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Teacher GuideWestern Canadian

Unit 2: Patterns in Additionand Subtraction

A D D I S O N W E S L E YA D D I S O N W E S L E Y Western

UNIT

“Can you do addition?” theWhite Queen asked. “What’sone and one and one and oneand one and one and one andone and one and one?” “I don’t know,” said Alice. “I lost count.”

Through the Looking Glass

Lewis Carroll

Mathematics Background

What Are the Big Ideas?

• Addition and subtraction are inverse operations.

• Addition and subtraction have certain properties. For example, there isthe commutative property of addition.

• Strategies for solving 1- and 2-digit addition and subtraction problemscan be used to solve problems involving numbers with increasingnumbers of digits.

How Will the Concepts Develop?

Students use patterns to develop strategies for addition and subtractionof 1-digit numbers, including finding missing numbers.

Students use Base Ten Blocks and place-value mats to add and subtract2-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-digitnumbers using the standard algorithm.

Why Are These Concepts Important?

The ability to recognize patterns assists students to recall basic factsproficiently. Fluency with computations involving the addition andsubtraction of whole numbers is essential in the world around us.Students should have a good understanding of number and themeanings of and the relationships between the operations of additionand subtraction. A solid foundation is necessary for learning andapplying math in higher grades.

FOCUS STRANDNumber Concepts and NumberOperations

SUPPORTING STRANDPatterns and Relations: Patterns

Patterns in Addition and Subtraction

ii Unit 2: Patterns in Addition and Subtraction

2

Unit 2: Patterns in Addition and Subtraction iii

Lesson 1:Patterns in an Addition ChartLesson 2:Addition StrategiesLesson 3:Subtraction StrategiesLesson 4:Related FactsLesson 5:Find the Missing Number

Curriculum Overview

General Outcomes• Students investigate, establish and

communicate rules for numerical ...patterns, ..., and use these rules tomake predictions.

• Students apply an arithmeticoperation (addition, subtraction, ...)on whole numbers, and illustrate itsuse in creating and solvingproblems.

Specific Outcomes• Students recall addition/subtraction

facts to 18 ... (N16)• Students verify solutions to addition

and subtraction problems, using theinverse operation. (N18)

• Students use objects and concretemodels to explain the rule for apattern, such as those found onaddition ... charts. (PR2)

• Students make predictions based onaddition ... patterns. (PR3)

LaunchNational Read-A-Thon

Cluster 1: Addition and Subtraction Facts

Show What You Know

Unit ProblemNational Read-A-Thon

General Outcomes• Students investigate, establish and

communicate rules for numerical ...patterns ... and use these rules tomake predictions.

• Students apply an arithmeticoperation (addition, subtraction, ...)on whole numbers, and illustrate itsuse in creating and solvingproblems.

• Students use and justify anappropriate calculation strategy ortechnology to solve problems.

Specific Outcomes• Students use manipulatives,

diagrams and symbols, in aproblem-solving context, todemonstrate and describe theprocesses of addition andsubtraction to 1000, with andwithout regrouping. (N14)

• Students verify solutions to additionand subtraction problems, usingestimation and calculators. (N17)

• Students verify solutions to additionand subtraction problems, using theinverse operation. (N18)

• Students justify the choice ofmethod for addition andsubtraction, using:– estimation strategies– mental mathematics strategies– manipulatives– algorithms– calculators. (N19)

• Students make predictions based onaddition ... patterns. (PR3)

Cluster 2: Adding and Subtracting 2- and 3-Digit Numbers

Lesson 6:Adding and Subtracting 2-Digit NumbersLesson 7:Using Mental Math to AddLesson 8:Using Mental Math to SubtractLesson 9:Strategies ToolkitLesson 10:Estimating Sums and DifferencesLesson 11:Adding 3-Digit NumbersLesson 12:Subtracting 3-Digit NumbersLesson 13:A Standard Method for AdditionLesson 14:A Standard Method for Subtraction

iv Unit 2: Patterns in Addition and Subtraction

Curriculum across the Grades

Grade 2

Students usemanipulatives, diagrams,and symbols todemonstrate and describethe processes of additionand subtraction ofnumbers to 100. Theyapply and explainmultiple strategies todetermine sums anddifferences of 2-digitnumbers, with andwithout regrouping.

Students apply a varietyof estimation and mentalmathematics strategies toaddition and subtractionproblems. They recalladdition and subtractionfacts to 10.

Grade 3

Students usemanipulatives, diagrams,and symbols, in aproblem-solving context,to demonstrate anddescribe the processes ofaddition and subtractionto 1000, with and withoutregrouping.

Students recalladdition/subtraction factsto 18. They verifysolutions to addition andsubtraction problems,using estimation andcalculators.

Students verify solutionsto addition andsubtraction problems,using the inverseoperation. They justify thechoice of method foraddition and subtraction,using estimationstrategies, mentalmathematics strategies,manipulatives,algorithms, andcalculators.

Grade 4

Students usemanipulatives, diagrams,and symbols, in aproblem-solving context,to demonstrate anddescribe the process ofaddition and subtractionof numbers up to 10 000.

Students demonstrate anunderstanding of additionand subtraction ofdecimals (tenths andhundredths), usingconcrete and pictorialrepresentations.

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.

Fastest FactsFor Extra Support (Appropriate for use after Lesson 2)Materials: Fastest Facts (Master 2.9), deck of cardswith 10s and face cards removed

The work students do: Students play in groups of3. One student is the dealer. The dealer shuffles the deckand turns over 2 cards for the two other players to see.The first player to correctly add the two numbers getsone point. The dealer continues to turn over 2 cards at atime until one player has accumulated 10 points. He orshe is the winner. Students repeat the activity, with thewinner becoming the dealer.

Take It Further: The dealer turns over 3 cards at atime and students add all three numbers.

Social/Mathematical Group Activity

Additional Activities

Tic-Tac-Toe SquaresFor 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

The work students do: Students play with apartner. Players decide who will be “X” and who will be“O.” Player X chooses a square, then uses Base TenBlocks and place-value mats to find the answer. Player Ouses a calculator to check the answer. If Player A iscorrect, he puts his mark on the square. Players switchroles. Players continue to take turns until one player gets3 Xs or 3 Os in a row.

Take It Further: Students create their own Tic-Tac-Toeboard with each question involving the addition of three3-digit numbers.

Logical/Interpersonal/Mathematical Partner Activity

First to 10For 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 with apartner. Player A rolls 2 number cubes to make a 2-digit number. Player A rolls the number cubes againto make another 2-digit number. She then uses Base TenBlocks and place-value mats to add the two 2-digitnumbers. Player B uses a calculator to check Player A’sanswer. If the answer is correct, Player A gets 1 point.Player B takes a turn. Players continue to take turns untilone player gets 10 points. He is the winner.

Take It Further: Students play the game again. This time, they subtract the lesser number from the greater number.

Logical/Mathematical/Social Partner Activity

Unit 2: Patterns in Addition and Subtraction v

Shopping Bags!For Extension (Appropriate for use after Lesson 13)Materials: Shopping Bags! (Master 2.12), classroomobjects, price tags, calculators

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 isthe cashier. The other students are the shoppers. Shopperschoose two objects to purchase, then use pencil andpaper to find the total cost. Each shopper records theirtotal on a piece of paper. The shoppers take theirpurchases 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¢, withoutgoing over, wins.

Logical/Mathematical/Kinesthetic/Social Group Activity

vi Unit 2: Patterns in Addition and Subtraction

Planning for Unit 2

Planning for Instruction

Lesson Time Materials Program Support

Suggested Unit time: 3–4 weeks

Unit 2: Patterns in Addition and Subtraction vii

Purpose Tools and Process Recording and Reporting

Planning for Assessment

Lesson Time Materials Program Support

2 Unit 2 • Launch • Student page 54

National Read-A-Thon

LESSON ORGANIZER

Curriculum Focus: Activate prior learning about addition andsubtraction.

10–15 min

L A U N C H

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 thebooks 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 55of 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 the4 weeks.)

Discuss the questions posed in the Student Book.(Sample answer: Sookal read the most pages, 276. Sunnyread the most books, 18. I can find out who read thefewest books or who read the most books in Week 1, orhow many more books Sunny read than Jenny.)

Ask questions, such as:• How did you find who read the most pages?

(I ordered the numbers of pages read from greatest toleast. Sookal had the greatest number.)

• How did you find who read the most books?(I added the number of books in each column, thenordered the numbers from greatest to least.)

• Did the student who read the most pagesread the most books? (No) Explain. (Sookalread 276 pages and 13 books. Sunny read 206 pagesand 18 books. Sunny’s books must have been short.)

Tell students that, in this unit, they will usepatterns to develop strategies for adding andsubtracting 1-digit numbers. They will use BaseTen Blocks and place-value mats to add andsubtract 2- and 3-digit numbers, and this willlead to the standard method of addition andsubtraction. At the end of the unit, studentswill use charts to obtain information, and thenreport on the Read-A-Thon.

LITERATURE CONNECTIONS FOR THE UNIT

Shark Swimathon by Stuart J. Murphy. Harper Trophy, 2000.ISBN: 006446735XA shark swim team practices subtraction of 2-digit numbers as ittries to reach a goal of 75 laps. The subtraction getsprogressively 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 JuvenileBooks, 1998.ISBN: 0064467163This 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 whileguessing the trucks’ final destination.

DIAGNOSTIC ASSESSMENT

What to Look For

✔ Students can recalladdition andsubtraction facts to 18.

✔ Students cancompare and orderwhole numbers.

What to Do

Extra Support:

Students who have difficulty recalling their addition and subtraction facts maybenefit 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 benefitfrom modelling the numbers with Base Ten Blocks or recording the numbers in aplace-value chart.Work on this skill during the Launch and the Unit Problem.

Unit 2 • Launch • Student page 55 3

Some students may benefit from using the virtualmanipulatives on the e-Tools CD-ROM. The

e-Tools appropriate for this unit include Place-Value Blocks. Thesecan be used in place of, or to support the use of, Base Ten Blocks.

