Extra Practice BLM 5.1

Extra Practice BLM 5.1

5.1 Introduction to Integers

Name: ______Date: ______

1. What integer does each group of counters represent? (A black counter represents +1 and a white counter represents –1.)

a) ____

b) ____

c) ____

d) ____

2. Write the opposite of each integer.

a) –2 ______b) +13 ______

c) 0 ______d) –8 ______

3. Represent each integer with counters in two different ways. Draw pictures to record your answers.

a) +2 b) –2 c) –4

4. Which of the following integers are greater than –3? Justify your answers.

–2, +1, –5, +7, +2, –1

______

5. Sidney Crosby, from Cole Harbour, NS, finished 6th in scoring in the NHL and had a season plus/minus rating of –1. His plus/minus totals for his last 5 games were:

• Game 1: plus one

• Game 2: plus two

• Game 3: minus one

• Game 4: plus three

• Game 5: even

a) Represent each score as an integer.

______

b) Which games did he have plus/minus scores that represent opposite integers?

______

c) What was Sidney’s net plus/minus score for his last five games?

______

6. The mean temperature was recorded each day during the first week of March in Yarmouth.

Day / 1 / 2 / 3 / 4 / 5 / 6 / 7
Temperature
(ºC) / –2 / –3 / –1 / +1 / +4 / –5 / –6

a) Make a scatter plot of these data.

b) Which days were colder than March3?

______

c) How much colder was the temperature on March 6 than on March 5?

______

d) What was the median temperature? On which day was it recorded?

______

Extra Practice BLM 5.2

5.2 Add Integers

This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

Name: ______Date: ______

1. Which group of counters shows
(–5) + (+8)? (A black counter represents +1 and a white counter represents –1.)

______

2. What sum is shown? Give each result.

______

3. Use coloured counters to model each sum. Draw pictures to record the steps.

a) (–3) + (+2) b) (+6) + (–4)

c) (–7) + (–2) d) (–2) + (+7)

e) (–9) + (–4) f) (–5) + (–1)

4. Use a number line to model each sum.

a) (–1) + (–9) b) (+3) + (–6)

c) (–6) + (+6) d) (+4) + (–5)

e) (–2) + (+3) f) (–1) + (+9)

5. Represent each situation as the sum of two integers. Find the result.

a) Jessica shot two over par one round, then six under par the next.

______

b) Adam earned $30 at his part-time job then spent $15 on take-out.

______

Extra Practice BLM 5.3

5.3 Subtract Integers

This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

Name: ______Date: ______

1. Use coloured counters to model each subtraction statement. Draw pictures to record the steps. What is the result?

a) (–5) – (–2) b) (+1) – (–6)

c) (+3) – (–4) d) (–7) – (+2)

2. Use a number line to find each difference.

a) (–4) – (+7) b) (+2) – (+6)

c) (–1) – (+5) d) (+7) – (–3)

3. Find each difference by adding the opposite.

a) (–2) – (+1) b) (–1) – (–8)

c) (+2) – (+6) d) (–4) – (+8)

4. Which expressions can you simplify mentally? Find each result, using coloured counters or a number line when necessary.

a) (+2) – (+1) b) (–3) – (+5)

c) (–3) – (–8) d) (–7) – (–4)

5. Find the missing integer in each.

a) (+2) – _____ = –7

b) (–3) – _____ = –8

c) (–4) – _____ = +6

d) _____ – (+2) = –5

6. Andy owed Silvia $6. Then he misplaced $4 he was going to give to her. What was Andy’s net worth after losing the $4? Find the result using three methods. Show your work.

______

7. Write each situation as an integer addition or subtraction statement. Give the outcome of each statement using an integer.

a) Alisa free-dove to the 7-m-below-sea-level mark in a diving tank. Then she swam up 3m.

______

b) There was 15 cm of snow on the ground but then 8 cm melted.

______

c) A loss of 11 points was followed by a loss of 6 points.

______

8. Sandra lives in Antigonish. Her aunt lives in Saskatoon, three time zones behind her. Sandra wants to call her aunt either before noon or after 9 P.M. Atlantic time. What times would these represent in Saskatoon? Why might Sandra want to call her aunt at these times? Explain your reasoning.

