TIPS4Math
Overall Expectations
Multiplication up to 7 x 7 and Division to 49 ÷ 7
Grade 3
Students will:
• Solve problems involving the addition and subtraction of single- and multi-digit whole numbers, using a variety of strategies, and
demonstrate an understanding of multiplication and division (3m10)
• Demonstrate an understanding of equality between pairs of expressions, using addition and subtraction of one- and two-digit
numbers (3m64)
Specific Expectations
Students will:
• Multiply to 7 x 7 and divide to 49 ÷ 7, using a variety of mental strategies (3m28)
• Identify, through investigation, the properties of zero and one in multiplication (i.e., any number multiplied by zero equals zero; any
number multiplied by 1 equals the original number) (3m73
Lesson
Decompose Numbers
into Groups of Equal
Size
EduGAINS-Mathematics
•
Learning Focus
Decompose numbers up to 50 using
objects
o partition a set of objects into equal-sized
groups
o write an addition statement
o explore and record other possibilities for
the same number
o repeat for a variety of numbers
o review the concept of even and odd
by identifying which numbers allow or
not allow two equal groups
Resource
mathies
• Colour Tiles
• Money Tool
• Rekenrek
• Set Tool
• Whole Number Rods
Page 1 of 15
TIPS4Math
Lesson
Multiplication up to 7 x 7 and Division to 49 ÷ 7 (continued)
Multiplication of Equal •
Quantities – Groups of
2, 5 and 10
•
•
Multiplication of Equal •
Quantities – 2, 5, or 10
Groups
•
EduGAINS-Mathematics
Learning Focus
Connect skip counting by 2s, 5s, 10s and
repeat addition to the multiplication
statement
Model multiplication representations as
groups of equal quantities of 2, 5, and 10
(e.g., 3 groups of 2, 7 groups of 2) using a
variety of tools e.g.,
o use ten frames with 2, 5 or 10 objects
and making multiple groups
o use Rekenrek with 5 or 10 beads on a
rack
o use the multiplier function of the mathies
Set Tool and mathies Colour Tiles
Represent the multiplication from the model
using standard notation and begin to build a
multiplication chart
Model multiplication representations as
2, 5, or 10 groups of equal quantities (e.g.,
2 groups of 3, 5 groups of 3, 10 groups of
3) using a variety of tools
Represent the multiplication from the model
using standard notation and record on a
multiplication chart
o identify patterns in the multiplication
chart and establish the commutative
property
Grade 3
Resource
mathies
• Colour Tiles
• Money Tool
• Rekenrek
• Set Tool
• Whole Number Rods
mathies
• Colour Tiles
• Money Tool
• Rekenrek
• Set Tool
• Whole Number Rods
Page 2 of 15
TIPS4Math
Lesson
Multiplication up to 7 x 7 and Division to 49 ÷ 7 (continued)
Add or Subtract One
or Two Groups On or
From 2 and 5
•
•
•
•
Multiplication Squares •
•
•
•
EduGAINS-Mathematics
Learning Focus
Model multiplication representations as 2
and 5 groups of equal quantities
Investigate the result of adding or
subtracting one or two groups, include:
o the special case of subtracting one
group from two groups to establish the
result of multiplying by one
o the special case of subtracting two
groups from two groups to establish the
result of multiplying by zero
Represent the multiplication model using
standard notation and record on a
multiplication chart
Look for patterns on the multiplication chart
and reinforce the commutative property
Build models of 2 x 2, 5 x 5, 7 x 7 using a
variety of tools that support arrays
Investigate other multiplication squares
using array model tools up to 7 x 7
Investigate the result of adding or
subtracting one group using a variety of
tools
Represent the multiplication from the
investigations using standard notation and
verify the product on the multiplication chart
Grade 3
Resource
Guide to Effective Instruction:
Patterning And Algebra K to 3
• pp 111 - 114 Zeros and Ones Game
mathies
• Colour Tiles
• Money Tool
• Rekenrek
• Set Tool
• Whole Number Rods
Guide to Effective Instruction: Number Sense and
Numeration Grades 1 to 3
• p 153 Finding Equal Groups
• pp 161 - 164 What’s the Relationship
• p 164 Arrays and Arrays!
