Download Unit 2 Patterns in Addition and Subtraction

ADDISON WESLEY
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Teacher Guide
Unit 2: Patterns in Addition
and Subtraction
UNIT
2
“Can you do addition?” the
White Queen asked. “What’s
one and one and one and one
and one and one and one and
one and one and one?”
“I don’t know,” said Alice.
“I lost count.”
Through the Looking Glass
Home
Patterns
inQuitAddition
and Subtraction
Mathematics Background
What Are the Big Ideas?
• Addition and subtraction are inverse operations.
• Addition and subtraction have certain properties. For example, there is
the commutative property of addition.
• Strategies for solving 1- and 2-digit addition and subtraction problems
can be used to solve problems involving numbers with increasing
numbers of digits.
Lewis Carroll
How Will the Concepts Develop?
FOCUS STRAND
Number Concepts and Number
Operations
SUPPORTING STRAND
Patterns and Relations: Patterns
Students use patterns to develop strategies for addition and subtraction
of 1-digit numbers, including finding missing numbers.
Students use Base Ten Blocks and place-value mats to add and subtract
2-digit numbers, and later to add and subtract 3-digit numbers.
Students use mental math to add and subtract. They estimate sums
and differences.
Students develop proficiency with adding and subtracting 3-digit
numbers using the standard algorithm.
Why Are These Concepts Important?
The ability to recognize patterns assists students to recall basic facts
proficiently. Fluency with computations involving the addition and
subtraction of whole numbers is essential in the world around us.
Students should have a good understanding of number and the
meanings of and the relationships between the operations of addition
and subtraction. A solid foundation is necessary for learning and
applying math in higher grades.
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Unit 2: Patterns in Addition and Subtraction
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Curriculum Overview
Launch
Cluster 1: Addition and Subtraction Facts
National Read-A-Thon
General Outcomes
Specific Outcomes
Lesson 1:
• Students investigate, establish and
communicate rules for numerical ...
patterns, ..., and use these rules to
make predictions.
• Students apply an arithmetic
operation (addition, subtraction, ...)
on whole numbers, and illustrate its
use in creating and solving
problems.
• Students recall addition/subtraction
facts to 18 ... (N16)
• Students verify solutions to addition
and subtraction problems, using the
inverse operation. (N18)
• Students use objects and concrete
models to explain the rule for a
pattern, such as those found on
addition ... charts. (PR2)
• Students make predictions based on
addition ... patterns. (PR3)
Patterns in an Addition Chart
Lesson 2:
Addition Strategies
Lesson 3:
Subtraction Strategies
Lesson 4:
Related Facts
Lesson 5:
Find the Missing Number
Cluster 2: Adding and Subtracting
2- and 3-Digit Numbers
General Outcomes
Specific Outcomes
Lesson 6:
• Students investigate, establish and
communicate rules for numerical ...
patterns ... and use these rules to
make predictions.
• Students apply an arithmetic
operation (addition, subtraction, ...)
on whole numbers, and illustrate its
use in creating and solving
problems.
• Students use and justify an
appropriate calculation strategy or
technology to solve problems.
• Students use manipulatives,
diagrams and symbols, in a
problem-solving context, to
demonstrate and describe the
processes of addition and
subtraction to 1000, with and
without regrouping. (N14)
• Students verify solutions to addition
and subtraction problems, using
estimation and calculators. (N17)
• Students verify solutions to addition
and subtraction problems, using the
inverse operation. (N18)
• Students justify the choice of
method for addition and
subtraction, using:
– estimation strategies
– mental mathematics strategies
– manipulatives
– algorithms
– calculators. (N19)
• Students make predictions based on
addition ... patterns. (PR3)
Adding and Subtracting
2-Digit Numbers
Lesson 7:
Using Mental Math to Add
Lesson 8:
Using Mental Math to Subtract
Lesson 9:
Strategies Toolkit
Lesson 10:
Estimating Sums and Differences
Lesson 11:
Adding 3-Digit Numbers
Lesson 12:
Subtracting 3-Digit Numbers
Lesson 13:
A Standard Method for Addition
Lesson 14:
A Standard Method
for Subtraction
Show What You Know
Unit Problem
National Read-A-Thon
Unit 2: Patterns in Addition and Subtraction
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Curriculum across the Grades
Grade 2
Grade 3
Grade 4
Students use
manipulatives, diagrams,
and symbols to
demonstrate and describe
the processes of addition
and subtraction of
numbers to 100. They
apply and explain
multiple strategies to
determine sums and
differences of 2-digit
numbers, with and
without regrouping.
Students use
manipulatives, diagrams,
and symbols, in a
problem-solving context,
to demonstrate and
describe the processes of
addition and subtraction
to 1000, with and without
regrouping.
Students use
manipulatives, diagrams,
and symbols, in a
problem-solving context,
to demonstrate and
describe the process of
addition and subtraction
of numbers up to 10 000.
Students apply a variety
of estimation and mental
mathematics strategies to
addition and subtraction
problems. They recall
addition and subtraction
facts to 10.
Students recall
addition/subtraction facts
to 18. They verify
solutions to addition and
subtraction problems,
using estimation and
calculators.
Students demonstrate an
understanding of addition
and subtraction of
decimals (tenths and
hundredths), using
concrete and pictorial
representations.
Students verify solutions
to addition and
subtraction problems,
using the inverse
operation. They justify the
choice of method for
addition and subtraction,
using estimation
strategies, mental
mathematics strategies,
manipulatives,
algorithms, and
calculators.
Materials for This Unit
Prepare triangular cards from cardboard (side length 6 cm) for Lesson 4.
Each pair of students will need about 20 cards.
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Unit 2: Patterns in Addition and Subtraction
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Additional Activities
Fastest Facts
First to 10
For Extra Support (Appropriate for use after Lesson 2)
Materials: Fastest Facts (Master 2.9), deck of cards
with 10s and face cards removed
For Extra Practice (Appropriate for use after Lesson 6)
Materials: First to 10 (Master 2.10), 2 number cubes,
Base Ten Blocks, place-value mats, calculator
The work students do: Students play in groups of
3. One student is the dealer. The dealer shuffles the deck
and turns over 2 cards for the two other players to see.
The first player to correctly add the two numbers gets
one point. The dealer continues to turn over 2 cards at a
time until one player has accumulated 10 points. He or
she is the winner. Students repeat the activity, with the
winner becoming the dealer.
The work students do: Students play with a
partner. Player A rolls 2 number cubes to make a
2-digit number. Player A rolls the number cubes again
to make another 2-digit number. She then uses Base Ten
Blocks and place-value mats to add the two 2-digit
numbers. Player B uses a calculator to check Player A’s
answer. If the answer is correct, Player A gets 1 point.
Player B takes a turn. Players continue to take turns until
one player gets 10 points. He is the winner.
Take It Further: The dealer turns over 3 cards at a
time and students add all three numbers.
Social/Mathematical
Group Activity
Take It Further: Students play the game again.
This time, they subtract the lesser number from
the greater number.
Logical/Mathematical/Social
Partner Activity
Tic-Tac-Toe Squares
Shopping Bags!
For Extra Practice (Appropriate for use after Lesson 11)
Materials: Tic-Tac-Toe Squares (Master 2.11),
Tic-Tac-Toe Board (Master 2.11b), Base Ten Blocks,
place-value mats (made from PM 18), calculator
For Extension (Appropriate for use after Lesson 13)
Materials: Shopping Bags! (Master 2.12), classroom
objects, price tags, calculators
The work students do: Students play with a
partner. Players decide who will be “X” and who will be
“O.” Player X chooses a square, then uses Base Ten
Blocks and place-value mats to find the answer. Player O
uses a calculator to check the answer. If Player A is
correct, he puts his mark on the square. Players switch
roles. Players continue to take turns until one player gets
3 Xs or 3 Os in a row.
Take It Further: Students create their own Tic-Tac-Toe
board with each question involving the addition of three
3-digit numbers.
Logical/Interpersonal/Mathematical
Partner Activity
The work students do: Students play in groups of 3.
Students put price tags on classroom objects they choose.
Prices should be between 25¢ and 50¢. One student is
the cashier. The other students are the shoppers. Shoppers
choose two objects to purchase, then use pencil and
paper to find the total cost. Each shopper records their
total on a piece of paper. The shoppers take their
purchases to the cashier who uses a calculator to check.
Take It Further: The cashier gives each shopper 99¢.
The shopper who comes closest to spending 99¢, without
going over, wins.
Logical/Mathematical/Kinesthetic/Social
Group Activity
Unit 2: Patterns in Addition and Subtraction
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Planning for Unit 2
Planning for Instruction
Lesson
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Time
Unit 2: Patterns in Addition and Subtraction
Suggested Unit time: 3–4 weeks
Materials
Program Support
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Lesson
Time
Materials
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Program Support
Planning for Assessment
Purpose
Tools and Process
Recording and Reporting
Unit 2: Patterns in Addition and Subtraction
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LAUNCH
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National Read-A-Thon
LESSON ORGANIZER
10–15 min
Curriculum Focus: Activate prior learning about addition and
subtraction.
ASSUMED PRIOR KNOWLEDGE
✓ Students can recall addition and subtraction facts to 18.
✓ Students can compare and order whole numbers.
ACTIVATE PRIOR LEARNING
Engage students in a discussion about the
books they like to read.
Ask:
• How many books did you read last week? (3)
• What kind of books do you like to read?
(I like to read mystery books.)
Invite students to examine the chart on page 55
of the Student Book.
Ask questions, such as:
• What does the chart show?
(How many books each student read)
• How can you find how many books Jeff read?
(Add up the number of books he read in each of the
4 weeks.)
Discuss the questions posed in the Student Book.
(Sample answer: Sookal read the most pages, 276. Sunny
read the most books, 18. I can find out who read the
fewest books or who read the most books in Week 1, or
how many more books Sunny read than Jenny.)
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Unit 2 • Launch • Student page 54
Ask questions, such as:
• How did you find who read the most pages?
(I ordered the numbers of pages read from greatest to
least. Sookal had the greatest number.)
• How did you find who read the most books?
(I added the number of books in each column, then
ordered the numbers from greatest to least.)
• Did the student who read the most pages
read the most books? (No) Explain. (Sookal
read 276 pages and 13 books. Sunny read 206 pages
and 18 books. Sunny’s books must have been short.)
Tell students that, in this unit, they will use
patterns to develop strategies for adding and
subtracting 1-digit numbers. They will use Base
Ten Blocks and place-value mats to add and
subtract 2- and 3-digit numbers, and this will
lead to the standard method of addition and
subtraction. At the end of the unit, students
will use charts to obtain information, and then
report on the Read-A-Thon.
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LITERATURE CONNECTIONS FOR THE UNIT
Shark Swimathon by Stuart J. Murphy. Harper Trophy, 2000.
ISBN: 006446735X
A shark swim team practices subtraction of 2-digit numbers as it
tries to reach a goal of 75 laps. The subtraction gets
progressively more difficult as the predictable story goes on.
Swordfish coach Blue explains the process in each example.
Animals on Board by Stuart J. Murphy. Harpercollins Juvenile
Books, 1998.
ISBN: 0064467163
This story lays out five simple addition problems. A truck driver,
Jill, watches as a series of trucks—all pulling different animals—
pass her by. The math gets worked into the story as Jill adds.
Using this pattern, the reader is able to practice addition while
guessing the trucks’ final destination.
REACHING ALL LEARNERS
Some students may benefit from using the virtual
manipulatives on the e-Tools CD-ROM. The
e-Tools appropriate for this unit include Place-Value Blocks. These
can be used in place of, or to support the use of, Base Ten Blocks.
DIAGNOSTIC ASSESSMENT
What to Look For
What to Do
✔ Students can recall
addition and
subtraction facts
to 18.
✔ Students can
compare and order
whole numbers.
Extra Support:
Students who have difficulty recalling their addition and subtraction facts may
benefit from using a number line, a 9 + 9 addition chart, or Base Ten Blocks.
Work on this skill during Lessons 1 to 5.
Students who have difficulty comparing and ordering whole numbers may benefit
from modelling the numbers with Base Ten Blocks or recording the numbers in a
place-value chart.
Work on this skill during the Launch and the Unit Problem.
Unit 2 • Launch • Student page 55
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LESSON 1
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Patterns in an
Addition Chart
40–50 min
LESSON ORGANIZER
Curriculum Focus: Describe properties of addition.
(PR2, PR3)
Teacher Materials
overhead transparency of Addition Chart 1 (Master 2.6)
Student Materials
Optional
addition charts (Master 2.6) Step-by-Step 1 (Master 2.13)
pencil crayons
Extra Practice 1 (Master 2.28)
Vocabulary: addition fact, sum, doubles
Assessment: Master 2.2 Ongoing Observations: Patterns in
Addition and Subtraction
Key Math Learnings
1. There are patterns in an addition chart.
2. When you add, the order does not matter.
3. When you add two numbers that are the same, you add
doubles. Doubles have a sum that is even.
Numbers Every Day
Encourage students to discuss the strategies they used. Students
should realize that the numbers you and I say have a sum of 10.
BEFORE
Get Started
Show students 2 quantities of the same item,
such as books or counters. Invite a volunteer to
add the 2 quantities, then record the addition
sentence on the board. Use the addition sentence
to introduce the terms addition fact and sum.
Show students an overhead transparency of an
addition chart. Demonstrate how to use the
chart to find 2 + 5 = 7.
Ask questions, such as:
• How would you use the chart to find 4 + 3?
(I would find 4 in the top row and 3 in the first
column. I would then find where the row and
column meet. They meet at 7. This is the sum.)
• How else can you find 4 + 3?
(I could find 3 in the top row and 4 in the first
column. I would then find where the row and
column meet.)
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Unit 2 • Lesson 1 • Student page 56
Present Explore. Encourage students to find all
the patterns they can, including patterns across
the rows, down the columns, and along the
diagonals. Suggest students use a different
colour to show each pattern.
DURING
Explore
Ongoing Assessment: Observe and Listen
Ask questions, such as:
• How do you know you have found a pattern?
(The numbers increase by 2 each time.)
• What pattern did you find in the rows?
(The numbers increase by 1 each time.)
• What pattern did you find in the columns?
(The numbers increase by 1 each time.)
• What pattern did you find in the diagonals
from top left to bottom right?
(The numbers in the white squares increase by
2 each time.)
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REACHING ALL LEARNERS
Early Finishers
Have students use addition facts in the chart to write sentences
with missing numbers, then trade them with a partner, who
completes the sentences.
Common Misconceptions
➤Students have difficulty finding a pattern on an addition chart
and choose a random selection of numbers.
How to Help: Provide students with the first 3 numbers in a
pattern and have students continue the pattern by colouring the
numbers on an addition chart. Students then describe the pattern.
ESL Strategies
Students for whom English is a second language may have
difficulty describing their patterns. Encourage these students
to use numbers and mathematical symbols (+, =) to describe
their patterns.
Sample Answers
1. The first number increases by 1 each time. The second number
decreases by 1 each time.
The two numbers add to 10.
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2. a) 0 + 13, 1 + 12, 2 + 11, 3 + 10, 4 + 9, 5 + 8, 6 + 7
b) 0 + 11, 1 + 10, 2 + 9, 3 + 8, 4 + 7, 5 + 6
c) 0 + 12, 1 + 11, 2 + 10, 3 + 9, 4 + 8, 5 + 7, 6 + 6
d) 0 + 15, 1 + 14, 2 + 13, 3 + 12, 4 + 11, 5 + 10, 6 + 9, 7 + 8
In each sum I used the pattern in the numbers. The first number
increases by 1 each time and the second number decreases by
1 each time. I kept listing the pairs until the numbers started to
repeat because when you add, order does not matter.
• What pattern do you see in the diagonals
from top right to bottom left? (The numbers in
the white squares are the same in each diagonal.)
• How did you record your patterns?
(We described a pattern and listed the facts that fit it.)
AFTER
Connect
Invite volunteers to describe their patterns to the
class. Have them explain how they found the
pattern and to tell how they know it is a pattern.
Ask questions, such as:
• What happens when you add zero to
a number? (The number does not change.)
• What pattern do you see when you add two
numbers that are the same?
(The pattern is 0, 2, 4, 6, 8, 10, 12, . . . .
The numbers increase by 2 each time.)
• What do you notice when you use the chart to
add 3 + 5 and 5 + 3? (The answer is the same, 8.)
Use Connect to introduce some of the properties
of addition. Tell students that when they add
doubles, the sum is always an even number.
Discuss how finding patterns could help
students with addition.
Practice
Have addition charts (Master 2.6) available for
all questions.
Assessment Focus: Question 6
Students understand the concept of even and
odd numbers. Students add pairs of even
numbers, and discover that all the answers are
even numbers. Some students may list the
numbers that never appear, while others may
also classify these numbers as odd numbers.
Unit 2 • Lesson 1 • Student page 57
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3. The first number in each sum starts at 1 and increases by
1 each time. The second number in each sum starts at 2 and
increases by 1 each time.
The sums start at 3 and increase by 2 each time.
The next two sums in the pattern are 4 + 5 = 9 and 5 + 6 = 11.