______

Extra Practice BLM 5.4

5.4 Multiply Integers

This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

Name: ______Date: ______

1. Write an integer multiplication statement to go with each model. Find each result. (A black counter represents +1 and a white counter represents –1.)

______

2. Multiply.

a) (+8) ´ (–6) = _____

b) (–7) ´ (–3) = _____

c) (+6) ´ (–13) = _____

d) (–9) ´ (–4) = _____

3. Match each phrase with a multiplication statement. Then find each product.

A receive eleven groups of 6 cups

B give away seven sets of 9 napkins

C net worth after losing four $20 bills

D take away six sets of 7 plates

E give away eight sets of 12 glasses

F buy thirteen sets of 5 stickers

a) (–8) ´ (+12) ______

b) (+13) ´ (+5) ______

c) (–6) ´ (+7) ______

d) (+4) ´ (–20) ______

e) (+11) ´ (+6) ______

f) (–7) ´ (+9) ______

4. Write each situation as an integer expression using multiplication. State the result and its meaning.

a) Andrea deposited $15 dollars into her bank account once a week for an entire year. How much money did she deposit?

______

b) For seven straight days, a slug climbed 13 cm up a tall bush. If it began at ground level, at what distance was the slug at the end?

______

5. List possible combinations of three different integers that have a product of –24.

______

Extra Practice BLM 5.5

5.5 Divide Integers

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Name: ______Date: ______

1. Which division statements will have a negative answer?

A (+72) ÷ (–9) B (–48) ÷ (–4)

C (+52) ÷ (+4) D (–48) ÷ (+8)

______

2. Use integer counters or a number line to find each quotient. Draw pictures to record the steps.

a) (–14) ÷ (–7) b) (+35) ÷ (+7)

c) (–8) ÷ (+2) d) (–48) ÷ (–6)

3. Draw a triangle for each multiplication statement. Then, write the related division statements.

a) (–4) ´ (+6) = –24

b) (–9) ´ (–4) = +36

c) (–27) ´ (+3) = –81

4. Divide.

a) (–28) ÷ (+7) b) (+38) ÷ (–2)

c) d)

5. Complete each statement to make it true.

a) +63 = _____ ´ (–7)

b) –36 = _____ ´ (–12)

c) _____ ´ (–5) = +70

d) _____ ´ (–9) = –90

6. List all the integers that divide evenly into each number.

a) –48 b) –60

______

7. Write an integer division expression for each situation. Evaluate and state what the answer means.

a) The temperature in Lunenburg increased by a total of 24°C over an 8-hour period. What was the mean hourly temperature increase?

______

b) Jamie owes his parents $54, to be paid in six equal installments. How much is each installment?

______

8. Six weeks ago, a stock price was $42. This week, the price is $24. What is the mean weekly decrease in the stock price over the six weeks?

______

9. Is it possible to use a number line to model (–24) ÷ (–6)? Why or why not? Explain your reasoning.

______

Extra Practice BLM 5.6

5.6 Order of Operations With Integers

This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

Name: ______Date: ______

1. Which integer expression represents the statement?

a) The difference between the square of 4 and the square of –3.

A (–3)2 – 42 B 42 – (–3)2

C 42 + (–3)2 D (4 – (–3))2

b) Double the sum of 4 and –6.

A 2 ´ 4 + (–6)

B (–2) ´ 4 + (–6)

C 2 ´ (4 ´ (–6))

D 2 ´ (4 + (–6))

c) Four times the difference between –5 and 2.

