5/6 chapter 3: adding and subtracting decimals &...

1 Math Focus 5/6 Combined-Grade Supplement Copyright © 2011 by Nelson Education Ltd.

Planning Chart Grade 5, Chapter 3: Adding and Subtracting Decimals

Grade 6, Chapter 2: Number Relationships

The outcomes and achievement indicators listed below are addressed in this chapter. When the outcome or achievement indicator is the focus of a lesson or feature, the lesson number or feature is indicated in brackets.

GRADE 5 GRADE 6

Strand: Number General Outcome: Develop number sense.

Specific Outcomes

N2. Use estimation strategies including:

• front‐end rounding

• compensation

• compatible numbers

in problem‐solving contexts. (1, 2, 3, MG, 7)

[C, CN, ME, PS, R, V]

Achievement Indicators

• Provide a context for when estimation is used to:

‐ make predictions (3)

‐ check reasonableness of an answer (3)

‐ determine approximate answers. (7)

• Describe contexts in which overestimating is important. (3)

• Determine the approximate solution to a given problem not requiring an exact answer. (1, 2, MG)

• Estimate a sum or product* using compatible numbers. (1, 2)

• Estimate the solution to a given problem using compensation and explain the reason for compensation. (1, 2, MG)

• Select and use an estimation strategy for a given problem. (1, 2, MG)

• Apply front‐end rounding to estimate

‐ sums (1, 2)

Specific Outcomes

N3. Demonstrate an understanding of factors and multiples by:

• determining multiples and factors of numbers less than 100

• identifying prime and composite numbers

• solving problems involving multiples. (1, 2, CM1, 3, MG1, 4, 5, 6)

[PS, R, V]


• Identify multiples for a given number and explain the strategy used to identify them. (2, CM1, 6)

• Determine all the whole‐number factors of a given number using arrays. (1, MG1)

• Identify the factors for a given number and explain the strategy used, e.g., concrete or visual representations, repeated division by prime numbers or factor trees. (1, MG1, 4, 5, 6)

• Provide an example of a prime number and explain why it is a prime number. (3, 4, 5)

• Provide an example of a composite number and explain why it is a composite number. (3, 4, 5)

• Sort a given set of numbers as prime and

Chapter 3: Adding and Subtracting Decimals & Number Relationships

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‐ differences (1, 2, MG)

‐ products*

‐ quotients*

N11. Demonstrate an understanding of addition and subtraction of decimals (limited to thousandths).

(3, 4, 5, 6, CM, 7, 8, MG)

[C, CN, ME, PS, R, V]


• Place the decimal point in a sum or difference using front‐end estimation. (4, 5, 7, 8, MG)

• Correct errors of decimal point placements in sums and differences without using paper and pencil. (5, 7, 8)

• Explain why keeping track of place value positions is important when adding and subtracting decimals. (5)

• Predict sums and differences of decimals using estimation strategies. (3, 4, 5, 7, 8, MG)

• Solve a given problem that involves addition and subtraction of decimals, limited to thousandths. (3, 4, 5, 6, CM, 7, 8, MG)

composite. (3)

• Solve a given problem involving factors or multiples. (1, 2, CM1, 3, 5, 6)

• Explain why 0 and 1 are neither prime nor composite. (3)

N7. Demonstrate an understanding of integers, concretely, pictorially and symbolically. (7, CM2, 8)

[C, CN, R, V]


• Extend a given number line by adding numbers less than zero and explain the pattern on each side of zero. (7, CM2)

• Place given integers on a number line and explain how integers are ordered. (8)

• Describe contexts in which integers are used, e.g., on a thermometer. (7, CM2)

• Compare two integers; represent their relationship using the symbols <, >, and =, and verify using a number line. (8)

• Order given integers in ascending or descending order. (8)

N9. Explain and apply the order of operations, excluding exponents, with and without technology (limited to whole numbers). (9, MG2)

[CN, ME, PS, T]


• Demonstrate and explain with examples why there is a need to have a standardized order of operations. (9)

• Apply the order of operations to solve multi‐step problems with or without technology, e.g., computer, calculator. (9, MG2)

Strand: Patterns and Relations General Outcome: Use patterns to describe the world and solve problems.

Specific Outcome

PR2. Solve problems involving single‐variable one‐step equations with whole number coefficients and whole number solutions. (3, 4, 8)

[C, CN, PS, R]


• Express a given problem in context as an equation where the unknown is represented by a letter variable.**

• Solve a given single‐variable equation with the


unknown in any of the terms. (3, 4, 8)

• Create a problem in context for a given equation.**

Mathematical Processes: C = Communication, CN = Connections, ME = Mental Mathematics and Estimation, PS = Problem Solving, R = Reasoning, T = Technology, V = Visualization

Features: CM = Curious Math, MG = Math Game

*Some aspects of N2 are covered in Ch. 6 Multiplication and Ch. 9 Division.