REACHING ALL LEARNERS

4 Unit 2 • Lesson 1 • Student page 56

Patterns in anAddition Chart

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, doublesAssessment: Master 2.2 Ongoing Observations: Patterns inAddition and Subtraction

40–50 min

L E S S O N 1

Key Math Learnings1. 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.

BEFORE Get S tar ted

Show students 2 quantities of the same item,such as books or counters. Invite a volunteer toadd the 2 quantities, then record the additionsentence on the board. Use the addition sentenceto introduce the terms addition fact and sum.

Show students an overhead transparency of anaddition chart. Demonstrate how to use thechart 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 firstcolumn. I would then find where the row andcolumn 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 firstcolumn. I would then find where the row andcolumn meet.)

Present Explore. Encourage students to find allthe patterns they can, including patterns acrossthe rows, down the columns, and along thediagonals. Suggest students use a differentcolour to show each pattern.

DURING Exp lore

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.)

Numbers Every DayEncourage students to discuss the strategies they used. Studentsshould realize that the numbers you and I say have a sum of 10.

Unit 2 • Lesson 1 • Student page 57 5

Early FinishersHave students use addition facts in the chart to write sentenceswith missing numbers, then trade them with a partner, whocompletes 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 apattern and have students continue the pattern by colouring thenumbers on an addition chart. Students then describe the pattern.

ESL StrategiesStudents for whom English is a second language may havedifficulty describing their patterns. Encourage these students to use numbers and mathematical symbols (+, =) to describetheir patterns.


• What pattern do you see in the diagonalsfrom top right to bottom left? (The numbers inthe 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 Connec t

Invite volunteers to describe their patterns to theclass. Have them explain how they found thepattern 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 toadd 3 + 5 and 5 + 3? (The answer is the same, 8.)

Use Connect to introduce some of the propertiesof addition. Tell students that when they adddoubles, the sum is always an even number.Discuss how finding patterns could helpstudents with addition.

Prac t i ce

Have addition charts (Master 2.6) available forall questions.

Assessment Focus: Question 6

Students understand the concept of even andodd numbers. Students add pairs of evennumbers, and discover that all the answers areeven numbers. Some students may list thenumbers that never appear, while others mayalso classify these numbers as odd numbers.

3

The two numbers add to 10.5

Sample Answers1. The first number increases by 1 each time. The second number

decreases by 1 each time.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 + 6c) 0 + 12, 1 + 11, 2 + 10, 3 + 9, 4 + 8, 5 + 7, 6 + 6d) 0 + 15, 1 + 14, 2 + 13, 3 + 12, 4 + 11, 5 + 10, 6 + 9, 7 + 8In each sum I used the pattern in the numbers. The first numberincreases by 1 each time and the second number decreases by1 each time. I kept listing the pairs until the numbers started torepeat because when you add, order does not matter.

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 andincreases 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 busaltogether? (Answer: 6 + 8 = 14)

6. 2 + 6 = 8, 2 + 4 = 6There are 7 different sums when you add 2 even numbers lessthan 10; 4, 6, 8, 10, 12, 14, 16. The odd numbers 1, 3, 5, 7, 9, 11, 13, 15, 17 never appear. The even numbers2 and 18 also do not appear. The only way to get 2 usingeven numbers is 2 + 0. The only way to get 18 using evennumbers is to add 10 + 8, but 10 is not a number less than10. The sum of 2 even numbers is always an even number.

REFLECT: The patterns in an addition chart help me remembersome of the addition facts. I know adding 0 does not changethe start number and when I add doubles, I know the sum isalways even. I also know that order does not matter. There arealso patterns when you look at all the ways to find a sum.When the first number increases by 1 each time, and thesecond number decreases by 1 each time, then the sum staysthe same each time.


ASSESSMENT FOR LEARNING

Recording and ReportingMaster 2.2 Ongoing Observations:Patterns in Addition and Subtraction

16 children

1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5

3

5

7

What to Look For

Understanding concepts ✔ Students understand that there are

patterns in an addition chart.

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 onan addition chart.

What to Do

Extra Support: Give students addition facts for one number,for example, 7. Have students colour an addition chart to showthese facts, then look for a pattern in the numbers.Students can use Step-by-Step 1 (Master 2.13) to completequestion 6.

Extra Practice: Have students work in pairs. One studentcolours a pattern on an addition chart. The other studentdescribes the pattern, then lists all the addition facts that fit thepattern. 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 ofnumbers beyond 9 + 9.


L E S S O N 2

Addition Strategies

Key Math Learnings1. 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.

LESSON ORGANIZER

Curriculum Focus: Use different strategies to recall basicaddition 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 crayonsVocabulary: near double, sums of 10Assessment: Master 2.2 Ongoing Observations: Patterns inAddition and Subtraction

40–50 min


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 onyour 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 that4 + 5 is 1 less than 5 + 5.)

Present Explore. Distribute copies of additioncharts (Master 2.7). Use an overheadtransparency of Addition Chart 2 todemonstrate the doubles along the diagonal.

Ensure students understand they are todescribe the patterns they see, then find waysto use the patterns to find other facts. Explainthat the number 10 is shaded yellow and bluebecause it lies on two diagonals.

DURING Exp lore


Ask questions, such as:• What pattern do you see in the blue diagonal?

(The numbers increase by 2 each time as you movefrom 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 adifferent sum for 10.)


• How can you remember the addition facts forthe pink squares? (They are doubles, plus 1.)

AFTER Connec t

Invite volunteers to describe the additionstrategies they found. Have them explain howthese strategies can help them recall basicaddition facts.

Use Connect to introduce the strategies for adding:“doubles,” “near doubles,” and “make 10.”Demonstrate how to use the strategy “neardoubles” to add 3 + 4. Tell students that to add 3 + 4, think of 3 + 3, plus another 1.

Explain how the basic facts for 10 can be usedto help figure out other facts. Show studentshow to find 9 + 3 by making 10 with 9 + 1,then adding another 2.

Write a variety of addition questions on theboard and have volunteers find the answers,describing the strategy they used each time.

Prac t i ce

Have addition charts (Master 2.6) available forall questions.


Students use their understanding of sums of 10. Students should first look for pairs ofnumbers that add to 10, then, if possible, break down the numbers in the pairs to findgroups of 3 and 4 numbers that add to 10.

Students who need extra support to completeAssessment Focus questions may benefit fromthe Step-by-Step masters (Masters 2.13–2.25).

Alternative ExploreMaterials: countersStudents use counters to show doubles. They add one morecounter to each double, then describe how they can use doublesto find near doubles. Students repeat the activity but remove onecounter from each double. Students record the additionstrategies they find.

Early FinishersHave 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 DayStudents 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,

435, 445, 455• 325, 350, 375, 400, 425, 450, 475, 500, 525, 550

101412

111513

16 17

Sample Answers4. I can use doubles for the first number and add 2 each time.

The first number increases by 1 each time. The second numberincreases 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, thenadded another 1.

6. 2 + 8; 3 + 7; 4 + 6; 1 + 2 + 7; 2 + 3 + 5; 1 + 4 + 5; 1 + 3 + 6; 1 + 2 + 3 + 4I know I have found all the ways because I have used all thecombinations of numbers that add to 10, without using thesame number more than once.

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.




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17 children

8 ways

What to Look For

Understanding concepts ✔ Students understand that patterns in

an addition chart can be used to helprecall basic addition facts.

Applying procedures✔ Students can use strategies,

such as “doubles,” “near doubles,”and “make 10” to recall basicaddition facts.

✔ Students can identify and extend apattern in an addition chart.

What to Do

Extra Support: Students can complete the Additional Activity,Fastest Facts (Master 2.9).Students can use Step-by-Step 2 (Master 2.14) to completequestion 6.

Extra Practice: Have students work in pairs. One studentmakes an addition question, and the other student uses countersto 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).

Extension: Challenge students to use these strategies to findaddition facts that involve the sums of 3 or more numbers.


Subtraction Strategies

Key Math Learnings1. 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.

LESSON ORGANIZER

Curriculum Focus: Use different strategies to recall basicsubtraction facts. (N16)Teacher Materials� overhead transparency of Addition Chart 1 (Master 2.6)� transparent countersStudent 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 factAssessment: Master 2.2 Ongoing Observations: Patterns inAddition and Subtraction

40–50 min

L E S S O N 3


Have a volunteer write an addition fact on theboard. Demonstrate how the addition fact can beused to find 2 subtraction facts. Tell studentssubtraction is the opposite of addition. Usetransparent counters on the overhead projectorto demonstrate this idea. Model the additionstatement 3 + 4 = 7. Show students how thesecounters 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 transparencyof an addition chart (Master 2.6) to demonstratehow to find subtraction facts. Colour the pathused for the subtraction fact 7 – 2 = 5. Have avolunteer list the other facts this path shows.

DURING Exp lore


Ask questions, such as:• How do you remember subtraction facts you

already know? (I think of the related addition facts. For example, Isay, “Three and what makes 8?”)

• What subtraction facts did you find that use10? (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 neardoubles. 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.)


AFTER Connec t

Invite volunteers to describe the subtractionstrategies they found. Have them explain howthese strategies can help them recall basicsubtraction facts. For example, some studentsmay find facts that subtract 5 are related tomake 10. For example, to find 9 – 5, think 10 – 5, then take away 1 more.

Use Connect to introduce other strategies forsubtracting. Demonstrate how to count upthrough 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 with12. Take away 2 to get 10. Since 5 is 2 + 3, takeaway 3 more; 10 – 3 = 7.

Write a variety of subtraction questions on theboard and have volunteers find the answers,describing the strategy they used each time.

Prac t i ce

Have Addition Chart 1 (Master 2.6) availablefor all questions.


Students should realize that to find allsubtraction facts that have an answer of 5, theyshould look down the column for 5 or acrossthe row for 5. They should discover they getthe same subtraction facts in both cases.Students will demonstrate their understandingof subtraction by explaining how they knowthey have found all the facts.

