anno’s Counting House
Mitsumasa Anno
Expressions, Equations
Dinosaur Deals
Stuart J. Murphy
Expressions, Equations
Ready, Set, Hop!
Stuart J. Murphy
Expressions, Equations
2x2=BOO! A Set of Multiplication Stories
Loreen Leedy
Multiplication
Recommended Read-Alouds
G3 - Bundle 3
Amanda Bean’s Amazing Dream: A Mathematical Story
Cindy Neuschwander
Multiplication
Bats on Parade
Appelt
Multiplication
Each Orange Has 8 Slices
Paul Giganti, Jr.
Multiplication
Multiplication Made Easy
Rebecca Wingard-Nelson
Multiplication
The Best of Times: Math Strategies that Multiply
Greg Tang
Multiplication
The King’s Commissioners
Aileen Friedman
Multiplication
Two of Everything
Lily T. Hong
Multiplication
Math Potatoes: Mind Stretching Brain Food
Greg Tang
Patterns
The Grapes of Math: Mind Stretching Math Riddles
Greg Tang
Patterns
Math
G3 - Bundle 3
CC/Learning Targets
3.2.2
-Five Easy Steps to a Balanced Math Program for Upper Elementary
Grades pp. 3-28
a. Represent the concept of
multiplication as equal groups using
pictures or objects.
-Each Orance Has 8 Slices by Paul Giganti, Jr.
-Bats on Parade by Appelt
-Amanda Bean’s Amazing Dream: A Mathematical Story by Cindy
Neuschwander
-The Best of Times: Math Strategies that Multiply by Greg Tang
-2x2=BOO! A Set of Multiplication Stories by Loreen Leedy
-Two of Everything by Lily T. Hong
-The King’s Commissioners by Aileen Friedman
b. Represent the concept of
multiplication as equal groups using
repeated addition.
c. Represent the concept of
multiplication as a rectangular array.
d. Represent the concept of
multiplication as equal hops on a number
line.
(3.OA.1)
(3.OA.3)
Resource of Ideas
Represent the concept of multiplication
as repeated addition.
Interpret products of whole
numbers, e.g., interpret 5 x
7 as the total number of
objects in 5 groups of 7
objects each.
Use multiplication and
division within 100 to solve
word problems in situations
involving equal groups,
arrays, and measurement
quantities, e.g., by using
drawings and equations
with a symbol for the
unknown number to
represent the problem
-Multiplication Practice
-Multiplication Games
-Mutliplication Activities
-Houghton Mifflin Math website
- IDOE Resources
rd
-3rd Grade Indiana Math Skills (click on Indiana, then click on 3 grade,
scroll down to the indicator of your choice)
-How Multiplying Works
-Math Multiplication and Division Activities
- enVisionMATH
Lessons 4.1 - 4.5
Lessons 5.1 - 5.7
Lessons 6.1 - 6.8
Lesson 7.3
Lesson 8.1, 8.6, 8.8
-Houghton Mifflin Math
Lessons 8.1 - 8.6
Lessons 9.2 - 9.6
Lessons 21.1 - 21.2, 21.7
Evidence of Learning
- enVisionMATH pp. 112-114,
136-138, 166-168, 186-188,
216-218
-Houghton Mifflin Math Chapter
Review/Test pp. 228-229
-Houghton Mifflin Math Chapter
Review/Test pp. 256-257
-Students create patterns using
symbols or shapes for a pattern to
solve
-Pocket Day (scroll down to pp.
11-13)
-Barnyard Legs (scroll down to p.
14)
-Tile Arrays activity from
Houghton Mifflin Math p. 208B
-Gravity and Weight activity from
Houghton Mifflin Math p. 236B
-Write number sentences to show
how many days in one week, in
two weeks, etc.
-Daily Math Review
Math
3.2.3
Represent the concept of division as
repeated subtraction, equal sharing, and
forming equal groups.
a. Represent the concept of division as
equal sharing.
b. Represent the concept of division as
forming equal groups.
c. Represent the concept of division as
repeated subtraction.
(3.OA.2)
(3.OA.3)
3.2.4
Interpret whole-number
quotients of whole numbers,
e.g., interpret 56 ÷ 8 as the
number of objects in each
share when 56 objects are
partitioned equally into 8
shares, or as a number of
shares when 56 objects are
partitioned into equal shares
of 8 objects each.