** Some aspects of PR2 are covered in Ch. 1 Patterns in Mathematics, Ch. 6 Multiplication, and Ch. 9 Division.


Lesson Sequence, Chapter 3 (Pacing: 16 days) Note: Read the Teacher Notes before the beginning of each lesson.

DAY GRADE 5 LESSON GRADE 6 LESSON TEACHER NOTES

1 Chapter Opener Chapter Opener The Chapter Opener photos engage students’ interest and give a preview of the chapter content.

Introduce the opening question for each grade. Ask Gr. 6 students to complete the opening task by using 12 linking cubes to model the straw bales in one wall of the Craik Eco-Centre building. While Gr. 6s are working on this opening task, elicit Gr. 5 students’ responses to their opening question. Ask students whether they need to calculate an exact distance or if an estimate would be sufficient.

The vocabulary terms used in Chapter 3 are different for each grade. Ask students to look through the chapter and add math word cards for their grade to the classroom Math Wall.

Use the Family Letter as a communication tool to help create a home environment that supports the learning at school. Read through the Family Letter with students before sending it home with them. Have students highlight key points and/or activities that they wish to do with a parent or sibling.

If possible, expand your classroom library or math centre with books related to the math in this chapter. Refer to TR p. 3 in both grades for a list of books that make connections to literature.

2 Getting Started: Going to the Movies What Do You Think?

Getting Started: Banner Designs What Do You Think?

Use the Getting Started activity as an initial assessment opportunity to judge Gr. 5 students’ prior knowledge of addition and subtraction of decimals, and of Gr. 6 students’ prior knowledge of factors, multiples, and number patterns.

What Do You Think? serves as an anticipation guide to activate students’ knowledge and understanding of personal strategies for estimating and calculating decimal sums and differences (Gr. 5), and

Chapter 35/6


of factors and multiples (Gr. 6). Explain to students that they are not expected to know the answers at this point. After reading the statements, students decide whether they agree or disagree with each one. Ask volunteers to explain the reasons for their choices.

3 3.1: Estimating Whole‐Number Sums and Differences

3.1: Identifying Factors Gr. 5: In this lesson, students explore a variety of strategies for estimating sums and differences (e.g., front-end rounding, compensation, compatible numbers).

This lesson features the reading strategy of “visualizing,” Visualizing the sum or difference on a number line reinforces students’ mental math skills.

Gr. 6: Students should already be familiar with the relationship between factors of a number and division of that number. To identify all the factors of a number and to help them visualize those factors, students can use arrays. An array is a pictorial or concrete model of a number in which the rows and columns of the rectangular array represent factors of the number.

Students can also show the factors of a number in a factor rainbow: they list all of a number’s factors in a row and pictorially link the factors that can be multiplied together to result in that number.

Note: Make copies of the Chapter Checklist (Gr. 5 MB p. 63, Gr. 6 MB p. 64) and use this assessment tool to help you track students’ progress throughout Chapter 3.

4 3.2: Communicating about Estimating and Calculating

3.2: Identifying Multiples

Gr. 5: In this lesson, students continue to estimate and calculate whole-number sums and differences. They use the mental math strategies from the previous lesson in problem-solving contexts. Most importantly, students are asked to improve upon their communication skills by fully explaining their thinking, showing their steps, and using appropriate mathematical language.

Gr. 6: In previous grades, students have multiplied factors to calculate a product. In this lesson, students approach multiplication from a different perspective as they calculate multiples of a number using known multiplication facts and skip counting. Ensure that students have access to number lines to help them visualize the pattern in the list of multiples.


5 3.3: Estimating Decimal Sums and Differences

Curious Math: String Art

Gr. 5: Today’s lesson introduces students to estimating sums and differences of decimal numbers. Students can use the same methods they used with whole numbers (e.g., front-end rounding, compatible numbers, compensation). Encourage students to try a variety of strategies to determine reasonable decimal estimates.

Gr. 6: In Curious Math, students are exposed to string art, or curve stitching. This is another visual representation of factors and multiples. Students identify the patterns formed in the string art and determine which numbers should be connected with each colour. Encourage students to see that all numbers connected by the same colour of string have at least one factor in common.