Alternative ExploreMaterials: number linesStudents use number lines to demonstrate addition facts, thenfind the corresponding subtraction facts. Students shoulddiscover subtraction is the opposite of addition, in that theymove to the right to add and to the left to subtract.

Early FinishersHave students use Addition Chart 2 (Master 2.7) to demonstratethe subtraction strategies “doubles,” “near doubles,” and“counting through 10.”

Common Misconceptions➤Students have difficulty when subtracting 0. For example, they

erroneously think 5 – 0 = 4 because subtraction must make anumber 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 DayStudents could use hundred charts.• 950, 948, 946, ..., 904, 902, 900• 950, 945, 940, ..., 850, 845, 840• 950, 940, 930, ..., 720, 710, 700• 950, 850, 750, ..., 250, 150, 50

78

7

96

97 9

777

999

7 9

Sample Answers2. When the first number increases by 1 each time, and the

second number increases by 1 each time, then the differencestays the same each time. Also, when the first numberdecreases by 1 each time, and the second number decreasesby 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 = 5I know I have found all the facts because I went down thecolumn for 5 on the addition chart and listed all thesubtraction facts with 5 as the answer.

9. Jenny’s mom sent 17 cookies to school with her. Jenny’sfriends ate 9 cookies. How many cookies were left? (Answer: 17 – 9 = 8)

REFLECT: I can think of subtraction as the opposite of addition.For example, when I see 9 – 3, I say, “Three and what makesnine?” Since 3 + 6 = 9, I know 9 – 3 = 6.




9 children

25

36

47

88

89

54

68

56

46

93

95

811

What to Look For

Understanding concepts ✔ Students understand that subtraction

is the opposite of addition.

Applying procedures✔ Students can use strategies, such as

“count up through 10” and “count back through 10,” to recall basicsubtraction facts.

✔ Students can use patterns in addition charts to help recall basicsubtraction facts.

What to Do

Extra Support: Students having difficulty finding subtractionfacts on the addition chart may benefit from finding additionfacts, then writing the corresponding subtraction facts.Students can use Step-by-Step 3 (Master 2.15) to completequestion 7.

Extra Practice: Have students work in pairs. One studentnames a subtraction strategy, and the other student writes asubtraction question that he would solve using that strategy. Thestudent 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 findsubtraction questions that involve 3 or more numbers (for example, 9 – 3 – 2).


L E S S O N 4

Related Facts

Key Math Learnings1. Some addition and subtraction facts are related.2. A doubles fact gives only one subtraction fact.

LESSON ORGANIZER

Curriculum Focus: Identify and apply relationships betweenaddition and subtraction. (N16)Teacher Materials� triangular cardsStudent Materials 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 factsAssessment: Master 2.2 Ongoing Observations: Patterns inAddition and Subtraction

40–50 min


Invite a volunteer to share an addition fact withthe class. Have students name other facts thatbelong with this fact. Tell students theseaddition 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 inan addition fact change the answer? (No)Why? (When you add, the order does not matter.)

• Given an addition fact, how can you find arelated 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 toeach pair of students. Model how to use a cardwith a set of related facts.

Introduce the Show and Share games to students.

DURING Exp lore


Ask questions, such as:• How did you make that card?

(We chose the numbers 3 and 4, then added them toget 7. We put one of these numbers in each of thethree 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 youwere shown 3 numbers? (I added the two lesser numbers to get their sum,which was the third number. This was the firstaddition fact. Then I said all the related facts.)


• When your partner showed you the relatedfacts, how did you find what numbersbelonged in the set? (I read the 3 numbers that were in one of the facts.)

AFTER Connec t

Invite volunteers to describe the strategies theyused in playing the games. Have students tellhow the games showed the relation betweenaddition and subtraction. Ask:• What other game can you play with these

cards? (One player covers one of the 3 numbers onthe front of the card, and the other player has to findthe 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)

• Why is there only one related fact for adoubles fact? (Because 2 of the numbers in the fact are the same.)

Use Connect to review the concept that additionand subtraction are related, and if you know onefact, you can use it to write other facts.

Prac t i ce



Students find an addition or subtraction factthat uses the number 5. They then find allrelated facts. Some students will find twonumbers that add to 5; others will find twonumbers that have a difference of 5, and otherswill find a fact in which 5 is not the sum ordifference, but one of the other two numbers.

Alternative ExploreMaterials: linking cubesHave students use linking cubes to demonstrate related additionand subtraction facts. Have them draw a picture to show each fact.

Early FinishersStudents use the triangular cards. One student covers up one of thethree numbers on the front of a card, and the other student findsthe 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 tomodel 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 DayStudents 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 is9 + 9, plus 2.

Sample Answers1. 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 = 5c) 9 + 9 = 18, 18 – 9 = 9d) 3 + 9 = 12, 9 + 3 = 12, 12 – 3 = 9, 12 – 9 = 3

2. a) 8 + 4 = 12, 4 + 8 = 12, 12 – 8 = 4b) 9 + 5 = 14, 14 – 5 = 9, 14 – 9 = 5c) 7 + 7 = 14d) 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 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 thecontainer.)

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 ofnumbers that add to 5, then finding pairs of numbers whosedifference is 5, and then finding other facts that have a 5, butdo not have an answer of 5.

REFLECT: 7 + 8 = 15, 8 + 7 = 15, 15 – 7 = 8, 15 – 8 = 7These facts are related because they all have the same numbers.



What to Look For

Understanding concepts ✔ Students understand that some

addition and subtraction facts are related.

✔ Students understand that a doublesfact gives only one related fact.

Applying procedures✔ Students can find all related facts for

a given fact.

✔ Students can list all related facts for aset of 3 numbers.

What to Do

Extra Support: Give students having difficulty finding relatedsubtraction 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 thecounters, then remove 7, and write the fact 13 – 7 = 6. Students can use Step-by-Step 4 (Master 2.16) to complete question 7.

Extra Practice: Have students make triangular cards for numbersbeyond 9 + 9.Students can complete Extra Practice 2 (Master 2.29).

Extension: Challenge students to use square cards to show factsthat involve more than 3 numbers.


7 children

20

++

–+

––

53 + 5 = 8, 5 + 3 = 8, 8 – 3 = 5, 8 – 5 = 3

118 + 3 = 11, 3 + 8 = 11,

11 – 3 = 8, 11 – 8 = 3

9 books

1619

17


Find the Missing Number

Key Math LearningTo find the missing term in a number sentence, think aboutrelated facts or think about the opposite operation.

LESSON ORGANIZER

Curriculum Focus: Find the value of the missing term in anumber 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 inAddition and Subtraction

40–50 min

L E S S O N 5


Write the number sentence 5 + 3 = 8 on theboard. 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 recordtheir number sentences as they play the game.

DURING Exp lore


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 had5 counters in her other hand.)

AFTER Connec t

Invite volunteers to describe the strategies theyused to find a missing number. Make a list ofthe strategies on the board.

Use the examples in Connect to introduce thestrategies “think of related facts” and “think about the opposite operation.”

Tell students that no matter which strategy theyuse to find a missing number, they shouldalways get the same answer.

Prac t i ce


Assessment Focus: Question 7Students could use addition charts. They findpairs of numbers that have a difference of 4.Some students may list pairs of numbers thathave more than 2 digits.

Numbers Every DayStudents should be systematic to ensure they do not miss any pairsof numbers. Students should recognize that after 7 + 8, the numbersentences repeat because when you add, order does not matter.


Alternative ExploreMaterials: Base Ten BlocksPlayer A uses Base Ten Blocks to model a number, then showsthem to Player B.Player B closes his eyes while Player A removes some blocks.Player B then finds how many blocks were removed.

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 sentencewith counters. Show students it does not make sense to add, asthe missing term would then be larger than 7.


Sample Answers4. I thought about related facts. I know 5 + 6 = 11.6. Calvin had 13 hockey cards. He gave Eric some of his cards.

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 couldbe 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 largenumbers, such as 204 and 200.

REFLECT: I used subtraction. I knew how many counters mypartner used. I looked at how many counters she had in herhand, then subtracted this number from the total. This gaveme the number of counters missing.

0 15

1 + 14 = 152 + 13 = 153 + 12 = 15

4 + 11 = 155 + 10 = 156 + 9 = 157 + 8 = 15

14 soccer balls

99

87

9

13

916 11

8

6

7 stickers


What to Look For

Understanding concepts ✔ Students understand that to find the

missing term in a number sentence,they can use related facts or theopposite operation.

Applying procedures✔ Students can use a variety of

strategies to find the missing term in anumber sentence.

Communicating✔ Students can explain the strategy they

used to find the missing term in anumber sentence.

What to Do

Extra Support: Students having difficulty finding the missingterm in a number sentence may benefit from using the triangularcards they made in Lesson 4.Students can use Step-by-Step 5 (Master 2.17) to completequestion 7.

Extra Practice: Have students make a set of triangular cardswith one term missing on each card. Students use the cards to playanother version of the game, How Many Are Missing?Students can complete Extra Practice 3 (Master 2.30).

Extension: Have students make number sentences with missingterms that go beyond 9 + 9.


I used doubles. 8 + 8 = 16

8ways


Adding and Subtracting2-Digit Numbers

Key Math Learnings1. 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.

LESSON ORGANIZER

Curriculum Focus: Add and subtract 2-digit numbers usingconcrete 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 cardsAssessment: Master 2.2 Ongoing Observations: Patterns inAddition and Subtraction

40–50 min

L E S S O N 6 L E S S O N 6


Have a student count the number of boys in theclass. Have another student count the numberof girls. Write these numbers on the board.Have a volunteer put Base Ten Blocks on theoverhead projector for the number of girls.Have another volunteer put the blocks on theprojector for the number of boys. Have a thirdvolunteer combine the two sets of blocks tocount how many students are in the class.

Ask students how they could find out howmany more girls or boys there are in the class.Students may have different strategies.

One strategy is to pair a boy with a girl (or dothis with blocks on the overhead), until yourun out of boys or girls. Then count the boys or girls who are not paired.

Present Explore. Distribute Base Ten Blocks andplace-value mats to students.