A 4 ´ (–5 – 2) B –4 ´ (–5 – 2)

C 4 ´ (–5) – 2 D 4 ´ (5 – 2)

2. Evaluate without using a calculator.

a) (–2) ´ 3 + (–5) b) 9 – 6 ÷ (–2)

c) (–3)2 – 4 ´ 2 d) (–8) ´ (–4) ÷ 2

e) (–5) – 2 ´ 42 f) (–6) + 3 ´ 2 – 1

3. Evaluate. Check your answers with a calculator.

a) 3 + (4 – 8) ´ (–2) _____

b) (–4)2 ´ 2 + 3 ´ 4 _____

c) –3[–4 + (–6)] ÷ (–5) _____

d) 3(–4 + 2) ÷ 6 _____

e) –6(22 – 32) ÷ (–5) _____

f) (4 + 3) ´ (–2) – 5 _____

4. Evaluate using a calculator.

a) 18(–3 – 4) _____

b) –4 – 3[42 + (–3)2] _____

c) –22(16 – 22) ÷ (–4) _____

d) –3[(–14)2 – 162] _____

5. Write an integer expression for each statement. Then, evaluate the expression.

a) Divide 4 into the product of –10 and 12.

______

b) Subtract the square of 7 from the square of 4.

______

c) Add –8 to 24 divided by –6.

______

6. a) Use the symbols +, –, ´, ÷, and ( ) to make each statement true.

• 4 ___ –2 = 2

• 2 ___ 3 ___ –4 = 2

• 6 ___ 4 ___ 3 = –6

• 20 ___ (–4) ___ 2 = 12

b) Is it possible to make any of the equations true in more than one way? Explain.

______

c) What strategies did you use to answer these questions? Which worked best?

______

Extra Practice BLM 5.7

5.7 Problem Solving With Integers

This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.

Name: ______Date: ______

1. An oriole was chasing insects. It flew up 5 m, caught one, then flew up another 5m eight more times to catch more insects. Finally, it flew down 4 m to land on a tree branch. If the branch is 56 m above ground, at what height did the oriole begin?

______

2. Samantha started a lawn-mowing business with a loan of $250 from her parents for a lawnmower and other expenses. She charges $8 a lawn. What will Samatha’s profit or loss be after mowing 45 lawns?

______

3. The length of the Caspian Sea, both the world’s largest and the world’s longest lake, is 542 km less than one thousand times the depth in metres of Lake Baikal, the world’s deepest lake. The depth of Lake Baikal is 1741 m.

a) What is the length of the Caspian Sea?

______

b) If the difference between the length of the Caspian Sea and one thousand times its depth is 253 km, what is the depth of the Caspian Sea?

______

4. A shoe store sells a brand of shoes for $170. At a clearance sale, each pair was offered at $18 off for every week of the sale, until it was sold. Sam bought a pair of the shoes for $62. How many weeks had the shoes been on sale?

______

5. The table shows the performance of two stocks (in dollars) on the stock exchange over five days last week. Stock A started the week at $37. If Stock B ended up $4 lower than Stock A, at what value did Stock B start?

Stock A / +2 / +5 / –1 / –3 / –7
Stock B / –1 / –3 / +2 / +4 / +6

______

6. James owes his parents $320. Every two weeks he pays them $12. If he has given them a total of $108, how many weeks has he been paying off his debt? How many more weeks does he have to make payments?

______

7. Amanda’s bank account balance was $218 at the beginning of February. During February, she made five equal withdrawals and two equal deposits, each deposit four times greater than each withdrawal. Her balance at the end of the month was $404.

a) What size was each withdrawal?

______

b) What size was each deposit?

______

Chapter 5 Extra Practice Answer Key

Get Ready

1. a) –75 b) +8 c) +9 d) –200 e) –4 f) +7 g) –5

2. Answers may vary.

3. a) –8 b) +1 c) –22 d) +13

4. a) +3 and +7; +3 < +7. b) –2 and –8; –2 > –8.

5. Answers may vary. –8 < –2 < +3 < +7. Negative eight is less than negative two which is less than positive three which is less than positive seven.

6. A (1, 2); B (–4, 4); C (–3, –4); D (–2, 0); E(4, 3); F (2, –2)

7. a), b), c)

8. a) 23 b) 34 c) 35

9. 12 ´ 7.5 = 90

10. a) 6 b) 19 c) 31 d) 50

12. a) 17 b) 2 c) 10 d) 5

13. a) 13 b) 52 c) 0

5.1 Introduction to Integers

1. a) –2 b) –1 c) –4 d) +5