TIPS4Math
Compose/Decompose, Represent, Compare and Order Numbers to 100
Grade 3
Overall Expectation
Students will:
• Read, represent, compare, and order whole numbers to [100]1000, and use concrete materials to represent fractions and [whole
number] money amounts to $10 (3m8)
Specific Expectations
Students will:
• Represent, compare, and order whole numbers to [100] 1000, using a variety of tools (3m11)
• Identify and represent the value of a digit in a number according to its position in the number (3m13)
• Compose and decompose three-digit numbers [up to 100] into hundreds, tens, and ones in a variety of ways, using concrete
materials (3m14)
• Round two-digit numbers to the nearest ten, in problems arising from real-life situations (3m15)
Lesson
Represent Numbers to •
100
•
EduGAINS-Mathematics
Learning Focus
Create representations of whole numbers
in a variety of ways using manipulatives
(concrete/digital) and pictures
o identify the strategy used to create the
representation (e.g., counting,
decomposing/composing, computational
strategies)
Communicate using pictures, words (oral
and written), symbols
Resource
Guide to Effective Instruction: Number Sense and
Numeration Grades 1 to 3
• pp 131 - 117 Mystery Bags
• p 135 Mystery Numbers
• p 138 Number Detective
mathies
• Catch a Bouncing Ball Representations - Whole
Numbers
• Colour Tiles
• Money Tool
• Number Line
• Rekenrek
• Set Tool
• Whole Number Rods
Page 1 of 12
TIPS4Math
Grade 3
Compose/Decompose, Represent, Compare and Order Numbers to 100 (continued)
Lesson
Compose and
Decompose Numbers
to 100
•
•
•
Represent Numbers to •
100 Using
Mathematical
Structures that
Reinforce Anchors of
5 and 10
Represent Numbers to •
100 Using
Mathematical
Structures that
Reinforce Anchors of
5 and 10 –
Continued
•
EduGAINS-Mathematics
Learning Focus
Create representations of whole numbers
Decompose a number in a variety of ways
Identify how the numbers were composed
and decomposed including:
o friendly numbers
o place value
o anchors of 5s and 10s
o two or more terms
o representations that involve the same
and different terms
Resource
Guide to Effective Instruction: Number Sense and
Numeration Grades 1 to 3
• p 135 Mystery Numbers
mathies
• Colour Tiles
• Money Tool
• Number Line
• Rekenrek
• Set Tool
• Whole Number Rods
mathies
• Rekenrek
• Set Tool
Create and read representations of whole
numbers in a variety of ways using:
o manipulatives with mathematical
structures that reinforce anchors of 5s
OERB
and 10s (concrete/digital)
• Street Crossing
o pictures
Identify the strategy used to create the
o OERB ID: ELO1298050
representation (e.g., counting,
decomposing/composing, computational
strategies)
o communicate using pictures, words (oral
and written), symbols
o compose and decompose into 10s and
1s
o identify how the components of the
representation connect to the digits in
the numerical representation
Identify a number that has been
represented concretely, digitally or
pictorially and provide reasoning
o relate numbers to anchors of 5s and 10s
Page 2 of 12
TIPS4Math
Grade 3
Compose/Decompose, Represent, Compare and Order Numbers to 100 (continued)
Lesson
Represent Numbers to •
100 Using Tools that
Support Place Value
Represent Numbers to
100 Using Tools that
Support Place Value Continued
•
EduGAINS-Mathematics
Learning Focus
Create and read representations of whole
numbers in a variety of ways using
concrete/digital manipulatives and/or
pictures that reinforce place value (e.g.