5. There are 6 children on the school bus. At the next school,
8 children get on the bus. How many children are on the bus
altogether? (Answer: 6 + 8 = 14)
6. 2 + 6 = 8, 2 + 4 = 6
There are 7 different sums when you add 2 even numbers less
than 10; 4, 6, 8, 10, 12, 14, 16. The odd numbers
1, 3, 5, 7, 9, 11, 13, 15, 17 never appear. The even numbers
2 and 18 also do not appear. The only way to get 2 using
even numbers is 2 + 0. The only way to get 18 using even
numbers is to add 10 + 8, but 10 is not a number less than
10. The sum of 2 even numbers is always an even number.
1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5
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16 children
REFLECT: The patterns in an addition chart help me remember
some of the addition facts. I know adding 0 does not change
the start number and when I add doubles, I know the sum is
always even. I also know that order does not matter. There are
also patterns when you look at all the ways to find a sum.
When the first number increases by 1 each time, and the
second number decreases by 1 each time, then the sum stays
the same each time.
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Understanding concepts
✔ Students understand that there are
patterns in an addition chart.
Extra Support: Give students addition facts for one number,
for example, 7. Have students colour an addition chart to show
these facts, then look for a pattern in the numbers.
Students can use Step-by-Step 1 (Master 2.13) to complete
question 6.
Applying procedures
✔ Students can identify and extend a
pattern on an addition chart.
✔ Students can make predictions based
on addition patterns.
Communicating
✔ Students use mathematical language
to describe the rules for patterns on
an addition chart.
Extra Practice: Have students work in pairs. One student
colours a pattern on an addition chart. The other student
describes the pattern, then lists all the addition facts that fit the
pattern. Students switch roles and continue the activity.
Students can complete Extra Practice 1 (Master 2.28).
Extension: Have students extend their patterns to find sums of
numbers beyond 9 + 9.
Recording and Reporting
Master 2.2 Ongoing Observations:
Patterns in Addition and Subtraction
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Unit 2 • Lesson 1 • Student page 58
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ESSON 2
Addition Strategies
40–50 min
LESSON ORGANIZER
Curriculum Focus: Use different strategies to recall basic
addition facts. (N16)(PR3)
Teacher Materials
overhead transparency of Addition Chart 2 (Master 2.7)
Student Materials
Optional
Addition Chart 1
Step-by-Step 2 (Master 2.14)
(Master 2.6)
Extra Practice 1 (Master 2.28)
Addition Chart 2
(Master 2.7)
pencil crayons
Vocabulary: near double, sums of 10
Assessment: Master 2.2 Ongoing Observations: Patterns in
Addition and Subtraction
Key Math Learnings
1. Patterns in addition charts can be used to help recall basic
addition facts.
2. Adding a number to its next counting number gives a
near double.
3. Strategies, such as “doubles,” “near doubles,” and “make 10”
can be used to recall basic addition facts.
BEFORE
Get Started
Invite students to examine the picture of
the ant on page 59 of the Student Book.
Have students think about the meaning of
the word double. Ask:
• What doubles fact does the ant show?
(The ant has 3 feet on each side of its body;
3 + 3 = 6.)
• Where do you find examples of doubles on
your own body? (I have 2 eyes, 2 hands, 2 ears,
2 feet, 2 arms, and 2 legs.)
• How do you know when something is
a double?
(When there are 2 of something, and they look alike.)
• How can you use doubles to find other facts?
(I can use 5 + 5 to help me find 4 + 5. I know that
4 + 5 is 1 less than 5 + 5.)
Present Explore. Distribute copies of addition
charts (Master 2.7). Use an overhead
transparency of Addition Chart 2 to
demonstrate the doubles along the diagonal.
Ensure students understand they are to
describe the patterns they see, then find ways
to use the patterns to find other facts. Explain
that the number 10 is shaded yellow and blue
because it lies on two diagonals.
DURING
Explore
Ongoing Assessment: Observe and Listen
Ask questions, such as:
• What pattern do you see in the blue diagonal?
(The numbers increase by 2 each time as you move
from top left to bottom right.)
• What pattern do you see in each row?
(The number in the green square is 1 less than
the number in the blue square. The number in
the pink square is 1 more than the number in
the blue square.)
• What is special about all the yellow squares?
(All the numbers are 10. Each number shows a
different sum for 10.)
Unit 2 • Lesson 2 • Student page 59
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REACHING ALL LEARNERS
Alternative Explore
Materials: counters
Students use counters to show doubles. They add one more
counter to each double, then describe how they can use doubles
to find near doubles. Students repeat the activity but remove one
counter from each double. Students record the addition
strategies they find.
Early Finishers
Have students use the patterns to complete Addition Chart 2
(Master 2.7). They then use the strategies to find more
addition facts.
Common Misconceptions
➤Students have difficulty relating near doubles to doubles.
How to Help: Demonstrate the concept using concrete materials.
For example, show students how close 5 + 6 is to 5 + 5.
Numbers Every Day
Students could use hundred charts.
Answers:
• 325, 327, 329, 331, 333, 335, 337, 339, 341, 343, 345,
347, 349
• 325, 330, 335, 340, 345, 350, 355, 360, 365, 370, 375
• 325, 335, 345, 355, 365, 375, 385, 395, 405, 415, 425,
10
14
12
11
15
13
16
17
435, 445, 455
• 325, 350, 375, 400, 425, 450, 475, 500, 525, 550
• How can you remember the addition facts for
the pink squares? (They are doubles, plus 1.)
AFTER
Write a variety of addition questions on the
board and have volunteers find the answers,
describing the strategy they used each time.
Connect
Invite volunteers to describe the addition
strategies they found. Have them explain how
these strategies can help them recall basic
addition facts.
Practice
Have addition charts (Master 2.6) available for
all questions.
Assessment Focus: Question 6
Use Connect to introduce the strategies for adding:
“doubles,” “near doubles,” and “make 10.”
Demonstrate how to use the strategy “near
doubles” to add 3 + 4. Tell students that to add
3 + 4, think of 3 + 3, plus another 1.
Students use their understanding of sums of
10. Students should first look for pairs of
numbers that add to 10, then, if possible,
break down the numbers in the pairs to find
groups of 3 and 4 numbers that add to 10.
Explain how the basic facts for 10 can be used
to help figure out other facts. Show students
how to find 9 + 3 by making 10 with 9 + 1,
then adding another 2.
Students who need extra support to complete
Assessment Focus questions may benefit from
the Step-by-Step masters (Masters 2.13–2.25).
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Unit 2 • Lesson 2 • Student page 60
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Sample Answers
15
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7
9
13
13
12
15
6
10
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4. I can use doubles for the first number and add 2 each time.
The first number increases by 1 each time. The second number
increases by 1 each time. The answer increases by 2 each time.
The second number in each fact is the first number plus 2.
5. I used near doubles. To add 9 + 8, I thought of 8 + 8, then
added another 1.
6. 2 + 8; 3 + 7; 4 + 6; 1 + 2 + 7; 2 + 3 + 5; 1 + 4 + 5;
1 + 3 + 6; 1 + 2 + 3 + 4
I know I have found all the ways because I have used all the
combinations of numbers that add to 10, without using the
same number more than once.
17 children
REFLECT: I use “near doubles.” For example, to add 7 + 8,
I think of 7 + 7, plus another 1. I also use “make 10.”
For example, to add 9 + 4, I think of 9 + 1, plus another 3.
8 ways
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Understanding concepts
✔ Students understand that patterns in
an addition chart can be used to help
recall basic addition facts.
Extra Support: Students can complete the Additional Activity,
Fastest Facts (Master 2.9).
Students can use Step-by-Step 2 (Master 2.14) to complete
question 6.
Applying procedures
✔ Students can use strategies,
such as “doubles,” “near doubles,”
and “make 10” to recall basic
addition facts.
Extra Practice: Have students work in pairs. One student
makes an addition question, and the other student uses counters
to demonstrate the strategy used to recall the addition fact.
Students switch roles and continue the activity.
Students can complete Extra Practice 1 (Master 2.28).
✔ Students can identify and extend a
pattern in an addition chart.
Extension: Challenge students to use these strategies to find
addition facts that involve the sums of 3 or more numbers.
Recording and Reporting
Master 2.2 Ongoing Observations:
Patterns in Addition and Subtraction
Unit 2 • Lesson 2 • Student page 61
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LESSON 3
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Subtraction Strategies
LESSON ORGANIZER
40–50 min
Curriculum Focus: Use different strategies to recall basic
subtraction facts. (N16)
Teacher Materials
overhead transparency of Addition Chart 1 (Master 2.6)
transparent counters
Student Materials
Optional
Addition Chart 1
Step-by-Step 3
(Master 2.6)
(Master 2.15)
pencil crayons
Extra Practice 2
(Master 2.29)
Vocabulary: subtraction fact
Assessment: Master 2.2 Ongoing Observations: Patterns in
Addition and Subtraction
Key Math Learnings
1. Subtraction is the opposite of addition.
2. Strategies, such as “count up through 10” and “count back
through 10,” can be used to recall basic subtraction facts.
3. Patterns in addition charts can be used to help recall basic
subtraction facts.
BEFORE
Get Started
Have a volunteer write an addition fact on the
board. Demonstrate how the addition fact can be
used to find 2 subtraction facts. Tell students
subtraction is the opposite of addition. Use
transparent counters on the overhead projector
to demonstrate this idea. Model the addition
statement 3 + 4 = 7. Show students how these
counters also show 7 – 4 = 3 and 7 – 3 = 4.
Ask:
• You know 4 + 5 = 9. What other facts do you
know from this addition fact?
(I know 9 – 5 = 4 and 9 – 4 = 5.)
• If you know 6 – 2 = 4, what else do
you know? (I know 6 – 4 = 2 and 2 + 4 = 6.)
Present Explore. Use an overhead transparency
of an addition chart (Master 2.6) to demonstrate
how to find subtraction facts. Colour the path
used for the subtraction fact 7 – 2 = 5. Have a
volunteer list the other facts this path shows.
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Unit 2 • Lesson 3 • Student page 62
DURING
Explore
Ongoing Assessment: Observe and Listen
Ask questions, such as:
• How do you remember subtraction facts you
already know?
(I think of the related addition facts. For example, I
say, “Three and what makes 8?”)
• What subtraction facts did you find that use
10? (I found 10 – 1 = 9, 10 – 9 = 1, 10 – 2 = 8,
10 – 8 = 2, 10 – 3 = 7, 10 – 7 = 3, 10 – 4 = 6,
10 – 6 = 4, and, 10 – 5 = 5.)
• What strategies do you use to subtract?
(I use doubles. For example, to find 8 – 4, I think
4 + 4 = 8, then I know 8 – 4 = 4. I also use near
doubles. For example, to find 7 – 3, I think
6 – 3 = 3, so 7 – 3 = 4; that is, 7 – 3 is 1 more than
6 – 3.)
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REACHING ALL LEARNERS
Alternative Explore
Materials: number lines
Students use number lines to demonstrate addition facts, then
find the corresponding subtraction facts. Students should
discover subtraction is the opposite of addition, in that they
move to the right to add and to the left to subtract.
Early Finishers
Have students use Addition Chart 2 (Master 2.7) to demonstrate
the subtraction strategies “doubles,” “near doubles,” and
“counting through 10.”
Common Misconceptions
7
8
9
6
7
7
9
7
7
7
7
AFTER
➤Students have difficulty when subtracting 0. For example, they
erroneously think 5 – 0 = 4 because subtraction must make a
number smaller.
How to Help: Use counters to demonstrate that if you have
5 counters and take away none, you still have 5 counters.
Numbers Every Day
Students could use hundred charts.
9
9
9
•
•
•
•
9
9
Connect
Invite volunteers to describe the subtraction
strategies they found. Have them explain how
these strategies can help them recall basic
subtraction facts. For example, some students
may find facts that subtract 5 are related to
make 10. For example, to find 9 – 5, think
10 – 5, then take away 1 more.
Use Connect to introduce other strategies for
subtracting. Demonstrate how to count up
through 10. Tell students that to subtract 12 – 8,
start with 8. You need 2 more to get 10, and
2 more to get 12, and 2 + 2 = 4.
So, 12 – 8 = 4
Demonstrate how to count back through 10.
Tell students that to subtract 12 – 5, start with
12. Take away 2 to get 10. Since 5 is 2 + 3, take
away 3 more; 10 – 3 = 7.
950, 948, 946, ..., 904, 902, 900
950, 945, 940, ..., 850, 845, 840
950, 940, 930, ..., 720, 710, 700
950, 850, 750, ..., 250, 150, 50
Write a variety of subtraction questions on the
board and have volunteers find the answers,
describing the strategy they used each time.
Practice
Have Addition Chart 1 (Master 2.6) available
for all questions.
Assessment Focus: Question 7
Students should realize that to find all
subtraction facts that have an answer of 5, they
should look down the column for 5 or across
the row for 5. They should discover they get
the same subtraction facts in both cases.
Students will demonstrate their understanding
of subtraction by explaining how they know
they have found all the facts.
Unit 2 • Lesson 3 • Student page 63
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Sample Answers
2. When the first number increases by 1 each time, and the
second number increases by 1 each time, then the difference
stays the same each time. Also, when the first number
decreases by 1 each time, and the second number decreases
by 1 each time, then the difference stays the same each time.
7. 5 – 0 = 5, 6 – 1 = 5, 7 – 2 = 5, 8 – 3 = 5, 9 – 4 = 5,
10 – 5 = 5, 11 – 6 = 5, 12 – 7 = 5, 13 – 8 = 5, 14 – 9 = 5
I know I have found all the facts because I went down the
column for 5 on the addition chart and listed all the
subtraction facts with 5 as the answer.
9. Jenny’s mom sent 17 cookies to school with her. Jenny’s
friends ate 9 cookies. How many cookies were left?
(Answer: 17 – 9 = 8)
2
5
3
6
4
7
8
8
8
9
5
4
6
8
5
6
4
6
9
3
9
5
8
11
REFLECT: I can think of subtraction as the opposite of addition.
For example, when I see 9 – 3, I say, “Three and what makes
nine?” Since 3 + 6 = 9, I know 9 – 3 = 6.
9 children
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Understanding concepts
✔ Students understand that subtraction
is the opposite of addition.
Extra Support: Students having difficulty finding subtraction
facts on the addition chart may benefit from finding addition
facts, then writing the corresponding subtraction facts.
Students can use Step-by-Step 3 (Master 2.15) to complete
question 7.
Applying procedures
✔ Students can use strategies, such as
“count up through 10” and “count
back through 10,” to recall basic
subtraction facts.
✔ Students can use patterns in
addition charts to help recall basic
subtraction facts.
Extra Practice: Have students work in pairs. One student
names a subtraction strategy, and the other student writes a
subtraction question that he would solve using that strategy. The
student then subtracts and explains how he used the strategy.
Students switch roles and continue the activity.
Students can complete Extra Practice 2 (Master 2.29).
Extension: Challenge students to use these strategies to find
subtraction questions that involve 3 or more numbers
(for example, 9 – 3 – 2).
Recording and Reporting
Master 2.2 Ongoing Observations:
Patterns in Addition and Subtraction
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Unit 2 • Lesson 3 • Student page 64
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ESSON 4
Related Facts
40–50 min
LESSON ORGANIZER
Curriculum Focus: Identify and apply relationships between
addition and subtraction. (N16)
Teacher Materials
triangular cards
Optional
triangular cards
Step-by-Step 4
(20 per pair)
(Master 2.16)
Addition Chart 1
Extra Practice 2
(Master 2.6)
(Master 2.29)
Vocabulary: related facts
Assessment: Master 2.2 Ongoing Observations: Patterns in
Addition and Subtraction
Student Materials
Key Math Learnings
1. Some addition and subtraction facts are related.
2. A doubles fact gives only one subtraction fact.
BEFORE
Get Started
Invite a volunteer to share an addition fact with
the class. Have students name other facts that
belong with this fact. Tell students these
addition and subtraction facts are related. Ask:
• How do you know the four facts are related?
(They use the same numbers.)
• If you are given an addition fact, how do you
find the related addition fact?
(Change the order of the numbers that are added.)
• Does changing the order of the numbers in
an addition fact change the answer? (No)
Why? (When you add, the order does not matter.)
• Given an addition fact, how can you find a
related subtraction fact?
(From the sum, subtract one number that was added.
The difference is the other number that was added.)
Present Explore. Distribute 20 triangular cards to
each pair of students. Model how to use a card
with a set of related facts.
Introduce the Show and Share games to students.
DURING
Explore
Ongoing Assessment: Observe and Listen
Ask questions, such as:
• How did you make that card?
(We chose the numbers 3 and 4, then added them to
get 7. We put one of these numbers in each of the
three corners of the card. On the back of the card,
we wrote all the related facts: 3 + 4 = 7, 4 + 3 = 7,
7 – 3 = 4, 7 – 4 = 3.)
• What happened when you used doubles?
(We only got 1 addition fact and 1 subtraction fact.)
• How did you find the related facts when you
were shown 3 numbers?
(I added the two lesser numbers to get their sum,
which was the third number. This was the first
addition fact. Then I said all the related facts.)
Unit 2 • Lesson 4 • Student page 65
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REACHING ALL LEARNERS
Alternative Explore
Materials: linking cubes
Have students use linking cubes to demonstrate related addition
and subtraction facts. Have them draw a picture to show each fact.
Early Finishers
Students use the triangular cards. One student covers up one of the
three numbers on the front of a card, and the other student finds
the missing number. Students switch roles and play again.