DURING Exp lore


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 for1 rod and kept 4 unit cubes. Then I counted 6 rods.46 + 18 = 64)

28 bottles

Students require place-value mats for this lesson. If you donot have place-value mats, turn a 2-column chart (PM 17)sideways and label the columns “Tens” and “Ones.” Makephotocopies. You may wish to laminate the mats.

Math Note

64 drinks


• How did you use a place-value mat to subtract46 – 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 tento leave 2 tens. 46 – 18 = 28)

• What other strategy could you use to findhow 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 theblocks: 1 orange rod and 1 green rod; I traded 1orange rod for 10 orange cubes; then paired 8 orangecubes with 8 green cubes. I had no green blocks left. I had 2 orange rods and 8 orange cubes left. Thistells me how many more bottles of juice I had.)

AFTER Connec t

Invite students to share the strategies they usedto add 46 + 18 and to subtract 46 – 18. Havestudents demonstrate these strategies withoverhead Base Ten Blocks and place-value mats.

Write the numbers 29 and 38 on the board. Usethe overhead Base Ten Blocks and place-valuemats to model how to add 29 + 38. Tellstudents since there are 17 ones, we can use 10 ones to make 10, leaving 7 ones. We thenadd the tens and the ones to get 6 tens and 7 ones, or 67.

Use the overhead Base Ten Blocks and place-value 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 thestrategies 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)

Early FinishersStudents write story problems that require both addition andsubtraction, 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 ofones regardless of which is the greater number.

How to Help: Have students use Base Ten Blocks to model thelarger number, then take away the blocks that represent the numberbeing subtracted. Students will “see” when there is a need to trade.


Your curriculum requires that students use the inverse operationto verify solutions to addition and subtraction problems (N17).The Curriculum Focus Activities, Checking Addition (Master2.12a) and Checking Subtraction (Master 2.12b) are providedto accommodate this outcome. You may wish to have studentscomplete these activities after this lesson. The answers to theseactivities can be found on page 20 of this Lesson.Remind students frequently to check their answers by using theinverse operation.

Curr i cu lum Focus

Prac t i ce

Have students use their calculators to checktheir answers to questions 1 to 5.Questions 7 and 8 also require calculators. Question 12 requires index cards. Have BaseTen Blocks and place-value mats available forall questions.


Students add all possible combinations of 2-digit numbers. Students should realize that tosubtract, the top number must be greater thanthe bottom number. Students then order thesums from greatest to least to find the greatestsum. They order the differences from least togreatest to find the least difference.


Sample Answers6. 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 numberincreases by 10 each time. Since you are subtracting 10 more each time, the answers start at 35 and decreaseby 10 each time.

7. 10 + 20, 11 + 19, 12 + 18, 13 + 17, 14 + 16, 15 + 15I know I have found all the ways because I started with 10,the least 2-digit number, and added 1 each time until thenumbers started to repeat.

8. 99 – 14, 98 – 13, 97 – 12, 96 – 11, 95 – 10I know I have found all the ways because I started with 99, the greatest 2-digit number, and subtracted 1 each timefrom 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 childrendid not finish? (Answer: 11 children; 36 – 25 = 11)

= 38 = 78 = 58 = 78

= 52 = 62 = 32 = 72

= 14 = 24 = 34 = 44

= 26 = 66 = 36 = 76

84 27 27 74

54 27 94 27

= 85 = 35= 83 = 25= 81 = 15= 79 = 5

6 ways

Answers to Curriculum Focus Activities:Curriculum Focus Activity 1– Master 2.12a1. a) 58 b) 136 c) 103

d) 143 e) 101 f) 141g) 77 h) 82 i) 108j) 111

Curriculum Focus Activity 2– Master 2.12b1. a) 71 b) 31 c) 55

d) 47 e) 20 f) 29g) 46 h) 54 i) 36j) 24

Curr i cu lum Focus

12. There are 12 addition problems: 53 + 74, 53 + 47, 54 + 37, 54 + 73, 57 + 34, 57 + 43, 35 + 74, 35 + 47, 34 + 75, 37 + 45, 45 + 73, 43 + 75There 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 thesums 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 TenBlocks or place-value charts. To add, model the numbers, thenadd the ones. If there are more than 10 ones, trade 10 onesfor 1 ten, then add the tens. To subtract, model the numbers,then subtract the ones. If there are not enough ones to takeaway from, trade 1 ten for 10 ones before you subtract theones. Subtract the tens.



What to Look For

Understanding concepts ✔ Students understand the strategies

for adding and subtracting 2-digit numbers.

Applying procedures✔ Students can use Base Ten Blocks and

place-value mats to add and subtract2-digit numbers.

✔ Students can solve problems involving the addition or subtractionof 2-digit numbers.

What to Do

Extra Support: Have students add or subtract two 2-digitnumbers where no trading is required, to build confidence.Students can use Step-by-Step 6 (Master 2.18) to completequestion 12.

Extra Practice: Students can play the Additional Activity, First to 10 (Master 2.10).Students can complete Extra Practice 3 (Master 2.30).

Extension: Have students find the missing digits in the sum and difference below.

4"+ 5 – 2"


9 boys

5 ways

86 bottles

"3

4 46 8"

Numbers Every DaySome students might write number sentences that involve otheroperations, 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


Using Mental Math to Add

Key Math LearningWhen you add in your head, you do mental math.

LESSON ORGANIZER

Curriculum Focus: Mentally add 1-digit and 2-digitnumbers. (PR3)(N19)Student Materials Optional

� Step-by-Step 7 (Master 2.19)

� Extra Practice 4 (Master 2.31)


40–50 min

L E S S O N 7 L E S S O N 7


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 thesteps they used to add the numbers.

DURING Exp lore


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 toadd when one of the numbers has a zero.)

AFTER Connec t

Invite volunteers to share their strategies with the class.

Use Connect to introduce the strategies “add ontens, then add on ones,” and “take from one togive to the other.” Invite volunteers to use thesestrategies to add 28 + 34.

Ask:• When would you use the strategy “take from

one to give to the other?” (When one of thenumbers being added is very close to a number of tens)

Prac t i ce


If students cannot think of ideas for a storyproblem, have them read the questions in Explore, Connect, and questions 6 and 7 for suggestions.

84 days

Numbers Every DayIn the first part, students could break down the second number in each statement into 2 numbers, one of which is given.



What to Look For

Understanding concepts ✔ Students can describe at least two

different strategies for addingnumbers mentally.

✔ Students understand when it isappropriate to use mental math to add.

Applying procedures✔ Students can mentally add two

2-digit numbers.

Communicating✔ Students can describe their strategies

clearly and precisely usingappropriate language.

What to Do

Extra Support: Provide students with questions where studentsadd 10 or multiples of 10 to build confidence.Students can use Step-by-Step 7 (Master 2.19) to completequestion 8.

Extra Practice: Students make 20 cards with a different two-digitnumber on each card. Students place the cards face down on atable. Students take turns to turn over 2 cards, then use mentalmath to add the numbers.Students can complete Extra Practice 4 (Master 2.31).

Extension: Students use mental math to add three 2-digit numbers.


Early FinishersStudents use a deck of cards with the tens and face cards removed.Students draw 4 cards. They use the cards to form two 2-digitnumbers. Students use mental math to add the two numbers formed.

Common Misconceptions➤Students have difficulty using the strategy “take from one

number to give to the other.”How to Help: Have students model the two numbers withcounters. Students take counters away from one number andgive the counters to the other number. Students will then “see”what happens to each number.


= 42 = 52 = 62 = 72= 66 = 76 = 86 = 96

= 78 = 88 = 68 = 78

= 71 = 71 = 71 = 71

= 64 = 66 = 90 = 71

Sample Answers1. In each part, as the second number increases by 10, the

answer increases by 10.5. I can add on tens, then add on ones: 29 + 50 + 5 = 84

I can take from one to give to the other: 29 + 1 + 54 = 30 + 54 = 84I can add 1 to 29 to get 30, then add the numbers and takeaway 1 from the answer: 30 + 55 = 85, 85 – 1 = 84

8. Andrew went to the car show with his mother. They saw 45 bluecars and 37 green cars. How many cars did they see altogether?(Answer: They saw 82 cars: 45 + 35 + 2 = 80 + 2 = 82)

REFLECT:+ +

27

13121272

82 licence plates

83 cars


Using Mental Math to Subtract

Key Math LearningStrategies, such as “take away tens, then take away ones,” and“add to match the ones, then subtract,” can be used to mentallysubtract 1-digit and 2-digit numbers.

LESSON ORGANIZER

Curriculum Focus: Mentally subtract 1-digit and 2-digitnumbers. (N19)Student Materials Optional

� Step-by-Step 8 (Master 2.20)

� Extra Practice 4 (Master 2.31)


40–50 min

L E S S O N 8


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 thenumbers are easy to handle.

Present Explore. Remind students to solve theproblem without using materials.

DURING Exp lore

Ongoing Assessment: Observe and ListenAsk questions, such as:• How did you find the difference?

(27 is 3 less than 30. I subtracted 30 from 43 to get13, then added 3 to get 16.)

• How else could you find the difference? (I could subtract the tens, 43 – 20 = 23, thensubtract the ones, 23 – 7 = 16.)

AFTER Connec t

Invite volunteers to share their strategies withthe class.

Use Connect to introduce the mental mathstrategies for subtraction. Invite volunteers touse 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 Itook away the 6 I added; 20 – 6 = 14.)

Prac t i ce


Students find a pair of numbers whosedifference is 43. A few students may even write a problem involving 3 numbers, such as 59 – 9 – 7.

16 people

2845365267Numbers Every Day

Make sure students understand the order of the numbers canbe switched in addition. To add: in each case, one ones digit is0, so the sum is the number formed by the tens digit and thenon-zero ones digit.



What to Look For

Understanding concepts ✔ Students can describe at least two

different strategies for subtractingnumbers mentally.

✔ Students understand when it isappropriate to use mental math to subtract.

Applying procedures✔ Students can mentally subtract two

2-digit numbers.

