Fractions and Decimals

CHAPTER 2 Key Words benchmark unit fraction repeating decimal period length of the period terminating decimal Fractions and Decimals Specific Curricu...
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CHAPTER 2 Key Words benchmark unit fraction repeating decimal period length of the period terminating decimal

Fractions and Decimals Specific Curriculum Outcomes Major Outcomes A7 A8 A9 B1 B2 B3 B4 B5 B6 B7

apply patterns in renaming numbers from fractions and mixed numbers to decimal numbers rename single-digit and double-digit repeating decimals to fractions through the use of patterns, and use these patterns to make predictions compare and order proper and improper fractions, mixed numbers, and decimal numbers use estimation strategies to assess and judge the reasonableness of calculation results for integers and decimal numbers use mental math strategies for calculations involving integers and decimal numbers demonstrate an understanding of the properties of operations with decimal numbers and integers determine and use the most appropriate computational method in problem situations involving whole numbers and/or decimals apply the order of operations for problems involving whole and decimal numbers estimate the sum or difference of fractions when appropriate multiply mentally a fraction by a whole number and vice versa

Contributing Outcomes D1 G6

identify, use, and convert among the SI units to measure, estimate, and solve problems that relate to length, area, volume, mass, and capacity use fractions, decimals, and percents as numerical expressions to describe probability

Chapter Problem A chapter problem is introduced in the chapter opener. This chapter problem has students use the context of an amusement park to apply fractions and decimals in various ways. The chapter problem is revisited in section 2.1 question 17, section 2.2 question 14, section 2.5 questions 10 to 12, and section 2.6 question 12. You may wish to have students complete the chapter problem revisits that occur throughout the chapter. These simpler versions provide scaffolding for the chapter problem and offer struggling students some support. The revisits will assist students in preparing their response for the Chapter Problem Wrap-Up on page 107. Alternatively, you may wish to assign only the Chapter Problem Wrap-Up when students have completed Chapter 2. The Chapter Problem Wrap-Up is a summative assessment.

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Planning Chart Section Suggested Timing Chapter Opener • 15 min (optional) Get Ready • 90 min

Teacher’s Resource Blackline Masters

Assessment Tools

Adaptations

Materials and Technology Tools

• BLM 2GR Parent Letter • BLM 2GR Extra Practice

2.1 Estimate Sums and • BLM 2.1 Extra Practice Formative Assessment: Differences of Fractions • BLM 2.1 Assessment • 120 min Question #16

• Fraction Factory pieces • grid paper • rulers • coloured pencils

2.2 Multiply a Whole Number by a Fraction and Vice Versa • 60 min

• coloured counters • pattern blocks • Fraction Factory pieces

• BLM 2.2 Extra Practice Formative Assessment: • BLM 2.2 Assessment Question #15

2.3 Changing Form: • BLM 2.3 Extra Practice Formative Assessment: Fractions and Decimals • BLM 2.3 Assessment • 120 min Question #16

• centimetre grid paper • ten thousands grids • scissors • glue sticks • coloured pencils • calculators

2.4 Compare and Order • BLM 2.4 Extra Practice Formative Assessment: Fractions and Decimals • BLM 2.4 Assessment • 60 min Question #13

• Fraction Factory pieces • linking cubes • coloured counters • pattern blocks • Cuisenaire rods • grid paper • calculators • base-10 materials

2.5 Operating With Decimals • 60 min

• BLM 2.5 Extra Practice Formative Assessment: • BLM 2.5 Assessment Question #7

2.6 Solve Problems Involving Decimals • 60 min

• BLM 2.6 Extra Practice Formative Assessment: • BLM 2.6 Assessment Question #9

Chapter 2 Review • 60 min

• BLM 2R Extra Practice

Chapter 2 Practice Test • 60 min

Summative Assessment: • BLM 2PT Chapter 2 Test

Chapter Problem WrapUp • 30 min

• BLM 2CP Chapter Problem Wrap-Up Rubric

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Get Ready WA R M - U P

Related Resources • BLM 2GR Parent Letter • BLM 2GR Extra Practice Suggested Timing 90 min

Write each mixed number as an improper fraction. 1. 2

3 5


5

2. 1

7 8


8

Write each improper fraction as a mixed number. 1 11 2 25 4. 3 3 6 6 5. Which expression has the same answer as 43.2 ÷ 0.4? A 43.2 ÷ 4 B 432 ÷ 4 C 432 ÷ 0.04 3.

Evaluate. 6. 1.8 ÷ 0.3 8. 7  0.3



7. 4 ÷ 0.1 9. 9  0.07

Find each amount. 10. 0.1 of 30 12. 0.01 of 700 14. 0.001 of 8000

11. 0.2 of 30 13. 0.01 of 1200 15. 0.5 of 26

16. Estimate to place the decimal point in the product.

8.8  4.5 = 3 9 6



ASSESSMENT FOR LEARNING Before starting Chapter 2, explain that the topic is fractions and decimals. Engage students in a brief brainstorming session in which they identify as many everyday instances of fractions and decimals as they can. The work of this chapter leads directly into Chapter 3, Percent, and these topics are very closely related. Discuss with students when they have used fractions and decimals before, and what they know about equivalent fractions and comparing numbers using a number line. You may wish to brainstorm and develop a mind map for each topic or start a graphic organizer to be used throughout the chapter. After students have discussed the concepts, have them complete the assessment suggestions below in pairs or individually. This assessment is designed to provide you and your students with information about their readiness for the chapter. After strengths and weaknesses have been identified, students can work on appropriate sections of the Get Ready. Method 1: Have students develop a journal entry to explain what they know about the topics and how they use fractions and decimals in their everyday language or in their everyday lives. Method 2: Challenge students to show how much they know about each topic. Encourage them to use words, numbers, and diagrams to show what they know.

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Reinforce the Concepts Have those students who need more reinforcement of the prerequisite skills complete BLM 2GR Extra Practice.

TEACHING SUGGESTIONS The Get Ready provides students with the skills they need to fully understand the topics developed in Chapter 2. All the topics except for Represent Decimals are needed at the beginning the chapter. Represent Decimals should be done near the midway point of the chapter. Provide students with a variety of manipulatives. In Understand Fractions, when students are making different representations of a fraction (as in question 3) you should check that they draw parts of the whole that are the same size. If you do not have base-10 materials for Represent Decimals, refer to Mathematics Blackline Masters Grade P to 9, pages 10 to 14, for base-10 materials BLMs. Many students struggle with simple operations involving decimals such as: 3.43 + 6 7.4 – 3.72 0.3  0.2 6.43 ÷ 0.05 Some practice with these types of questions may be helpful.