Common Misconceptions
➤Students think all facts have 3 related facts.
How to Help: Show students a doubles fact. Use counters to
model the 4 related facts. Point out to students that the
2 addition facts are the same and the 2 subtraction facts are
the same. A doubles fact has only one other related fact.
Numbers Every Day
Students should recognize 9 + 8 is 9 + 9, take away 1;
9 + 10 is 9 + 9, plus 1; 9 + 7 is 9 + 9, take away 2; 9 + 11 is
9 + 9, plus 2.
• When your partner showed you the related
facts, how did you find what numbers
belonged in the set?
(I read the 3 numbers that were in one of the facts.)
AFTER
Connect
Invite volunteers to describe the strategies they
used in playing the games. Have students tell
how the games showed the relation between
addition and subtraction. Ask:
• What other game can you play with these
cards? (One player covers one of the 3 numbers on
the front of the card, and the other player has to find
the missing number.)
Write a doubles fact on the board, such as
6 + 6 = 12. Have volunteers list all related facts.
Ask:
• How many related facts does a doubles fact
have? (1)
14
Unit 2 • Lesson 4 • Student page 66
• Why is there only one related fact for a
doubles fact?
(Because 2 of the numbers in the fact are the same.)
Use Connect to review the concept that addition
and subtraction are related, and if you know one
fact, you can use it to write other facts.
Practice
Have Addition Chart 1 (Master 2.6) available
for all questions.
Assessment Focus: Question 7
Students find an addition or subtraction fact
that uses the number 5. They then find all
related facts. Some students will find two
numbers that add to 5; others will find two
numbers that have a difference of 5, and others
will find a fact in which 5 is not the sum or
difference, but one of the other two numbers.
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Sample Answers
+
+
–
+
–
–
5
3 + 5 = 8, 5 + 3 = 8, 8 – 3 = 5, 8 – 5 = 3
11
8 + 3 = 11, 3 + 8 = 11,
11 – 3 = 8, 11 – 8 = 3
1. a) 7 + 4 = 11, 4 + 7 = 11, 11 – 4 = 7, 11 – 7 = 4
b) 6 + 5 = 11, 5 + 6 = 11, 11 – 5 = 6, 11 – 6 = 5
c) 9 + 9 = 18, 18 – 9 = 9
d) 3 + 9 = 12, 9 + 3 = 12, 12 – 3 = 9, 12 – 9 = 3
2. a) 8 + 4 = 12, 4 + 8 = 12, 12 – 8 = 4
b) 9 + 5 = 14, 14 – 5 = 9, 14 – 9 = 5
c) 7 + 7 = 14
d) 7 + 5 = 12, 12 – 7 = 5, 12 – 5 = 7
4. c) In part a, I found the difference between 8 and 3. In part b,
I found the sum of 8 and 3.
6. The girl’s basketball team brought a container of
9 books
7 children
17
19
16
20
15 basketballs to the practice. The team used 9 basketballs.
How many basketballs were left in the container?
(Answer: 15 – 9 = 6; there were 6 basketballs left in the
container.)
7. The other numbers could be 1 and 4, 1 + 4 = 5; 2 and 3,
2 + 3 = 5; 1 and 6, 6 – 1 = 5; 7 and 2, 7 – 2 = 5; 8 and 3,
8 – 3 = 5; 9 and 4, 9 – 4 = 5; 10 and 5, 10 – 5 = 5; 1 and 6,
1 + 5 = 6; 2 and 7, 2 + 5 = 7; 3 and 8, 3 + 5 = 8; 4 and 9,
4 + 5 = 9; and so on. I found the numbers by finding pairs of
numbers that add to 5, then finding pairs of numbers whose
difference is 5, and then finding other facts that have a 5, but
do not have an answer of 5.
REFLECT: 7 + 8 = 15, 8 + 7 = 15, 15 – 7 = 8, 15 – 8 = 7
These facts are related because they all have the same numbers.
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Understanding concepts
✔ Students understand that some
addition and subtraction facts
are related.
Extra Support: Give students having difficulty finding related
subtraction facts an addition fact, such as 6 + 7 = 13. Use counters.
To find the related subtraction facts, remove 6 counters from 13,
have students say what is left, and write 13 – 6 = 7. Replace the
counters, then remove 7, and write the fact 13 – 7 = 6.
Students can use Step-by-Step 4 (Master 2.16) to complete
question 7.
✔ Students understand that a doubles
fact gives only one related fact.
Applying procedures
✔ Students can find all related facts for
a given fact.
Extra Practice: Have students make triangular cards for numbers
beyond 9 + 9.
Students can complete Extra Practice 2 (Master 2.29).
✔ Students can list all related facts for a
set of 3 numbers.
Extension: Challenge students to use square cards to show facts
that involve more than 3 numbers.
Recording and Reporting
Master 2.2 Ongoing Observations:
Patterns in Addition and Subtraction
Unit 2 • Lesson 4 • Student page 67
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LESSON 5
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Find the
Missing Number
40–50 min
LESSON ORGANIZER
Curriculum Focus: Find the value of the missing term in a
number sentence. (N16, N18)
Student Materials
Optional
counters
Step-by-Step 5
Addition Chart 1
(Master 2.17)
(Master 2.6)
Extra Practice 3
(Master 2.30)
Assessment: Master 2.2 Ongoing Observations: Patterns in
Addition and Subtraction
Key Math Learning
To find the missing term in a number sentence, think about
related facts or think about the opposite operation.
Numbers Every Day
Students should be systematic to ensure they do not miss any pairs
of numbers. Students should recognize that after 7 + 8, the number
sentences repeat because when you add, order does not matter.
BEFORE
Get Started
Write the number sentence 5 + 3 = 8 on the
board. Erase the 3. Ask:
• How could you find the missing number?
(I could use guess and check or I could
use subtraction.)
Present Explore. Encourage students to record
their number sentences as they play the game.
DURING
Explore
AFTER
Connect
Invite volunteers to describe the strategies they
used to find a missing number. Make a list of
the strategies on the board.
Use the examples in Connect to introduce the
strategies “think of related facts” and
“think about the opposite operation.”
Tell students that no matter which strategy they
use to find a missing number, they should
always get the same answer.
Ongoing Assessment: Observe and Listen
Practice
Ask questions, such as:
• How many counters did you use? (14) How
many counters were in one hand? (9)
• How did you find how many counters were
in your partner’s other hand?
(I counted on by 1s from 9 until I got to 14. She had
5 counters in her other hand.)
Have Addition Chart 1 (Master 2.6) available
for all questions.
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Unit 2 • Lesson 5 • Student page 68
Assessment Focus: Question 7
Students could use addition charts. They find
pairs of numbers that have a difference of 4.
Some students may list pairs of numbers that
have more than 2 digits.
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REACHING ALL LEARNERS
Alternative Explore
8
7
9
9
9
Materials: Base Ten Blocks
Player A uses Base Ten Blocks to model a number, then shows
them to Player B.
Player B closes his eyes while Player A removes some blocks.
Player B then finds how many blocks were removed.
9
13
16
11
8
I used doubles. 8 + 8 = 16
Common Misconceptions
➤Students erroneously use the opposite operation to find the
missing term in a number sentence of the form 7 –
= 2.
They add 7 + 2 to get 9.
How to Help: Encourage students to model the number sentence
with counters. Show students it does not make sense to add, as
the missing term would then be larger than 7.
6
7 stickers
Sample Answers
4. I thought about related facts. I know 5 + 6 = 11.
6. Calvin had 13 hockey cards. He gave Eric some of his cards.
14 soccer balls
0 15
1 + 14 = 15
2 + 13 = 15
3 + 12 = 15
4
5
6
7
+
+
+
+
8
ways
11 = 15
10 = 15
9 = 15
8 = 15
Calvin has 6 cards left. How many cards did he give Eric?
(Answer: 7 cards; 13 – 7 = 6.)
7. There are many ways to do this. The missing numbers could
be 4 and 0, 5 and 1, 6 and 2, 7 and 3, 8 and 4, 9 and 5,
10 and 6, and so on. The numbers could also be large
numbers, such as 204 and 200.
REFLECT: I used subtraction. I knew how many counters my
partner used. I looked at how many counters she had in her
hand, then subtracted this number from the total. This gave
me the number of counters missing.
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Understanding concepts
✔ Students understand that to find the
missing term in a number sentence,
they can use related facts or the
opposite operation.
Extra Support: Students having difficulty finding the missing
term in a number sentence may benefit from using the triangular
cards they made in Lesson 4.
Students can use Step-by-Step 5 (Master 2.17) to complete
question 7.
Applying procedures
✔ Students can use a variety of
strategies to find the missing term in a
number sentence.
Extra Practice: Have students make a set of triangular cards
with one term missing on each card. Students use the cards to play
another version of the game, How Many Are Missing?
Students can complete Extra Practice 3 (Master 2.30).
Communicating
✔ Students can explain the strategy they
used to find the missing term in a
number sentence.
Extension: Have students make number sentences with missing
terms that go beyond 9 + 9.
Recording and Reporting
Master 2.2 Ongoing Observations:
Patterns in Addition and Subtraction
Unit 2 • Lesson 5 • Student page 69
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ESSON 6
Adding and Subtracting
2-Digit Numbers
40–50 min
LESSON ORGANIZER
Curriculum Focus: Add and subtract 2-digit numbers using
concrete materials. (N14, N17)
Teacher Materials
overhead Base Ten Blocks
place-value mat (made from PM 17)
Student Materials
Optional
Base Ten Blocks
Step-by-Step 6
place-value mats
(Master 2.18)
(made from PM 17)
Extra Practice 3
calculators
(Master 2.30)
index cards
Assessment: Master 2.2 Ongoing Observations: Patterns in
Addition and Subtraction
64 drinks
28 bottles
Key Math Learnings
1. You can use Base Ten Blocks or place-value mats to add and
subtract 2-digit numbers.
2. The strategies for adding and subtracting 2-digit numbers
are based on place-value concepts.
Math Note
Students require place-value mats for this lesson. If you do
not have place-value mats, turn a 2-column chart (PM 17)
sideways and label the columns “Tens” and “Ones.” Make
photocopies. You may wish to laminate the mats.
BEFORE
Get Started
Have a student count the number of boys in the
class. Have another student count the number
of girls. Write these numbers on the board.
Have a volunteer put Base Ten Blocks on the
overhead projector for the number of girls.
Have another volunteer put the blocks on the
projector for the number of boys. Have a third
volunteer combine the two sets of blocks to
count how many students are in the class.
Ask students how they could find out how
many more girls or boys there are in the class.
Students may have different strategies.
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Unit 2 • Lesson 6 • Student page 70
One strategy is to pair a boy with a girl (or do
this with blocks on the overhead), until you
run out of boys or girls. Then count the boys
or girls who are not paired.
Present Explore. Distribute Base Ten Blocks and
place-value mats to students.
DURING
Explore
Ongoing Assessment: Observe and Listen
Ask questions, such as:
• How did you model 46?
(I used 4 rods and 6 unit cubes.)
• How did you model 18?
(I used 1 rod and 8 unit cubes.)
• How did you use Base Ten Blocks to add
46 + 18?
(I counted 14 unit cubes. I traded 10 unit cubes for
1 rod and kept 4 unit cubes. Then I counted 6 rods.
46 + 18 = 64)
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REACHING ALL LEARNERS
Early Finishers
Students write story problems that require both addition and
subtraction, then solve their problems.
Common Misconceptions
➤Students fail to trade 1 ten for 10 ones when subtracting, and
subtract the lesser number of ones from the greater number of
ones regardless of which is the greater number.
How to Help: Have students use Base Ten Blocks to model the
larger number, then take away the blocks that represent the number
being subtracted. Students will “see” when there is a need to trade.
Curriculum Focus
Your curriculum requires that students use the inverse operation
to verify solutions to addition and subtraction problems (N17).
The Curriculum Focus Activities, Checking Addition (Master
2.12a) and Checking Subtraction (Master 2.12b) are provided
to accommodate this outcome. You may wish to have students
complete these activities after this lesson. The answers to these
activities can be found on page 20 of this Lesson.
Remind students frequently to check their answers by using the
inverse operation.
• How did you use a place-value mat to subtract
46 – 18?
(I placed 4 ten rods and 6 ones on the mat. I traded
1 rod for 10 ones. Then I had 3 rods and 16 ones.
I took away 8 ones to leave 8 ones. I took away 1 ten
to leave 2 tens. 46 – 18 = 28)
• What other strategy could you use to find
how many more bottles of juice than water?
(I used Base Ten Blocks of two different colours;
orange for juice and green for water. I paired the
blocks: 1 orange rod and 1 green rod; I traded 1
orange rod for 10 orange cubes; then paired 8 orange
cubes with 8 green cubes. I had no green blocks left.
I had 2 orange rods and 8 orange cubes left. This
tells me how many more bottles of juice I had.)
AFTER
Connect
Invite students to share the strategies they used
to add 46 + 18 and to subtract 46 – 18. Have
students demonstrate these strategies with
overhead Base Ten Blocks and place-value mats.
Write the numbers 29 and 38 on the board. Use
the overhead Base Ten Blocks and place-value
mats to model how to add 29 + 38. Tell
students since there are 17 ones, we can use
10 ones to make 10, leaving 7 ones. We then
add the tens and the ones to get 6 tens and
7 ones, or 67.
Use the overhead Base Ten Blocks and placevalue mats to model how to subtract 50 – 26.
We cannot take 6 ones from 0 ones, so trade
1 ten rod for 10 ones. We then have 4 tens and
10 ones from which we subtract 2 tens and
6 ones, to leave 2 tens and 4 ones, or 24.
Use the examples in Connect to review the
strategies for adding and subtracting. Ask:
• When do you need to trade 10 ones for 1 ten?
(When I add the ones and have more than 10 ones)
• When do you need to trade 1 ten for 10 ones?
(When I have to take away more ones than I have)
Unit 2 • Lesson 6 • Student page 71
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Sample Answers
6. a) The first number starts at 50 and decreases by 1 each
time. The second number starts at 35 and decreases by
1 each time. The answers start at 85 and decrease by
2 each time.
b) The first number is always 91. The second number
increases by 10 each time. Since you are subtracting
10 more each time, the answers start at 35 and decrease
by 10 each time.
7. 10 + 20, 11 + 19, 12 + 18, 13 + 17, 14 + 16, 15 + 15
I know I have found all the ways because I started with 10,
the least 2-digit number, and added 1 each time until the
numbers started to repeat.
8. 99 – 14, 98 – 13, 97 – 12, 96 – 11, 95 – 10
I know I have found all the ways because I started with
99, the greatest 2-digit number, and subtracted 1 each time
from each number until the number being subtracted was
10, which is the least 2-digit number.
11. 36 children brought their bikes to the bike-a-thon.
25 children completed the bike-a-thon. How many children
did not finish? (Answer: 11 children; 36 – 25 = 11)
= 38
= 78
= 52
= 58
= 62
= 14
= 32
= 24
= 26
= 34
= 66
27
74
54
27
94
27
85
83
81
79
=
=
=
=
35
25
15
5
Curriculum Focus
Have students use their calculators to check
their answers to questions 1 to 5.
Questions 7 and 8 also require calculators.
Question 12 requires index cards. Have Base
Ten Blocks and place-value mats available for
all questions.
Answers to Curriculum Focus Activities:
Curriculum Focus Activity 1– Master 2.12a
b) 136
c) 103
1. a) 58
d) 143
e) 101
f) 141
g) 77
h) 82
i) 108
j) 111
20
Unit 2 • Lesson 6 • Student page 72
= 76
27
Practice
Students add all possible combinations of
2-digit numbers. Students should realize that to
subtract, the top number must be greater than
the bottom number. Students then order the
sums from greatest to least to find the greatest
sum. They order the differences from least to
greatest to find the least difference.
= 44
= 36
6 ways
Assessment Focus: Question 12
= 72
84
=
=
=
=
Curriculum Focus Activity 2– Master 2.12b
b) 31
c) 55
e) 20
f) 29
h) 54
i) 36
1. a) 71
d) 47
g) 46
j) 24
= 78
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12. There are 12 addition problems: 53 + 74, 53 + 47,
5 ways
86 bottles
9 boys
54 + 37, 54 + 73, 57 + 34, 57 + 43, 35 + 74, 35 + 47,
34 + 75, 37 + 45, 45 + 73, 43 + 75
There are 12 subtraction problems: 53 – 47, 54 – 37,
57 – 43, 57 – 34, 45 – 37, 47 – 35, 75 – 34, 75 – 43,
73 – 45, 73 – 54, 74 – 35, 74 – 53
When I solved my addition problems, I found that some of the
sums are the same. There are only 6 different sums:
127, 118, 109, 100, 91, 82. The greatest sum is 127.
There are 12 differences: 6, 8, 12, 14, 17, 19, 21, 23, 28,
32, 39, 41. The least difference is 6.
REFLECT: To add or subtract 2-digit numbers, use Base Ten
Blocks or place-value charts. To add, model the numbers, then
add the ones. If there are more than 10 ones, trade 10 ones
for 1 ten, then add the tens. To subtract, model the numbers,
then subtract the ones. If there are not enough ones to take
away from, trade 1 ten for 10 ones before you subtract the
ones. Subtract the tens.