Use multiplication and
division within 100 to solve
word problems in situations
involving equal groups,
arrays, and measurement
quantities, e.g., by using
drawings and equations
with a symbol for the
unknown number to
represent the problem
Know and use the inverse relationship
G3 - Bundle 3
-Five Easy Steps to a Balanced Math Program for Upper Elementary
Grades pp. 3-28
-Divide and Ride by Stuart J. Murphy
-The Doorbell Rang by Pat Hutchins
-A Remainder of One by Elinor J. Pinczes
-One Hundred Hungry Ants by Elinor J. Pinczes
-Great Divide by Hutchins
-One of Each by Mary Ann Hoberman
-The Rainbow Fish by Marcus Pfister
-Cheetah Math Learning About Division from Baby Cheetahs by Ann
Whitehead Nagda
-The Best Vacation Ever by Stuart J. Murphy
- enVisionMATH pp. 186-188,
216-218
-Houghton Mifflin Math Chapter
Review/Test pp. 282-283
-Houghton Mifflin Math Chapter
Review/Test pp. 314-315
-Multiply or Divide Tiles activity
from Houghton Mifflin Math p.
264B
-Daily Math Review
-Division Practice
-Division Activities
-Houghton Mifflin Math website
-IDOE Resource
rd
-3rd Grade Indiana Math Skills (click on Indiana, then click on 3 grade,
scroll down to the indicator of your choice)
-Math Multiplication and Division Activities
- enVisionMATH
Lessons 7.1 - 7.6
Lessons 8.1 - 8.9
-Houghton Mifflin Math
Lessons 10.1 - 10.2, 10.4, 10.6 - 10.7, 10.9
Lessons 11.3 - 11.5, 11.7 - 11.9
Lessons 22.1 - 22.2
-Five Easy Steps to a Balanced Math Program for Upper Elementary
- enVisionMATH pp. 186-188,
Math
G3 - Bundle 3
between multiplication and division facts.
Grades pp. 3-28
a. Explain the inverse relationship
between multiplication and division facts.
-Houghton Mifflin Math website
-IDOE Resource
-IDOE Resource
rd
-3rd Grade Indiana Math Skills (click on Indiana, then click on 3 grade,
scroll down to the indicator of your choice)
(3.OA.7)
b. Write a related division fact for a give
multiplication fact.
c. Write a related multiplication fact for a
given division fact.
216-218
-Houghton Mifflin Math Chapter
Review/Test pp. 282-283
-Houghton Mifflin Math Chapter
Review/Test pp. 314-315
-Fact Family Fun activity from
Houghton Mifflin Math p. 288B
-Daily Math Review
- enVisionMATH
Lesson 7.3
Lesson 8.1
-Houghton Mifflin Math
Lesson 10.3
Lessons 11.1 - 11.2
3.2.5
Show mastery of multiplication facts for
2, 5, and 10.
(3.OA.7)
a. Show mastery of multiplication facts
for two.
b. Show mastery of multiplication facts
for five.
c. Show mastery of multiplication facts
for ten.
3.2.7
Use estimation to decide whether
answers are reasonable in addition and
subtraction problems.
a. Determine whether answers are
-Houghton Mifflin Math website
-IDOE Resource
rd
-3rd Grade Indiana Math Skills (click on Indiana, then click on 3 grade,
scroll down to the indicator of your choice)
-Crickweb Math Teacher's Toolkit (click on tables tester, or click on
double
dutch counting machine)
- enVisionMATH
Lessons 5.1, 5.4 - 5.5
-Houghton Mifflin Math
Lessons 8.3, 8.5 - 8.6
-Five Easy Steps to a Balanced Math Program for Upper Elementary
Grades pp. 3-28
-Houghton Mifflin Math website
rd
-3rd Grade Indiana Math Skills (click on Indiana, then click on 3 grade,
- enVisionMATH pp. 136-138
-See Appendix
-Houghton Mifflin Math Chapter
Review/Test pp. 228-229
-Multiplication Top-It activity from
Houghton Mifflin Math p. 202D
-Soccer Math activity from
Houghton Mifflin Math p. 230D
-Daily Math Review
-Play a game of Around the World
-Play a game of I Have-Who Has
-enVisionMATH pp. 60-62
-Houghton Mifflin Math Chapter
Review/Test pp. 104-105
-Houghton Mifflin Math Chapter
Review/Test pp. 132-133
Math
reasonable in addition and subtraction
problems using rounding, front-end
estimation and convenient (sometimes
called friendly or compatible) numbers.