Common Errors • Rx • Rx

Students may mix up the numerator and denominator when describing a part-to-whole comparison. Use concrete models, Fraction Factory pieces, or pattern blocks, to review the terminology using some simple examples. Students may incorrectly convert mixed numbers to improper fractions. 2 Use concrete materials to model simple examples, such as 1 . A visual 3 representation will quickly show if an answer is unreasonable.

• Students struggle with the correct order of operations. Rx Provide a series of order of operation exercises where students first analyse the question then number the parts that should be calculated to indicate the order.

Journal At the end of a class or a unit you might pose questions in the form of an “exit pass” to help students consolidate their understanding of the topic. The exit pass also allows students who are having difficulties to inform the teacher privately and arrange for extra help. If the exit pass shows that many students have a similar problem, the teacher can arrange a remedial lesson.

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Exit Pass • • • • •

This is how I feel about [decimals, fractions, etc.] … I do well on … But I still have difficulty with _____ because … I [need / do not need] extra help. I think I need extra help with …

G e t Ready Answers 1 1 7 1 3 1 1 1 b) c) d) 1 2. a) b) 1 c) d) 1 2 4 10 2 4 4 3 2 3. Diagrams may vary. a) 1 whole, one third shaded; 2 wholes divided into thirds, two thirds shaded b) 1 whole, four fifths shaded; 10 wholes divided in halves, eight halves shaded c) 1 whole, three tenths shaded; 2 wholes divided into fifths, three fifths shaded d) 1 whole, five sixths shaded; 2 wholes divided into thirds, five thirds shaded e) 2 wholes divided into quarters, five quarters shaded; 4 shapes, where two shapes equals one whole, divided into halves, five halves shaded f) 4 wholes divided into halves, seven halves shaded; 8 shapes, where two shapes equals one whole, seven shapes shaded 3 1 5 5 11 23 4. a) 3 b) 4 c) 1 5. a) b) c) 4 5 8 2 3 5 1. a)

6.

0.4

1 0.75 –1 4– 2

0.9

0

1

1 2

2– 1.8 2

3

3.9

3

4

7. a) 3 is a whole number, so place on 3 b)

1 is halfway between 0 and 1 2

1 1 1 is halfway between 0 and d) 2 is halfway between 2 and 3 4 2 2 1 1 e) 0.75 is halfway between and 1 f) 0.4 is slightly less than 2 2 g) 0.9 is slightly less than 1 h) 1.8 is slightly less than 2 i) 3.9 is slightly less than 4 a) > b) < c) < d) < 9. a) 0.8 b) 0.06 c) 0.124 d) 1.003 a) 6 flats; 6 tenths b) 2 flats, 4 rods; 24 hundredths c) 7 rods; 7 hundredths d) 4 flats, 8 rods, 5 unit cubes; 485 thousandths e) 4 unit cubes; 4 thousandths f) 3 flats, 7 unit cubes; 307 thousandths a) 4 flats b) 4 flats, 2 rods c) 1 rod, 7 unit cubes d) 2 flats, 5 rods e) 5 flats f) 1 large cube, 2 flats Explanations may vary. a), c), d) yes b) no Answers may vary. c)

8. 10.

11. 12. 13.

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2.1

Estimate Sums and Differences of Fractions WA R M - U P

Materials • Fraction Factory pieces • grid paper • rulers • coloured pencils Related Resources • BLM 2.1 Assessment Question • BLM 2.1 Extra Practice Specific Curriculum Outcomes B6 estimate the sum or difference of fractions when appropriate Suggested Timing 120 min Link to Get Ready Students should have demonstrated understanding of Understand Fractions, Mixed Numbers and Improper Fractions, and Compare Numbers Using a Number Line in the Get Ready prior to beginning this section.

Find the number that makes each number sentence true. 1. 4  72 = 4  70 + 4  䊏 2. 7  39 = 7  40 – 䊏  1 3. 5  8.3 = 5  䊏 + 5  0.3

Evaluate. 4. 6. 8. 10. 12. 14.

3  19 9  28 6  84 9  44 9  48 6  47



5. 7. 9. 11. 13. 15.

6  43 7  64 8  52 4  26 11  35 5  23



Front-End Multiplic ation When finding a product, such as 6  53, break 53 into parts: 50 + 3. Now start at the “front end” and multiply 6 by 50 and 6 by 3, then add. 6  50 = 300 6  3 = + 18 318

TEACHING SUGGESTIONS In this section, students continue to develop number sense for proper and improper fractions and mixed numbers. They apply a variety of strategies to estimate sums and differences. Have students focus on these strategies rather than using algorithms, which will be taught in grade 8. Encourage students to use manipulatives when working through the problems. To introduce the chapter, discuss the concept of a fraction representing a partto-whole comparison. Have students identify examples of this in their everyday lives. The chapter problem, introduced on page 53, uses an amusement park to explore problems involving fractions and decimals.

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D i s cove r t h e M at h The activity encourages students to apply different techniques for estimating fractions and their sums and differences. Have students work in pairs through the activities, especially for Part A. In Part A, students are asked to estimate the location of a proper fraction on a number line, relative to 0 and 1. The activity is framed in the form of a game or a friendly challenge. Fraction Factory pieces are used to check estimates and determine the winner of each point. As students continue to play, their estimation abilities should improve. Grid paper might be useful for drawing the number lines. Or supply enlarged copies of the blank number lines in Mathematics Blackline Masters Grades P to 9, pages 201 and 202, and have students measure and mark 18 cm lengths. In Part B, specific strategies are introduced for rounding fractions to easy-to1 use benchmark values of 0, , and 1. In The Unit Fractions, students discover that 2 one piece (a numerator of 1) of an increasingly larger whole (the denominator) gives a value that is increasingly closer to zero. In The Nearly Ones, students discover that one part less than a whole becomes closer to one as both numerator and denominator increase. By examining The Close-to-Halves, students will learn to recognize 1 fractions that are close to and to judge whether they are above or below this value. 2 Part C provides an opportunity for students to see how rounding fractions to benchmark values can help them arrive at a reasonable estimate of the sum of two fractions. This concept is extended in the Examples that follow.

D i s cover t h e M at h An s we r s Part A 4. Answers may vary.