Communicating✔ Students can describe their strategies

clearly and precisely usingappropriate language.

What to Do

Extra Support: Provide students with questions where studentssubtract 10 or multiples of 10 to build confidence.Students can use Step-by-Step 8 (Master 2.20) to completequestion 7.

Extra Practice: Students make 10 cards, each with a 2-digitnumber greater than 40. Students make another 10 cards, eachwith a 2-digit number less than 40. Students take turns to take onecard 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 bysubtracting 2-digit numbers. They then solve the problem.


Common Misconceptions➤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 withcounters. Students add 3 counters to 24 to match the ones; 24 + 3 = 27. Students then subtract; 27 – 17 = 10. Tell studentsthey must get the counters they added back so they must takeaway 3 counters from 10 to get 7.


Sample Answers2. The number being subtracted from increases by 10 each time;

the number being subtracted decreases by 10 each time; andthe answer increases by 20 each time.

5. I can take away tens, then take away ones: 81 – 50 = 31, 31 – 8 = 23I can add to match the ones, then subtract: 81 + 7 = 88, 88 – 58 = 30, 30 – 7 = 23I 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. Icould take away the tens, then take away the ones. Forexample, to subtract 55 – 27, I first subtract the tens; 55 – 20 = 35. I then subtract the ones; 35 – 7 = 28. I couldalso add to match the ones, then subtract. For example, I couldadd 2 to 55 to make 57; 57 – 27 = 30. I then take away the 2 I added; 30 – 2 = 28.

= 49 = 57 = 78= 39 = 67 = 58= 29 = 77 = 38= 19 = 87 = 18

= 22 = 42 = 62 = 82

32 22 12 2

18 74 29 38

29 geese flew in.


Strategies Toolkit

Key Math LearningA “guess and check” strategy can be used to solve many problems.

LESSON ORGANIZER

Curriculum Focus: Interpret a problem and select anappropriate strategy. (N14)Teacher Materials� overhead countersStudent Materials� countersAssessment: PM 1 Inquiry Process Check List, PM 3 Self-Assessment: Problem Solving

40–50 min

L E S S O N 9


Present Explore. Have counters available forstudents to model the problem. Encouragestudents to think about what strategy they willuse before they begin.

DURING Exp lore

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 thestrategy “use a model.” I put 25 counters on my desk.I took away one counter each time until there were11 more counters in one pile than in the other. Ginahad 7 foreign stamps and 18 Canadian stamps.)

AFTER Connec t

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 wouldthere be? (14) Is the total 23? (Yes, 9 + 14 = 23)

• If you started by guessing the number oftrucks, what would you do differently? (I would subtract 5 to find the number of cars.)

• How could you solve this problem anotherway? (I could model the number 23 with counters. Icould remove one counter at a time until the differencebetween the number of counters in each pile was 5.)

Prac t i ce

Encourage students to refer to the Strategies listto choose an appropriate strategy.

9 cars

7 foreign stamps


There are two possible answers.There are 2 tricycles and 6 bicycles OR there are 4 tricycles and 3 bicycles.


What to Look For

Understanding concepts ✔ Students understand that “guess

and check” is a strategy to solve many problems.

Problem Solving✔ Students can select an appropriate

strategy to solve a problem.

Communicating✔ Students can describe their strategy

clearly, using appropriate language.

What to Do

Extra Support: Provide play money (coins) for students to use inPractice question 2.

Extra Practice: Have students write problems similar to thequestions in Practice for others to solve.

Extension: Challenge students to solve each of the Practicequestions using a different strategy. They check to see that theiranswers are the same each time.

Recording and ReportingPM 1 Inquiry Process Check ListPM 3 Self-Assessment: Problem Solving

Early FinishersHave 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. Havestudents use counters to model the total number of stamps.Students then arrange the counters into 2 groups until it lookslike one group has about 11 more counters than the othergroup. Students count the counters to check their answers. Ifnecessary, students adjust the counters and guess again.


Sample Answer

REFLECT: To answer Practice question 1, I used “guess andcheck.” 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 guessedKumail had won 9 cards. I then added 6 to find how manycards 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.

Sasha has won 15 cards and Kumailhas won 9 cards.

Margaret used 5 dimes and 3 nickels.


Estimating Sums and Differences

Key Math Learnings1. When you do not need an exact answer, you estimate.2. Strategies, such as “rounding first” and “front-end

estimation,” can be used to estimate.

LESSON ORGANIZER

Curriculum Focus: Use estimation to add and subtract.(N19)Student Materials Optional� calculators � Step-by-Step 10

(Master 2.21)� Extra Practice 5

(Master 2.32)Vocabulary: estimate, differenceAssessment: Master 2.2 Ongoing Observations: Patterns inAddition and Subtraction

40–50 min

L E S S O N 1 0


Have students read the introduction to the lessonon page 80 of the Student Book. Introduce theterm estimate as being close to an amount orvalue, but not exact. Invite students to giveexamples of situations in which an exact numbermight be used (recipes, test marks). Talk aboutother situations where an estimate might be used(the distance to the store, the number of pages in a book).

Present Explore. Ensure students understandthey are to estimate, not calculate.

DURING Exp lore


Ask questions, such as:• How do you know you have to estimate?

(The question asks “About how many?”)

• How did you estimate the number ofpennies? (I rounded 213 to 200 and I rounded488 to 500. I then added 200 and 500 to get 700.)

• About how many more than Jeff does Mayhave? 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 andMay to plan what they can buy? How do youknow? (Yes, if I use a calculator to add 213 + 488,I get 701. This is very close to my estimate of 700.)

AFTER Connec t

Invite students to share the strategies they usedto estimate.

Ask:• Why did you round to the nearest hundred?

(Because the numbers are easy to add and subtract)

About 300

About 700

34 + 28 = 62

Numbers Every DayStudents could use the strategy “add on tens, then add on ones:”34 + 20 = 54, 54 + 8 = 62Students could use the strategy “take from one to give to theother:” 34 + 6 = 40, 28 – 6 = 22; so, 34 + 28 = 40 + 22 = 62

• How do you know your answer is close tothe exact answer? (Because I rounded onenumber up and the other number down. Bothnumbers were close to a number of hundreds.)

Introduce the term difference as the result of asubtraction. Tell students that in the numbersentence 9 – 5 = 4, 4 is the difference.

Review the strategies in Connect. Havevolunteers 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 addedand subtracted the numbers; 300 + 600 = 900 and 600 – 300 = 300.)

• How did you use the strategy “front-endestimation?” (I used the digits in the hundredsplace and ignored all other digits; 322 became 300and 586 became 500. I then added and subtractedthe numbers; 300 + 500 = 800, 500 – 300 = 200.)

• Which strategy gave the better estimate? Why? (“Rounding first” gave the better estimate; 322 is closeto 300 and 586 is close to 600. In “front-endestimation,” 586 is far away from 500, so the estimateis not very close to the exact answer.)

Prac t i ce

Question 4 requires a calculator.


Students should round each number to thenearest 10 and then find pairs of numbers thatadd to 200. Students then look at how thenumbers were rounded. Students shouldrealize if one number was rounded up, theother number should be rounded down to givethe closest estimate.


Alternative ExploreMaterials: department store flyersTell students they have $40 to spend. They can buy what theywant, as long as they do not go over $40. Have studentsestimate as they shop, making a list of items they buy. Studentsuse a calculator to find the actual cost of their items, thencompare their estimate to the actual cost.

Early FinishersHave students estimate the sum of 251 + 323 in as manydifferent 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. Studentslocate the number on the line and “see” which ten it is closer to.


Sample Answers1. 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 onesplace add to 7, when both numbers are rounded down, theestimate 60 is not closer; 70 is better.

c) 600; 327 rounds down to 300 and 254 rounds up to 300,300 + 300 = 600.

3. I rounded all the numbers to the nearest 10, and found50 + 150 = 200. I then looked at the two numbers thatrounded to 150. 148 rounded up to 150 and 153 roundeddown to 150. Since 53 rounded down to 50, I chose thenumber that rounded up to 150: 148. The 2 numbers that willgive 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 estimatethat I add 145 six times to get 900. I checked with acalculator: 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 hisfriends a CD instead of a loot bag. His mother did not wantany CDs left over but she wanted to be sure that everyone gota CD. Matthew invited 12 girls and 12 boys to his party. Howmany CDs does he need? (Answer: 12 + 12 = 24)

REFLECT: When I guess, I choose a number without reallyknowing. When I estimate, I look at the numbers, then roundthem to get an answer that is close to the exact answer. Forexample, 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.



What to Look For

Understanding concepts ✔ Students understand that an estimate

is close to an amount or value, butnot exact.

✔ Students understand when an estimateis appropriate.

Applying procedures✔ Students can use strategies, such as

“rounding first” and “front-endestimation,” to estimate sums and differences.

What to Do

Extra Support: Give students number lines to help them estimatebefore they add or subtract.Students can use Step-by-Step 10 (Master 2.21) to completequestion 3.

Extra Practice: Have students refer to Lesson 6, Practice question5. Students estimate each sum or difference, then compare theirestimates to the exact answers.Students can also complete Extra Practice 5 (Master 2.32).

Extension: Challenge students to estimate the sum of 3 or more numbers.


No

53 and 148

both

both


L E S S O N 1 1

Adding 3-DigitNumbers

Key Math Learnings1. 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.

LESSON ORGANIZER

Curriculum Focus: Add 3-digit numbers with and withoutregrouping, using concrete materials. (N14, N17, N18)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 inAddition and Subtraction

40–50 min

Students require place-value mats for this lesson andfuture lessons. If you do not have place-value mats, turn a3-column chart (PM 18) sideways and label the columns“Hundreds,” “Tens,” and “Ones.” Make photocopies. Youmay wish to laminate the mats.

Math Note


Ask students how they add 284 + 328. Havestudents talk about the strategies they coulduse. 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 andplace-value mats to students.

DURING Exp lore


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 andkept 1 rod. I counted 4 flats. 236 + 175 = 411)

• How else could you add 236 + 175? (I coulduse counters but I would need a lot of counters.)