Numbers Every Day
Some students might write number sentences that involve other
operations, such as subtraction. Some possible sentences are:
32 = 10 + 10 + 10 + 2;
32 = 20 + 6 + 4 + 2;
32 = 40 – 6 – 2;
32 = 33 – 1;
32 = 1 + 2 + 3 + 4 + 4 + 5 + 6 + 7
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Understanding concepts
✔ Students understand the strategies
for adding and subtracting
2-digit numbers.
Extra Support: Have students add or subtract two 2-digit
numbers where no trading is required, to build confidence.
Students can use Step-by-Step 6 (Master 2.18) to complete
question 12.
Applying procedures
✔ Students can use Base Ten Blocks and
place-value mats to add and subtract
2-digit numbers.
Extra Practice: Students can play the Additional Activity,
First to 10 (Master 2.10).
Students can complete Extra Practice 3 (Master 2.30).
✔ Students can solve problems
involving the addition or subtraction
of 2-digit numbers.
Extension: Have students find the missing digits in the sum
and difference below.
4"
"3
+ "5
– 2"
68
44
Recording and Reporting
Master 2.2 Ongoing Observations:
Patterns in Addition and Subtraction
Unit 2 • Lesson 6 • Student page 73
21
Home
LESSON 7
Quit L
ESSON 7
Using Mental Math
to Add
40–50 min
LESSON ORGANIZER
Curriculum Focus: Mentally add 1-digit and 2-digit
numbers. (PR3)(N19)
Student Materials
Optional
Step-by-Step 7
(Master 2.19)
Extra Practice 4
(Master 2.31)
Assessment: Master 2.2 Ongoing Observations: Patterns in
Addition and Subtraction
84 days
Key Math Learning
When you add in your head, you do mental math.
Numbers Every Day
In the first part, students could break down the second number
in each statement into 2 numbers, one of which is given.
BEFORE
Get Started
Have students find each sum mentally:
10 + 5, 10 + 20, 20 + 5 (15, 30, 25) Ask:
• Why were these sums easy to find mentally?
(At least one of the numbers in each sum had a zero.)
• Name another pair of numbers that would be
easy to add mentally. (25 and 10)
Present Explore. Remind students to record the
steps they used to add the numbers.
DURING
Explore
Ongoing Assessment: Observe and Listen
Ask questions, such as:
• How did you find the sum?
(I added 30 to 48 by counting on by tens to get
78, then I added 6 to get 84.)
• How else could you find the sum?
(I could add 40 to 48, then take away 4.)
• Why did you use that strategy? (It is easier to
add when one of the numbers has a zero.)
22
Unit 2 • Lesson 7 • Student page 74
AFTER
Connect
Invite volunteers to share their strategies
with the class.
Use Connect to introduce the strategies “add on
tens, then add on ones,” and “take from one to
give to the other.” Invite volunteers to use these
strategies to add 28 + 34.
Ask:
• When would you use the strategy “take from
one to give to the other?” (When one of the
numbers being added is very close to a number
of tens)
Practice
Assessment Focus: Question 8
If students cannot think of ideas for a story
problem, have them read the questions
in Explore, Connect, and questions 6 and 7
for suggestions.
Home
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REACHING ALL LEARNERS
Early Finishers
= 42
= 66
= 52
= 76
= 62
= 86
Students use a deck of cards with the tens and face cards removed.
Students draw 4 cards. They use the cards to form two 2-digit
numbers. Students use mental math to add the two numbers formed.
= 72
= 96
Common Misconceptions
= 78
= 88
= 68
= 78
= 71
= 71
= 71
= 71
= 64
= 66
= 90
= 71
➤Students have difficulty using the strategy “take from one
number to give to the other.”
How to Help: Have students model the two numbers with
counters. Students take counters away from one number and
give the counters to the other number. Students will then “see”
what happens to each number.
Sample Answers
1. In each part, as the second number increases by 10, the
answer increases by 10.
82 licence plates
5. I can add on tens, then add on ones: 29 + 50 + 5 = 84
83 cars
2
7
13
12
12
72
I can take from one to give to the other:
29 + 1 + 54 = 30 + 54 = 84
I can add 1 to 29 to get 30, then add the numbers and take
away 1 from the answer: 30 + 55 = 85, 85 – 1 = 84
8. Andrew went to the car show with his mother. They saw 45 blue
cars and 37 green cars. How many cars did they see altogether?
(Answer: They saw 82 cars: 45 + 35 + 2 = 80 + 2 = 82)
REFLECT:
+
+
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Understanding concepts
✔ Students can describe at least two
different strategies for adding
numbers mentally.
✔ Students understand when it is
appropriate to use mental math to add.
Extra Support: Provide students with questions where students
add 10 or multiples of 10 to build confidence.
Students can use Step-by-Step 7 (Master 2.19) to complete
question 8.
Applying procedures
✔ Students can mentally add two
2-digit numbers.
Communicating
✔ Students can describe their strategies
clearly and precisely using
appropriate language.
Extra Practice: Students make 20 cards with a different two-digit
number on each card. Students place the cards face down on a
table. Students take turns to turn over 2 cards, then use mental
math to add the numbers.
Students can complete Extra Practice 4 (Master 2.31).
Extension: Students use mental math to add three
2-digit numbers.
Recording and Reporting
Master 2.2 Ongoing Observations:
Patterns in Addition and Subtraction
Unit 2 • Lesson 7 • Student page 75
23
Home
LESSON 8
Quit
Using Mental Math
to Subtract
40–50 min
LESSON ORGANIZER
Curriculum Focus: Mentally subtract 1-digit and 2-digit
16 people
numbers. (N19)
Optional
Step-by-Step 8
(Master 2.20)
Extra Practice 4
(Master 2.31)
Assessment: Master 2.2 Ongoing Observations: Patterns in
Addition and Subtraction
Student Materials
Key Math Learning
Strategies, such as “take away tens, then take away ones,” and
“add to match the ones, then subtract,” can be used to mentally
subtract 1-digit and 2-digit numbers.
28
45
36
52
67
Numbers Every Day
Make sure students understand the order of the numbers can
be switched in addition. To add: in each case, one ones digit is
0, so the sum is the number formed by the tens digit and the
non-zero ones digit.
BEFORE
Get Started
Have students find each difference mentally:
20 – 10, 15 – 5, 25 – 5 (10, 10, 20) Ask:
• Why were these differences easy to find
mentally? (Because in each subtraction question,
the ones digits were the same.)
Emphasize that we use mental math when the
numbers are easy to handle.
Present Explore. Remind students to solve the
problem without using materials.
DURING
Explore
Ongoing Assessment: Observe and Listen
Ask questions, such as:
• How did you find the difference?
(27 is 3 less than 30. I subtracted 30 from 43 to get
13, then added 3 to get 16.)
• How else could you find the difference?
(I could subtract the tens, 43 – 20 = 23, then
subtract the ones, 23 – 7 = 16.)
24
Unit 2 • Lesson 8 • Student page 76
AFTER
Connect
Invite volunteers to share their strategies with
the class.
Use Connect to introduce the mental math
strategies for subtraction. Invite volunteers to
use these strategies to subtract 31 – 17.
Ask:
• How did you use the strategy “add to match
the ones, then subtract” to subtract 31 – 17?
(I added 6 to 31 to make 37; 37 – 17 = 20. Then I
took away the 6 I added; 20 – 6 = 14.)
Practice
Assessment Focus: Question 7
Students find a pair of numbers whose
difference is 43. A few students may even
write a problem involving 3 numbers,
such as 59 – 9 – 7.
Home
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REACHING ALL LEARNERS
Common Misconceptions
=
=
=
=
49
39
29
19
=
=
=
=
= 22
57
67
77
87
=
=
=
=
= 42
➤Students have difficulty using the strategy “add to match the
ones, then subtract” to subtract numbers such as 24 – 17.
How to Help: Have students model the two numbers with
counters. Students add 3 counters to 24 to match the ones;
24 + 3 = 27. Students then subtract; 27 – 17 = 10. Tell students
they must get the counters they added back so they must take
away 3 counters from 10 to get 7.
78
58
38
18
= 62
= 82
Sample Answers
2. The number being subtracted from increases by 10 each time;
32
22
12
2
18
74
29
38
29 geese flew in.
the number being subtracted decreases by 10 each time; and
the answer increases by 20 each time.
5. I can take away tens, then take away ones: 81 – 50 = 31,
31 – 8 = 23
I can add to match the ones, then subtract: 81 + 7 = 88,
88 – 58 = 30, 30 – 7 = 23
I can add to make a friendly number: 81 – 58 = 83 – 60 = 23
7. Some possible problems are: 44 – 1, 45 – 2, . . ., 86 – 43,
87 – 44, 88 – 45, ..., 100 – 57, 101 – 58, 102 – 59,
and so on.
REFLECT: There are two strategies that I use to subtract mentally. I
could take away the tens, then take away the ones. For
example, to subtract 55 – 27, I first subtract the tens;
55 – 20 = 35. I then subtract the ones; 35 – 7 = 28. I could
also add to match the ones, then subtract. For example, I could
add 2 to 55 to make 57; 57 – 27 = 30. I then take away the
2 I added; 30 – 2 = 28.
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Understanding concepts
✔ Students can describe at least two
different strategies for subtracting
numbers mentally.
✔ Students understand when it is
appropriate to use mental math
to subtract.
Extra Support: Provide students with questions where students
subtract 10 or multiples of 10 to build confidence.
Students can use Step-by-Step 8 (Master 2.20) to complete
question 7.
Applying procedures
✔ Students can mentally subtract two
2-digit numbers.
Communicating
✔ Students can describe their strategies
clearly and precisely using
appropriate language.
Extra Practice: Students make 10 cards, each with a 2-digit
number greater than 40. Students make another 10 cards, each
with a 2-digit number less than 40. Students take turns to take one
card from each pile and subtract the numbers.
Students can also complete Extra Practice 4 (Master 2.31).
Extension: Students write a story problem that can be solved by
subtracting 2-digit numbers. They then solve the problem.
Recording and Reporting
Master 2.2 Ongoing Observations:
Patterns in Addition and Subtraction
Unit 2 • Lesson 8 • Student page 77
25
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LESSON 9
Quit
Strategies Toolkit
40–50 min
LESSON ORGANIZER
Curriculum Focus: Interpret a problem and select an
appropriate strategy. (N14)
Teacher Materials
7 foreign stamps
overhead counters
Student Materials
counters
Assessment: PM 1 Inquiry Process Check List,
PM 3 Self-Assessment: Problem Solving
Key Math Learning
A “guess and check” strategy can be used to solve
many problems.
BEFORE
Get Started
Present Explore. Have counters available for
students to model the problem. Encourage
students to think about what strategy they will
use before they begin.
DURING
Explore
Ongoing Observations: Observe and Listen
Ask questions, such as:
• What are some pairs of numbers that add to
25? (1 + 24, 2 + 23, 3 + 22, 4 + 21,
5 + 20, 6 + 19, 7 + 18, 8 + 17, and so on.)
• Which two numbers have a difference of 11?
(18 and 7)
• How did you solve the problem? (I used the
strategy “use a model.” I put 25 counters on my desk.
I took away one counter each time until there were
11 more counters in one pile than in the other. Gina
had 7 foreign stamps and 18 Canadian stamps.)
26
Unit 2 • Lesson 9 • Student page 78
9 cars
AFTER
Connect
Review the example in Connect.
Ask:
• If you guess 10 cars, how many trucks would
there be? (15) Is the total 23?
(No, the total is 25.)
• If you guess 9 cars, how many trucks would
there be? (14) Is the total 23? (Yes, 9 + 14 = 23)
• If you started by guessing the number of
trucks, what would you do differently?
(I would subtract 5 to find the number of cars.)
• How could you solve this problem another
way? (I could model the number 23 with counters. I
could remove one counter at a time until the difference
between the number of counters in each pile was 5.)
Practice
Encourage students to refer to the Strategies list
to choose an appropriate strategy.
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REACHING ALL LEARNERS
Early Finishers
Have students repeat Explore. This time Gina has 37 stamps,
and she has 15 more foreign stamps than Canadian stamps.
How does this change affect the answers?
(Gina has 26 foreign stamps and 11 Canadian stamps.)
Common Misconceptions
➤Students have difficulty making an initial guess when using the
“guess and check” strategy.
How to Help: Use the Explore problem as an example. Have
students use counters to model the total number of stamps.
Students then arrange the counters into 2 groups until it looks
like one group has about 11 more counters than the other
group. Students count the counters to check their answers. If
necessary, students adjust the counters and guess again.
Sasha has won 15 cards and Kumail
has won 9 cards.
Sample Answer
REFLECT: To answer Practice question 1, I used “guess and
Margaret used 5 dimes and 3 nickels.
There are two possible answers.
There are 2 tricycles and 6 bicycles OR there are 4 tricycles and 3 bicycles.
check.” I guessed Kumail had won 10 cards. I then added
6 to find how many cards Sasha had won; 10 + 6 = 16.
I checked to see if the total was 24; 16 + 10 = 26.
This is too much. So, I chose a lesser number and I guessed
Kumail had won 9 cards. I then added 6 to find how many
cards Sasha had won; 9 + 6 = 15. I checked to see if the
total was 24; 15 + 9 = 24. The total was 24, so my answer
is correct.
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Understanding concepts
✔ Students understand that “guess
and check” is a strategy to solve
many problems.
Extra Support: Provide play money (coins) for students to use in
Practice question 2.
Problem Solving
✔ Students can select an appropriate
strategy to solve a problem.
Extension: Challenge students to solve each of the Practice
questions using a different strategy. They check to see that their
answers are the same each time.
Extra Practice: Have students write problems similar to the
questions in Practice for others to solve.
Communicating
✔ Students can describe their strategy
clearly, using appropriate language.
Recording and Reporting
PM 1 Inquiry Process Check List
PM 3 Self-Assessment: Problem Solving
Unit 2 • Lesson 9 • Student page 79
27
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LESSON 10
Quit
Estimating Sums
and Differences
40–50 min
LESSON ORGANIZER
Curriculum Focus: Use estimation to add and subtract.
(N19)
Optional
Step-by-Step 10
(Master 2.21)
Extra Practice 5
(Master 2.32)
Vocabulary: estimate, difference
Assessment: Master 2.2 Ongoing Observations: Patterns in
Addition and Subtraction
Student Materials
calculators
Key Math Learnings
1. When you do not need an exact answer, you estimate.
2. Strategies, such as “rounding first” and “front-end
34 + 28 = 62
estimation,” can be used to estimate.
Numbers Every Day
About 700
Students could use the strategy “add on tens, then add on ones:”
34 + 20 = 54, 54 + 8 = 62
Students could use the strategy “take from one to give to the
other:” 34 + 6 = 40, 28 – 6 = 22; so, 34 + 28 = 40 + 22 = 62
BEFORE
Get Started
About 300
Present Explore. Ensure students understand
they are to estimate, not calculate.
• How did you estimate the number of
pennies? (I rounded 213 to 200 and I rounded
488 to 500. I then added 200 and 500 to get 700.)
• About how many more than Jeff does May
have? How do you know?
(About 300; I subtracted 200 from 500.)
• Which other strategy could you use?
(I could round each number to the nearest ten.)
• Is your estimate close enough for Jeff and
May to plan what they can buy? How do you
know? (Yes, if I use a calculator to add 213 + 488,
I get 701. This is very close to my estimate of 700.)
DURING
AFTER
Have students read the introduction to the lesson
on page 80 of the Student Book. Introduce the
term estimate as being close to an amount or
value, but not exact. Invite students to give
examples of situations in which an exact number
might be used (recipes, test marks). Talk about
other situations where an estimate might be used
(the distance to the store, the number of pages in a book).
Explore
Ongoing Assessment: Observe and Listen
Ask questions, such as:
• How do you know you have to estimate?
(The question asks “About how many?”)
28
Unit 2 • Lesson 10 • Student page 80
Connect
Invite students to share the strategies they used
to estimate.
Ask:
• Why did you round to the nearest hundred?
(Because the numbers are easy to add and subtract)
Home
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REACHING ALL LEARNERS
Alternative Explore
Materials: department store flyers
Tell students they have $40 to spend. They can buy what they
want, as long as they do not go over $40. Have students
estimate as they shop, making a list of items they buy. Students
use a calculator to find the actual cost of their items, then
compare their estimate to the actual cost.
Early Finishers
Have students estimate the sum of 251 + 323 in as many
different ways as they can.
Common Misconceptions
➤Students have difficulty rounding a number to the nearest ten.
How to Help: Provide students with a number line. Students
locate the number on the line and “see” which ten it is closer to.
Sample Answers
1. a) 80; 61 rounds down to 60 and 22 rounds down to 20,
60 + 20 = 80.
b) 60; 54 rounds down to 50 and 13 rounds down to 10,
50 + 10 = 60. Alternatively, since the numbers in the ones
place add to 7, when both numbers are rounded down, the
estimate 60 is not closer; 70 is better.
c) 600; 327 rounds down to 300 and 254 rounds up to 300,
300 + 300 = 600.
• How do you know your answer is close to
the exact answer? (Because I rounded one
number up and the other number down. Both
numbers were close to a number of hundreds.)
Introduce the term difference as the result of a
subtraction. Tell students that in the number
sentence 9 – 5 = 4, 4 is the difference.