Part B 1 1 b) It gets closer to zero. c) 12 99 11 a) b) The numerator is always 1 less than the denominator. It gets closer to 1. 12 99 c) Each fraction is one unit fraction less than 1. d) 100 2 3 4 5 6 7 3 5 a) , , , , . They are all equivalent fractions. b) , , 4 6 8 10 12 12 5 8 8 10 50 12 7 10 44 1.5 2.5 3.5 5.5 7.5 12.5 c) , , , d) , , e) , , , , , 16 20 100 24 16 22 90 3 5 7 11 15 25 4 50 f) , 7 99 1 3 0 1 4 1 2 ,3 ,3 ,3 ,4 ,5 4 4 3 5 10 4 1 a) It is halfway between the benchmarks 0 and . 2 1 3 b) Answers may vary. is halfway between the benchmarks and 1. 4 2 Down, because he rounded 3 of the 5 fractions up and only 1 down.

3. a) 4.

5.

6. 7.

8.

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Part C 1 b) yes 2 2. Answers may vary. Compare 7 brown pieces and 2 green pieces to 1 black piece and 1 orange piece. 1 1 3. a) 2 . Subtract 1 cups from 4 cups. b) Diagrams may vary. 2 2 4. a), b) Estimate each fraction by rounding to the closest benchmark, then add or subtract. Examples may vary. 1. a) 1

Example 1 shows two methods for estimating a sum of fractions. In Method 1, whole and fraction parts are added separately and then combined. This is an application of the associative property of addition. In Method 2, the addends are rounded to benchmarks first and then added together, applying number sense to perform the addition. The visual aids reinforce the rounding and adding processes. Students should compare the merits of each method. Example 2 shows two methods for estimating the difference of two fractions. Method 1 uses the technique of rounding to benchmarks and then subtracting by applying number sense. Method 2 uses concrete and visual models to compare the sizes of two quantities and estimate the difference. Suggest students use Fraction Factory pieces. Students will benefit from seeing and exploring this method.

Com m u n i c ate t h e Key I d e a s Consider having some groups present their solutions to the class and invite discussion. Ask if any groups applied a different approach or used different tools. Invite and encourage a variety of solution methods. Use this opportunity to assess student readiness for the Check Your Understanding questions.

Com m u n i c ate t h e Key I d e a s An s we r s 1 , 1. Numbers that are easy to remember and work with. 2 b) They make comparing fractions and estimating amounts easier. 1 3 1 7 1 7 a) is almost and is just over ; about 1 b) is almost 1 and is just 8 2 12 2 8 6 5 1 over 0; about 1. c) 1 is just over 1 and is almost 1; about 2 8 6 1 9 3 7 2 1 a) is almost 1; almost b) is almost 1 and is just over ; about 10 4 8 3 2 2 1 3 1 11 c) 2 is almost 2 and is almost 1; 1 8 2 12 2 Answers may vary. 5. Answers may vary. Answers may vary. No. It is easier to add the fractions without rounding since they are between benchmark amounts. Up. He has already rounded one fraction down.

1. a) 0,

2.

3.

4. 6. 7.

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Ongoing Assessment •

Can students use benchmarks and number sense to estimate the sums and differences of fractions?

Check Your Understanding Question Planning Chart Level 1 Knowledge and Understanding

Level 2 Comprehension of Concepts and Procedures

Level 3 Application and Problem Solving

1–3, 6, 8

4, 5, 7, 9

10–18

Encourage students to use manipulatives or their number lines from the Discover the Math activity. For question 10, refer to the Did You Know? box at the bottom of the page. Questions 10 to 12 and 16 could be solved efficiently using either benchmarks or combining and comparing concrete models. Encourage a variety of approaches when discussing these solutions. Question 13 involves a comparison of The Unit Fractions, which were explored in Discover the Math. Part B. For question 17, a handout of an enlarged map of the park may be useful.

Common Errors •

Rx

Students think unit fractions increase as the denominator increases. 1 1 For example, students may think is greater than . 5 4 Use a visual model, such as a circle diagram, fraction strips, or Fraction Factory pieces, to show that one part of a larger whole gives a smaller amount.

Inter vention •

For some students, you may need to review part-to-whole relationships using a variety of visual and physical models.

ASSESSMENT Qu es t i o n 1 6 , p ag e 6 6 , An s we r s a) Underfoot

b) Skidmark

c) about 2

d) about 1

A D A P TAT I O N S BLM 2.1 Assessment Question provides scaffolding for question 16. BLM 2.1 Extra Practice provides additional reinforcement for those who need it.

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Visual/Perce ptual/Spatial/Motor •

Encourage students to use Fraction Factory pieces, fraction strips, or fraction circles.

Ex tension Assign question 18. You may wish to reduce the number of Check Your Understanding questions to provide students with extra time to work on the Extend question. Encourage students to explore different possibilities. Some additional estimation may need to be inferred.

Check Your Understanding Answers 1 1 1 1 1 c) d) 0 2. a) b) 0 c) d) e) 0 f) 1 2 2 2 2 2 1 3. a) greater than b) greater than 1 2 1 5 3 4. greater than 3; is almost 1 and is almost 6 8 2 4 7 5. less than 1; is closer than is to 1 8 5 1 1 1 6. a) 2 b) 1 c) 1 d) 6 e) 9 f) 9 7. Answers may vary. 2 2 2 1 1 1 8. a) 0 b) c) 1 d) 1 e) f) 1 2 2 2 9. Answers may vary. 10. about 4 light-years 11. about 9 h 1 1 12. Answers may vary. About a page. 13. a) Leah b) about 2 2 14. a), b) Answers may vary. 15. Answers may vary. 1 17. a) about 2 h b) Answers may vary. About 1 h. c) about 1:00 P.M. 2 18. a) Wild Ride, back to Sling Shot, Mind Warp, Cannonball, Water Park, and 1 finally the Food Court. b) Answers may vary. About 3 h. c) Answers may vary. 2 1. a) 1 b)

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2.2

Multiply a Whole Number by a Fraction and Vice Versa WA R M - U P

Materials • coloured counters • pattern blocks • Fraction Factory pieces Related Resources • BLM 2.2 Assessment Question • BLM 2.2 Extra Practice Specific Curriculum Outcomes A9 compare and order proper and improper fractions, mixed numbers, and decimal numbers B7 multiply mentally a fraction by a whole number and vice versa Suggested Timing 60 min

Evaluate. 1. 62 + 32

2. 82 – 72





Each 3-digit number is missing a digit. If the number is divisible by the number shown, what is the missing digit? (There may be more than one answer.) 3. 56䊏 is divisible by 3

4. 80䊏 is divisible by 6



Evaluate. Use the order of operations. 5. 22 + 5  3



6. 9 + 82



How much change would be received from $10 for each purchase? 7. $3.98 9. Write

17 as a mixed number. 5

10. Write 7

8. $8.46



2 5

3 as an improper fraction. 8


8

Which is the better estimate for each sum or difference?