411 T-shirts


AFTER Connec t

Invite students to share the strategies they usedto add 236 + 175. Have students demonstratethese strategies with overhead Base Ten Blocksand 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 meaningof addition is still the same, no matter how large thenumbers are.)

• Why do we start adding in the ones place?(So that we know if we have to regroup 10 ones forone rod)

• Could we start by adding in the hundredsplace? (Yes; I have 3 flats, 11 rods, and 12 unitcubes. I trade 10 unit cubes for 1 rod, leaving 2 unitcubes, then trade 10 rods for 1 flat, leaving 2 rods. Iend up with 4 flats, 2 rods, and 2 unit cubes.)

Write the numbers 329 and 285 on the board.Use the overhead Base Ten Blocks and place-value mats to model how to add 329 + 285.(Answer: 6 hundreds 1 ten 4 ones, or 614)

Prac t i ce

Question 7 requires a calculator. Have Base Ten Blocks and place-value mats available forall questions. Encourage students to check theiranswers using estimation, a calculator, or theinverse operation.


Students should be systematic to ensure theydo not miss any pairs of numbers. Bothnumbers must be 3-digit numbers. Studentsshould start with 100 as the first number, thenincrease the first number by 1 each time.Students should recognize that after 108 + 109,the number sentences repeat because when youadd, order does not matter.

Alternative ExploreHave students solve this problem:Last year, Corinne went outside for 153 morning recesses and158 afternoon recesses. For how many recesses did Corinne gooutside altogether? Students use what they know about adding2-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 nomore than 9 rods in the tens column and no more than 9 unitcubes in the ones column of the place-value chart. If they havemore than 9 of either of these Base Ten Blocks, they must trade.

Early FinishersChallenge students to find two 3-digit numbers that have a sumthat is a 4-digit number (for example, 672 + 489).


Numbers Every DayFor 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.

486 416

9910059134

Sample Answers5. I modelled the numbers with Base Ten Blocks. I counted

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 cardsdoes 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 + 109I 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 numbersbecause you can use the same strategies. The only differenceis when I add 3-digit numbers, I sometimes have to trade 10 rods for 1 flat.



What to Look For

Understanding concepts ✔ Students understand that the same

strategies are used to add 3-digitnumbers as 2-digit numbers.

Applying procedures✔ Students can use Base Ten Blocks

and place-value mats to add 3-digit numbers.

✔ Students can solve problems involvingthe addition of 3-digit numbers.

✔ Students can choose an appropriatemethod for adding and for verifyingsolutions.

What to Do

Extra Support: Have students add two 3-digit numbers whereno regrouping is required, to build confidence.Students can use Step-by-Step 11 (Master 2.22) to completequestion 7.

Extra Practice: Students can do the Additional Activity, Tic-Tac-Toe Squares (Master 2.11).Students can complete Extra Practice 5 (Master 2.32).

Extension: Have students find the missing digits in this sum.4 " 3

+ " 8 "8 1 2


355 lunches

= 372 = 897 = 420= 432 = 792 = 714

610 730 530 530

= 851 = 851 = 851 = 851

9 ways

557 km


Subtracting 3-DigitNumbers

Key Math Learnings1. 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.

LESSON ORGANIZER

Curriculum Focus: Subtract 3-digit numbers with and withoutregrouping, 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 inAddition and Subtraction

40–50 min

L E S S O N 1 2


Use overhead Base Ten Blocks and atransparency of the place-value mat to reviewhow to subtract 2-digit numbers.

Invite students to examine the map on page 86of the Student Book. Ask:• What question can you ask that would

need the subtraction of 3-digit numbers toanswer it?(How much farther is it from Banff to Vancouverthan from Banff to Edmonton?)

• What strategy would you use to subtract two3-digit numbers? (I would use the same strategy that I used tosubtract two 2-digit numbers.)

Students should be familiar with subtractionquestions where they trade 1 ten for 10 ones.Tell students when they subtract 3-digitnumbers, it is often necessary to trade 1 hundred for 10 tens.

Present Explore. Distribute Base Ten Blocks andplace-value mats to students. Remind studentsthey should always model the greater numberwith Base Ten Blocks, then take away thelesser number.

DURING Exp lore


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 TenBlocks; 2 flats, 9 rods, and 0 unit cubes. I thensubtracted 128 by taking away 1 flat, 2 rods, and 8 unit cubes. There were not enough unit cubes to takeaway 8 unit cubes, so I traded 1 rod for 10 unit cubes,leaving 8 rods. Then I took away 8 unit cubes, leaving2 unit cubes. Then I took away 2 rods, leaving 6 rods;and 1 flat, leaving 1 flat. 290 – 128 = 162)

The Lee family 162 km


• 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 Connec t

Invite students to share the strategies they usedto subtract 290 – 128. Have studentsdemonstrate these strategies with overheadBase 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 trade1 ten for 10 ones.)

• What was the most important step thathelped you solve the problem? (When I traded 1 rod for 10 unit cubes)

Some students have difficulty subtracting froma number such as 400. Model this subtractionon the overhead projector: 400 – 156Have a volunteer place the blocks for 400: 4 flats. Write the number 156 along the bottomof the place-value mat, to show that this is thenumber we take away. Ask:• How do we take 156 away from 400?

(We want to take 6 ones from 0 ones, but wecannot. 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 withsubtracting hundreds, follow their strategy.This is a legitimate method.

Alternative ExploreMaterials: measuring tapes, Base Ten Blocks, place-value matsStudents use a measuring tape to measure the height of theirteacher and a fellow classmate, in centimetres. Students find thedifference 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 byusing place value to compare the numbers. Compare thehundreds digits. If they are the same, compare the tens digits.

Early FinishersHave students choose a 3-digit number as an answer to asubtraction question, then find 2 possible 3-digit numbers thatcould be subtracted to get that answer; that is, choose theanswer, then write the question.


Sample Answers6. 999 – 876, 998 – 875, 997 – 874, ..., 226 – 103,

225 – 102, 224 – 101, 223 – 1007. I modelled 475 with Base Ten Blocks. I traded 1 rod for

10 unit cubes, leaving 6 rods. I took 8 unit cubes away from15 unit cubes, leaving 7 unit cubes. I took 3 rods away from6 rods, leaving 3 rods. I took 2 flats away from 4 flats leaving2 flats. 475 – 238 = 237

8. 456 – 285 = 1719. The local school was holding a music concert. They printed

652 tickets. They had 328 tickets left over. How many peopleattended 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.

Prac t i ce

Question 6 requires a calculator. Have Base Ten Blocks and place-value mats available forall questions. As students are working, askthem to explain the method they are using tosubtract and to justify their choice of method.


There are 777 solutions. Students should findsome of these. Some students may select a“friendly” 3-digit number such as 423 andsubtract 123 from it to find the “missingnumber” (423 – 300 = 123). Other students mayrecognize a pattern that they can use togenerate other solutions (for example, bysuccessively subtracting 1 from the two 3-digitnumbers, they can find many solutions).


216 69

REFLECT: To subtract 157, I have to take away 1 hundred 5 tens7 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 tensfrom 9 tens, leaving 4 tens. I take 1 hundred from 2 hundreds, leaving 1 hundred; 300 – 157 = 143



What to Look For

Understanding concepts ✔ Students understand that the same

strategies are used to subtract 3-digitnumbers as 2-digit numbers.

Applying procedures✔ Students can use Base Ten Blocks

and place-value mats to subtract 3-digit numbers.

✔ Students can solve problems involvingthe subtraction of 3-digit numbers.

Communicating✔ Students can explain and justify their

methods for subtracting.

What to Do

Extra Support: Have students subtract two 3-digit numberswhere no regrouping is required, to build confidence. Students canuse Step-by-Step 12 (Master 2.23) to complete question 6.

Extra Practice: Students choose two 3-digit numbers to subtract,then make up a story problem they can solve by subtraction. Theysolve the problem.Students can complete Extra Practice 6 (Master 2.33).

Extension: Challenge students to find the least 3-digit numberthey can take away from 237 to get a 2-digit number.


118 117 116 215

= 853 = 913 = 613 = 513

= 707 = 809 = 648 = 905

= 327 = 327 = 327 = 327

237 km

171 comic books

9496

757377

Numbers Every DayStudents 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 theother sums.


A Standard Methodfor Addition

Key Math Learnings1. 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.

LESSON ORGANIZER

Curriculum Focus: Develop proficiency in adding 3-digitnumbers. (N14, N19)Student Materials Optional

� Base Ten Blocks� place-value mats

(made from PM 18)� Step-by-Step 13


(Master 2.33)Assessment: Master 2.2 Ongoing Observations: Patterns inAddition and Subtraction

40–50 min

L E S S O N 1 3


Initiate a discussion about the strategiesstudents use to add 2-digit and 3-digitnumbers. 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 theyare harder, I use blocks, or a calculator. If I do notneed an exact answer, I estimate.)

Have students think about how they could add2-digit and 3-digit numbers without usingconcrete materials.

Present Explore. Tell students they are to addusing only pencil and paper. Encouragestudents to share the strategies they used.

DURING Exp lore


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 thetens 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 thetens to get 9 tens. He then added the hundreds to get3 hundreds; 257 + 138 = 395.)

• How did you add 25 + 39? (I used mental math.I used the strategy “take from one to give to theother.” 25 + 39 = 24 + 39 + 1 = 24 + 40 = 64)

• How did you add 257 + 138? (I used mental math. I added on hundreds, thentens, and then ones; 257 + 100 + 30 + 8 = 395.)

• What are the “little 1s” written above some ofthe numbers? (Each represents 1 ten that has beentraded for 10 ones.)


AFTER Connec t

Invite students to share the strategies they usedto add the numbers in Explore. Have studentsdemonstrate these strategies on the board.

Use Connect to introduce the standard algorithmfor addition. Write the numbers 27 and 18 onthe 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 exactsum 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 asrounding down, the exact sum will be morethan 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 addingthe ones; 7 + 8 = 15. Since we have more than10 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 thisten. We then add the tens; 2 + 1 + 1 = 4. Thesum of 27 and 18 is 45.

