Number & Operations - Task Sheets - Grades 6-8 : Task Sheets 6-8 [1 ed.] 9781553198109, 9781553194705

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NUMBER AND OPERATIONS Principles & Standards of Math Series .................. Written by Nat Reed

GRADES 6 - 8

Classroom Complete Press P.O. Box 19729 San Diego, CA 92159 Tel: 1-800-663-3609 | Fax: 1-800-663-3608 Email: [email protected]

www.classroomcompletepress.com ISBN-13: 978-1-55319-470-5 © 2010 Permission to Reproduce Permission is granted to the individual teacher who purchases one copy of this book to reproduce the student activity material for use in his or her classroom only. Reproduction of these materials for colleagues, an entire school or school system, or for commercial sale is strictly prohibited. No part of this publication may be transmitted in any form or by any means, electronic, mechanical, recording or otherwise without the prior written permission of the publisher. We acknowledge the financial support of the Government of Canada through the Book Publishing Industry Development Program (BPIDP) for our publishing activities. Printed in Canada. All rights reserved.

Number and Operations CC3112

• recognize reasoning and proof as fundamental aspects of mathematics; • make and investigate mathematical conjectures; • develop and evaluate mathematical arguments and proofs; • select and use various types of reasoning and methods of proof.

• create and use representations to organize, record, and communicate mathematical ideas; • select, apply, and translate among mathematical representations to solve problems; • use representations to model and interpret physical, social, and mathematical phenomena.

• recognize and use connections among mathematical ideas; • understand how mathematical ideas interconnect and build on one another to produce a coherent whole; • recognize and apply mathematics in contexts outside of mathematics.

• organize and consolidate their mathematical thinking through communication; • communicate their mathematical thinking coherently and clearly to peers, teachers, and others; • analyze and evaluate the mathematical thinking and strategies of others; • use the language of mathematics to express mathematical ideas precisely.

• build new mathematical knowledge through problem solving; • solve problems that arise in mathematics and in other contexts; • apply and adapt a variety of appropriate strategies to solve problems; • monitor and reflect on the process of mathematical problem solving.

Instructional programs from prekindergarten through grade 12 should enable all students to:

Expectations

GOAL 1: Problem Solving

GOAL 5: Representation

2

GOAL 4: Connections

GOAL 3: Communication

GOAL 2: Reasoning & Proof



7

8

9 10 11 12 13 14 15

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

3 3 3

3 3 3

3 3 3



3 3 3

3 3 3 3 3 3 3 3 3 3 3 3

3 3 3 3 3 3 3

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

3 3

3 3 3 3 3 3 3 3 3 3 3 3

3 3 3 3 3 3 3 3 3 3 3 3

3 3 3 3 3

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3



3 3 3 3 3 3 3 3 3 3 3



3 3 3



3 3 3 3 3 3 3 3 3 3 3



3 3 3



3 3 3 3 3

3 3



3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

3 3 3

3 3 3

3 3 3 3 3 3 3 3 3 3

3 3 3

3 3 3

3 3

3 3 3 3 3 3 3 3

3 3 3

3 3 3

3 3 3 3 3

3 3

6

Drill Sheet 1

3 3 3 3 3

5

Drill Sheet 2

3 3 3 3 3 3 3

4

Review A

3 3 3 3 3 3 3 3 3 3 3 3

3

Review B

3 3 3 3 3 3 3

2

Review C

3 3 3 3 3 3 3 3 3 3 3 3

1

Exercise

Process Standards Rubric .................. Number and Operations

Number and Operations CC3112

Contents

.................. TEACHER GUIDE • NCTM Content Standards Assessment Rubric . ............................................ 4 • How Is Our Resource Organized? . ................................................................ 5 • The NCTM Principles & Standards................................................................ 6

STUDENT HANDOUTS • Exercises Task Sheet 1................................................................................................. 7 Task Sheet 2.................................................................................................... 8 Task Sheet 3.................................................................................................... 9 Task Sheet 4................................................................................................. 10 Task Sheet 5................................................................................................. 11 Task Sheet 6................................................................................................. 12 Task Sheet 7................................................................................................. 13 Task Sheet 8................................................................................................. 14 Task Sheet 9................................................................................................. 15 Task Sheet 10............................................................................................... 16 Task Sheet 11............................................................................................... 17 Task Sheet 12............................................................................................... 18 Task Sheet 13............................................................................................... 19 Task Sheet 14............................................................................................... 20 Task Sheet 15............................................................................................... 21

EZ

• Drill Sheets................................................................................................... 22 • Review......................................................................................................... 24 EASY MARKING™ ANSWER KEY . ........................................................... 27 MINI POSTERS .......................................................................................... 30

FREE!

4 6 BONUS Activity Pages! Additional worksheets for your students

NAME:

• Go to our website: www.classroomcompletepress.com/bonus • Enter item CC3112 • Enter pass code CC3112D for Activity Pages.

Student Worksheet

...................