Link to Get Ready Students should have demonstrated understanding of Understand Fractions, and Mixed Numbers and Improper Fractions in the Get Ready prior to beginning this section.

3 1 1 1 1 + or > (< ) 8 10 2 2 2 5 4 13. + 1 (>1) 9 7 5 1 15. 2 + 4 7 (>7) 2 6 11.

3 3 – 1 < 3 or >3 4 8 5 1 1 1 14. – < or > 8 3 2 2 12. 4

(>3) 1 (< ) 2

TEACHING SUGGESTIONS The focus in this section is to multiply mentally. There may be areas of this chapter that can be incorporated into the mental math program, reducing the time needed to complete the chapter. In this section, students use a variety of concrete materials to explore multiplication of whole numbers by fractions and vice versa. Symbolic algorithmic methods are left to grade 8. It is important for students to see a variety of concrete and visual representations. Have students work in pairs for the activities.

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D i s cove r t h e M at h In Part A, students use counters to multiply a fraction by a whole number using a grouping strategy. The type of counter is not important. The concrete model leads to a mental math approach. In Part B, students use pattern blocks to multiply a whole number by a fraction. Students discover that this type of product is commutative; the order of the factors does not matter. By the end of the activity students should be able to perform simple calculations of this sort mentally. As an alternate approach to Part B, students could explore how their answers change if a double hexagon is one unit, if these pieces are available.

D i s cove r t h e M at h An s we r s Part A 1. d) 8 students

1 1  24 = 6 b) 4 students;  24 = 4 4 6 3. Divide 24 by 4 or by 6. 4. a) 3 b) 2 c) 8 1 5. Calculate  20, then multiply the result by 3 to get 12. 5 6. a), b) Answers may vary. 2. a) 6 students;

Part B 1 1 1 , Rhombus: , Triangle: 2 3 6 4 9 12 12 2 12 2. a) ; 2 b) ; 3 c) ; 2 d) ; 2 e) ;4 2 3 6 5 5 3 3. Divide the numerator by the denominator. 4. a) 8 b) 3 c) 6 5. Answers may vary. 6. 6 thirds versus one third of 6. They are the same. 1. Trapezoid:

In Example 1, a variety of tools and strategies are applied to find the product of a whole number and a fraction. Money models are particularly effective when 1 1 1 working with fractions such as , , and . They provide a strong real-world 4 10 20 connection for many students. The purpose of this example is to consolidate the processes discovered in the previous activity. The variety of concrete and visual models is intended to reach a wide variety of learning styles. In Example 2, students are challenged to apply their skills and thinking to a contextual problem. The correct solution leads to a range of answers as opposed to a single answer. Discuss why a range of answers may be more desirable than a single best estimate. (For example, to provide information for contingency planning.)

Com m u n i c ate t h e Key I d e a s Have students work in pairs or small groups to answer and discuss all of the Communicate the Key Ideas questions. Use this opportunity to assess student readiness for the Check Your Understanding questions. You may wish to have some groups present their solutions to questions 1 to 3, and 5 to the rest of the class.

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Com m u n i c ate t h e Key I d e a s An s we r s 1. Diagrams may vary. a) five fifths to make 1 b) twelve shapes grouped in fours, one group circled to make 4 c) twelve shapes grouped in fours, two groups

3 e) sixteen shapes grouped in fours, 4 one group circled to make 4 f) sixteen shapes grouped in fours, three groups circled to make 12 Multiply the numerator by the number, and then divide the numerator by the denominator. Diagrams may vary. Twenty eight shapes grouped in sevens, one group circled to make 7. 1 4  = 2 5. Answers may vary. 2 Answers may vary. Calculate 2  18, then divide the result by 3, to get 12. circled to make 8 d) three fourths to make

2. 3.

4. 6.

Ongoing Assessment • •

Can students multiply a whole number by a fraction and vice versa? Can students use estimation and benchmarks to check that their answers are reasonable?

Check Your Understanding Question Planning Chart Level 1 Knowledge and Understanding

Level 2 Comprehension of Concepts and Procedures

Level 3 Application and Problem Solving

1–7

8–10, 12

11, 13–18

Some questions ask students to use a specific manipulative while others allow students to select a manipulative of their choice. Have many types of manipulatives (Fraction Factory pieces, pattern blocks, base-10 blocks, coloured counters, etc.) available for students to use. Encourage students to represent the products in questions 2, 4, 6, and 7 in as many different ways as they can. For question 14, a range of values is desired. Have students refer to Example 2, as needed.

Common Errors •

Rx

Students try to apply false mechanical methods. For example, 21 1 2 = 4 24 Encourage application of number sense. Refrain from introducing the symbolic algorithm for this type of multiplication, which will be learned in Grade 8. Try to use different visual models with a variety of concrete materials, as illustrated in Example 1.

Inter vention •

Some students may benefit from using manipulatives such as Fraction Factory pieces to reinforce their understanding of the magnitude of a fraction.

48 MHR • M athematics 7: Fo cus on Understanding Te acher ’s Resource

ASSESSMENT Q u e s t i o n 1 5 , p ag e 7 5 , An s we r s a) minimum: 1 h; maximum: 2 h b) minimum:

1 h; maximum: 1 h 2

A D A P TAT I O N S BLM 2.2 Assessment Question provides scaffolding for question 15. BLM 2.2 Extra Practice provides additional reinforcement for those who need it.

Visual/Perce ptual/Spatial/Motor •

Have students try a variety of manipulatives and let them use the ones that are the simplest for them.

Ex tension Assign questions 16 to 18. You may wish to reduce the number of Check Your Understanding questions to provide students with extra time to work on the Extend questions. Question 18 lends itself to building linear (length) models; supply Cuisenaire rods, if available.

Check Your Understanding Answers 1 1 1 3 1 = 3 b)  12 = 4 c) 3  = d) 9  = 3 2 3 8 8 3 a) 4 b) 5 c) 3 d) 3 3. Divide the numerator by the denominator. a) 2 b) 10 Multiply the number by the fraction then divide the numerator by the denominator. 3 1 2 1 a) 2 b) 6 7. 8. a) 3  b) 4  9. 4 cups; 8  =4 2 4 3 2 a) 2 h b) 14 h a), b) Answers may vary. c) The commutative property of multiplication. 6 blocks. Assume she walks to school and back 5 days a week. a) $37.50 b) $262.50 c) Answers may vary. a), b) Answers may vary. c) Answers may vary. Assume that the ride’s claim is true for students in your school. Diagrams may vary. Answers may vary. a) B b) F c) K d) R

1. a) 6  2. 4. 5.