Review the strategies in Connect. Have
volunteers use these strategies to add
322 + 586 and to subtract 586 – 322. Ask:
• How did you use the strategy “rounding
first?” (I rounded each number to the nearest 100.
I rounded 322 to 300 and 586 to 600, then added
and subtracted the numbers; 300 + 600 = 900 and
600 – 300 = 300.)
• How did you use the strategy “front-end
estimation?” (I used the digits in the hundreds
place and ignored all other digits; 322 became 300
and 586 became 500. I then added and subtracted
the numbers; 300 + 500 = 800, 500 – 300 = 200.)
• Which strategy gave the better estimate? Why?
(“Rounding first” gave the better estimate; 322 is close
to 300 and 586 is close to 600. In “front-end
estimation,” 586 is far away from 500, so the estimate
is not very close to the exact answer.)
Practice
Question 4 requires a calculator.
Assessment Focus: Question 3
Students should round each number to the
nearest 10 and then find pairs of numbers that
add to 200. Students then look at how the
numbers were rounded. Students should
realize if one number was rounded up, the
other number should be rounded down to give
the closest estimate.
Unit 2 • Lesson 10 • Student page 81
29
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3. I rounded all the numbers to the nearest 10, and found
50 + 150 = 200. I then looked at the two numbers that
rounded to 150. 148 rounded up to 150 and 153 rounded
down to 150. Since 53 rounded down to 50, I chose the
number that rounded up to 150: 148. The 2 numbers that will
give the sum that is closest to 200 are 53 and 148.
4. I rounded 145 to the nearest 10 and got 150. Since
150 + 150 = 300, and 300 + 300 + 300 = 900, I estimate
that I add 145 six times to get 900. I checked with a
calculator: 145 + 145 + 145 + 145 + 145 + 145 = 870.
870 is close to 900, so my estimate is close.
5. No, Faizal is not close. To estimate 136 – 25, I rounded
136 to 140 and 25 to 30, then subtracted the numbers;
140 – 30 = 110. Faizal has about 110 books.
6. Matthew had a birthday party. He was to give each of his
friends a CD instead of a loot bag. His mother did not want
any CDs left over but she wanted to be sure that everyone got
a CD. Matthew invited 12 girls and 12 boys to his party. How
many CDs does he need? (Answer: 12 + 12 = 24)
both
both
53 and 148
No
REFLECT: When I guess, I choose a number without really
knowing. When I estimate, I look at the numbers, then round
them to get an answer that is close to the exact answer. For
example, if I guess 143 + 466, I would say 700. If I estimate,
I would round 143 to 100 and 466 to 500, then add
100 + 500 to get 600.
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Understanding concepts
✔ Students understand that an estimate
is close to an amount or value, but
not exact.
Extra Support: Give students number lines to help them estimate
before they add or subtract.
Students can use Step-by-Step 10 (Master 2.21) to complete
question 3.
✔ Students understand when an estimate
is appropriate.
Extra Practice: Have students refer to Lesson 6, Practice question
5. Students estimate each sum or difference, then compare their
estimates to the exact answers.
Students can also complete Extra Practice 5 (Master 2.32).
Applying procedures
✔ Students can use strategies, such as
“rounding first” and “front-end
estimation,” to estimate sums
and differences.
Extension: Challenge students to estimate the sum of 3 or
more numbers.
Recording and Reporting
Master 2.2 Ongoing Observations:
Patterns in Addition and Subtraction
30
Unit 2 • Lesson 10 • Student page 82
Home
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ESSON 11
Adding 3-Digit
Numbers
40–50 min
LESSON ORGANIZER
Curriculum Focus: Add 3-digit numbers with and without
regrouping, using concrete materials. (N14, N17, N18)
411 T-shirts
Teacher Materials
overhead Base Ten Blocks
place-value mat (made from PM 18)
Student Materials
Optional
Base Ten Blocks
Step-by-Step 11
place-value mats
(Master 2.22)
(made from PM 18)
Extra Practice 5
calculators
(Master 2.32)
Assessment: Master 2.2 Ongoing Observations: Patterns in
Addition and Subtraction
Key Math Learnings
1. You can use Base Ten Blocks with or without place-value mats
to add 3-digit numbers.
2. The strategies for adding 3-digit numbers are based on
place-value concepts.
3. The same strategies are used to add 3-digit and
2-digit numbers.
Math Note
Students require place-value mats for this lesson and
future lessons. If you do not have place-value mats, turn a
3-column chart (PM 18) sideways and label the columns
“Hundreds,” “Tens,” and “Ones.” Make photocopies. You
may wish to laminate the mats.
BEFORE
Get Started
Ask students how they add 284 + 328. Have
students talk about the strategies they could
use. Ask:
• What materials could you use to help
you add?
(I could use Base Ten Blocks and place-value mats.)
• How do you add?
(I add the ones, add the tens, and add the hundreds.)
• How do you regroup 12 ones?
(12 ones can be regrouped as 1 ten and 2 ones.)
• How do you regroup 11 tens?
(11 tens can be regrouped as 1 hundred and 1 ten.)
• How many hundreds?
(2 hundreds + 3 hundreds + 1 hundred is 600.)
• What is the sum? (612; 6 hundreds 1 ten 2 ones)
Present Explore. Distribute Base Ten Blocks and
place-value mats to students.
DURING
Explore
Ongoing Assessment: Observe and Listen
Ask questions, such as:
• How did you model 236?
(I used 2 flats, 3 rods, and 6 unit cubes.)
• How did you model 175?
(I used 1 flat, 7 rods, and 5 unit cubes.)
• How did you use Base Ten Blocks to add
236 + 175? (I counted 11 unit cubes. I traded
10 unit cubes for 1 rod and kept 1 unit cube. Next,
I counted 11 rods. I traded 10 rods for 1 flat and
kept 1 rod. I counted 4 flats. 236 + 175 = 411)
• How else could you add 236 + 175? (I could
use counters but I would need a lot of counters.)
Unit 2 • Lesson 11 • Student page 83
31
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REACHING ALL LEARNERS
Alternative Explore
Have students solve this problem:
Last year, Corinne went outside for 153 morning recesses and
158 afternoon recesses. For how many recesses did Corinne go
outside altogether? Students use what they know about adding
2-digit numbers to solve this problem. (Answer: 311 recesses)
Common Misconceptions
➤Students forget to trade when adding.
How to Help: Tell students when they add, they can have no
more than 9 rods in the tens column and no more than 9 unit
cubes in the ones column of the place-value chart. If they have
more than 9 of either of these Base Ten Blocks, they must trade.
Early Finishers
Challenge students to find two 3-digit numbers that have a sum
that is a 4-digit number (for example, 672 + 489).
Numbers Every Day
For 57 + 42, students could add on tens, then add on ones:
57 + 40 + 2 = 99.
For 49 + 51, students could take from one to give to the other:
49 + 1 + 50 = 50 + 50 = 100.
For 25 + 34, students could add on tens, then add on ones:
25 + 30 + 4 = 59.
For 85 + 49, students could take from one to give to the other:
84 + 49 + 1 = 84 + 50 = 134.
AFTER
Connect
Invite students to share the strategies they used
to add 236 + 175. Have students demonstrate
these strategies with overhead Base Ten Blocks
and place-value mats.
Review the problem in Connect. Ask:
• What did you discover about the strategies
for adding 2-digit and 3-digit numbers?
(The strategies are the same.) Why? (The meaning
of addition is still the same, no matter how large the
numbers are.)
• Why do we start adding in the ones place?
(So that we know if we have to regroup 10 ones for
one rod)
• Could we start by adding in the hundreds
place? (Yes; I have 3 flats, 11 rods, and 12 unit
cubes. I trade 10 unit cubes for 1 rod, leaving 2 unit
cubes, then trade 10 rods for 1 flat, leaving 2 rods. I
end up with 4 flats, 2 rods, and 2 unit cubes.)
32
Unit 2 • Lesson 11 • Student page 84
99
100
59
134
486
416
Write the numbers 329 and 285 on the board.
Use the overhead Base Ten Blocks and placevalue mats to model how to add 329 + 285.
(Answer: 6 hundreds 1 ten 4 ones, or 614)
Practice
Question 7 requires a calculator. Have Base
Ten Blocks and place-value mats available for
all questions. Encourage students to check their
answers using estimation, a calculator, or the
inverse operation.
Assessment Focus: Question 7
Students should be systematic to ensure they
do not miss any pairs of numbers. Both
numbers must be 3-digit numbers. Students
should start with 100 as the first number, then
increase the first number by 1 each time.
Students should recognize that after 108 + 109,
the number sentences repeat because when you
add, order does not matter.
Home
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Sample Answers
= 372
= 432
610
= 851
= 897
= 792
5. I modelled the numbers with Base Ten Blocks. I counted
= 420
= 714
730
530
530
= 851
= 851
= 851
355 lunches
15 unit cubes. I traded 10 unit cubes for 1 rod and kept
5 unit cubes. Next, I counted 5 rods and 3 flats.
218 + 137 = 355
6. Tracy has a collection of baseball cards. She collected
157 cards last year and 276 cards this year. How many cards
does Tracy have altogether?
(Answer: 157 + 276 = 433 cards)
7. 9 ways: 100 + 117, 101 + 116, 102 + 115, 103 + 114,
104 + 113, 105 + 112, 106 + 111, 107 + 110, 108 + 109
I know I have found all the ways because I started with
100, the least 3-digit number, and added 1 each time until
the numbers started to repeat.
REFLECT: Adding 3-digit numbers is like adding 2-digit numbers
9 ways
because you can use the same strategies. The only difference
is when I add 3-digit numbers, I sometimes have to trade
10 rods for 1 flat.
557 km
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Understanding concepts
✔ Students understand that the same
strategies are used to add 3-digit
numbers as 2-digit numbers.
Extra Support: Have students add two 3-digit numbers where
no regrouping is required, to build confidence.
Students can use Step-by-Step 11 (Master 2.22) to complete
question 7.
Applying procedures
✔ Students can use Base Ten Blocks
and place-value mats to add
3-digit numbers.
Extra Practice: Students can do the Additional Activity,
Tic-Tac-Toe Squares (Master 2.11).
Students can complete Extra Practice 5 (Master 2.32).
✔ Students can solve problems involving
the addition of 3-digit numbers.
✔ Students can choose an appropriate
method for adding and for verifying
solutions.
Extension: Have students find the missing digits in this sum.
4"3
+"8"
812
Recording and Reporting
Master 2.2 Ongoing Observations:
Patterns in Addition and Subtraction
Unit 2 • Lesson 11 • Student page 85
33
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LESSON 12
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Subtracting 3-Digit
Numbers
LESSON ORGANIZER
40–50 min
Curriculum Focus: Subtract 3-digit numbers with and without
regrouping, using concrete materials. (N14, N19)
Teacher Materials
overhead Base Ten Blocks
place-value mat (made from PM 18)
Student Materials
Optional
Base Ten Blocks
Step-by-Step 12
place-value mats
(Master 2.23)
(made from PM 18)
Extra Practice 6
calculators
(Master 2.33)
Assessment: Master 2.2 Ongoing Observations: Patterns in
Addition and Subtraction
The Lee family
162 km
Key Math Learnings
1. You can use Base Ten Blocks with or without place-value mats
to subtract 3-digit numbers.
2. The strategies for subtracting 3-digit numbers are based on
place-value concepts.
3. The same strategies are used to subtract 3-digit and
2-digit numbers.
BEFORE
Get Started
Use overhead Base Ten Blocks and a
transparency of the place-value mat to review
how to subtract 2-digit numbers.
Invite students to examine the map on page 86
of the Student Book. Ask:
• What question can you ask that would
need the subtraction of 3-digit numbers to
answer it?
(How much farther is it from Banff to Vancouver
than from Banff to Edmonton?)
• What strategy would you use to subtract two
3-digit numbers?
(I would use the same strategy that I used to
subtract two 2-digit numbers.)
Students should be familiar with subtraction
questions where they trade 1 ten for 10 ones.
Tell students when they subtract 3-digit
numbers, it is often necessary to trade
1 hundred for 10 tens.
34
Unit 2 • Lesson 12 • Student page 86
Present Explore. Distribute Base Ten Blocks and
place-value mats to students. Remind students
they should always model the greater number
with Base Ten Blocks, then take away the
lesser number.
DURING
Explore
Ongoing Assessment: Observe and Listen
Ask questions, such as:
• Which family travelled farther?
(The Lee family, because 290 is greater than 128)
• How did you find how much farther the Lee
family travelled? (I modelled 290 with Base Ten
Blocks; 2 flats, 9 rods, and 0 unit cubes. I then
subtracted 128 by taking away 1 flat, 2 rods, and
8 unit cubes. There were not enough unit cubes to take
away 8 unit cubes, so I traded 1 rod for 10 unit cubes,
leaving 8 rods. Then I took away 8 unit cubes, leaving
2 unit cubes. Then I took away 2 rods, leaving 6 rods;
and 1 flat, leaving 1 flat. 290 – 128 = 162)
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REACHING ALL LEARNERS
Alternative Explore
Materials: measuring tapes, Base Ten Blocks, place-value mats
Students use a measuring tape to measure the height of their
teacher and a fellow classmate, in centimetres. Students find the
difference in the heights.
Common Misconceptions
➤Students model the lesser number with Base Ten Blocks instead
of the greater number.
How to Help: Have students identify the greater number by
using place value to compare the numbers. Compare the
hundreds digits. If they are the same, compare the tens digits.
Early Finishers
Have students choose a 3-digit number as an answer to a
subtraction question, then find 2 possible 3-digit numbers that
could be subtracted to get that answer; that is, choose the
answer, then write the question.
• How did you record your work?
(I drew pictures. I drew a square for 100,
a stick for 10, and a dot for 1.)
AFTER
Connect
Invite students to share the strategies they used
to subtract 290 – 128. Have students
demonstrate these strategies with overhead
Base Ten Blocks and place-value mats.
Review the problems in Connect. Ask:
• Why do we start subtracting in the ones place?
(If there are not enough ones, we will need to trade
1 ten for 10 ones.)
• What was the most important step that
helped you solve the problem?
(When I traded 1 rod for 10 unit cubes)
Some students have difficulty subtracting from
a number such as 400. Model this subtraction
on the overhead projector: 400 – 156
Have a volunteer place the blocks for 400:
4 flats. Write the number 156 along the bottom
of the place-value mat, to show that this is the
number we take away. Ask:
• How do we take 156 away from 400?
(We want to take 6 ones from 0 ones, but we
cannot. There are no 10 rods to trade, so use
1 flat. Trade 1 flat for 10 rods, then trade 1 rod
for 10 ones. Subtract 6 ones from 10 ones, leaving
4 ones. Subtract 5 tens from 9 tens, leaving 4 tens.
Subtract 1 hundred from 3 hundreds, leaving
2 hundreds. So, 400 – 156 = 244)
When students suggest how to subtract
400 – 156, if they wish to begin with
subtracting hundreds, follow their strategy.
This is a legitimate method.
Unit 2 • Lesson 12 • Student page 87
35
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Sample Answers
6. 999 – 876, 998 – 875, 997 – 874, ..., 226 – 103,
225 – 102, 224 – 101, 223 – 100
7. I modelled 475 with Base Ten Blocks. I traded 1 rod for
10 unit cubes, leaving 6 rods. I took 8 unit cubes away from
15 unit cubes, leaving 7 unit cubes. I took 3 rods away from
6 rods, leaving 3 rods. I took 2 flats away from 4 flats leaving
2 flats. 475 – 238 = 237
8. 456 – 285 = 171
9. The local school was holding a music concert. They printed
652 tickets. They had 328 tickets left over. How many people
attended the concert?
(Answer: 652 – 328 = 324)
To solve the problem, I modelled 652 with Base Ten Blocks,
then took away 3 flats, 2 tens, and 8 ones. I had to trade
1 rod for 10 ones because I could not take 8 ones from
2 ones.
216
Practice
Question 6 requires a calculator. Have Base
Ten Blocks and place-value mats available for
all questions. As students are working, ask
them to explain the method they are using to
subtract and to justify their choice of method.
Assessment Focus: Question 6
There are 777 solutions. Students should find
some of these. Some students may select a
“friendly” 3-digit number such as 423 and
subtract 123 from it to find the “missing
number” (423 – 300 = 123). Other students may
recognize a pattern that they can use to
generate other solutions (for example, by
successively subtracting 1 from the two 3-digit
numbers, they can find many solutions).
36
Unit 2 • Lesson 12 • Student page 88
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REFLECT: To subtract 157, I have to take away 1 hundred 5 tens
= 853
= 913
= 613
= 513
= 707
= 809
= 648
= 905
= 327
= 327
= 327
= 327
118
117
116
7 ones. There are no tens and no ones to take away from.
I trade 1 hundred for 10 tens, then trade 1 ten for 10 ones.
I then take 7 ones from 10 ones, leaving 3 ones. I take 5 tens
from 9 tens, leaving 4 tens. I take 1 hundred from
2 hundreds, leaving 1 hundred; 300 – 157 = 143
Numbers Every Day
215
Students should recognize that 49 + 45 is 1 less than 50 + 45,
and that 51 + 45 is 1 more than 50 + 45. In the second part,
students should find 40 + 35, then use the results to find the
other sums.
237 km
171 comic books
94
96
75
73
77
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Understanding concepts
✔ Students understand that the same
strategies are used to subtract 3-digit
numbers as 2-digit numbers.