base ten blocks, money - penny, dime; or
loonie, $10 bill, mathies Colour Tiles – x1,
x10)
o identify the strategy used to create the
representation (e.g., counting,
decomposing/composing, computational
strategies)
o communicate using pictures, words (oral
and written), symbols
o compose and decompose into 10s and
1s
o identify how the components of the
representation connect to the digits in
the numerical representation
Identify a number that has been
represented concretely, digitally or
pictorially and provide reasoning
Resource
Guide to Effective Instruction: Number Sense and
Numeration Grades 1 to 3
• p 135 Countdown to Zero
• p 139 Let’s Get Loonie
mathies
• Colour Tiles
• Money Tool
Page 3 of 12
TIPS4Math
Grade 3
Compose/Decompose, Represent, Compare and Order Numbers to 100 (continued)
Lesson
Represent Numbers to •
100 in Flexible Ways
Represent Numbers to
100 in Flexible Ways –
Continued
•
•
•
EduGAINS-Mathematics
Learning Focus
Create and read representations of whole
numbers in a variety of ways using
concrete/digital manipulatives and/or
pictures which allow the user to compose
representations in flexible ways
Identify the strategy used to create a
representation (e.g., relationship to other
numbers including to the nearest ten,
counting, decomposing/composing,
computational strategies)
o communicate using pictures, words (oral
and written), symbols
Recompose a representation into 10s and
1s
o identify how the components of the
representation connect to the digits in
the numerical representation
Identify a number that has been
represented concretely, digitally or
pictorially and provide reasoning
Resource
Guide to Effective Instruction:
Number Sense and Numeration Grades 1 to 3
• p 138 Number Detective
mathies
• Colour Tiles
• Money Tool
• Rekenrek
• Set Tool
• Whole Number Rods
Page 4 of 12
TIPS4Math
Grade 3
Compose/Decompose, Represent, Compare and Order Numbers to 100 (continued)
Lesson
Compare and Order
•
Numbers to 100 Based
on Quantity
•
•
•
•
EduGAINS-Mathematics
Learning Focus
Read numbers represented in various
formats (numerical, pictorial, concrete/
digital) and compare those numbers with
reasoning
o same representation model
o different representation model
Explain why one number is greater than, less
than or equal to another number
Identify values between any two given
numbers
Identify the multiples of ten that are directly
less than and greater than a given number
o name the closest multiple of ten
Order numbers presented in various formats
(numerical, pictorial, concrete/digital) and
explain reasoning
o least to greatest and greatest to least
Resource
Guide to Effective Instruction: Number Sense and
Numeration Grades 1 to 3
• p 138 Luck of the Draw
mathies
• Diamond Drop - Whole Numbers
• Colour Tiles
• Money Tool
• Rekenrek
• Set Tool
• Whole Number Rods
Page 5 of 12
TIPS4Math
Grade 3
Compose/Decompose, Represent, Compare and Order Numbers to 100 (continued)
Lesson
Represent Numbers to •
100 Using a Number
Line
•
•
•
EduGAINS-Mathematics
Learning Focus
Represent and read a whole number as a
position relative to zero on a number line
o paper/digital
o variety of scales starting from zero
o without all ticks identified
Represent and read a whole number as a
distance from zero on a number line
o paper/digital
o variety of scales starting from zero
o without all ticks identified
Identify the strategy used to represent a
number on a number line (e.g., relationship
to other numbers including to the nearest ten,
counting, decomposing/composing,
computational strategies)
o communicate using pictures, words (oral
and written), symbols
Represent numbers presented in various
formats (numerical, pictorial, concrete/digital)
on a number line and explain reasoning
o variety of scales from zero
o with and without all ticks identified
Resource
mathies
• Catch a Bouncing Ball Representations Whole Numbers
• Number Line
Page 6 of 12
TIPS4Math
Grade 3
Compose/Decompose, Represent, Compare and Order Numbers to 100 (continued)
Lesson
Compare and Order
•
Numbers to 100 Using
a Number Line
•
•
•
•
EduGAINS-Mathematics
Learning Focus
Resource
mathies
Compare numbers represented on a number
• Number Line
line
• Comparison Tool - Whole Numbers
o use comparative language and symbols
o provide reasoning (e.g., distance from zero,
further to the right on the number line,
relationships to benchmarks)
Read numbers represented in various formats
(numerical, pictorial, concrete/digital) and
compare those numbers using a number line
o use comparative language and symbols
o provide reasoning (e.g., distance from zero,
further to the right on the number line,
relationships to benchmarks)
Identify values between any two given
numbers
Identify the multiples of ten that are directly
less than and greater than a given number
o name the closest multiple of ten
Read numbers represented in various formats
(numerical, pictorial, concrete/digital) and order
those numbers using a number line
o least to greatest and greatest to least
o provide reasoning
Page 7 of 12
TIPS4Math
Grade 3
Compose/Decompose, Represent, Compare and Order Numbers to 100 (continued)
Lesson
Learning Focus
Solve Problems
•
Involving Rounding to
the Nearest Ten
Solve problems from real-life situations where
a number is compared to given consecutive
multiples of ten (e.g., Robin is 34 years old. Is
Robin closer in age to Tobias who is 30 or to
Noa who is 40?)
o represent the numbers using an appropriate
format (numerical, pictorial, concrete/digital)
o compare the numbers
o provide reasoning
•
Solve problems from real-life situations where
a two-digit number is rounded to the nearest
ten (e.g., Kumiko has 27 stickers. Round the
number of stickers to the nearest ten. By what
amount did you round up or down?)