6. 10. 11. 12. 13. 14. 16. 17. 18.

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2.3

Changing Form: Fractions and Decimals WA R M - U P

Materials • centimetre grid paper • ten thousands grids • scissors • glue sticks • coloured pencils • calculators Related Resources • BLM 2.3 Assessment Question • BLM 2.3 Extra Practice Specific Curriculum Outcomes A7 apply patterns in renaming numbers from fractions and mixed numbers to decimal numbers A8 rename single-digit and double-digit repeating decimals to fractions through the use of patterns, and use these patterns to make predictions

Find the number that makes each number sentence true. 1. 4  3.1 = 4  3 + 4  䊏 2. 8  3.9 = 8  3 – 䊏  0.9 3. 6  8.9 = 6  䊏 – 6  0.1

Evaluate. 4. 6. 8. 10. 12. 14.

3  1.9 5  2.8 6  9.8 7  4.1 9  3.9 6  4.9



5. 7. 9. 11. 13. 15.

7  4.1 6  7.2 8  5.2 4  2.9 11  3.2 5  12.3



Compensation Strategy for Multiplic ation When finding a product, such as 8  6.9, multiply 8 by 7 then compensate for the change that was made by subtracting the product 8  0.1 (6.9 is 0.1 less than 7). 8  7 = 56 – 8  0.1 = – 0.8 55.2

Suggested Timing 120 min Link to Get Ready Students should have demonstrated understanding of Understand Fractions, Mixed Numbers and Improper Fractions, and Represent Decimals in the Get Ready prior to beginning this section.

TEACHING SUGGESTIONS In this section, students extend their understanding of fractions and decimals, and how they are related. Repeating decimals are introduced using concrete materials. Students learn techniques for converting from fractions to decimals and vice versa. Have students do the Discover the Math activities in pairs or small groups, alternately gathering the whole class in teacher-led discussions for the Examples that appear between them.

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D i s cove r t h e M at h In Part A, students represent fractions visually and convert fractions to equivalent fractions with denominators of 10 or 100. They also write fractions as terminating decimals and use a calculator to convert a fraction to a terminating decimal. Most of this work with fractions is review from grade 6. Example 1 shows how to write a mixed number as a terminating decimal. First, the fractional part is converted to an equivalent fraction having a denominator of 100, then it is converted to a decimal. The thought bubble shows how to use a calculator to divide the numerator by the denominator. The decimal part of the number is then added to the whole part. Example 2 shows a formal method for writing a decimal as a fraction in simplest form: convert to a fraction over 10, 100, etc., then reduce to lowest terms.

D i s cove r t h e M at h In Part B, students discover how certain types of fractions give repeating decimals. Using ten thousands grid paper (see Mathematics Blackline Masters Grades P to 9, page 105) and base-10 blocks can provide a concrete/visual model that will help many students understand why a repeating decimal occurs. Students can work individually or in groups of three. Example 3 demonstrates some of the different types of repeating decimals. Students are introduced to repeating decimal notation and vocabulary (i.e. period, length of the period).

D i s cove r t h e M at h In Part C, students explore repeating decimals in greater depth. Certain families of repeating decimals have longer periods and exhibit some interesting patterns. By examining these patterns, students can make predictions about other fractions and their repeating decimal equivalents. Students can also use a given pattern of repeating decimals to write equivalent fractions. It is strongly recommended that students use calculators to explore these patterns.

D i s cove r t h e M at h An s we r s Part A 1 d) Diagrams may 5 2 vary. The same whole divided into tenths, two tenths shaded. e) 10 f) Each person gets the same portion of brownies from both pans. g) 0.2 1 a) 4 b) Diagrams may vary. A whole divided into fourths. c) d) Diagrams may 4 vary. The same whole divided into hundredths, twenty five hundredths shaded. 25 e) f) Each person gets the same portion of brownies from both pans. g) 0.25 100 a) 0.2 b) 0.25 a) Question 1 is the same as 3a); question 2 is the same as 3b). b) Divide the numerator by the denominator. c) Examples may vary. d) yes Answers may vary.

1. a) 5 b) Diagrams may vary. A whole divided into fifths. c)

2.

3. 4. 5.

Chapter 2 • MHR

51

Part B 1.

1 3

3. a) 0.333... b) Yes. Continue cutting each remaining strip into thirds. 4. a) They are equal. b), c) Its digits repeat without end. d) 0.666... The last digit is 7

on a calculator because the calculator rounds the last digit up. 5. Answers may vary.

Part C 7 8 2 6 9 , d) Answers may vary. , e) ; 1 9 9 3 9 9 2. a) 0.142857142…; repeating decimal b) 0.285714285…; 0.428571428…; 0.571428571… c) There is a pattern of 6 repeating digits. d) 0.714285714…; 0.857142857… f) yes 1 3. Answers may vary. The repeating decimal for starts at the tenths place 90 1 0.0111… and the repeating decimal for starts at the hundredth place 900 0.00111…. 4. Answers may vary. 1. a) 0.111…; 0.222…; 0.333… b) 0.555… c)

Journal Students could use this prompt for Part B, question 5. • It is better to use a [fraction / decimal number] when …

Com m u n i c ate t h e Key I d e a s Questions 1 to 4 could be used as journal entries. Have students discuss questions 5 and 6 with a partner or in small groups to aim for a consensus response. Some responses should then be shared with the class for discussion. Use this opportunity to assess student readiness for the Check Your Understanding questions.

Com m u n i c ate t h e Key I d e a s An s we r s 1. Answers may vary. 2. Write the decimal as an equivalent fraction with a denominator of 10, 100, or 1000. 3. a) A decimal number with a sequence of digits that repeat forever. b) A decimal

number whose digits end. 4. Period is the digits that repeat: 285; length of the period is the number of digits in each period: 3. 5. a) 0. 4 b) 0.35 c) 0. 516 d) 0.413 6. Denzel. Roberto’s calculator has rounded the last digit.

Ongoing Assessment • •

Can students use mental math to convert frequently used fractions to decimals and vice versa? Do students know when to use mental math and when to use a calculator?