Extra Support: Have students subtract two 3-digit numbers
where no regrouping is required, to build confidence. Students can
use Step-by-Step 12 (Master 2.23) to complete question 6.
Applying procedures
✔ Students can use Base Ten Blocks
and place-value mats to subtract
3-digit numbers.
✔ Students can solve problems involving
the subtraction of 3-digit numbers.
Extra Practice: Students choose two 3-digit numbers to subtract,
then make up a story problem they can solve by subtraction. They
solve the problem.
Students can complete Extra Practice 6 (Master 2.33).
Extension: Challenge students to find the least 3-digit number
they can take away from 237 to get a 2-digit number.
Communicating
✔ Students can explain and justify their
methods for subtracting.
Recording and Reporting
Master 2.2 Ongoing Observations:
Patterns in Addition and Subtraction
Unit 2 • Lesson 12 • Student page 89
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LESSON 13
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A Standard Method
for Addition
40–50 min
LESSON ORGANIZER
Curriculum Focus: Develop proficiency in adding 3-digit
numbers. (N14, N19)
Student Materials
Optional
Base Ten Blocks
place-value mats
(made from PM 18)
Step-by-Step 13
(Master 2.24)
Extra Practice 6
(Master 2.33)
Assessment: Master 2.2 Ongoing Observations: Patterns in
Addition and Subtraction
Key Math Learnings
1. Three-digit numbers can be added using the standard
algorithm.
2. The strategies for adding 2-digit and 3-digit numbers are
based on place-value concepts.
BEFORE
Get Started
Initiate a discussion about the strategies
students use to add 2-digit and 3-digit
numbers.
Ask:
• What methods have you used to add 2-digit
and 3-digit numbers?
(Base Ten Blocks, place-value mats, calculators,
mental math, estimation, paper and pencil)
• How do you decide which method to use?
(If the numbers are easy, I use mental math. If they
are harder, I use blocks, or a calculator. If I do not
need an exact answer, I estimate.)
Have students think about how they could add
2-digit and 3-digit numbers without using
concrete materials.
Present Explore. Tell students they are to add
using only pencil and paper. Encourage
students to share the strategies they used.
38
Unit 2 • Lesson 13 • Student page 90
DURING
Explore
Ongoing Assessment: Observe and Listen
Ask questions, such as:
• How did Tio add 25 + 39?
(He added the ones to get 14 ones, then traded
10 ones for 1 ten, leaving 4 ones. He then added the
tens to get 6 tens; 25 + 39 = 64.)
• How did Tio add 257 + 138?
(He added the ones to get 15 ones, then traded
10 ones for 1 ten, leaving 5 ones. He then added the
tens to get 9 tens. He then added the hundreds to get
3 hundreds; 257 + 138 = 395.)
• How did you add 25 + 39? (I used mental math.
I used the strategy “take from one to give to the
other.” 25 + 39 = 24 + 39 + 1 = 24 + 40 = 64)
• How did you add 257 + 138?
(I used mental math. I added on hundreds, then
tens, and then ones; 257 + 100 + 30 + 8 = 395.)
• What are the “little 1s” written above some of
the numbers? (Each represents 1 ten that has been
traded for 10 ones.)
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REACHING ALL LEARNERS
Alternative Explore
Have students write down the first 2 digits of the year in which
they were born to make a 2-digit number. Students write down
the last 2 digits of the year in which they were born to make
another 2-digit number. Students add these 2 numbers without
using concrete materials. Have students write down the first
3 digits of their phone number and the last 3 digits, then add the
two 3-digit numbers using pencil and paper.
Common Misconceptions
➤Students do not align the digits correctly when they add.
How to Help: Have students use 1-cm grid paper. Students write
each digit in one square on the paper. This places the digits in
columns. Students can then add.
Early Finishers
Challenge students to add 694 + 528. Finding this sum involves
trading 10 ones for 1 ten, 10 tens for 1 hundred, and
10 hundreds for 1 thousand.
AFTER
Connect
Invite students to share the strategies they used
to add the numbers in Explore. Have students
demonstrate these strategies on the board.
Use Connect to introduce the standard algorithm
for addition. Write the numbers 27 and 18 on
the board. Have students estimate the sum first.
Use rounding.
27 rounds to 30.
18 rounds to 20.
So, 30 + 20 = 50
Since we rounded both numbers up, the exact
sum will be less than 50.
Use front-end estimation.
27 becomes 20.
18 becomes 10.
So, 20 + 10 = 30
Since front-end estimation is the same as
rounding down, the exact sum will be more
than 30. The sum 27 + 18 is between 30 and 50.
Use the algorithm to model how to add
27 + 18. Tell students that we start by adding
the ones; 7 + 8 = 15. Since we have more than
10 ones, we trade 10 ones for 1 ten, leaving
5 ones. We write a “little 1” (in the tens place)
above the 2 in the number 27 to represent this
ten. We then add the tens; 2 + 1 + 1 = 4. The
sum of 27 and 18 is 45.
Model 3-digit addition on the board using the
standard algorithm.
Ask questions, such as:
• How are adding with the standard method
and adding with Base Ten Blocks the same?
(In both ways, I add the ones and trade 10 ones for
1 ten if necessary. Then I add the tens and trade
10 tens for 1 hundred if necessary.)
• Why is it a good idea to estimate
before adding?
(If the estimate is close to my answer, my answer
is reasonable.)
Unit 2 • Lesson 13 • Student page 91
39
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Sample Answers
1. To add 27 + 39, I can:
Add on the tens, then add on the ones:
20 + 30 + 7 + 9 = 50 + 16 = 66
Take from one number to give to the other:
27 + 39 = 26 + 39 + 1 = 26 + 40 = 66
Use the standard method for addition:
26
39
19
1
27
+ 39
66
2. The first number in each question increases by 10 each time.
The second number in each question increases by 1 each
time. In the answers, the tens digit starts at 6 and increases by
1 each time, and the ones digit starts at 1 and increases by
1 each time; that is, the sum increases by 11 each time.
Numbers Every Day
Leah took away a number that had the same ones digit as 52.
Then she took away the extra ones.
Some students might start by adding on the
left, adding the hundreds, the tens, and then
the ones, then combining the results using the
standard method for addition. This is an
acceptable strategy.
Practice
Have Base Ten Blocks and place-value mats
available for all questions. Remind students
to use an appropriate method for verifying
their answers.
40
Unit 2 • Lesson 13 • Student page 92
61
72
83
94
88
90
92
94
407
507
607
707
84
65
106
113
600
500
400
700
549
631
832
832
Assessment Focus: Question 10
Students should be systematic to ensure they
do not miss any numbers. Students could start
with 2 as the hundreds digit and find all
possible 3-digit numbers. Students repeat with
3, then 4 as the hundreds digit. Students then
add pairs of numbers in a systematic way and
compare the sums.
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8. I added the ones, 6 + 1 = 7. I added the tens; 5 + 7 = 12.
627 tulips
44 children
71 children
6
13 different sums
I traded 10 tens for 1 hundred, leaving 2 tens. I added the
hundreds; 2 + 3 + 1 = 6. 256 + 371 = 627
9. b) 44 + 27 = 71
10. I can make six 3-digit numbers:
234, 243, 324, 342, 423, 432
I added pairs of numbers: 234 + 243 = 477,
234 + 324 = 558, 234 + 342 = 576, 234 + 423 = 657,
234 + 432 = 666, 243 + 324 = 567, 243 + 342 = 585,
243 + 423 = 666, 243 + 432 = 675, 324 + 342 = 666,
324 + 423 = 747, 324 + 432 = 756, 342 + 423 = 765,
342 + 432 = 774, 423 + 432 = 855
There are 15 sums, but 3 of the sums are the same.
12. There were 2 showings of a movie on opening night. Three
hundred fifty-six people saw the early show and 248 people
saw the late show. How many people saw the movie on
opening night?
(Answer: 604 people)
REFLECT: I like to use the standard method best because I
402 things
always get an exact answer and I can get the answer faster
as I do not have to get any materials, such as Base Ten
Blocks, before I add. If I do the addition in my head, I might
make a mistake.
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Understanding concepts
✔ Students understand that the
strategies for adding 2-digit and
3-digit numbers are based on
place-value concepts.
Extra Support: Have students work in pairs. One student models
the addition with Base Ten Blocks, and the other student records the
steps on paper, using numbers.
Students can use Step-by-Step 13 (Master 2.24) to complete
question 10.
Applying procedures
✔ Students can use the standard
algorithm for addition to add 2-digit
and 3-digit numbers.
Extra Practice: Students use a set of digit cards numbered
from 0 to 9. Students use the cards to make two 3-digit
numbers, then add the numbers. Students repeat the activity with
2 different numbers.
Students can complete Extra Practice 6 (Master 2.33).
✔ Students can use more than one
strategy to add 2-digit and
3-digit numbers.
Extension: Students can complete the Additional Activity,
Shopping Bags! (Master 2.12).
Recording and Reporting
Master 2.2 Ongoing Observations:
Patterns in Addition and Subtraction
Unit 2 • Lesson 13 • Student page 93
41
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LESSON 14
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A Standard Method
for Subtraction
40–50 min
LESSON ORGANIZER
Curriculum Focus: Develop proficiency in subtracting 3-digit
numbers. (N14)
Optional
Base Ten Blocks
place-value mats
(made from PM 18)
Step-by-Step 14
(Master 2.25)
Extra Practice 7
(Master 2.34)
Assessment: Master 2.2 Ongoing Observations: Patterns in
Addition and Subtraction
Student Materials
Yes
Key Math Learnings
1. Three-digit numbers can be subtracted using paper and
pencil and a standard algorithm.
2. The strategies for subtracting 2-digit and 3-digit numbers are
based on place-value concepts.
BEFORE
Get Started
Initiate a discussion about the strategies
students use to subtract 2-digit numbers and
3-digit numbers.
Ask:
• What methods did you use to subtract 2-digit
numbers and 3-digit numbers?
(Base Ten Blocks, place-value mats, calculators)
Have students think about how they could
subtract 2-digit numbers and 3-digit numbers
without using concrete materials.
Present Explore. Tell students they are to subtract
using only pencil and paper. Encourage
students to share the strategies they used.
42
Unit 2 • Lesson 14 • Student page 94
DURING
Explore
Ongoing Assessment: Observe and Listen
Ask questions, such as:
• How did Joe find how many pages he still
has to read?
(Joe’s book has 42 pages. He is on page 18. To find
how many pages he has left to read, Joe subtracted
18 from 42. Joe could not subtract 8 ones from
2 ones, so he traded 1 ten for 10 ones, making 3 tens
and 12 ones; 12 – 8 = 4. Joe then subtracted the tens
to get 2 tens; 3 – 1 = 2. 42 – 18 = 24)
• Is Joe correct? (Yes) How do you know?
(I used mental math to check. I added 2 to 18 to get
20, which is an easy number to take away:
42 – 20 = 22. Since I took away 2 more than I
should have, I add 2 to the answer to get 24.)
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REACHING ALL LEARNERS
Early Finishers
Challenge students to check their answers by adding.
Common Misconceptions
69 + 8 = 77 or 80 – 3 = 77
80 – 22 = 58
➤Students trade 1 ten for 10 ones or 1 hundred for 10 tens, but
forget to take one away from the number of tens or the
number of hundreds.
How to Help: Tell students when they trade, they do an
exchange. Have them model the subtraction with Base Ten
Blocks, then exchange one rod for 10 unit cubes or exchange
one flat for 10 rods, as necessary.
Numbers Every Day
Encourage students to experiment with their calculators. Students
should recognize that Julia needs to add or subtract to show
77 on her calculator. Students could find several ways to display
77 without using the 7 key. For example, Julia could subtract
3 from 80 or she could add 69 + 8. To calculate 75 – 17,
students should realize that if they change both numbers in a
subtraction problem in the same way, the difference does not
change. For example, students could add 5 to each number, then
use the calculator to find 80 – 22.
• How did Joe find how many pages Angie
still has to read? (Angie’s book has 245 pages.
Angie is on page 164. To find how many pages
Angie has left to read, Joe subtracted 164 from 245.
Joe subtracted the ones; 5 – 4 = 1. Joe could not
subtract 6 tens from 4 tens, so he traded 1 hundred
for 10 tens, making 1 hundred and 14 tens. Joe
subtracted the tens: 14 – 6 = 8. Joe then subtracted
the hundreds; 1 – 1 = 0. 245 – 164 = 81)
• Is Joe correct? (Yes) How do you know?
(I used mental math to check. I subtracted the
hundreds, then the tens, and then the ones;
245 – 100 = 145, 145 – 60 = 85, 85 – 4 = 81.)
AFTER
Connect
Invite students to share their ideas about Joe’s
method of subtraction with the class.
Use Connect to introduce the standard algorithm
for subtraction. Write the numbers 27 and 18
on the board. Use the standard algorithm for
subtraction to model how to subtract 27 – 18.
Tell students we start by subtracting the ones.
Since there are not enough ones to subtract
from, trade 1 ten for 10 ones, leaving 1 ten.
We cross out the 2 and write a “little 1” above
the 2 to show we have traded 1 ten for 10 ones
and we have 1 ten left. We cross out the 7 then
write a “little 17” above the 7 to show we have
added the 10 ones to the 7 in the ones column.
Show students how to add to check; that is,
add the number that was subtracted to the
difference. If the difference is correct, this sum
is the top number in the subtraction. That is,
27 – 18 = 9; to check, add 9 + 18. The answer
is 27.
Anticipate difficulty in problems that involve a
zero, especially if the zero is in the number
being subtracted from. Model 3-digit
subtraction on the board using the standard
method, using an example such as 402 – 139.
Unit 2 • Lesson 14 • Student page 95
43
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Sample Answers
1. Start at 85. The first number in each question decreases by
10 each time. Start at 23. The second number in each
question increases by 1 each time. The answers start at
62 and decrease by 11 each time.
3. To subtract 75 – 37, I can:
Take away tens, then take away ones:
75 – 30 = 45, 45 – 7 = 38
Add to match the ones, then subtract:
75 + 2 = 77, 77 – 37 = 40, 40 – 2 = 38
Use the standard method for subtraction:
6 15
75
– 37
38
Ask questions, such as:
• How did we subtract the ones?
(There were not enough ones to subtract from so we
traded. There were no tens to trade from, so we
traded 1 hundred for 10 tens, leaving 3 hundreds. We
then traded 1 ten for 10 ones, leaving 9 tens. We had
12 ones; 12 – 9 = 3.)
• How did we take away 3 tens?
(We had 9 tens; 9 – 3 = 6.)
• How did we take away 1 hundred?
(We had 3 hundreds; 3 – 1 = 2.)
• What were we left with?
(2 hundreds 6 tens 3 ones, or 263)
Again, show students how to check by adding
the difference to the number that was subtracted.
44
Unit 2 • Lesson 14 • Student page 96
62
51
40
29
69
48
27
6
222
115
242
632
275
356
183
212
Practice
Have Base Ten Blocks and place-value mats
available for all questions.
Assessment Focus: Question 10
Students should realize in part a, they must
find the difference between Michelle’s score
and Sunny’s score. In part b, students should
realize they must find the difference between
Zane’s score and Michelle’s score and the
difference between Zane’s score and Sunny’s
score. Some students might make up a problem
that involves both the addition and subtraction
of 3-digit numbers.
Home
= 179
= 148
= 218
Quit
7. a) I compared the tens digits. Since 8 > 4, $82 > $49
8. 90 – 25 – 50 = 15, 15 + 19 = 34
10. a) 84 points; 369 – 285 = 84
b) Michelle needs 87 points; 456 – 369 = 87.
= 118
Sunny needs 171 points; 456 – 285 = 171.
c) How many more points did Michelle and Sunny score in
Prya
$33
total than Zane?
(Answer: 198 points; 369 + 285 = 654, 654 – 456 = 198)
11. Last year, 167 Grade 3 students participated in the Terry Fox
Run. This year, 214 students participated. How many more
students participated this year than last?
(Answer: 47 students; 214 – 167 = 47)
34¢
REFLECT: When I subtract 2 numbers , I need to trade 1 ten for
230 sticks
84 points
87 points,
171 points
10 ones if there are not enough ones to take away from. For
example, to subtract 45 – 16, there are not enough ones to
take away 6.
I need to trade 1 hundred for 10 tens if there are not enough
tens to take away from. For example, to subtract 327 – 281,
there are not enough tens to take away 8.
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Understanding concepts
✔ Students understand that the
strategies for subtracting 2-digit
and 3-digit numbers are based on
place-value concepts.
Extra Support: Have students use Base Ten Blocks, then model
what they do with the blocks as they use the standard algorithm
for subtraction.
Students can use Step-by-Step 14 (Master 2.25) to complete
question 10.
Applying procedures
✔ Students can use the standard
algorithm for subtraction to subtract
2-digit and 3-digit numbers.
Extra Practice: Students find the total number of pages in their
math book, then subtract the page they are on to find how many
pages they have left to learn.
Students can complete Extra Practice 7 (Master 2.34).
✔ Students can use more than one
strategy to subtract 2-digit and
3-digit numbers.