6 3.4: Adding Decimals Using Mental Math

3.3: Prime and Composite Numbers

Gr. 5: To add decimals using mental math, students redistribute tenths, hundredths, or thousandths from one addend to the other to create decimal numbers that are easier to add. In order to determine which parts to move from one addend to the other, students first identify a number that is close to one addend and convenient for adding. Then they ask themselves, “How many parts do I need to make ______ ?”

Gr. 6: In this lesson, students formalize their understanding of prime and composite numbers as they use reasoning to identify numbers that can be arranged in only one rectangular array. By arranging counters in arrays, students are able to visualize numbers that can be arranged in only one row or column; these numbers are prime, as their only factors are 1 and themselves. Numbers that can be arranged in more than one array are composite; each array represents two factors.

7 3.5: Adding Decimals by Regrouping

Math Game: Colouring Factors 3.4: Identifying Factors by Dividing

Gr. 5: This lesson is an extension of the previous lesson in which students used mental math to add decimals and solve problems. In today’s lesson, students discover that using a mental math strategy is not always reasonable or efficient. In some cases, using a more traditional algorithm to determine a sum (e.g., using regrouping) makes more sense.

Gr. 6: Students can play the Math Game while you teach the Gr. 5 lesson. This math


game helps students consolidate their understanding of factors, prime numbers, and composite numbers.

In today’s lesson, students use their reasoning ability to identify a prime number that is a factor of a given number. This can be done by repeated division or by using factor trees.

8 Mid‐Chapter Review

3.5: Creating Composite Numbers

Gr. 5: Use the Mid-Chapter Review to assess individual students’ understanding of the concepts developed in the chapter so far. This review also allows you to monitor the progress of the class and see where re-teaching may be required.

To help students monitor their own progress, ask them to use the Frequently Asked Questions worksheet to summarize and reflect on their learning. They can check their answers against the possible responses on SB p. 98. Assign Mid-Chapter Review questions and point out that the questions are organized by lesson, making it easy for students to go back to the lesson indicated to review the concepts for each question.

Gr. 6: Introduce today’s exploratory lesson by asking students to determine the prime numbers from 1 to 50. Remind students that prime numbers have only two factors and that composite numbers have more than two factors. As students solve today’s problem, they recognize that prime numbers can be multiplied to make any composite number from 2 to 50. Refer to TR p. 37 for sample solutions.

9 3.6: Exploring Problems That Involve Decimals

Mid‐Chapter Review Gr. 5: In this exploratory lesson, students make connections to the previous five lessons by activating and applying what they know about estimation and calculation of whole number and decimal sums and differences. Students use these skills in the context of a single, rich problem-solving situation. No one approach to the problem should be suggested; encourage students to choose their own strategies. Circulate and observe students as they work. Ask probing questions such as the ones listed on TR p. 41.

Note: Students will continue working on this exploration on the following day. At that time, provide an opportunity for students to share their solutions and to explain their


personal strategies to their classmates.


To help students monitor their own progress, ask them to use the Frequently Asked Questions worksheet to summarize and reflect on their learning. Students can check their answers against the possible responses on SB p. 86.

10 3.6: Exploring Problems That Involve Decimals (cont’d)

3.6: Solving Problems Using an Organized List

Gr. 5: Students continue working on the exploration from the previous day. Provide the opportunity for students to share and communicate about their work. Ask students to describe to their classmates how they solved the problem, using their chart paper as an organizing tool for other students to follow. Encourage students to identify similarities and differences among their methods.

Gr. 6: Discuss with students the reasons for making an organized list to solve a problem (e.g., no possible solution overlooked or eliminated in error). Also point out that, when there is more than one condition to be satisfied in order to solve a problem, making an organized list is an appropriate strategy. The conditions that students work with in this lesson involve multiples, prime and composite numbers, and factors.

The reading strategy of “finding important information” is featured in this lesson.

11 Curious Math: Subtracting Decimals Using a Whole Number 3.7: Subtracting Decimals by Regrouping

3.7: Representing Integers Gr. 5: Ask students to work on the Curious Math activity while you introduce the Gr. 6 lesson. The Curious Math provides students with a non-traditional method for subtracting decimals using mental math. This sets the stage for Lesson 7, which presents the more conventional process of subtracting decimals by regrouping. In this lesson, students discover that they can do all the regrouping at once before subtracting, or they can regroup in stages starting from the right.

Note: The terms composition and decomposition are also acceptable terms to use when adding or subtracting whole or decimal numbers.