Activity Six NAME:

Student Worksheet

6a) If A:B = 7:3 What is B if A is 35? ................... Answer: ______________

Activity Five NAME:

Student Worksheet

Activity Four NAME:

NAME:

Student Worksheet

i) 7 x

b) If C:D = 5:1 What is C if D is 5? Answer: ______________

d) If C:D = 6:2 What is C if D is 16?

If A:B = 1:11 What is B if A is 4?

b)

Answer: ______________

- 6 = 40 + 3

ii) 9 x 3 +

= 46 – 16

Answer: ______________

iii) 89 + 32 x e)= 11What are the reciprocals of the following fractions?

i) 3/5 ________ Sammy has a total of twenty toy trucks in his collection. Seven of them were red, three

ii) 9/10 ________

iii) 1/2 ________

Answer: ____________

worth by then?

c)

3a) Complete the following chart. ...................

Show your Work

Round the following to the nearest thousands. i) 64 237 ____________

ii) 3 672.12 ____________

i) 12/3 x 21/3 = ___

ii) 45/8 x 21/2 = ___

iii) 987 ____________

Activity Two

Answer: Decimal Percent Fraction d) Calculate the following. 0.75 30% ii) 3/4 / 2/3 = _______ iii) 5/8 / 3/8 = _______ i) 1/3 / 1/3 = _______ 2 /5 b) Two unknown numbers have a sum of 8 and a product of 15. What are the two numbers? car’s odometer reading. He is careful about traveling the whole way at about the0.85 same e) What number is missing from this pattern? 8, ___, 26, 35, 44 15% speed and makes only one 30 minute stop to stretch his legs and gas up. 1.25 Answer: __________ Time Reading (miles) Reading (kilometers) Answer: ____________ 9:00 am 12 344 19 866 g) What number does 2² x 5 x 3³ represent? b) Calculate the percent for each of the following. 1a) Jenna, Charmaine, Rhonda and Aubrey go shopping for the afternoon at the mall. c) Determine which of the following pairs of fractions is larger by including either > or or sign between each pair of fractions to indicate which is greater.



i) 5/8 __

c)

Replace each blank with the correct digit.



i) 21__ 341 + 8567 = 218908

d)

Mrs. Wormstead baked a batch of chocolate chip cookies. Each batch has a total of 15 cookies. Mrs. Wormstead’s son, Steadfast, came home and ate 1/3 of this batch. If she then baked three more batches, what is the total number of cookies that Mrs. Wormstead has?



i) 40

e)

Meredith finishes a race in 39.761 seconds. Her friend Amanda also ran in the same race. We know the following about Amanda’s results:



•

The number in the thousandths column is twice that of Meredith’s



•

The digit in the tens column was six more than Meredith’s



•

The number in the tenths column was five less than Meredith’s



What is Amanda’s time?



Answer =

f)

The following numbers are written in expanded form. Rewrite them in standard form.



i) 4 x 10³ + 3 x 10² + 5 x 10 =

©

/8

7

ii) 2/3 __

/8

5

ii) 55

iii) 1/3 __

/8

3

iv) 1/2 __

ii) 23.074 – 12.7__1 = 10.353

iii) 60

/8

5

v) 3/6 __

/7

3

iii) 9.2 x 6.__ = 58.88

iv) 45

ii) 7 x 10³ + 8 x 10² + 2 x 10 = 25

Number and Operations CC3112

NAME:

...................

Review C a)

Your dinner bill at a restaurant comes to $18.75. You decide to leave a 15% tip. What will be your total bill?

Show your Work Answer:

b)

Show each of the following fractions as a percent.



i) 4/25 =

c)

What is the least common multiple (LCM) of the following numbers.



i) 8 and 32 =

d)

7



i) 0

e)

Samantha works for a moving company. The following table shows her annual salary for the next five years.

ii) 2/9 =



iii) 17/19 =





ii) 15 and 45 =

/9 x 1/9 is closest to what integer? ii) 1

Year 1 2 3 4 5

iii) 7

iv) 2

Salary 28 000 30 600 33 200 35 800 38 400



If this continues, what will Samantha’s salary be by Year 9?



Answer =

©



26

Number and Operations CC3112

©

100

200

c)

300

400

500

7

175 [Various ways of arriving at this answer i.e. 2x – 150 = 200 2x = 200 + 150 x = 175

200

400

600

800

1000

1200

1400

b)

8

c) iii) 304,151,346

b) NO - The total of the other 9 countries is 1 056 318 541 – smaller than China’s population.

Germany 82,400,996 Egypt 80,264,543 Iran 65,397,521 Thailand 65,068,149 Canada 33,390,141

China 1,321,851,888 United States 301,139,947 Indonesia 234,693,997 Mexico 108,700,891 Vietnam 85,262,356

a)

a)

100 - $50 200 - $350 300 - $650 400 - $950 500 - $1250

2.

1.

9

9963 - 47643066

234 - 1118988

3107 - 14857674

3428 - 16392696

c) iv) 280 + 249 + 415 + 196 + 312 = 1452 / 5 = 290.4 hours

TOTAL i) $155.60

Monthly fee x 4 $104.00

February 280 hours $12.00 March 249 hours $7.35 April 415 hours $32.25 May 196 hours 0

b) i) 155.60

a) 112 x .15¢ = $16.80 + $26.00 = $42.80

3.