52 MHR • M athematics 7: Fo cus on Understanding Te acher ’s Resource

Check Your Understanding Question Planning Chart Level 1 Knowledge and Understanding

Level 2 Comprehension of Concepts and Procedures

Level 3 Application and Problem Solving

1–9

10–15

16–18

When dealing with a mixed number, as in question 9, parts g) and h), students may forget how to handle the whole number part. Refer to Example 1 for a reminder. As an alternate approach, encourage students to use a calculator to apply the order of operations. If the students’ calculators do not follow the order of operations, they must add brackets. Questions 11 to 13, 16, and 17 are good opportunities for students to use a calculator as an exploratory tool. Consider having students work in pairs for these questions.

Common Errors • Rx •

Rx

Students use too many digits when writing repeating decimal notation. For example, 0.33. Review the concepts of period and the length of the period, and reinforce the convention of writing the period exactly once. Students are careless in the placement of decimals. For example, they may 2 write = 0.2 . 90 Review the concept of place value and stress the importance of attention to detail. Remind students to use number sense to judge the reasonableness of a calculator result.

Inter vention • •

For some students, you may need to review place value. Use concrete models, such as base-10 materials, as described in the Get Ready section. Some students might find memory aids useful, such as flash cards with common fractions and their decimal equivalents. Also useful would be a list showing which fractions can be converted to decimals using mental math skills and which should be converted using a calculator.

ASSESSMENT Q u e s t i o n 1 6 , p ag e 8 3 , An s we r s a) 0.0 6 ; 0.13

b) 0.2

c) yes

d) 0.26 ; 0.3 , 0.4

9 12 15 , , ; 15 15 15 7 8 10 11 13 14 repeating decimals: , , , , , 15 15 15 15 15 15

e) terminating decimals:

f) 0.4 6 , 0.5 3, 0.6, 0. 6 ; 0.7 3, 0.8, 0.8 6, 0.9 3, 1 Chapter 2 • MHR

53

A D A P TAT I O N S BLM 2.3 Assessment Question provides scaffolding for question 16. BLM 2.3 Extra Practice provides additional reinforcement for those who need it.

Visual/Perce ptual/Spatial/Motor See the Nova Scotia Department of Education’s Mathematics Grade 7: A Teaching Resource, pages 53 to 61, for additional related activities.

Ex tension Assign question 18. You may wish to reduce the number of Check Your Understanding questions to provide students with extra time to work on the Extend question. Most calculators produce evidence that is inconclusive so suggest students use long division. By studying the patterns produced, students will find clear evidence that a repeating decimal is produced.

Literac y Connec tions Suggest students work in groups to create concentration game cards that match fractional forms to their decimal equivalents. Creating and then playing the game will reinforce students’ understanding of converting forms.

Check Your Understanding Answers 1. a) 0.7; terminating b) 0. 45 ; repeating c) 0. 6 ; repeating d) 0.625; terminating 2. a) 0.9 b) 0.49 c) 0.25 d) 0.8 e) 0.74 f) 0.84 g) 1.1 h) 3.2

3 7 23 9 31 9 7 1 b) c) d) e) 4 f) 2 5. a) b) 10 100 1000 1000 10 100 2 4 7. a) 0. 5 b) 0. 26 c) 0.9 3 d) 0. 724 6. a) 5; 1 b) 26; 2 c) 3; P 1 d) 724; 3 8. a), c), d) e) repeating b), f) terminating 4. a)

9. a) 0. 27 b) 0.1 2 c) 0.9 7 d) 0.1 36 e) 0.108 3 f) 0. 384615 g) 2. 3 h) 1. 6 10. Examine other fractions that have 13 as a denominator. Examples may vary. 11. a) 0.1 2; 0.1 3; 0.1 4 b) 0.1 5; 0.1 6 c)

16 17 , 90 90

12. a) 0.1 9 b) 0.2; yes c) 0.2 1; 0. 2 , 0.2 3 d) yes

22 26 32 b) c) 14. Aceena. Examples may vary. 90 90 90 15. Lei Mei. Explanations may vary. 17. Answers may vary. 13. a)

54 MHR • M athematics 7: Fo cus on Understanding Te acher ’s Resource

18. repeating decimal

2.4

Compare and Order Fractions and Decimals WA R M - U P

Materials • Fraction Factory pieces • linking cubes • coloured counters • pattern blocks • Cuisenaire rods • grid paper • calculators • base-10 materials Related Resources • BLM 2.4 Assessment Question • BLM 2.4 Extra Practice Specific Curriculum Outcomes A9 compare and order proper and improper fractions, mixed numbers, and decimal numbers B4 determine and use the most appropriate computational method in problem situations involving whole numbers and/or decimals

Evaluate. 1. 3  72 3. 7  58



2. 32 + 42 + 52 4. 9  6.3

How much change would be received from $20 for each purchase? 5. $11.89



6. $7.32



Which is the better estimate for each sum or difference? 1 11 1 1 1 – < or > (> ) 12 5 2 2 2 2 3 8. + 1 (3) 3 8 7.

Multiply. 1  27 3 3 12. 24  8 10.



4  45 5 5 13.  63 9 11.



Change the fractions to decimals then add. Give your answer as a decimal. 14.

3 1 + 10 2



15.

1 2 + 4 5



Suggested Timing 60 min Link to Get Ready Students should have demonstrated understanding of Understand Fractions, Mixed Numbers and Improper Fractions, Compare Numbers Using a Number Line, and Represent Decimals in the Get Ready prior to beginning this section.

Chapter 2 • MHR

55

TEACHING SUGGESTIONS In this section, students extend their understanding of the relative magnitudes of fractions and decimals. Pose and discuss real-world scenarios involving fractions and decimals. Ask students questions to prompt discussion. Where are decimals or fractions found in everyday life? When is one form preferred over another? When is a combination of forms used? How can we compare these quantities?

D i s cove r t h e M at h In this activity, students write fractions to compare athletic performance. Such scenarios are quite common in sports. Encourage students to develop concrete models to illustrate quantities visually. Have a wide array of manipulatives available. Encourage students to apply different approaches to modelling and solving the problem. Have groups present their methods to the class.

D i s cover t h e M at h An s we r s 1. 2. 3. 5. 6.

a) Singh b) No. It also depends on the number of attempts. a) Jones b) No. It also depends on the number of attempts. Diagrams may vary. 4. Jones, Dunbar, Matsu, Singh.