Gr. 6: Students are familiar with the set of whole numbers, which includes the counting numbers and zero. In this lesson, students are introduced to the set of integers, which includes positive and negative whole numbers and zero. Students use a number line as a visualization tool for the set of integers.

12 3.8: Subtracting Decimals by Renaming

Curious Math: Countdown Clock 3.8: Comparing and Ordering Integers

Gr. 5: In this lesson, students use number sense to look at the minuend in different ways before subtracting. Help students formalize the important concepts of renaming before subtracting by discussing the ideas in Math Background on TR p. 50.

Gr. 6: Ask students to work on the Curious Math activity while you introduce the Gr. 5 lesson. Many students will be familiar with the idea of a countdown clock, where the time before an event has a negative value, the time of the event is assigned a zero, and time after the event has a positive value. Students make connections to existing knowledge as they work with positive and negative integers in real-life contexts.

In today’s lesson, students compare and order integers. Refer to TR p. 53 for some key ideas about comparing integers.

13 Math Game: Close Call Problem of the Week

3.9: Order of Operations Math Game: Four in a Row

Gr. 5: Today’s Math Game provides students with an opportunity to practise their mental math skills related to the estimation and calculation of decimal differences. Students determine a strategy that will enable them to earn the maximum number of points during each round of play.

After playing a few rounds of the Math Game, students choose a Problem of the Week from the selection on TR p. 3 and work with a partner to solve it.

Gr. 6: In this lesson, students use both mental math skills and technology to calculate the answers to problems involving many operations. The rules for order of operations tell which operation should be performed first. The purpose of the order of operations is to ensure that the same answer is reached regardless of who performs the calculations.

Students who have demonstrated an understanding of how to use the order of operations may play the Math Game on SB


p. 101. 14 Chapter Review Chapter Review Use the Chapter Review to consolidate and

assess students’ understanding of the concepts developed in the chapter.

15, 16

Chapter Task: Gold Coins and/or Chapter Test Cumulative Review: Chapters 1–3

Chapter Task: A Block Dropping Game and/or Chapter Test Cumulative Review: Chapters 1–3

Use the Chapter Task and/or Chapter Test as assessment of students’ understanding of the concepts and skills covered in Chapter 3.

The Cumulative Review provides practice with multiple-choice questions while reviewing the concepts developed in Chapters 1 to 3.


Chapter Opener

Comparison of Lessons

The Chapter Opener photos engage students’ interest and give a preview of the chapter content.

Introduce the opening question for each grade. Ask Gr. 6 students to complete the opening task by using 12 linking cubes to model the straw bales in one wall of the Craik Eco-Centre building. While Gr. 6s are working on this opening task, elicit Gr. 5 students’ responses to their opening question. Ask students whether they need to calculate an exact distance or if an estimate would be sufficient.

The vocabulary terms used in Chapter 3 are different for each grade. Ask students to look through the chapter and add math word cards for their grade to the classroom Math Wall.

Use the Family Letter as a communication tool to help create a home environment that supports the learning at school. Read through the Family Letter with students before sending it home with them. Have students highlight key points and/or activities that they wish to do with a parent or sibling.

If possible, expand your classroom library or math centre with books related to the math in this chapter. Refer to TR p. 3 in both grades for a list of books that make connections to literature.

Grade 5 Goal

Combined Goals• Discuss chapter

goals. • Introduce key

vocabulary terms.

• Foster home–school communication with the Family Letter.

Grade 6 Goal

Chapter 3 DAY 1

5/6

Chapter Opener SB pp. 78–79 TR p. 8 • Family Letter p.

67 Masters Booklet • (optional) Review

of Essential Skills: Chapter 3: Adding and Subtracting Decimals pp. 5–6

(Answers: p. 19)

Chapter OpenerSB pp. 66–67 TR pp. 8 • Family Letter p.

74 Masters Booklet • (optional) Review

of Essential Skills: Chapter 3: Number Relationships p. 5 (Answers: p. 19)


Getting Started Comparison of Lessons

Use the Getting Started activity as an initial assessment opportunity to judge Gr. 5 students’ prior knowledge of addition and subtraction of decimals, and of Gr. 6 students’ prior knowledge of factors, multiples, and number patterns.

What Do You Think? serves as an anticipation guide to activate students’ knowledge and understanding of personal strategies for estimating and calculating decimal sums and differences (Gr. 5), and of factors and multiples (Gr. 6). Explain to students that they are not expected to know the answers at this point. After reading the statements, students decide whether they agree or disagree with each one. Ask volunteers to explain the reasons for their choices.

Grade 5 Goal • Activate

knowledge about addition and subtraction of decimals.