G3 - Bundle 3
scroll down to the indicator of your choice)
-Comparing Numbers Activity (click on comparing numbers or click on
estimate)
-Math Songs
- enVisionMATH
Lessons 2.6 - 2.7, 2.9
3.3.1
Represent relationships of quantities in
the form of a numeric expression or
equation.
a. Identify an expression and an
equation.
b. Write an expression and an equation
with an unknown quantity (variable) to
match a given situation.
3.3.2
Solve problems involving numeric
equations.
a. Solve for an unknown quantity
(variable) when given an equation.
-Houghton Mifflin Math
Enrichment p. 67
Lessons 4.2, 4.9
Lesson 5.3
-Five Easy Steps to a Balanced Math Program for Upper Elementary
Grades pp. 3-28
-Ready, Set, Hop! by Stuart J. Murphy
-Anno’s Counting House by Mitsumasa Anno
-Dinosaur Deals by Stuart J. Murphy
-Houghton Mifflin Math website
-Indiana Resource
-IDOE Resource
rd
-3rd Grade Indiana Math Skills (click on Indiana, then click on 3 grade,
scroll down to the indicator of your choice)
- enVisionMATH
Lesson 7.4
Lessons 8.6, 8.8
-Five Easy Steps to a Balanced Math Program for Upper Elementary
Grades pp. 3-28
-Ready, Set, Hop! by Stuart J. Murphy
-Anno’s Counting House by Mitsumasa Anno
-The Great Take-Away by Louise Mathews
-Match numbers with estimated
answers
-Observe students playing Roll
and
Play activity from Houghton Mifflin
Math p. 72D
-Daily Math Review
- enVisionMATH pp. 186-188,
216-218
-Students create simple
expressions or equations for
partners to solve
-Daily Math Review
-Quiz
-Have students create numeric
expressions or equations for a
partner to solve
-Students create simple
expressions or equations for
partners to solve
-Daily Math Review
-Quiz
- enVisionMATH pp. 186-188,
Math
G3 - Bundle 3
-Twelve Ways to Get to Eleven by Eve Merriam
-Dinosaur Deals by Stuart J. Murphy
-Houghton Mifflin Math website
-Indiana Resource
-IDOE Resource
rd
-3rd Grade Indiana Math Skills (click on Indiana, then click on 3 grade,
scroll down to the indicator of your choice)
216-218
-Houghton Mifflin Math Chapter
Review/Test pp. 256-257
-Have students create numeric
expressions or equations for a
partner to solve
- enVisionMATH
Lesson 7.4
Lessons 8.6, 8.8 - 8.9
3.3.4
(3.OA.5)
(3.OA.7)
Understand and use the commutative
and associative properties of
multiplication.
-Houghton Mifflin Math
Lesson 9.8
-Five Easy Steps to a Balanced Math Program for Upper Elementary
Grades pp. 3-28
-Multiplication Made Easy by Rebecca Wingard-Nelson
Apply properties of
operations as strategies to
multiply and divide.
Fluently multiply and divide
within 100, using strategies
such as the relationship
between multiplication and
division (e.g., knowing that
8 x 5 = 40, one knows 40 ÷
5 = 8) or properties of
operations. By the end of
Grade 3, know from
memory all products of two
one-digit numbers.
-Houghton Mifflin Math website
-IDOE Resource
rd
-3rd Grade Indiana Math Skills (click on Indiana, then click on 3 grade,
scroll down to the indicator of your choice)
- enVisionMATH
Lesson 4.3
Lesson 6.6
-Houghton Mifflin Math
Lesson 8.8
Lesson 9.8
- enVisionMATH pp. 112-114,
166-168
-Houghton Mifflin Math Chapter
Review/Test pp. 228-229
-Houghton Mifflin Math Chapter
Review/Test pp. 256-257
-Students create examples for
partner or class to decide which
property they used
-Daily Math Review
Math
3.3.5
G3 - Bundle 3
Create, describe, and extend number
patterns using multiplication.
-Five Easy Steps to a Balanced Math Program for Upper Elementary
Grades pp. 3-28
a. Extend number patterns using
multiplication.