Methods may vary. a), b) Answers may vary. c) Answers may vary. Compare fractions using

benchmarks. For decimal numbers, compare each digit. In Example 1, another sports statistic is used to compare and rank data presented in various forms. The scores are converted to decimals then ordered by comparing place values. Use base-10 blocks to show the comparisons visually. Ask why the statistic is called a batting average, and what a value of 0.302 means in this context. You could briefly introduce the concept of percent, the subject of the next chapter. Example 2 offers students an opportunity to apply the number sense strategies for comparing fractions that they learned in section 2.1: The Unit Fractions, The Nearly Ones, The Close-to-Halves and other benchmark fractions. In Example 3, students apply additional strategies to compare and order fractions. These strategies include rewriting the fractions with a common denominator or numerator, or as decimals. A variety of different visual models are presented to complement the written explanations. As these examples are discussed, students should be encouraged to recognize situations where one or more of these strategies can be applied. Example 4 shows two methods for comparing and ordering decimals and fractions. In Method 1, all the values are converted to decimals, a method that works in every situation. Method 2 shows a case where the values can be converted to easy-tocompare fractions. Seeing both methods will help students appreciate that there is often more than one valid solution method. Caution students against an overreliance on technology.

Com m u n i c ate t h e Key I d e a s Have students work in pairs or small groups to answer and discuss all of the Communicate the Key Ideas questions. Use this opportunity to assess student readiness for the Check Your Understanding questions.

56 MHR • M athematics 7: Fo cus on Understanding Te acher ’s Resource

Com m u n i c ate t h e Key I d e a s An s we r s 1. a) Answers may vary. When the denominators are the same, order the fractions

by the numerators. When the numerators and denominators are different, use benchmarks to compare. b) Examples may vary. 2. a) Answers may vary. Write in expanded form then compare each digit. b) 0.4, 0.44, 0. 4, 0.45, 0.5 3. a) Answers may vary. Convert all the fractions to decimals then compare each digit. b) Examples may vary.

Ongoing Assessment •

Can students use benchmarks to accurately compare and order decimals and fractions?

Check Your Understanding Question Planning Chart Level 1 Knowledge and Understanding

Level 2 Comprehension of Concepts and Procedures

Level 3 Application and Problem Solving

1–3

4–12

13–15

For questions 6 to 8, if Cuisenaire rods are not available, make them out of coloured Bristol board, using the lengths shown in the text.

Common Errors •

Students incorrectly order repeating decimals written in repeating notation.

For example they might conclude that 2.5 < 2.53 because it looks like it is less. Rx Write repeating decimals in expanded notation, and align placeholders vertically for easy comparison. For example: 2.555… 2.53 • Students make incorrect judgments on values measured in different units. Rx If quantities are given with units, instruct students to convert to common units before making comparisons. Remind them that the choice of unit does not matter, as long as all quantities are expressed in the same unit.

Inter vention •

For some students, you may need to review place value using manipulatives, such as base-10 materials.

ASSESSMENT Q u e s t i o n 1 3 , p ag e 9 1 , An s we r s a) Answers may vary.

b) Mrs. Cheng’s class

Chapter 2 • MHR

57

A D A P TAT I O N S BLM 2.4 Assessment Question provides scaffolding for question 13. BLM 2.4 Extra Practice provides additional reinforcement for those who need it.

Visual/Perce ptual/Spatial/Motor •

Students with weak visual or fine motor skills may find it useful to write the numbers on large grid paper when comparing decimal numbers with several place values.

Ex tension Assign question 15. You may wish to reduce the number of Check Your Understanding questions to provide students with extra time to work on the Extend question. Encourage students to estimate first before doing any research, and to explain their thinking. Then encourage them to refine their estimates based on their research. You could have some students debate the relative merits of their estimates, using examples.

Check Your Understanding Answers 1 1 1 1 1 5 5 5 5 5 1 4 6 5 89 , , , , b) , , , , c) , , , , 6 5 4 3 2 7 6 5 4 3 20 9 11 6 90 1 3 1 7 9 1 1 2 5 d) , , , , e) , , , , 1 10 10 2 10 10 6 3 3 6 2. a) 0.777, 0. 7, 0.778, 0.78, 0.8 b) 3. 2, 3.23, 3. 23, 3.3, 3.3 2 3 4 1 8 7 1 6 9 4 2 3. a) , , , , b) 1 , , , , 1 8 9 2 15 12 6 5 7 3 5 1 1 1 2 0.02 – 4. a) 0.02, 0. 02 , , , b) 0.02 5 45 5 9 1. a)

0

1

1 –– 45

5. 7. 8.

9. 10. 11. 12.

14.

15.

2 – 9

– 2

2 4 3 4 3 1 ; ; greatest: ; least: 6. a) ; 0.5 b) ; 2.0 5 6 5 6 2 1 a) green b) brown c) dark blue Answers may vary. a) orange and green b) orange and yellow c) orange and brown d) orange and purple 3 7 5 4 3 9 a) b) , , , c) Numerator and denominator are decreasing. d) 2 6 4 3 2 8 Lundergard, Stiles. They had the lowest number of goals per game. a) Evan b) Evan, Gianetta, Dora 6 5 7 1 a) 6.77, 6 , 6 , 6 , 6 , 6.31 8 7 20 3 b) Answers may vary. For example, change each fraction to decimal form. 1 1 2 1 a) 1 h, 1 h, 1 h, 1 h; 1.25 h, 1. 3 h, 1.4 h, 1.5 h; 75 min, 80 min, 4 3 5 2 1 84 min, 90 min b) h; 0.25 h; 15 min 4 Answers may vary.

58 MHR • M athematics 7: Fo cus on Understanding Te acher ’s Resource

2.5

Operating With Decimals WA R M - U P

Related Resources • BLM 2.5 Assessment Question • BLM 2.5 Extra Practice Specific Curriculum Outcomes B2 use mental math strategies for calculations involving integers and decimal numbers B4 determine and use the most appropriate computational method in problem situations involving whole numbers and/or decimals B5 apply the order of operations for problems involving whole and decimal numbers Suggested Timing 60 min Link to Get Ready Students should have demonstrated understanding of all topics in the Get Ready prior to beginning this section.

Find the number that makes each number sentence true. 1. 4.8 – 3.7 = 4.8 – 4 + 䊏 2. 7.2 – 3.9 = 7.2 – 4 + 䊏 3. 9.4 – 8.8 = 9.4 – 䊏 + 0.2

Evaluate. 4. 6. 8. 10. 12. 14.

3.8 – 1.9 9.1 – 2.8 6.3 – 4.8 9.6 – 4.9 9.5 – 4.8 6.4 – 4.7



5. 7. 9. 11. 13. 15.