Combined Goal• Reactivate prior

learning through introductory activities.

Grade 6 Goal • Activate

knowledge about number relationships.

Getting Started & What Do You Think? SB pp. 80–81 TR pp. 9–12 • Movie Gift

Cards p. 68 • (optional)

Scaffolding for Getting Started pp. 69–70

(Answers: p. 81)

Masters Booklet • (optional) Initial

Assessment Summary p. 56

Getting Started & What Do You Think? SB pp. 68–69 TR pp. 9–12 • (optional)

Scaffolding for Getting Started pp. 75–76

(Answers: p. 89) Masters Booklet • 2 cm Grid Paper

p. 23 • (optional) Initial

Assessment Summary p. 57

Materials • pencil crayons

5/6 Day 2 Chapter 3


Lessons 3.1 and 3.1 Comparison of Lessons

Gr. 5: In this lesson, students explore a variety of strategies for estimating sums and differences (e.g., front-end rounding, compensation, compatible numbers).

This lesson features the reading strategy of “visualizing.” Visualizing the sum or difference on a number line reinforces students’ mental math skills.

Gr. 6: Students should already be familiar with the relationship between factors of a number and division of that number. To identify all the factors of a number and to help them visualize those factors, students can use arrays. An array is a pictorial or concrete model of a number in which the rows and columns of the rectangular array represent factors of the number.

Students can also show the factors of a number in a factor rainbow: they list all of a number’s factors in a row and pictorially link the factors that can be multiplied together to result in that number.

Note: Make copies of the Chapter Checklist (Gr. 5 MB p. 63, Gr. 6 MB p. 64) and use this assessment tool to help you track students’ progress throughout Chapter 3.

Grade 5 Goal • Estimate sums

and differences to solve problems.

Combined Goal

Grade 6 Goal • Identify factors

to solve problems.

3.1: Estimating Whole-Number Sums and Differences SB pp. 82–85 TR pp. 13–17 • (optional)

Scaffolding for Lesson 1, Question 3 p. 71 (Answers: p. 81)

Masters Booklet • Number Lines p.

35 • (optional) Chapter

Checklist: Chapter 3 p. 63

Materials • (optional) base ten

blocks • (optional) pencil

crayons Assessment • Key Question 6

3.1: Identifying Factors SB pp. 70–73 TR pp. 13–17 Masters Booklet • (optional) 1 cm

Grid Paper p. 22 • (optional) Chapter

Checklist: Chapter 3 p. 64

Materials • (optional) counters • (optional) linking

cubes Assessment • Key Question 5

5/6 DAY 3 Chapter 3


Lessons 3.2 and 3.2 Comparison of Lessons

Gr. 5: In this lesson, students continue to estimate and calculate whole number sums and differences. They use the mental math strategies from the previous lesson in problem-solving contexts. Most importantly, students are asked to improve upon their communication skills by fully explaining their thinking, showing their steps, and using appropriate mathematical language.

Gr. 6: In previous grades, students have multiplied factors to calculate a product. In this lesson, students approach multiplication from a different perspective as they calculate multiples of a number using known multiplication facts and skip counting. Ensure that students have access to number lines to help them visualize the pattern in the list of multiples.

Grade 5 Goal • Explain clearly

how to estimate and calculate.

Combined Goal

Grade 6 Goal • Identify

multiples to solve problems.

3.2: Communicating about Estimating and Calculating SB pp. 86–87 TR pp. 18–21 Assessment • Key Question 2

3.2: Identifying Multiples SB pp. 74–76 TR pp. 18–21 • (optional)


Masters Booklet • Number Lines p.

33 Materials • rulers • (optional) counters Assessment • Key Question 5

5/6

DAY 4 Chapter 3


Lesson 3.3 and Curious Math Comparison of Lessons

Gr. 5: Today’s lesson introduces students to estimating sums and differences of decimal numbers. Students can use the same methods they used with whole numbers (e.g., front-end rounding, compatible numbers, compensation). Encourage students to try a variety of strategies to determine reasonable decimal estimates.

Gr. 6: In Curious Math, students are exposed to string art, or curve stitching. This is another visual representation of factors and multiples. Students identify the patterns formed in the string art and determine which numbers should be connected with each colour. Encourage students to see that all numbers connected by the same colour of string have at least one factor in common.

Grade 5 Goal • Estimate sums

and differences with decimals.

Combined Goal

Grade 6 Goal • Create and

describe a visual representation of multiples and factors.