-The Grapes of Math: Mind Stretching Math Riddles by Greg Tang
-Math Potatoes: Mind Stretching Brain Food by Greg Tang
b. Create number patterns using
multiplication.
-Number Sequencing
-Finding the Next Number
-Houghton Mifflin Math website
-IDOE Resources
rd
-3rd Grade Indiana Math Skills (click on Indiana, then click on 3 grade,
scroll down to the indicator of your choice)
-Comparing Numbers Activity (click on patterns, counting stick, snowflake
sequences, or cheeky monkey number sentences)
-Math Pattern Activities
c. Describe the patterns created and
extended using multiplication.
- enVisionMATH pp. 112-114,
136-138
-Houghton Mifflin Math Chapter
Review/Test pp. 256-257
-Students create examples for
partner or class to decide which
property they used
-Draw to Count By activity from
Houghton Mifflin Math p. 202D
-Count Up activity from
Houghton Mifflin Math p. 204D
-Daily Math Review
-Students create patterns using
symbols or shapes for a pattern to
solve
- enVisionMATH
Lesson 4.5
Lessons 5.1 - 5.5
-Houghton Mifflin Math
Lesson 1.5 (Find a Number Pattern)
Lessons 9.1, 9.5
3.3.6
Solve simple problems involving a
functional relationship between two
quantities.
a. Solve simple problems involving a
functional relationship between two
quantities.
-Five Easy Steps to a Balanced Math Program for Upper Elementary
Grades pp. 3-28
-Number Sequencing
-Finding the Next Number
-Houghton Mifflin Math website
-IDOE Resources
rd
-3rd Grade Indiana Math Skills (click on Indiana, then click on 3 grade,
scroll down to the indicator of your choice)
- enVisionMATH pp. 136-138,
186-188
-Daily Math Review
-Quiz
Math
G3 - Bundle 3
- enVisionMATH
Lesson 5.7
Lesson 7.4
3.6.13.6.9
Problem Solving
-Houghton Mifflin Math
Lesson 21.8
Lesson 22.8
-The Problem Solver 3: Activities for Learning Problem-Solving
Strategies
-Five Easy Steps to a Balanced Math Program for Upper Elementary
Grades pp. 29-69, 131-139
rd
-3rd Grade Indiana Math Skills (click on Indiana, then click on 3 grade,
scroll down to the indicator of your choice)
- enVisionMATH
Lesson 4.5
Lesson 6.9
Lessons 7.4, 7.6
Lessons 8.5, 8.9
3.OA.4
3.OA.6
Determine the unknown whole number in
a multiplication or division equation
relating three whole numbers. For
example, determine the unknown
number that makes the equation true in
each of the equations 8 × ? = 48, 5 = ÷
3, 6 × 6 = ?.
Understand division as an unknownfactor problem. For example, find 32 ÷ 8
by finding the number that makes 32
-Houghton Mifflin Math
Lesson 18.4 (Make it Simpler with Multistep Problems)
Lesson 19.3 (Act It Out)
-Houghton Mifflin Math
Lesson 10.3
Lesson 11.2
-Houghton Mifflin Math
Lesson 10.3
Lesson 11.2
-See Problem Solving Template in
Appendix
-Problem Solver Activities
-Evidence in a math journal
-Observation of students
participating in Poster Method
problem solving
Math
G3 - Bundle 3
when multiplied by 8.
3.OA.8
3.OA.9
Solve two-step word problems using the
four operations. Represent these
problems using equations with a letter
standing for the unknown quantity.
Assess the reasonableness of answers
using mental computation and estimation
strategies including rounding.
Identify arithmetic patterns (including
patterns in the addition table or
multiplication table), and explain them
using properties of operations. For
example, observe that 4 times a number
is always even, and explain why 4 times
a number can be decomposed into two
equal addends.
Correlating CC/Learning Targets
3.1.1
3.1.2
3.2.1
3.2.8
3.3.3
3.4.6
3.4.7
3.NBT.2
3.5.1
3.MD.4
-Houghton Mifflin Math
Multiplication; Lessons 8.1,8.3, 8.4, 8.6, 9.3, 9.5
Teacher Notes
Five Easy Steps to a Balanced Math Program for Upper Elementary Grades pp. 71-96