Model 3-digit addition on the board using thestandard 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 for1 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.)

Alternative ExploreHave students write down the first 2 digits of the year in whichthey were born to make a 2-digit number. Students write downthe last 2 digits of the year in which they were born to makeanother 2-digit number. Students add these 2 numbers withoutusing concrete materials. Have students write down the first 3 digits of their phone number and the last 3 digits, then add thetwo 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 writeeach digit in one square on the paper. This places the digits incolumns. Students can then add.

Early FinishersChallenge students to add 694 + 528. Finding this sum involvestrading 10 ones for 1 ten, 10 tens for 1 hundred, and 10 hundreds for 1 thousand.


Sample Answers1. To add 27 + 39, I can:

Add on the tens, then add on the ones: 20 + 30 + 7 + 9 = 50 + 16 = 66Take from one number to give to the other: 27 + 39 = 26 + 39 + 1 = 26 + 40 = 66Use the standard method for addition:

2. The first number in each question increases by 10 each time.The second number in each question increases by 1 eachtime. In the answers, the tens digit starts at 6 and increases by1 each time, and the ones digit starts at 1 and increases by 1 each time; that is, the sum increases by 11 each time.

27+ 39

66

1

Some students might start by adding on theleft, adding the hundreds, the tens, and thenthe ones, then combining the results using thestandard method for addition. This is anacceptable strategy.

Prac t i ce

Have Base Ten Blocks and place-value matsavailable for all questions. Remind students to use an appropriate method for verifying their answers.


Students should be systematic to ensure theydo not miss any numbers. Students could startwith 2 as the hundreds digit and find allpossible 3-digit numbers. Students repeat with3, then 4 as the hundreds digit. Students thenadd pairs of numbers in a systematic way andcompare the sums.


Numbers Every DayLeah took away a number that had the same ones digit as 52.Then she took away the extra ones.

61 72 83 94

88 90 92 94

407 507 607 707

84 65 106 113

600 500 400 700

549 631 832 832

263919

8. I added the ones, 6 + 1 = 7. I added the tens; 5 + 7 = 12. I traded 10 tens for 1 hundred, leaving 2 tens. I added thehundreds; 2 + 3 + 1 = 6. 256 + 371 = 627

9. b) 44 + 27 = 7110. I can make six 3-digit numbers:

234, 243, 324, 342, 423, 432I 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 = 855There are 15 sums, but 3 of the sums are the same.

12. There were 2 showings of a movie on opening night. Threehundred fifty-six people saw the early show and 248 peoplesaw the late show. How many people saw the movie onopening night?(Answer: 604 people)

REFLECT: I like to use the standard method best because Ialways get an exact answer and I can get the answer fasteras I do not have to get any materials, such as Base TenBlocks, before I add. If I do the addition in my head, I mightmake a mistake.



What to Look For

Understanding concepts ✔ Students understand that the

strategies for adding 2-digit and 3-digit numbers are based on place-value concepts.

Applying procedures✔ Students can use the standard

algorithm for addition to add 2-digitand 3-digit numbers.

✔ Students can use more than onestrategy to add 2-digit and 3-digit numbers.

What to Do

Extra Support: Have students work in pairs. One student modelsthe addition with Base Ten Blocks, and the other student records thesteps on paper, using numbers.Students can use Step-by-Step 13 (Master 2.24) to completequestion 10.

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).

Extension: Students can complete the Additional Activity,Shopping Bags! (Master 2.12).


627 tulips

44 children

71 children

6

13 different sums

402 things


A Standard Methodfor Subtraction

Key Math Learnings1. 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.

LESSON ORGANIZER

Curriculum Focus: Develop proficiency in subtracting 3-digitnumbers. (N14)Student Materials Optional

� Base Ten Blocks� place-value mats

(made from PM 18)� Step-by-Step 14


(Master 2.34)Assessment: Master 2.2 Ongoing Observations: Patterns inAddition and Subtraction

40–50 min

L E S S O N 1 4


Initiate a discussion about the strategiesstudents use to subtract 2-digit numbers and 3-digit numbers. Ask:

• What methods did you use to subtract 2-digitnumbers and 3-digit numbers? (Base Ten Blocks, place-value mats, calculators)

Have students think about how they couldsubtract 2-digit numbers and 3-digit numberswithout using concrete materials.

Present Explore. Tell students they are to subtractusing only pencil and paper. Encouragestudents to share the strategies they used.

DURING Exp lore


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 findhow 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 tensand 12 ones; 12 – 8 = 4. Joe then subtracted the tensto 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 get20, which is an easy number to take away: 42 – 20 = 22. Since I took away 2 more than Ishould have, I add 2 to the answer to get 24.)

Yes


• How did Joe find how many pages Angiestill 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 notsubtract 6 tens from 4 tens, so he traded 1 hundredfor 10 tens, making 1 hundred and 14 tens. Joesubtracted the tens: 14 – 6 = 8. Joe then subtractedthe hundreds; 1 – 1 = 0. 245 – 164 = 81)

• Is Joe correct? (Yes) How do you know? (I used mental math to check. I subtracted thehundreds, then the tens, and then the ones; 245 – 100 = 145, 145 – 60 = 85, 85 – 4 = 81.)

AFTER Connec t

Invite students to share their ideas about Joe’smethod of subtraction with the class.Use Connect to introduce the standard algorithmfor subtraction. Write the numbers 27 and 18on the board. Use the standard algorithm forsubtraction to model how to subtract 27 – 18.

Tell students we start by subtracting the ones.Since there are not enough ones to subtractfrom, trade 1 ten for 10 ones, leaving 1 ten. We cross out the 2 and write a “little 1” abovethe 2 to show we have traded 1 ten for 10 onesand we have 1 ten left. We cross out the 7 thenwrite a “little 17” above the 7 to show we haveadded 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 thedifference. If the difference is correct, this sumis 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 azero, especially if the zero is in the numberbeing subtracted from. Model 3-digitsubtraction on the board using the standardmethod, using an example such as 402 – 139.

Early FinishersChallenge students to check their answers by adding.

Common Misconceptions➤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 thenumber of hundreds.

How to Help: Tell students when they trade, they do anexchange. Have them model the subtraction with Base TenBlocks, then exchange one rod for 10 unit cubes or exchangeone flat for 10 rods, as necessary.


Numbers Every DayEncourage students to experiment with their calculators. Studentsshould recognize that Julia needs to add or subtract to show 77 on her calculator. Students could find several ways to display77 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 asubtraction problem in the same way, the difference does notchange. For example, students could add 5 to each number, thenuse the calculator to find 80 – 22.

69 + 8 = 77 or 80 – 3 = 77

80 – 22 = 58

Sample Answers1. Start at 85. The first number in each question decreases by

10 each time. Start at 23. The second number in eachquestion 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 = 38Add to match the ones, then subtract: 75 + 2 = 77, 77 – 37 = 40, 40 – 2 = 38Use the standard method for subtraction:

75– 37

38

6 15

Ask questions, such as:• How did we subtract the ones?

(There were not enough ones to subtract from so wetraded. There were no tens to trade from, so wetraded 1 hundred for 10 tens, leaving 3 hundreds. Wethen traded 1 ten for 10 ones, leaving 9 tens. We had12 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 addingthe difference to the number that was subtracted.

Prac t i ce

Have Base Ten Blocks and place-value matsavailable for all questions.


Students should realize in part a, they mustfind the difference between Michelle’s scoreand Sunny’s score. In part b, students shouldrealize they must find the difference betweenZane’s score and Michelle’s score and thedifference between Zane’s score and Sunny’sscore. Some students might make up a problemthat involves both the addition and subtractionof 3-digit numbers.


62 51 40 29

69 48 27 6

222 115 242 632

275 356 183 212

7. a) I compared the tens digits. Since 8 > 4, $82 > $498. 90 – 25 – 50 = 15, 15 + 19 = 34

10. a) 84 points; 369 – 285 = 84b) Michelle needs 87 points; 456 – 369 = 87.

Sunny needs 171 points; 456 – 285 = 171.c) How many more points did Michelle and Sunny score in

total than Zane?(Answer: 198 points; 369 + 285 = 654, 654 – 456 = 198)

11. Last year, 167 Grade 3 students participated in the Terry FoxRun. This year, 214 students participated. How many morestudents participated this year than last?(Answer: 47 students; 214 – 167 = 47)

REFLECT: When I subtract 2 numbers , I need to trade 1 ten for 10 ones if there are not enough ones to take away from. Forexample, to subtract 45 – 16, there are not enough ones totake away 6. I need to trade 1 hundred for 10 tens if there are not enoughtens to take away from. For example, to subtract 327 – 281,there are not enough tens to take away 8.



What to Look For

Understanding concepts ✔ Students understand that the

strategies for subtracting 2-digit and 3-digit numbers are based on place-value concepts.

Applying procedures✔ Students can use the standard

algorithm for subtraction to subtract2-digit and 3-digit numbers.

✔ Students can use more than onestrategy to subtract 2-digit and 3-digit numbers.

What to Do

Extra Support: Have students use Base Ten Blocks, then modelwhat they do with the blocks as they use the standard algorithm for subtraction.Students can use Step-by-Step 14 (Master 2.25) to completequestion 10.

Extra Practice: Students find the total number of pages in theirmath book, then subtract the page they are on to find how manypages they have left to learn.Students can complete Extra Practice 7 (Master 2.34).