3.3: Estimating Decimal Sums and Differences SB pp. 88–91 TR pp. 22–25 Masters Booklet • Thousandths

Grids p. 38 Materials • pencil crayons Assessment • Key Question 3

Curious Math: String Art SB p. 77 TR pp. 22–23 • String Art p. 78 Materials • pencil crayons • rulers

5/6

DAY 5 Chapter 3


Lessons 3.4 and 3.3


Gr. 5: To add decimals using mental math, students redistribute tenths, hundredths, or thousandths from one addend to the other to create decimal numbers that are easier to add. In order to determine which parts to move from one addend to the other, students first identify a number that is close to one addend and convenient for adding. Then they ask themselves, “How many parts do I need to make ______?”

Gr. 6: In this lesson, students formalize their understanding of prime and composite numbers as they use reasoning to identify numbers that can be arranged in only one rectangular array. By arranging counters in arrays, students are able to visualize numbers that can be arranged in only one row or column; these numbers are prime, as their only factors are 1 and themselves. Numbers that can be arranged in more than one array are composite; each array represents two factors.

Grade 5 Goal • Solve problems

by using mental math to add decimals.

Combined Goal

Grade 6 Goal • Identify prime

and composite numbers.

3.4: Adding Decimals Using Mental Math SB pp. 92–93 TR pp. 26–29 Masters Booklet • Thousandths

Grids p. 38 Materials • pencil crayons Assessment • Key Question 3

3.3: Prime and Composite Numbers SB pp. 78–80 TR pp. 24–28 Masters Booklet • 100 Chart p. 30 • 2 cm Grid Paper

p. 23 Materials • counters Assessment • Key Question 4

5/6

DAY 6 Chapter 3


Lesson 3.5 and Math Game/Lesson 3.4


Gr. 5: This lesson is an extension of the previous lesson in which students used mental math to add decimals and solve problems. In today’s lesson, students discover that using a mental math strategy is not always reasonable or efficient. In some cases, using a more traditional algorithm to determine a sum (e.g., using regrouping) makes more sense.

Gr. 6: Students can play the Math Game while you teach the Gr. 5 lesson. This math game helps students consolidate their understanding of factors, prime numbers, and composite numbers.

In today’s lesson, students use their reasoning ability to identify a prime number that is a factor of a given number. This can be done by repeated division or by using factor trees.

Grade 5 Goal • Solve problems

by adding decimals.

Combined Goal

Grade 6 Goals • Identify factors

of whole numbers.

• Identify factors by dividing composite numbers by primes.

3.5: Adding Decimals by Regrouping SB pp. 94–97 TR pp. 30–34 Masters Booklet • Decimal Place

Value Chart p. 44 • (optional) 1 cm

Grid Paper p. 22 • Manipulatives

Substitute: Base Ten Blocks pp. 39–42

Materials • base ten blocks Assessment • Key Question 3

Math Game: Colouring Factors 3.4: Identifying Factors by Dividing SB pp. 81, 82–84 TR pp. 29–30, 31–34 Masters Booklet • 100 Chart p. 30 Materials • pencil crayons • number cards 40

to 50 • (optional) counters Assessment • Key Question 4

5/6 DAY 7 Chapter 3


Mid-Chapter Review and Lesson 3.5 Comparison of Lessons


To help students monitor their own progress, ask them to use the Frequently Asked Questions worksheet to summarize and reflect on their learning. They can check their answers against the possible responses on SB p. 98. Assign Mid-Chapter Review questions and point out that the questions are organized by lesson, making it easy for students to go back to the lesson indicated to review the concepts for each question.

Gr. 6: Introduce today’s exploratory lesson by asking students to determine the prime numbers from 1 to 50. Remind students that prime numbers have only two factors and that composite numbers have more than two factors. As students solve today’s problem, they recognize that prime numbers can be multiplied to make any composite number from 2 to 50. Refer to TR p. 37 for sample solutions.

Grade 5 Goals• Review terms

and concepts studied in Lessons 3.1 to 3.5.

• Assess students’ understanding of the concepts developed in the chapter so far.

Combined Goal

Grade 6 Goal • Multiply

combinations of factors to create composite numbers.