o verify the solution
establish the convention that when the ones
digit is five round up
EduGAINS-Mathematics
Resource
mathies
• Colour Tiles
• Money Tool
• Number Line
• Rekenrek
• Set Tool
• Whole Number Rods
Page 8 of 12
TIPS4Math
Represent Numbers to 100
Resource
Guide to Effective Instruction: Number
Sense and Numeration Grades 1 to 3
mathies:
Catch a Bouncing Ball Representations
– Whole Numbers
mathies:
Colour Tiles
mathies:
Money Tool
mathies:
Number Line
mathies:
Rekenrek
mathies:
Set Tool
mathies:
Whole Number Rods
EduGAINS-Mathematics
Grade 3
URL
http://oame.on.ca/eduproject/ontariomathedresources/files/Number%20Sense%20and%20
Numeration%201-3%20Revised.pdf
http://mathies.ca/games.php#Cc0
http://mathies.ca/learningTools.php
http://mathies.ca/learningTools.php#Mm0
http://mathies.ca/learningTools.php#Nn0
http://mathies.ca/learningTools.php#Rr0
http://mathies.ca/learningTools.php#Ss1
http://mathies.ca/learningTools.php#Ww0
Page 9 of 12
TIPS4Math
Compose and Decompose Numbers to 100
Resource
URL
Guide to Effective Instruction: Number
Sense and Numeration Grades 1 to 3
mathies:
Colour Tiles
mathies:
Money Tool
mathies:
Rekenrek
mathies:
Set Tool
mathies:
Whole Number Rods
Grade 3
http://oame.on.ca/eduproject/ontariomathedresources/files/Number%20Sense%20and%20
Numeration%201-3%20Revised.pdf
http://mathies.ca/learningTools.php
http://mathies.ca/learningTools.php#Mm0
http://mathies.ca/learningTools.php#Rr0
http://mathies.ca/learningTools.php#Ss1
http://mathies.ca/learningTools.php#Ww0
Represent Numbers to 100 Using Mathematical Structures that Reinforce Anchors of 5 and 10
Resource
URL
mathies:
Rekenrek
mathies:
Set Tool
OERB:
Street Crossing
http://mathies.ca/learningTools.php#Rr0
http://mathies.ca/learningTools.php#Ss1
https://download.elearningontario.ca/repository/12/1298050000/streetCrossing%20-%20v02.
html
Represent Numbers to 100 Using Tools that Support Place Value
Resource
URL
Guide to Effective Instruction: Number
Sense and Numeration Grades 1 to 3
mathies:
Colour Tiles
mathies:
Money Tool
EduGAINS-Mathematics
http://oame.on.ca/eduproject/ontariomathedresources/files/Number%20Sense%20and%20
Numeration%201-3%20Revised.pdf
http://mathies.ca/learningTools.php
http://mathies.ca/learningTools.php#Mm0
Page 10 of 12
TIPS4Math
Represent Numbers to 100 in Flexible Ways
Resource
URL
Guide to Effective Instruction: Number
Sense and Numeration Grades 1 to 3
mathies:
Colour Tiles
mathies:
Money Tool
mathies:
Rekenrek
mathies:
Set Tool
mathies:
Whole Number Rods
Grade 3
http://oame.on.ca/eduproject/ontariomathedresources/files/Number%20Sense%20and%20
Numeration%201-3%20Revised.pdf
http://mathies.ca/learningTools.php
http://mathies.ca/learningTools.php#Mm0
http://mathies.ca/learningTools.php#Rr0
http://mathies.ca/learningTools.php#Ss1
http://mathies.ca/learningTools.php#Ww0
Compare and Order Numbers to 100 Based on Quantity
Resource
URL
Guide to Effective Instruction: Number
Sense and Numeration Grades 1 to 3
mathies:
Colour Tiles
mathies:
Money Tool
mathies:
Rekenrek
mathies:
Set Tool
mathies:
Whole Number Rods
EduGAINS-Mathematics
http://oame.on.ca/eduproject/ontariomathedresources/files/Number%20Sense%20and%20
Numeration%201-3%20Revised.pdf
http://mathies.ca/learningTools.php
http://mathies.ca/learningTools.php#Mm0
http://mathies.ca/learningTools.php#Rr0
http://mathies.ca/learningTools.php#Ss1
http://mathies.ca/learningTools.php#Ww0
Page 11 of 12
TIPS4Math
Represent Numbers to 100 Using a Number Line
Resource
URL
Grade 3
mathies:
http://mathies.ca/games.php#Cc0
Catch a Bouncing Ball Representations
– Whole Numbers
mathies:
http://mathies.ca/learningTools.php#Nn0
Number Line
Compare and Order Numbers to 100 Using a Number Line
Resource
URL
mathies:
Number Line
mathies:
Comparison Tool – Whole Numbers
http://mathies.ca/learningTools.php#Nn0
http://mathies.ca/learningTools.php
Solve Problems Involving Rounding to the Nearest Ten
Resource
URL
mathies:
Colour Tiles
mathies:
Money Tool
mathies:
Number Line
mathies:
Rekenrek
mathies:
Set Tool
mathies:
Whole Number Rods
EduGAINS-Mathematics
http://mathies.ca/learningTools.php
http://mathies.ca/learningTools.php#Mm0
http://mathies.ca/learningTools.php#Nn0
http://mathies.ca/learningTools.php#Rr0
http://mathies.ca/learningTools.php#Ss1
http://mathies.ca/learningTools.php#Ww0
Page 12 of 12