• p 165 Arrays Around Us
• p 165 Roll an Array
mathies
• Colour Tiles
• Rekenrek
• Set Tool
• Whole Number Rods
Page 3 of 15
TIPS4Math
Lesson
Multiplication up to 7 x 7 and Division to 49 ÷ 7 (continued)
Decompose Using
Factors of 2 or 5
•
•
Model Multiplication
Using a Number Line
EduGAINS-Mathematics
•
Learning Focus
Model multiplication as 3, 6, and 7 groups
of equal quantities
o investigate decomposing the models
using the factors of 2 and 5
o decompose 3 into 2 and 1
o decompose 6 into 5 and 1
o decompose 7 into 5 and 2
Model multiplication as 4 groups of equal
quantities
o investigate decomposing the models
using the factor of 2
o decompose 4 as 2 and 2
o investigate the use of the halving and
doubling strategy
o make connections between the two
strategies
Multiply whole numbers up to 7 x 7 using
the number line
o notice and name the multiplication
strategies used
o demonstrate flexibility in selecting
strategies based on the numbers given
Grade 3
Resource
mathies
• Colour Tiles
• Money Tool
• Rekenrek
• Set Tool
• Whole Number Rods
mathies
• Number Line
• Catch a Bouncing Ball Operations – Whole Numbers
Page 4 of 15
TIPS4Math
Lesson
Multiplication up to 7 x 7 and Division to 49 ÷ 7 (continued)
Multiply Using a
Variety of Mental
Strategies
•
Learning Focus
Multiply whole numbers up to 7 x 7
o verify using a variety of tools including
the multiplication chart
o identify the mental strategies used
Grade 3
Resource
Guide to Effective Instruction: Number Sense and
Numeration Grades 1 to 3
• p 149 What Comes in 2’s, 3’s, and 4’s?
• p 153 Circles and Dots Game
• p 154 The Broken Calculator Key
mathies
• Colour Tiles
• Money Tool
• Number Line
• Rekenrek
• Set Tool
• Whole Number Rods
• Catch a Bouncing Ball Operations – Whole Numbers
OERB
• Batter Up
o OERB ID: ELO1295400
EduGAINS-Mathematics
Page 5 of 15
TIPS4Math
Lesson
Multiplication up to 7 x 7 and Division to 49 ÷ 7 (continued)
Investigate
•
Partitioning into Equal
Groups (Division)
Division as Equal
Sharing – Finding the
Number of Items in a
Group
•
•
EduGAINS-Mathematics
Learning Focus
Through investigation, establish that one
way of thinking about division is as
partitioning into equal groups
o use up to 50 concrete or digital objects
o explore all the possible ways to partition
the set of objects into equal-sized
groups
o describe each partition in terms of
the number of groups and the size of
the group
o compare and contrast the different
ways of partitioning [factors] (e.g., 1
group of 12 or 12 groups of 1, 6
groups of 2 or 2 groups of 6, 3
groups of 4 or 4 groups of 3)
o repeat for a variety of numbers
o review the concept of even and odd
by identifying which numbers allow or
not allow the partitioning into two
equal groups
Through investigation, establish division as
the sharing of a quantity equally by:
o identify how many items there would be
in each group when a quantity of up
to 50 concrete/digital items is shared
equally amongst 2, 3, 4, 5, 6, or 7
groups with no leftovers
o state the number of items in each
group
Represent the division from the
investigations using standard notation and
relate it to the multiplication facts on the
multiplication chart
Grade 3
Resource
Guide to Effective Instruction: Number Sense and
Numeration Grades 1 to 3
• p 161 What’s the Relationship
• p 165 Roll an Array
mathies
• Colour Tiles
• Money Tool
• Rekenrek
• Set Tool
• Whole Number Rods
OERB
• Let’s Share
o OERB ID: ELO1161190
Guide to Effective Instruction: Number Sense and
Numeration Grades 1 to 3
• p 171 How Can You Share?