Mid-Chapter Review SB pp. 98–99 TR pp. 35–39 • Mid-Chapter

Review—Frequently Asked Questions p. 72

Masters Booklet • (optional)

Thousandths Grids p. 38

• (optional) Decimal Place Value Chart p. 44

• Manipulatives Substitute: Base Ten Blocks: Ones, Tenths, Hundredths, Thousandths pp. 39–42


blocks

3.5: Creating Composite Numbers SB p. 85 TR pp. 35–38 Masters Booklet • (optional) 100

Chart p. 30 • (optional) 1 cm

Grid Paper p. 22 Materials • (optional) chart

paper and markers

Assessment • entire exploration

5/6

DAY 8 Chapter 3


Lesson 3.6 and Mid-Chapter Review


Gr. 5: In this exploratory lesson, students make connections to the previous five lessons by activating and applying what they know about estimation and calculation of whole number and decimal sums and differences. Students use these skills in the context of a single, rich problem-solving situation. Do not suggest an approach to the problem; encourage students to choose their own strategies. Circulate and observe students as they work. Ask probing questions such as the ones listed on TR p. 41.

Note: Students will continue working on this exploration on the following day. At that time, provide an opportunity for students to share their solutions and to explain their personal strategies to their classmates.


To help students monitor their own progress, ask them to use the Frequently Asked Questions worksheet to summarize and reflect on their learning. Students can check their answers against the possible responses on SB p. 86.

Grade 5 Goal • Use your own

strategies to solve a problem that involves adding and subtracting decimals.

Combined Goal

Grade 6 Goals • Review terms

and concepts studied in Lessons 3.1 to 3.5.

• Assess students’ understanding of the concepts developed in

the chapter so far.

3.6: Exploring Problems That Involve Decimals SB p. 100 TR pp. 40–42 Masters Booklet • (optional) Decimal

Place Value Chart p. 44


blocks • (optional) chart

paper and markers

Assessment • entire exploration

Mid-Chapter Review SB pp. 86–87 TR pp. 39–42 • Mid-Chapter

Review—Frequently Asked Questions p. 79 Materials

• (optional) counters

5/6

DAY 9 Chapter 3


Lessons 3.6 (cont’d) and 3.6


Gr. 5: Students continue working on the exploration from the previous day. Provide the opportunity for students to share and communicate about their work. Ask students to describe to their classmates how they solved the problem, using their chart paper as an organizing tool for other students to follow. Encourage students to identify similarities and differences among their methods.

Gr. 6: Discuss with students the reasons for making an organized list to solve a problem (e.g., no possible solution overlooked or eliminated in error). Also point out that, when there is more than one condition to be satisfied in order to solve a problem, making an organized list is an appropriate strategy. The conditions that students work with in this lesson involve multiples, prime and composite numbers, and factors.

The reading strategy of “finding important information” is featured in this lesson.

Grade 5 Goal • Use your own

strategies to solve a problem that involves adding and subtracting decimals.

Combined Goal

Grade 6 Goal • Use an

organized list to solve problems that involve number relationships.

3.6: Exploring Problems That Involve Decimals (cont’d) SB p. 100 TR pp. 40–42 Masters Booklet • (optional)

Decimal Place Value Chart p. 44

Materials • (optional) base

ten blocks • (optional) chart

paper and markers

Assessment • entire

exploration

3.6: Solving Problems Using an Organized List SB pp. 88–89 TR pp. 43–46 Masters Booklet • (optional) 100

Chart p. 30 Assessment • Key Question 6

5/6

DAY 10 Chapter 3


Curious Math/Lesson 3.7 and Lesson 3.7


Gr. 5: Ask students to work on the Curious Math activity while you introduce the Gr. 6 lesson. The Curious Math provides students with a non-traditional method for subtracting decimals using mental math. This sets the stage for Lesson 7, which presents the more conventional process of subtracting decimals by regrouping. In this lesson, students discover that they can do all the regrouping at once before subtracting, or they can regroup in stages starting from the right.

Note: The terms composition and decomposition are also acceptable terms to use when adding or subtracting whole or decimal numbers.

Gr. 6: Students are familiar with the set of whole numbers, which includes the counting numbers and zero. In this lesson, students are introduced to the set of integers, which includes positive and negative whole numbers and zero. Students use a number line as a visualization tool for the set of integers.

Grade 5 Goals• Subtract

decimals using a whole number.

• Regroup to solve subtraction problems.

Combined Goal

Grade 6 Goal • Use integers to

describe situations.

Curious Math: Subtracting Decimals Using a Whole Number 3.7: Subtracting Decimals by Regrouping SB pp. 101, 102–105 TR pp. 43–44, 45–49 • (optional)


Masters Booklet • Number Lines p. 35 • Decimal Place Value

Chart p. 44 • (optional) 1 cm Grid

Paper p. 22 • Manipulatives


Materials • base ten blocks Assessment • Key Question 4

3.7: Representing Integers SB pp. 90–92 TR pp. 47–50 Masters Booklet • Number Lines p.