6.6 – 4.9 7.6 – 6.9 8.1– 5.9 4.7 – 2.8 11.2 – 3.9 5.6 – 2.8

Compensation Strategy for Subtrac tion When finding a difference between decimals, subtract a “nice” number then compensate by adding. For example, for 4.6 – 2.9, the “nice” number is 3, then add 0.1 because 2.9 is 0.1 less than 3. 4.6 – 2.9 = (4.6 – 3) + 0.1 = 1.7

TEACHING SUGGESTIONS In this section students apply various strategies for mentally calculating and estimating in contextual problems involving decimals. Emphasize the importance of deciding when an exact answer is needed or when an estimate is sufficient. Ask students for examples of situations that need exact answers or estimates.

D i s cove r t h e M at h In this activity, students estimate the amount to withdraw from a bank machine. Students should apply rounding skills in working out their estimates. Then, students calculate the exact amount needed to pay the bill. It is recommended that calculators not be used for this activity. Encourage students to share the methods they used for estimating and calculating the exact amount.

D i s cove r t h e M at h An s we r s 1. Heather: $10.00, Shannon: $10.00 3. $18.86 4. Strategies may vary.

2. Heather: $8.93, Shannon: $9.93 Chapter 2 • MHR

59

Example 1 shows a situation where an estimate is sufficient. The clustering method is used. This is a good technique for adding a group of numbers that are close in value. Students should recall that multiplication is an efficient method of repeated addition. In Example 2, part a), two methods are used to add a grocery bill. In Method 1, each value is rounded to a benchmark value and then added to estimate the total. In Method 2, dollar values and cent values are grouped, the cent values are rounded to benchmarks, each group is totalled and then combined. These calculations should be done mentally, without a calculator. A table is a good visual organizer to keep track of all the subtotals. In part b), a scientific calculator is used to find the exact amount. Students could also apply mental math strategies to find the subtotals and totals given in the solution using the distributive property. Example 3 demonstrates a variety of approaches to the halve/double strategy, which is useful for multiplying two numbers. One factor is converted to a value that is equal to or close to a multiple of 10 to allow for mental calculation of the product. If one factor is doubled and the other factor is halved, the resulting product will remain unchanged. Example 4 shows the double/double strategy, which is useful when finding the quotient of two numbers. The idea is similar to the halve/double strategy: the divisor is converted to a value that is equal to or close to a multiple of 10. This method is based on the concept of equivalent fractions. Encourage students to use mental estimation to check the reasonableness of their results.

Com m u n i c ate t h e Key I d e a s Have students work in pairs to discuss and answer all of the Communicate the Key Ideas questions. Use this opportunity to assess student readiness for the Check Your Understanding questions.

Com m u n i c ate t h e Key I d e a s An s we r s 1. a), b) Answers may vary. 2. a) clustering b) $6 3. a), b) halve/double strategy 4. halve/halve strategy

Ongoing Assessment • •

Can students use a variety of estimation strategies? Can students use mental math to find estimates and to check that their answers are reasonable?

Check Your Understanding Question Planning Chart Level 1 Knowledge and Understanding

Level 2 Comprehension of Concepts and Procedures

Level 3 Application and Problem Solving

1, 3a), 4–7

2, 3b), c), 8, 9, 11, 12

10, 13, 14

You might need to review how to identify the important information in the word problems. Suggest students apply strategies such as underlining key words, summarizing, and using visual organizers. You may wish to work through a couple of questions with the class to demonstrate these strategies. In question 8, part c), students may assume one or more of the following: that Roberto attends school five days each

60 MHR • M athematics 7: Fo cus on Understanding Te acher ’s Resource

week for the full month with no days off, that he gets no rides, and that he travels directly to school and back every day.

Common Errors • Students do not know how to start a word problem. Rx Encourage students to break up the problem: identify what the question is asking for, find the important information, and think of solution strategies. Alternatively, put students in pairs or small groups and encourage them to discuss the questions together.

Inter vention •

Some students may have difficulty with the language in the word problems. Pair weak readers with stronger readers and have students work in pairs to discuss and answer several questions.

ASSESSMENT Q u e s t i o n 7 , p ag e 9 7 , An s we r s a) 300 ÷ 10

b) $30

c) $29.80

A D A P TAT I O N S BLM 2.5 Assessment Question provides scaffolding for question 7. BLM 2.5 Extra Practice provides additional reinforcement for those who need it.

Ex tension Assign questions 13 and 14. You may wish to reduce the number of Check Your Understanding questions to provide students with extra time to work on the Extend questions. These questions allow students to extend the calculation strategies they learned in this section to develop a refined clustering strategy that gives precise answers. Encourage students to invent and share their own strategies.

Check Your Understanding Answers 1. 2. 3. 4. 6. 8. 9. 10. 11. 12.

a) about $18 b) Round each cost, add, then multiply by 3. c) Answers may vary.

Yes. An estimate. a) about $500 b) Find pairs of numbers that add to an easy number. c) about $5200 $240 5. $150 a) about $61 b) Answers may vary. a) about 15 km b) about 60 km c) Assume he walks to school 5 days a week and

4 weeks each month. a) about 8 m2; about 9 m2 b) triangular garden; about 1 m2 larger c) Round to the closest number. a) Cannonball: $4.50, Mind Warp: $6.00, Slingshot: $7.50, Wild Rider: $9.00. b) $27.00 Answers may vary. Yes, if you are planning on riding each ride at least once. a) 3 times b) $2.00 13. a) $8.97 b) $4.90 14. a) $8.08 b) $60.00 Chapter 2 • MHR

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2.6

Solve Problems Involving Decimals WA R M - U P

Related Resources • BLM 2.6 Assessment Question • BLM 2.6 Extra Practice Specific Curriculum Outcomes B2 use mental math strategies for calculations involving integers and decimal numbers B4 determine and use the most appropriate computational method in problem situations involving whole numbers and/or decimals B5 apply the order of operations for problems involving whole and decimal numbers Suggested Timing 60 min

How much change would be received from $20 for each purchase? 1. $6.75



2. $3.52



Multiply. 3. 9  4.3



4. 6  7.99



Choose the better estimate for each sum or difference. 3 2 5 1 5. 1 – 1 ( 10 3 2 2

1 (< ) 2

Multiply. 4. 36 

1 3



5.

3  35 5



6.

7  32 8



Change the fractions to decimals then add or subtract. Give your answer as a decimal. 7.

2 1 – 5 10



8.

3 1 + 100 4

9.

7 1 – 10 2



(