Extension: Have students use pencil and paper to subtract:
362 – 177 – 96
(Answer: 89)
Recording and Reporting
Master 2.2 Ongoing Observations:
Patterns in Addition and Subtraction
Unit 2 • Lesson 14 • Student page 97
45
S H O W W H AT Y O U K NHome
OW
LESSON ORGANIZER
Quit
40–50 min
Student Materials
addition charts (Master 2.6)
counters
Base Ten Blocks
place-value mats (made from PM 18)
Show What You Know Chart (Master 2.8)
Assessment: Masters 2.1 Unit Rubric: Patterns in Addition
and Subtraction, 2.4 Unit Summary: Patterns in Addition
and Subtraction
14
15
14
18
6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16
9
9
8
8
7
9
8
8
15
11
21 24
23 26
61
69
Sample Answers
4. a) 9 – 8, 8 – 7, 7 – 6, 6 – 5, 5 – 4, 4 – 3, 3 – 2,
2 – 1, 1 – 0
b) 11 – 9, 10 – 8, 9 – 7, 8 – 6, 7 – 5, 6 – 4, 5 – 3,
4 – 2, 3 – 1, 2 – 0
c) 12 – 9, 11 – 8, 10 – 7, 9 – 6, 8 – 5, 7 – 4, 6 – 3,
5 – 2, 4 – 1, 3 – 0
d) 13 – 9, 12 – 8, 11 – 7, 10 – 6, 9 – 5, 8 – 4, 7 – 3,
6 – 2, 5 – 1, 4 – 0
Most students will use the 9 + 9 addition chart to
answer this question. If some students decide to go
beyond this chart, there is no limit to the answers.
I know I have found all the facts because I used the
addition chart. For example, for a difference of 3,
I went down the column for 3 and listed all the
subtraction facts with 3 as the answer.
6. In each row, the numbers increase by 3 each time.
In each column, the numbers increase by 5 each time.
In the diagonals going from top left to bottom right, the
numbers increase by 8 each time.
In the diagonals going from top right to bottom left, the
numbers increase by 2 each time.
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Unit 2 • Show What You Know • Student page 98
66
69
26 29
17 20
19 22
13
28 31 34
30 33 36 39
32 35 38 41 44
388
616
70
69
9. a) I took from one to give to the other:
38 + 2 + 43 = 40 + 43 = 83
b) I took away tens, then took away ones:
50 – 10 = 40, 40 – 8 = 32
14. Using addition and 3-digit numbers, the problem
could be:
100 + 276, 101 + 275, 102 + 274, 103 + 273, . . .,
187 + 189, 188 + 188.
Using subtraction and 3-digit numbers, the problem
could be:
999 – 623, 998 – 622, 997 – 621, . . ., 476 – 100.
If students use 1-digit and 2-digit numbers, many more
answers are possible.
15. The greatest possible sum is 1795:
953 + 842, 943 + 852, 853 + 942, 952 + 843
The least possible sum is 607:
248 + 359, 249 + 358, 258 + 349, 259 + 348
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Read the Question
Encourage students to read each question carefully, and look for
clues about the operation that is required.
83
For example, words such as “difference” and “how many more”
would indicate subtraction is required to solve the problem.
Words such as “sum,” “altogether,” and “in all” would indicate
addition is required to solve the problem.
32
37 and 62
89 and 37
861 tiles
55
38
129
313
498 children
ASSESSMENT FOR LEARNING
What to Look For
Reasoning; Applying concepts
✔ Questions 4 and 6: Student understands there are patterns in an addition chart.
✔ Question 5: Student understands that to find the missing term in a number sentence, related facts or the
opposite operation can be used.
✔ Question 10: Student understands the difference between an exact answer and an estimate.
Accuracy of procedures
✔ Questions 8 and 9: Student can mentally add and subtract two 2-digit numbers.
✔ Questions 1 and 3: Student can recall basic addition and subtraction facts.
✔ Questions 7 and 12: Student can add and subtract 2-digit and 3-digit numbers, with and without
concrete materials.
Problem Solving
✔ Questions 11 and 13: Student can solve problems involving the addition and subtraction of 3-digit numbers.
Recording and Reporting
Master 2.1 Unit Rubric: Patterns in Addition and Subtraction
Master 2.4 Unit Summary: Patterns in Addition and Subtraction
Unit 2 • Show What You Know • Student page 99
47
UNIT PROBLEM
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National Read-A-Thon
LESSON ORGANIZER
40–50 min
Student Grouping: 2
Student Materials
Base Ten Blocks
place-value mats (made from PM 18)
Assessment: Masters 2.3 Performance Assessment Rubric:
National Read-A-Thon, 2.4 Unit Summary: Patterns in
Addition and Subtraction
Sample Response
Part 1
I estimate Woodlawn Public School read the most pages.
For each school, I rounded the number of pages read by each
child to the nearest hundred, then added.
Roseville Public School: 200 + 100 + 300 + 200 = 800
Woodlawn Public School: 200 + 200 + 300 + 200 = 900
900 is greater than 800.
Jeff and Sookal read 419 pages altogether; 143 + 276 = 419.
LaToya read 61 more pages than Jadan; 298 – 237 = 61.
LaToya read more books than Jadan. I added the number of
books read by Jadan (4 + 2 + 0 + 3 = 9). I added the number
of books read by LaToya (5 + 6 + 3 + 2 = 16). Since 16 is
greater than 9, LaToya read more books.
Have students turn to the Unit Launch on pages
54 and 55 of the Student Book.
Use the lists of Learning Goals and Key Words
to review the key learnings of the unit.
Tell students they will use the skills they
have learned in this unit to complete the
Unit Problem.
Present the Unit Problem. Have volunteers read
the 3 parts of the problem aloud. Answer any
questions students might have.
Invite a student to read aloud the Check List.
Explain these are the criteria against which
their work will be assessed. Have students
work in pairs.
48
Unit 2 • Unit Problem • Student page 100
Ensure students understand they must
collaborate in pairs to complete all parts of the
activity. One student could keep her book open
at pages 54 and 55, so the table there is readily
available.
Encourage students to use the algorithms for
addition and subtraction, but have Base Ten
Blocks and place-value mats available. In
Part 3, ensure students understand they are to
explain the new prize as well as explain how
they figured out to whom it was awarded.
Tell students they can draw a picture of the
new prize.
As an extension, students could hold a class
Read-A-Thon, then decide who would get
each prize.
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Part 2
Children who have read from 10 to 15 books:
Sookal: 4 + 4 + 3 + 2 = 13
Jenny: 5 + 4 + 3 + 2 = 14
Stanley: 2 + 3 + 4 + 1 = 10
Children who have read from 15 to 20 books:
Sunny: 6 + 4 + 3 + 5 = 18
LaToya: 5 + 6 + 3 + 2 = 16
Part 3
A prize could be awarded to the child who reads the most
pages at each school. The prize could be a gift certificate for a
book store. The winners would be:
Roseville Public School:
Sookal, since 276 is the greatest number.
Woodlawn Public School:
LaToya, since 298 is the greatest number.
Reflect on the Unit
I know there are many strategies for adding and subtracting,
such as using mental math, estimation, Base Ten Blocks, placevalue mats, or the standard method. I know that I can use
addition to check the answer to a subtraction question. I also
know how to trade 10 ones for 1 ten, and 10 tens for 1 hundred
when adding, and how to trade 1 ten for 10 ones, and
1 hundred for 10 tens when subtracting. For example,
1 1
632
+ 299
931
6 13 12
742
– 288
454
ASSESSMENT FOR LEARNING
What to Look For
What to Do
Understanding concepts
✔ Students understand the difference
between an exact answer and
an estimate.
Extra Support: Make the problem accessible.
Applying procedures
✔ Students can add and subtract 2-digit
and 3-digit numbers.
Problem Solving
✔ Students can solve problems involving
the addition and subtraction of
whole numbers.
Some students may have difficulty deciding whether they are to
add or subtract. Tell students that when the question uses the
word “altogether,” they are to add. When the question asks,
“How many more?” they are to subtract.
Some students may have difficulty comparing the 3-digit
numbers. Remind students about using place value to compare
numbers, or have them use a number line.
Communicating
✔ Students use mathematical language
to explain answers.
Recording and Reporting
Master 2.3 Performance Assessment Rubric: National Read-A-Thon
Master 2.4 Unit Summary: Patterns in Addition and Subtraction
Unit 2 • Unit Problem • Student page 101
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Evaluating Student Learning: Preparing to Report:
Unit 2 Patterns in Addition and Subtraction
This unit provides an opportunity to report on the Number Concepts and Number Operations strand.
Master 2.4: Unit Summary: Patterns in Addition and Subtraction provides a comprehensive format for
recording and summarizing evidence collected.
Here is an example of a completed summary chart for this Unit:
Key:
1 = Not Yet Adequate
2 = Adequate
3 = Proficient
4 = Excellent
Strand:
Number Concepts/
Number Operations
Reasoning;
Applying
concepts
Accuracy of
procedures
Problem
solving
Communication
Overall
Ongoing Observations
3
4
3
4
3/4
Strategies Toolkit
not assesed
Work samples or
portfolios; conferences
3
4
3
4
3/4
Show What You Know
4
Unit Test
Unit Problem
National Read-A-Thon
3
4
4
4
4
4
4
4
4
3
Achievement Level for reporting
4
4
4
4
Recording
How to Report
Ongoing Observations
Use Master 2.2 Ongoing Observations: Patterns in Addition and Subtraction to determine the
most consistent level achieved in each category. Enter it in the chart. Choose to summarize
by achievement category, or simply to enter an overall level.
Observations from late in the unit should be most heavily weighted.
Strategies Toolkit
(problem solving)
Use PM 1: Inquiry Process Check List with the Strategies Toolkit (Lesson 9). Transfer results
to the summary form. Teachers may choose to enter a level in the Problem solving column
and/or Communication.
Portfolios or collections of
work samples; conferences,
or interviews
Use Master 2.1 Unit Rubric: Patterns in Addition and Subtraction to guide evaluation of
collections of work and information gathered in conferences. Teachers may choose to focus
particular attention on the Assessment Focus questions.
Work from late in the unit should be most heavily weighted.
Show What You Know
Master 2.1 Unit Rubric: Patterns in Addition and Subtraction may be helpful in determining
levels of achievement.
#1, 3, 7, 8, 9, and 12 provide evidence of Accuracy of procedures; #4, 5, 6, and 10 provide
evidence of Reasoning; Applying concepts; #11 and 13 provide evidence of Problem solving;
all provide evidence of Communication.
Unit Test
Master 2.1 Unit Rubric: Patterns in Addition and Subtraction may be helpful in determining
levels of achievement.
Part A provides evidence of Accuracy of procedures; Part B provides evidence of Reasoning;
Applying concepts; Part C provides evidence of Problem solving; all parts provide evidence
of Communication.
Unit performance task
Use Master 2.3 Performance Assessment Rubric: National Read-A-Thon. The Unit Problem
offers a snapshot of students’ achievement. In particular, it shows their ability to synthesize
and apply what they have learned.
Student Self-Assessment
Note students’ perceptions of their own progress. This may take the form of an oral or written
comment, or a self-rating.
Comments
Analyse the pattern of achievement to identify strengths and needs. In some cases, specific
actions may need to be planned to support the learner.
Learning Skills
Ongoing Records
PM 4: Learning Skills Check List
PM 10: Summary Class Records: Strands
PM 11: Summary Class Records: Achievement Categories
PM 12: Summary Record: Individual
Use to record and report evaluations of student achievement over
several clusters, a reporting period, or a school year.
These can also be used in place of the Unit Summary.
Use to record and report throughout a reporting period,
rather than for each unit and/or strand.
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Unit Rubric: Patterns in Addition and Subtraction
Not Yet
Adequate
Adequate
Proficient
Excellent
may be unable to
demonstrate, apply, or
explain:
– patterns in addition
and subtraction
– relationships
between addition
and subtraction
– strategies for
addition and
subtraction
– place value
– estimation strategies
– choice of operations
– choice of method for
adding or
subtracting
partially able to
demonstrate, apply, or
explain:
– patterns in addition
and subtraction
– relationships between
addition and
subtraction
– strategies for addition
and subtraction
– place value
– estimation strategies
– choice of operations
– choice of method for
adding or subtracting
able to demonstrate,
apply, and explain:
– patterns in addition
and subtraction
– relationships between
addition and
subtraction
– strategies for addition
and subtraction
– place value
– estimation strategies
– choice of operations
– choice of method for
adding or subtracting
in various contexts,
appropriately
demonstrates, applies,
and explains:
– patterns in addition
and subtraction
– relationships between
addition and
subtraction
– strategies for addition
and subtraction
– place value
– estimation strategies
– choice of operations
– choice of method for
adding or subtracting
limited accuracy;
omissions or major
errors in:
– addition and
subtraction to 1000
– recalling addition
and subtraction facts
to 18
– verifying solutions
partially accurate;
omissions or frequent
minor errors in:
– addition and
subtraction to 1000
– recalling addition and
subtraction facts to 18
– verifying solutions
generally accurate;
makes few errors in:
– addition and
subtraction to 1000
– recalling addition and
subtraction facts to 18
– verifying solutions
accurate; makes no
errors in:
– addition and
subtraction to 1000
– recalling addition and
subtraction facts to 18
– verifying solutions
may be unable to use
appropriate strategies
to solve and create
problems involving
addition and
subtraction of whole
numbers
with limited help, uses
some appropriate
strategies to solve and
create problems
involving addition and
subtraction of whole
numbers; partially
successful
uses appropriate
strategies to solve and
create problems involving
addition and subtraction
of whole numbers
successfully
uses appropriate, often
innovative, strategies to
solve and create
problems involving
addition and subtraction
of whole numbers
successfully
• explains reasoning and
procedures clearly,
including appropriate
terminology
unable to explain
reasoning and
procedures clearly
partially explains
reasoning and
procedures
explains reasoning and
procedures clearly
explains reasoning and
procedures clearly,
precisely, and confidently
• presents work clearly
work is often unclear
presents work with
some clarity
presents work clearly
presents work clearly and
precisely
Reasoning; Applying
concepts
• shows understanding by
applying and explaining:
– processes of addition
and subtraction
– patterns in addition
and subtraction
– relationships between
addition and
subtraction
– place value
– estimation strategies
for sums and
differences
– which operation(s)
can be used to solve
a particular problem
• justifies choice of
operations, and choice
of method for addition
and subtraction
Accuracy of
procedures
• accurately adds and
subtracts to 1000
• recalls addition and
subtraction facts to 18
• verifies solutions to
addition and subtraction
problems using
estimation, calculators,
and inverse operations
Problem-solving
strategies
• chooses and carries out
a range of strategies
(e.g., estimation, using
manipulatives to model,
drawing pictures,
making place-value
charts, creating
organized lists, guess
and check, using
patterns, calculators) to
create and solve
problems involving
addition and subtraction
of whole numbers
Communication
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Ongoing Observations: Patterns in Addition
and Subtraction
The behaviours described under each heading are examples; they are not intended to be an exhaustive list of all
that might be observed. More detailed descriptions are provided in each lesson under Assessment for Learning.
STUDENT ACHIEVEMENT: Patterns in Addition and Subtraction*
Student
Reasoning; Applying
concepts
Applies and explains
concepts related to
the addition and
subtraction of whole
numbers
Accuracy of
procedures
Accurately adds
and subtracts
1-, 2-, and 3-digit
numbers
Uses a variety of
strategies to verify
solutions to addition
and subtraction
problems
*Use locally or provincially approved levels, symbols, or numeric ratings.
52 Copyright © 2005 Pearson Education Canada Inc.
Problem solving
Uses appropriate
strategies to solve
and create problems
involving the addition
and subtraction of
whole numbers
Communication
Presents work clearly
Explains reasoning
and procedures
clearly, including
appropriate
terminology
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Master 2.3
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Performance Assessment Rubric:
National Read-A-Thon
Not Yet
Adequate
Adequate
Proficient
Excellent
Reasoning; Applying
concepts
does not apply
required concepts of
addition, subtraction,
and estimation
appropriately; may be
incomplete or indicate
misconceptions
applies some of the
required concepts of
addition, subtraction,
and estimation
appropriately; may
indicate some
misconceptions
applies the required
concepts of addition,
subtraction, and
estimation
appropriately;
explanations may
show minor flaws in
reasoning
applies the required
concepts of addition,
subtraction, and
estimation effectively
throughout; indicates
thorough
understanding
limited accuracy;
makes omissions or
major errors in
adding, subtracting,
and comparing
somewhat accurate;
some omissions or
minor errors in
adding, subtracting,
and comparing
generally accurate; few
minor errors in adding,
subtracting, and
comparing
accurate and precise;
no errors in adding,
subtracting, and
comparing
uses few appropriate
strategies; does not
adequately create a
prize or determine
who would get it
uses some
appropriate strategies,
with partial success,
to create a very
simple prize and
determine who would
get it; may be some
flaws
uses appropriate and
successful strategies
to create an
appropriate prize and
determine who would
get it
uses innovative and
effective strategies to
create a prize, with
some complexity, and
determine who would
get it
• explains solutions
clearly as required,
using mathematical
terminology correctly
(e.g., sum,
difference, estimate)
little clear explanation;
uses few appropriate
mathematical terms
gives partial
explanations; may be
unclear or incomplete;
uses some
appropriate
mathematical terms
explains answers as
required; uses
appropriate
mathematical terms
explains answers
clearly and precisely,
using a range of
appropriate
mathematical terms
• work is clearly
presented
does not present work
clearly
presents work with
some clarity; may be
hard to follow in
places
presents work clearly
presents work clearly
and precisely
• shows understanding
by applying the
required concepts of
addition, subtraction,
and estimation to:
– solve the word
problems (Part 1)
– decide who should
win the prizes
(Part 2)
– design a new prize
(Part 3)
Accuracy of
procedures
• adds, subtracts, and
compares correctly
Problem-solving
strategies
• uses appropriate
strategies to create
another prize and
decide who would
get it (Part 3)
Communication
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Master 2.4
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Unit Summary: Patterns in Addition
and Subtraction
Review assessment records to determine the most consistent achievement levels for the assessments conducted.