Extension: Have students use pencil and paper to subtract:362 – 177 – 96 (Answer: 89)


87 points,171 points

= 179 = 148 = 218 = 118

Prya$33

34¢

230 sticks

84 points

46 Unit 2 • Show What You Know • Student page 98

LESSON ORGANIZER

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 Additionand Subtraction, 2.4 Unit Summary: Patterns in Addition and Subtraction

40–50 min

SHOW WHAT YOU KNOW

Sample Answers4. a) 9 – 8, 8 – 7, 7 – 6, 6 – 5, 5 – 4, 4 – 3, 3 – 2,

2 – 1, 1 – 0b) 11 – 9, 10 – 8, 9 – 7, 8 – 6, 7 – 5, 6 – 4, 5 – 3,

4 – 2, 3 – 1, 2 – 0c) 12 – 9, 11 – 8, 10 – 7, 9 – 6, 8 – 5, 7 – 4, 6 – 3,

5 – 2, 4 – 1, 3 – 0d) 13 – 9, 12 – 8, 11 – 7, 10 – 6, 9 – 5, 8 – 4, 7 – 3,

6 – 2, 5 – 1, 4 – 0Most students will use the 9 + 9 addition chart toanswer this question. If some students decide to gobeyond this chart, there is no limit to the answers.I know I have found all the facts because I used theaddition chart. For example, for a difference of 3, I went down the column for 3 and listed all thesubtraction 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, thenumbers increase by 8 each time.In the diagonals going from top right to bottom left, thenumbers increase by 2 each time.

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 problemcould be: 999 – 623, 998 – 622, 997 – 621, . . ., 476 – 100.If students use 1-digit and 2-digit numbers, many moreanswers are possible.

15. The greatest possible sum is 1795: 953 + 842, 943 + 852, 853 + 942, 952 + 843The least possible sum is 607: 248 + 359, 249 + 358, 258 + 349, 259 + 348

61 66 388 616

14 15 14 18

9 8 8 9

9 7 8 15

6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16

8

13

23

11

21

26

19

24

17

22

32

20

30

35

28

33

38

26

31

36

41

29

34

39

44

69 69 70 69

Unit 2 • Show What You Know • Student page 99 47

55 38 129 313


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 ReportingMaster 2.1 Unit Rubric: Patterns in Addition and SubtractionMaster 2.4 Unit Summary: Patterns in Addition and Subtraction

83 32

37 and 62

89 and 37

861 tiles

498 children

Read the QuestionEncourage students to read each question carefully, and look forclues about the operation that is required.

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 indicateaddition is required to solve the problem.

SHOW YOUR BEST

48 Unit 2 • Unit Problem • Student page 100

National Read-A-Thon

LESSON ORGANIZER

Student Grouping: 2Student 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 inAddition and Subtraction

40–50 min

U N I T P R O B L E M

Have students turn to the Unit Launch on pages54 and 55 of the Student Book.

Use the lists of Learning Goals and Key Wordsto 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 readthe 3 parts of the problem aloud. Answer anyquestions students might have.

Invite a student to read aloud the Check List.Explain these are the criteria against whichtheir work will be assessed. Have studentswork in pairs.

Ensure students understand they mustcollaborate in pairs to complete all parts of theactivity. One student could keep her book openat pages 54 and 55, so the table there is readilyavailable.

Encourage students to use the algorithms foraddition and subtraction, but have Base TenBlocks and place-value mats available. In Part 3, ensure students understand they are toexplain the new prize as well as explain howthey figured out to whom it was awarded. Tell students they can draw a picture of thenew prize.

As an extension, students could hold a classRead-A-Thon, then decide who would get each prize.

Sample ResponsePart 1

I estimate Woodlawn Public School read the most pages. For each school, I rounded the number of pages read by eachchild to the nearest hundred, then added.Roseville Public School: 200 + 100 + 300 + 200 = 800Woodlawn Public School: 200 + 200 + 300 + 200 = 900900 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 ofbooks read by Jadan (4 + 2 + 0 + 3 = 9). I added the numberof books read by LaToya (5 + 6 + 3 + 2 = 16). Since 16 isgreater than 9, LaToya read more books.

Part 2

Children who have read from 10 to 15 books:Sookal: 4 + 4 + 3 + 2 = 13Jenny: 5 + 4 + 3 + 2 = 14Stanley: 2 + 3 + 4 + 1 = 10Children who have read from 15 to 20 books:Sunny: 6 + 4 + 3 + 5 = 18LaToya: 5 + 6 + 3 + 2 = 16Part 3

A prize could be awarded to the child who reads the mostpages at each school. The prize could be a gift certificate for abook 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 UnitI know there are many strategies for adding and subtracting,such as using mental math, estimation, Base Ten Blocks, place-value mats, or the standard method. I know that I can useaddition to check the answer to a subtraction question. I alsoknow how to trade 10 ones for 1 ten, and 10 tens for 1 hundredwhen adding, and how to trade 1 ten for 10 ones, and 1 hundred for 10 tens when subtracting. For example,

742– 288

454

632+ 299

931

11 13 126

Unit 2 • Unit Problem • Student page 101 49


What to Look For

Understanding concepts ✔ Students understand the difference

between an exact answer and an estimate.

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.

Communicating✔ Students use mathematical language

to explain answers.

What to Do

Extra Support: Make the problem accessible.

Some students may have difficulty deciding whether they are toadd or subtract. Tell students that when the question uses theword “altogether,” they are to add. When the question asks,“How many more?” they are to subtract.

Some students may have difficulty comparing the 3-digitnumbers. Remind students about using place value to comparenumbers, or have them use a number line.

Recording and ReportingMaster 2.3 Performance Assessment Rubric: National Read-A-ThonMaster 2.4 Unit Summary: Patterns in Addition and Subtraction

Copyright © 2005 Pearson Education Canada Inc. 50

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 4 4 4 4 Unit Test 3 4 4 4 Unit Problem National Read-A-Thon

4 4 3 4 4

Achievement Level for reporting 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

PM 4: Learning Skills Check List Use to record and report throughout a reporting period, rather than for each unit and/or strand.

Ongoing Records

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.


Name Date

Unit Rubric: Patterns in Addition and Subtraction

Not Yet Adequate Adequate Proficient Excellent


• 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

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






able to demonstrate, apply, and explain: – patterns in addition






in various contexts, appropriately demonstrates, applies, and explains: – patterns in addition







• 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

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



accurate; makes no errors in: – addition and



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

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

Communication • 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

Master 2.1


Name Date

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 Accuracy of procedures

Problem solving Communication

Applies and explains concepts related to the addition and subtraction of whole numbers

Accurately adds and subtracts 1-, 2-, and 3-digit numbers Uses a variety of

strategies to verify solutions to addition and subtraction problems

Uses appropriate strategies to solve and create problems involving the addition and subtraction of whole numbers

Presents work clearly Explains reasoning

and procedures clearly, including appropriate terminology

*Use locally or provincially approved levels, symbols, or numeric ratings.

Master 2.2


Name Date

Performance Assessment Rubric: National Read-A-Thon

Not Yet

Adequate Adequate Proficient Excellent


• 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)

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


• adds, subtracts, and compares correctly

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

Problem-solving strategies

• uses appropriate strategies to create another prize and decide who would get it (Part 3)

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

Communication • 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

Master 2.3


Name Date

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



Problem solving

Communication Overall

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)

Master 2.4


Name Date

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.

Master 2.5


Name Date

Addition Chart 1

Master 2.6


Name Date

Addition Chart 2

Master 2.7


Name Date

Show What You Know Chart

Master 2.8


Name 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.

Master 2.9


Name Date

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.

Master 2.10


Name Date

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.

Master 2.11


Name Date

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 =

Master 2.11b


Name Date

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.

Master 2.12

Copyright © 2005 Pearson Education Canada Inc. Activity Focus: Use the inverse operation to verify solutions. 64

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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 68 68 – 45 or – 23 23 45 1. Add, then check by subtracting.

a) 25 b) 52 c) 47 d) 64 e) 84 + 33 + 84 + 56 + 79 + 17 f) 78 g) 19 h) 28 i) 36 j) 43 + 63 + 58 + 54 + 72 + 68

Master 2.12a

Subtract one of these numbers from 68. Your answer should be the other number.

Activity Focus: Use the inverse operation to verify solutions. Copyright © 2005 Pearson Education Canada Inc. 65

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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

24 + 63

87 1. Subtract, then add to check.

a) 94 b) 58 c) 94 d) 64 e) 38 – 23 – 27 – 39 – 17 – 18 f) 86 g) 75 h) 88 i) 61 j) 43 – 57 – 29 – 34 – 25 – 19

Master 2.12b

These 2 numbers should add to this number.


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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? _____________

________________________________________________________

Master 2.13


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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? _____________

Master 2.14


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Step-by-Step 3


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?

________________________________________________________ _________________________________________________________________

Master 2.15


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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 + ________ = ________


Step 3 Write numbers to make a subtraction fact: ________ – ________ = 5


Step 4 Write numbers to make a subtraction fact: 5 – ________ = ________


Step 5 Write numbers to make a subtraction fact: ________ – 5 = ________


Step 6 Explain how you found the numbers to make the facts.

________________________________________________________

________________________________________________________

Master 2.16


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Step-by-Step 5


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? ________________________

Master 2.17


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Step-by-Step 6


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? _____________________

Master 2.18


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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.

Master 2.19


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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

Master 2.20


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Step-by-Step 10


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?

________________________________________________________

________________________________________________________

________________________________________________________

________________________________________________________

Master 2.21


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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?

________________________________________________________ ________________________________________________________

Master 2.22


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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?

Master 2.23


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Step-by-Step 13


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.


Use 4 as the hundreds digit.


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? ___________________

Master 2.24


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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.

Master 2.25


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Unit Test: Unit 2 Patterns in Addition and Subtraction

Part A 1. Find each missing number.

a) 7 + 9 = b) 17 – 8 = c) 4 + = 11 d) 15 – = 9 2. Add or subtract.

a) 34 b) 67 c) 227 d) 300 + 26 – 26 + 169 – 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.

Master 2.26a


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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?

Master 2.26b


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Sample Answers Unit Test – Master 2.26 Part A 1. a) 16 b) 9 c) 7 d) 6 2. a) 60 b) 41 c) 396 d) 123 3. a) 91 b) 21 4. a) 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.

b) 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 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)

Part C 7. a) Sample answer: 135 and 456

b) 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.

Master 2.27


Extra Practice Masters 2.28–2.35 Go to the CD-ROM to access editable versions of these Extra Practice Masters

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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