mathies
• Colour Tiles
• Money Tool
• Rekenrek
• Set Tool
• Whole Number Rods
OERB
• Galaxy Divide
o OERB ID: ELO1298130
Page 6 of 15
TIPS4Math
Lesson
Multiplication up to 7 x 7 and Division to 49 ÷ 7 (continued)
Division as Equal
Sharing – Finding the
Number of Groups for
a Set of Items
•
•
Model Division Using
a Number Line
EduGAINS-Mathematics
•
Learning Focus
Through investigation, establish division as
the sharing of a quantity equally by:
o identify how many groups a set of up to
50 concrete/digital items can be equally
shared into when the number of items in
each group is 2, 3, 4, 5, 6, or 7 with no
leftovers
o state the number of groups for each
number of items
Represent the division from the
investigations using standard notation and
relate it to the multiplication facts on the
multiplication chart
Divide whole numbers up to 49 using the
number line
o notice and name the division strategies
used
o demonstrate flexibility in selecting
strategies based on the numbers given
Grade 3
Resource
mathies
• Colour Tiles
• Money Tool
• Rekenrek
• Set Tool
• Whole Number Rods
mathies
• Catch a Bouncing Ball Operations – Whole Numbers
• Number Line
Page 7 of 15
TIPS4Math
Lesson
Multiplication up to 7 x 7 and Division to 49 ÷ 7 (continued)
Multiply and Divide
Using a Variety of
Mental Strategies
•
•
Learning Focus
Multiply whole numbers up to 7 x 7 and
divide whole numbers up to 49 ÷ 7
o vary the location of the unknown (e.g.,
3 x ? = 6, ? x 2 = 6, ? ÷ 2 = 3)
o demonstrate flexibility in selecting a
strategy based on the numbers given
o notice and name the mental strategies
used
o verify using a variety of tools including
the multiplication chart
Make connections between multiplication
and division
Grade 3
Resource
Guide to Effective Instruction: Number Sense and
Numeration Grades 1 to 3
• p 154 Graphs and Multiplication
• p 154 Create a Problem
• p 165 Roll an Array
• p 166 What’s Missing?
mathies
• Colour Tiles
• Money Tool
• Rekenrek
• Set Tool
• Whole Number Rods
• Catch a Bouncing Ball Operations – Whole Numbers
OERB
• Batter Up
o OERB ID: ELO1295400
• Planet Multiply
o OERB ID: ELO1245620
EduGAINS-Mathematics
Page 8 of 15
TIPS4Math
Decompose Numbers into Groups of Equal Size
Resource
URL
mathies:
Colour Tiles
mathies:
Money Tool
mathies:
Number Line
mathies:
Set Tool
mathies:
Whole Number Rods
Grade 3
http://mathies.ca/learningTools.php
http://mathies.ca/learningTools.php#Mm0
http://mathies.ca/learningTools.php#Nn0
http://mathies.ca/learningTools.php#Ss1
http://mathies.ca/learningTools.php#Ww0
Multiplication of Equal Quantities – Groups of 2, 5 and 10
Resource
URL
mathies:
Colour Tiles
mathies:
Money Tool
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#Rr0
http://mathies.ca/learningTools.php#Ss1
http://mathies.ca/learningTools.php#Ww0
Page 9 of 15
TIPS4Math
Multiplication of Equal Quantities – 2, 5, or 10 Groups
Resource
URL
mathies:
Colour Tiles
mathies:
Money Tool
mathies:
Number Line
mathies:
Set Tool
mathies:
Whole Number Rods
Grade 3
http://mathies.ca/learningTools.php
http://mathies.ca/learningTools.php#Mm0
http://mathies.ca/learningTools.php#Nn0
http://mathies.ca/learningTools.php#Ss1
http://mathies.ca/learningTools.php#Ww0
Add or Subtract One or Two Groups On or From 2 and 5
Resource
URL
Guide to Effective Instruction:
Patterning and Algebra K-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/Patterning%20and%20Algebra%20K-3.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 10 of 15
TIPS4Math
Multiplication Squares
Resource
Guide to Effective Instruction: Number
Sense and Numeration Grades 1 to 3
mathies:
Colour Tiles
mathies:
Rekenrek
mathies:
Set Tool
mathies:
Whole Number Rods
Grade 3
URL
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#Rr0
http://mathies.ca/learningTools.php#Ss1
http://mathies.ca/learningTools.php#Ww0
Decompose Using Factors of 2 or 5
Resource
URL
mathies:
Colour Tiles
mathies:
Money Tool
mathies:
Rekenrek
mathies:
Set Tool
mathies:
Whole Number Rods
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
Model Multiplication Using a Number Line
Resource
URL
mathies:
Number Line
mathies:
Catch a Bouncing Ball Operations –
Whole Numbers
EduGAINS-Mathematics
http://mathies.ca/learningTools.php#Nn0
http://mathies.ca/games.php#Cc0
Page 11 of 15
TIPS4Math
Multiply Using a Variety of Mental Strategies
Resource
URL
Guide to Effective Instruction: Number
Sense and Numeration Grades 1 to 3
mathies:
Catch a Bouncing Ball Operations –
Whole Numbers
mathies:
Colour Tiles
mathies:
Number Line
mathies:
Money Tool
mathies:
Rekenrek
mathies:
Set Tool
mathies:
Whole Number Rods
OERB:
Batter Up
EduGAINS-Mathematics
Grade 3
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#Nn0
http://mathies.ca/learningTools.php#Mm0
http://mathies.ca/learningTools.php#Rr0
http://mathies.ca/learningTools.php#Ss1
http://mathies.ca/learningTools.php#Ww0
https://download.elearningontario.ca/repository/12/1295400000/Batter%20Up%20-%20v02.
html
Page 12 of 15
TIPS4Math
Investigate Partitioning into Equal Groups (Division)
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
OERB:
Let’s Share
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
https://download.elearningontario.ca/repository/1161190000/01_letsShare.html
Division as Equal Sharing – Finding the Number of Items in a Group
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
OERB:
Galaxy Divide
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
https://download.elearningontario.ca/repository/12/1298130000/LO_4005%20-%20v03.html
Page 13 of 15
TIPS4Math
Division as Equal Sharing – Finding the Number of Groups for a Set of Items
Resource
URL
mathies:
Colour Tiles
mathies:
Money Tool
mathies:
Rekenrek
mathies:
Set Tool
mathies:
Whole Number Rods
Grade 3
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
Model Division Using a Number Line
Resource
URL
mathies:
Catch a Bouncing Ball Operations –
Whole Numbers
mathies:
Number Line
EduGAINS-Mathematics
http://mathies.ca/games.php#Cc0
http://mathies.ca/learningTools.php#Nn0
Page 14 of 15
TIPS4Math
Multiply and Divide Using a Variety of Mental Strategies
Resource
URL
Guide to Effective Instruction: Number
Sense and Numeration Grades 1 to 3
mathies:
Catch a Bouncing Ball Operations –
Whole Numbers
mathies:
Colour Tiles
mathies:
Money Tool
mathies:
Number Line
mathies:
Rekenrek
mathies:
Set Tool
mathies:
Whole Number Rods
OERB:
Batter Up
OERB:
Planet Multiply
EduGAINS-Mathematics
Grade 3
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
https://download.elearningontario.ca/repository/12/1295400000/Batter%20Up%20-%20v02.
html
https://download.elearningontario.ca/repository/1245620000/LO_4004.html
Page 15 of 15