Some cells may be blank. Overall achievement levels may be recorded in each row, rather than identifying
levels for each achievement category.
Most Consistent Level of Achievement*
Strand:
Number Concepts/
Number Operations
Reasoning;
Applying
concepts
Accuracy of
procedures
Problem
solving
Ongoing Observations
Strategies Toolkit
(Lesson 9)
Work samples or
portfolios; conferences
Show What You Know
Unit Test
Unit Problem
National Read-A-Thon
Achievement Level for reporting
*Use locally or provincially approved levels, symbols, or numeric ratings.
Self-Assessment:
Comments: (Strengths, Needs, Next Steps)
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Communication
Overall
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To Parents and Adults at Home …
Your child’s class is starting a mathematics unit on patterns in addition and
subtraction. Your child will develop strategies for adding and subtracting whole
numbers by using addition charts, mental math, estimation, Base Ten Blocks,
place-value mats, and pencil and paper.
In this unit, your child will:
• Describe properties of addition.
• Recall basic addition and subtraction facts.
• Identify and apply relationships between addition and subtraction.
• Add and subtract 2-digit numbers.
• Use mental math to add and subtract.
• Estimate sums and differences.
• Add and subtract 3-digit numbers.
The ability to use a variety of strategies to add and subtract leads to the
development of a strong sense of number. Numbers are all around us and the
skills taught in this unit are essential for daily living.
Here are some suggestions for activities you can do with your child.
Play Store with your child. Price some of the items in your home in whole
dollars (for example, the microwave is $149 and the telephone is $35). You are
the Shopper and your child is the Cashier. Have your child add the cost of the
items you buy.
Roll a number cube 4 times. Use the numbers rolled to make two
2-digit numbers. Have your child subtract the lesser number from the greater
number. Repeat the activity, this time rolling the number cube 6 times, making
two 3-digit numbers.
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Master 2.6
Addition Chart 1
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Addition Chart 2
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Show What You Know Chart
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Date
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Master 2.9
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Date
Additional Activity 1:
Fastest Facts
Play in groups of 3.
You will need a deck of cards with the 10s and face cards removed.
An ace counts as 1.
One person is the dealer. The others are the players.
The object of the game is to be the first player to get 10 points.
How to play:
• The dealer shuffles the deck, then turns over 2 cards.
• The players add the numbers on the cards.
The first player to add the numbers correctly gets 1 point.
• The dealer turns over 2 more cards.
• The first player to get 10 points is the winner.
• Repeat the activity. The winner is now the dealer.
Take It Further: The dealer turns over 3 cards. The players add all 3 numbers.
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Master 2.10
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Additional Activity 2:
First to 10
Play with a partner.
You will need 2 number cubes, Base Ten Blocks, place-value mats,
and a calculator.
How to play:
Player A rolls the number cubes.
Use the numbers to make a 2-digit number.
Record the number.
Player A rolls the number cubes again.
Use the numbers to make another 2-digit number.
Record the number.
Player A uses Base Ten Blocks and place-value mats to
add the two 2-digit numbers.
Player B checks the answer using a calculator.
If the answer is correct, Player A gets 1 point.
Player B takes a turn.
Players continue to take turns.
The first player to get 10 points is the winner.
Take It Further: Play the game again. This time, subtract the lesser number
from the greater number.
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Additional Activity 3:
Tic-Tac-Toe Squares
Play with a partner.
You will need a Tic-Tac-Toe board, Base Ten Blocks, place-value mats,
and a calculator.
How to play:
Decide who will be “X” and who will be “O.”
Player “X” chooses a square on the board.
Use Base Ten Blocks and place-value mats to find the answer.
Player “O” uses a calculator to check the answer.
If the answer is correct, Player “X” puts her mark on the square.
Switch roles.
The first player to get 3 Xs or 3 Os in a row is the winner.
Take It Further: Make your own Tic-Tac-Toe board.
Each addition question should have three 3-digit numbers.
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Tic-Tac-Toe Board
TIC
TAC
TOE
836 + 129 =
456 + 365 =
321 + 383 =
625 + 345 =
234 + 432 =
459 + 222 =
535 + 449 =
734 + 137 =
823 + 129 =
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Master 2.12
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Additional Activity 4:
Shopping Bags!
Play in groups of 3.
You will need classroom objects, price tags, and a calculator.
Choose objects in the class to be for sale. Put price tags on each object.
Each price should be more than 25¢, but less than 50¢.
Decide who will be the cashier and who will be the shoppers.
Each shopper chooses 2 objects to buy.
Use paper and pencil to find the total cost of your objects.
Record the total on a piece of paper.
Take your objects to the cashier.
The cashier uses a calculator to find each total.
Show the cashier the piece of paper with your total on it.
If your total matches the calculator, you win.
Switch roles and play again.
Take It Further: The cashier gives each shopper 99¢.
The shopper who comes closest to spending 99¢ without going over
is the winner.
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Master 2.12a
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Curriculum Focus Activity 1:
Checking Addition
You know that subtraction is the opposite of addition.
7 + 6 = 13
So, 13 – 6 = 7 and 13 – 7 = 6
You can check an addition question by subtracting.
23
+ 45
68
Subtract one of these numbers from 68.
Your answer should be the other number.
68
– 45
23
68
– 23
45
or
1. Add, then check by subtracting.
64
a)
25
+ 33
b)
52
+ 84
c)
47
+ 56
d)
64
+ 79
e)
84
+ 17
f)
78
+ 63
g)
19
+ 58
h)
28
+ 54
i)
36
+ 72
j)
43
+ 68
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Activity Focus: Use the inverse operation to verify solutions.
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Curriculum Focus Activity 2:
Checking Subtraction
You know that addition is the opposite of subtraction.
14 – 6 = 8
So, 8 + 6 = 14 and 6 + 8 = 14
You can check a subtraction question by adding.
87
– 24
63
These 2
numbers should
add to this number.
24
+ 63
87
1. Subtract, then add to check.
a)
94
– 23
b)
58
– 27
c)
94
– 39
d)
64
– 17
e)
38
– 18
f)
86
– 57
g)
75
– 29
h)
88
– 34
i)
61
– 25
j)
43
– 19
Activity Focus: Use the inverse operation to verify solutions.
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Master 2.13
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Step-by-Step 1
Lesson 1, Question 6
Step 1 Write the numbers from 1 to 10.
________________________________________________________
Which of these numbers are even? ___________________________
Step 2 Choose 2 even numbers from Step 1. ____________
What is their sum? __________
Step 3 Choose 2 different even numbers from Step 1. ____________
What is their sum? __________
Step 4 Repeat Step 3 as many times as you can.
How many different sums can you find?
________________________________________________________
Step 5 Which numbers never appear? _______________________________
Why do you think these numbers never appear? _____________
________________________________________________________
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Master 2.14
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Step-by-Step 2
Lesson 2, Question 6
1, 2, 3, 4, 5, 6, 7, 8
Use the numbers above.
Step 1 Find pairs of numbers that add to 10.
______ + ______ = 10
______ + ______ = 10
______ + ______ = 10
How do you know you have found all the ways?
________________________________________________________
Step 2 Find groups of 3 numbers that add to 10.
______ + ______ + ______ = 10
______ + ______ + ______ = 10
______ + ______ + ______ = 10
______ + ______ + ______ = 10
How do you know you have found all the ways?
________________________________________________________
Step 3 Can you find 4 numbers that add to 10?
______ + ______ + ______ + ______ = 10
Step 4 How many different ways did you find to make 10? _____________
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Name
Master 2.15
Date
Step-by-Step 3
Lesson 3, Question 7
Step 1 Colour all the numbers in the column for 5.
The first number you coloured was 5.
The subtraction fact is 5 – 0 = 5.
Write the subtraction fact for the second number, 6.
______ – ______ = 5
Step 2 Write the subtraction facts for the other numbers you coloured.
______ – ______ = 5
______ – ______ = 5
______ – ______ = 5
______ – ______ = 5
______ – ______ = 5
______ – ______ = 5
______ – ______ = 5
______ – ______ = 5
Step 3 How do you know you have found all the facts?
________________________________________________________
_________________________________________________________________
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Master 2.16
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Date
Step-by-Step 4
Lesson 4, Question 7
Step 1 Write numbers to make an addition fact: ________ + ________ = 5
What are the related facts?
Step 2 Write numbers to make an addition fact: 5 + ________ = ________
What are the related facts?
Step 3 Write numbers to make a subtraction fact: ________ – ________ = 5
What are the related facts?
Step 4 Write numbers to make a subtraction fact: 5 – ________ = ________
What are the related facts?
Step 5 Write numbers to make a subtraction fact: ________ – 5 = ________
What are the related facts?
Step 6 Explain how you found the numbers to make the facts.
________________________________________________________
________________________________________________________
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Name
Master 2.17
Date
Step-by-Step 5
Lesson 5, Question 7
Step 1 Fill in the blanks to make a subtraction fact: ________ – ________ = 4
Step 2 Repeat Step 1.
Find a different pair of numbers that subtract to leave 4.
Try to do this as many ways as you can.
Step 3 How many different ways did you find? ________________________
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Master 2.18
Date
Step-by-Step 6
Lesson 6, Question 12
5
3
7
4
Step 1 Arrange the numbers to make an addition problem.
Add the numbers.
Step 2 Arrange the numbers in different ways.
Add the numbers.
How many sums did you find? _______________
What is the greatest sum? ________________
Step 3 Arrange the numbers to make a subtraction problem.
Subtract the numbers.
Step 4 Arrange the numbers in different ways.
Subtract the numbers.
How many differences did you find? _______________
What is the least difference? _____________________
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Master 2.19
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Date
Step-by-Step 7
Lesson 7, Question 8
Step 1 Write two 2-digit numbers you can add using mental math.
________________________________________________________
Step 2 Write a story problem using the numbers from Step 1.
Make sure your story problem is an addition problem.
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
Step 3 Solve your problem.
Show your work.
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Master 2.20
Date
Step-by-Step 8
Lesson 8, Question 7
Step 1 Choose a 2-digit number that is greater than 43. _________
Step 2 Write the number from Step 1 in the first space.
_______ – _______ = 43
Step 3 Use a mental math strategy to find the number to subtract.
Write the number in the second space in Step 2.
Step 4 Find other pairs of numbers with a difference of 43.
Show your work.
______ – ______ = 43
______ – ______ = 43
______ – ______ = 43
______ – ______ = 43
______ – ______ = 43
______ – ______ = 43
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Master 2.21
Date
Step-by-Step 10
Lesson 10, Question 3
26, 53, 95, 148, 153, 256
Step 1 Round each number to the nearest 10.
26 rounds to ______.
53 rounds to ______.
95 rounds to ______.
148 rounds to ______.
153 rounds to ______.
256 rounds to ______.
Step 2 Use the rounded numbers.
Find two numbers with a sum of 200. ________________________
Find two other numbers with a sum of 200. ____________________
Step 3 Use the answers to Step 2. Use the exact numbers.
Which two numbers have the sum that is closest to 200? __________
How do you know?
________________________________________________________
________________________________________________________
________________________________________________________
________________________________________________________
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Master 2.22
Date
Step-by-Step 11
Lesson 11, Question 7
Step 1 Fill in the missing number: 100 + ______ = 217
Step 2 Add 1 to 100: ______
Use your answer to make another addition sentence:
______ + ______ = 217
Step 3 Add 2 to 100: ______
Use your answer to make another addition sentence:
______ + ______ = 217
Step 4 Continue the pattern.
Keep adding to 100.
Use the new number to write an addition sentence with a sum of 217.
Step 5 How many ways did you find? _________
How do you know if you have found all the ways?
________________________________________________________
________________________________________________________
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Name
Master 2.23
Date
Step-by-Step 12
Lesson 12, Question 6
Use a calculator to help.
Step 1 Fill in the missing number: 999 – ______ = 123
Step 2 Subtract 1 from 999: ______
Use your answer to make another subtraction sentence:
______ – ______ = 123
Step 3 Subtract 2 from 999: ______
Use your answer to make another subtraction sentence:
______ – ______ = 123
Step 4 Continue the pattern.
Keep subtracting from 999.
Use the new number to write a subtraction sentence with
a difference of 123.
Step 5 How many ways did you find?
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Master 2.24
Date
Step-by-Step 13
Lesson 13, Question 10
Use these digits:
2, 3, 4
Step 1 Use 2 as the hundreds digit.
Make two 3-digit numbers. ______, ______
Use 3 as the hundreds digit.
Make two 3-digit numbers. ______, ______
Use 4 as the hundreds digit.
Make two 3-digit numbers. ______, ______
How many 3-digit numbers did you make? ____________________
Step 2 Choose any two numbers from Step 1. Add the numbers.
Record the sum: _________
Step 3 Choose a different pair of numbers. Add the numbers.
Record the sum. _________
Step 4 Continue to add different pairs of numbers. Record the sums.
________________________________________________________
________________________________________________________
Step 5 How many different sums did you get? ___________________
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Master 2.25
Date
Step-by-Step 14
Lesson 14, Question 10
Step 1 How many points does Michelle have? ________________
How many points does Sunny have? __________________
What is the difference between the scores? ____________
How many points does Sunny need to tie Michelle? ____________
Step 2 How many points does Zane have? ___________
How many points does Michelle have? ___________
What is the difference between the scores? ___________
How many points does Michelle need to tie Zane? ____________
Step 3 How many points does Zane have? ___________
How many points does Sunny have? ___________
What is the difference between the scores? ___________
How many points does Sunny need to tie Zane? ____________
Step 4 Make up your own problem about these scores.
________________________________________________________
________________________________________________________
________________________________________________________
________________________________________________________
Step 5 Solve your problem.
Show your work.
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Master 2.26a
Date
Unit Test: Unit 2
Patterns in Addition and Subtraction
Part A
1. Find each missing number.
a) 7 + 9 =
b) 17 – 8 =
2. Add or subtract.
a) 34
b) 67
+ 26
– 26
c) 4 +
c)
227
+ 169
= 11
d) 15 –
=9
d) 300
– 177
3. Use mental math to find the sum and the difference.
a) 57 + 34 =
b) 40 – 19 =
4. Estimate the sum and the difference in 2 ways.
Did you get the same answer both times? Explain.
a) 313 + 479
b) 443 – 212
Part B
5. A subway was carrying two hundred thirty-five people.
At the next stop, 116 people got off and 87 people got on.
How many people were now on the subway?
Show your work.
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Name
Master 2.26b
Date
Unit Test continued
6. Use the digits 4, 5, and 7.
a) How many 3-digit numbers can you make?
b) Add pairs of these numbers.
What is the greatest sum you can get? Show your work.
c) Make up your own subtraction problem using two of your 3-digit
numbers. Solve your problem.
Part C
7. a) Two numbers, when using front-end estimation, add to 500.
The same two numbers, when rounded to the nearest 100, add to 600.
What could the numbers be?
b) Suppose one of the numbers is 248.
What is the least that the second number could be?
What is the greatest that the second number could be?
How do you know?
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Master 2.27
Sample Answers
Unit Test – Master 2.26
Part A
1. a)
c)
2. a)
c)
3. a)
4. a)
b)
Date
16
b) 9
7
d) 6
60
b) 41
396
d) 123
91
b) 21
Rounding to nearest 100: 800
Front-end estimation: 700
I did not get the same answer because in
the first estimate, 479 rounded to 500. In
the second estimate, 479 became 400.
Rounding to nearest 100: 200
Front-end estimation: 200
I got the same answer because each of the
numbers changed in the same way.
Part C
7. a)
b)
Sample answer: 135 and 456
Least number: 350
This is the least number that would round
to 400 when rounding to the nearest
hundred, and would be 300 using
front-end estimation.
Greatest number: 399
This is the greatest number that would
round to 400 when rounding to the nearest
hundred, and would be 300 using
front-end estimation.
Part B
5. 206 people: 235 – 116 + 87 = 206
6. a) 6 numbers: 457, 475, 547, 574, 745, 754
b) 1499; 745 + 754 = 1499
c) While on her summer vacation, Maya
travelled 457 km on the first day and
574 km on the second day. How much
farther did Maya travel on the second day?
(Answer: 117 km; 574 – 457 = 117)
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Extra Practice Masters 2.28–2.35
Go to the CD-ROM to access editable versions of these Extra Practice Masters
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Program Authors
Peggy Morrow
Ralph Connelly
Steve Thomas
Jeananne Thomas
Maggie Martin Connell
Don Jones
Michael Davis
Angie Harding
Ken Harper
Linden Gray
Sharon Jeroski
Trevor Brown
Linda Edwards
Susan Gordon
Manuel Salvati
Copyright © 2005 Pearson Education Canada Inc.
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