33 Assessment • Key Question 4

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DAY 11 Chapter 3


Lesson 3.8 and Curious Math/Lesson 3.8


Gr. 5: In this lesson, students use number sense to look at the minuend in different ways before subtracting. Help students formalize the important concepts of renaming before subtracting by discussing the ideas in Math Background on TR p. 50.

Gr. 6: Ask students to work on the Curious Math activity while you introduce the Gr. 5 lesson. Many students will be familiar with the idea of a countdown clock, where the time before an event has a negative value, the time of the event is assigned a zero, and time after the event has a positive value. Students make connections to existing knowledge as they work with positive and negative integers in real-life contexts.

In today’s lesson, students compare and order integers. Refer to TR p. 53 for some key ideas about comparing integers.

Grade 5 Goal • Rename

decimals to make subtraction easier.

Combined Goal

Grade 6 Goals • Describe

contexts in which integers are used.

• Use a number line to compare and order integers.

3.8: Subtracting Decimals by Renaming SB pp. 106–108 TR pp. 50–54 • (optional)


Assessment • Key Questions 3

and 4

Curious Math: Countdown Clock 3.8: Comparing and Ordering Integers SB pp. 93, 94–97 TR pp. 51–52, 53–57 Masters Booklet • Number Lines p.

33 Assessment • Key Question 6

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DAY 12 Chapter 3


Math Game/Problem of the Week and Lesson 3.9/Math Game


Gr. 5: Today’s Math Game provides students with an opportunity to practise their mental math skills related to the estimation and calculation of decimal differences. Students determine a strategy that will enable them to earn the maximum number of points during each round of play.

After playing a few rounds of the Math Game, students choose a Problem of the Week from the selection on TR p. 3 and work with a partner to solve it.

Gr. 6: In this lesson, students use both mental math skills and technology to calculate the answers to problems involving many operations. The rules for order of operations tell which operation should be performed first. The purpose of the order of operations is to ensure that the same answer is reached regardless of who performs the calculations.

Students who have demonstrated an understanding of how to use the order of operations may play the Math Game on SB p. 101.

Grade 5 Goals• Estimate and

calculate differences of decimals.

• Solve problems involving addition and subtraction of decimals.

Combined Goal

Grade 6 Goals • Apply the rules

for order of operations with whole numbers.

• Apply the order of operations to solve multi-step problems with or without technology.

Math Game: Close Call Problem of the Week SB p. 109 TR pp. 3, 55–56 Materials • dice

3.9: Order of Operations Math Game: Four in a Row SB pp. 98–100, 101 TR pp. 58–61, 62–63 • Four in a Row

Game Board p. 80 • Calculation Cards

pp. 81–82 Materials • calculators • coloured counters Assessment • Key Question 5

5/6 DAY 13 Chapter 3


Chapter Review

GRADE 5 GRADE 6

Chapter Review SB pp. 110–112 TR pp. 57–61 • Chapter Review—Frequently

Asked Questions p. 75 Masters Booklet • (optional) Number Lines p. 35 • (optional) Thousandths Grids

p. 38 • (optional) Decimal Place Value

Chart p. 44 • (optional) Manipulatives


Materials • (optional) base ten blocks

Chapter Review SB pp. 102–104 TR pp. 64–68 • Chapter Review—Frequently

Asked Questions p. 83 Masters Booklet • (optional) Number Lines p. 33 Materials • (optional) counters

Use the Chapter Review to consolidate and assess students’ understanding of the concepts developed in the chapter.

DAY 14 Chapter 3

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Assessment of Learning

Work with Each Grade

GRADE 5 GRADE 6

Chapter Task Gold Coins

SB p. 113 TR pp. 62–64 • Chapter Task pp. 79–80

Chapter Task A Block Dropping Game

SB p. 105 TR pp. 69–71 • Chapter Task pp. 87–88

Chapter Test TR pp. 76–78 (Answers: pp. 82–83)

Chapter Test TR pp. 84–86 (Answers: pp. 89–91)

Cumulative Review: Chapters 1–3

SB pp. 114–115

TR pp. 65–66 Cumulative Review: Chapters 1–3

SB pp. 106–107

TR pp. 72–73

Use the Chapter Task and/or Chapter Test as assessment of students’ understanding of the concepts and skills covered in Chapter 3.

The Cumulative Review provides practice with multiple-choice questions while reviewing the concepts developed in Chapters 1 to 3.

DAYS 15, 16 Chapter 3

5/6

5/6 chapter 3: adding and subtracting decimals &...

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