11

128 + 64=192 miles (206 + 103 = 309 kilometers)

d)

c) 6400

(.12 meters/hr)

b) 16 hours he only progresses 1/8 yd/hr.

a) 5 hours

5.

10

c) Large - $12.30 Medium - $10.70 Small - $7.95

b) 1 - .24 2 - .25 3 - .13

12

ii) 15 x .50¢ = $7.50

b) i) .25¢

iii) $27.60

ii) $21

i) $36

a)

a) Large – 48; Medium – 84; Small – 126

6.

4.

13

e) $38.99

d) iv) 3 phones, 4 planes

c) 80

b) 10

a) iii) 40%

7.

EZ

Number and Operations CC3112

©

14

d) Treadmill – 20%; Bicycle – 10%; Stepper – 25%; Elliptical – 15%; HypoCycloidal – 30%

c) 315 / 6 = 52.5 min.

b) 100 min.

a) Mean = 35.71 Median = 35 Mode = 40

8.

15

e) Answers will vary.

d) $18.50 + 32.50 = $51.00

c) Signing bonus is $2500. Amount per comic = $400 / 2000 = .20¢

b) i) $49.95

a) Beef 45; Shrimp 90; Chicken 180; Vegetarian 135.

9.

16

- $720.00

b) Bichon Frise $240.00 French Bulldog - $420.00 Irish Wolfhound

•The Bichon Frise came within her $1000 budget

$146.25 $1121.25

$135 $1035

a) $105 $805

10.

18

d) 18

c) 21

b) 5

Stephen – 18.8

a) Caleb – 19.6

12.

17

c) There are 36 flowers (3 dozen) - .75¢ x 3 = $2.25

iii) 40%

ii) 10%

b) i) E

$70.00 - $69.55 = .45¢

a) $65 x 1.07 = $69.55

11.

19

40.0 = 40.00

8/20 = .40

40%= .40

2/5 = .40

d) 40.0 is not equivalent -

c) 4/9 ~ halfway between 2/9 and 6/9

b) -26, -14, -12, -4, 2, 17, 121

a) 0.6, 67%. ¾, 2 ½, 2.7 – convert to decimals ~ .6, .67, .75, 2.5, 2.7

13.

20

d) $12.50 x 7.5 x 5.5 x 8 = $4125.00

8³ = 8 x 8 x 8 = 512 while 8 x 3 = 24

c) No.

b) $20.00 – [$2.50 x 5 = $12.50][ .95¢ x 4 = $3.80] = $3.70

a) iii) 8 feet (2.4 meters) Reduce by 20% with each bounce. 20 – 16 – 12.8 – 10.24 – 8.192

14.

EZ

Number and Operations CC3112

©

21

ii) 7.9%

c) i) 13

b) ii) 138 100 kilometers (85 811 miles)

88 856 (143 000km) Saturn 77 671 (125 000km) Uranus 31 752 (51 100km) Neptune 30 758 (49 500km) Earth 7 954 (12 800km) Venus 7 519 (12 100km) Mars 4 225 (6 800km) Mercury 3 045 (4 900km)

a) Jupiter

15.

v) 784 d) i) 282

iv) < d) 35321 668424.6 9802345

22

g) i) 978 764

f) iii) 1000

e) i) 1/5 ii) 1/3 iii) 2/15 iv) 9/10 v) 3/5

iv) 3375

iii)


c) i) 25

iii) 234.31

ii) 23 556

b) i) 989 100

iv) 42, 40, 38, 26, 34

ii) 144



a)

Drill Sheet 2

c) i) >

b) iv) 269

a) i) 10/15

Drill Sheet 1

24

d) i) 226 days

c) 2

b) Answers may vary.

a) Answers may vary.

Review A

25

f) i) 4,350 ii) 7,820

e) 45.262

d) ii) 55

c) i) 0 ii) 2 iii) 4

b) i) < ii) > iii) < iv) < v) >

a) mean = 344.71; mode = 125; median = 298

Review B

26

e) $48 800

a) i) 0

c) i) 32 ii) 45

iii) 89%

ii) 22%

b) i) 16%

a) $21.56

Review C

EZ

Number and Operations CC3112

©

1A

d) 310 m/hr (499 km/hr)

c) Answers will vary (i.e. 400 – 24 = 376)

b) Laurie – Bert – Ken – Shawn

a) Convert to decimals. Jenna has .40 left, Charmaine .30 left, Rhonda .28 left and Aubrey .35 left. Therefore Jenna has the most left.

1.

2A

d) $212.50 x 6 = $1275 + $375 + $408.25 = $2058.25

c) $678 - $240.00 = $438 / $36.50 = 12 hours.

b) 9+8+7+65+4+3+2+1 = 99

a) 75% ¾

a) Between noon and 1:00 p.m. [Then he travels only 33 miles (53 km), compared to 50+ miles (80 km.) at all other times.] /100 or 3/20

0.15

3A

c) $20.00 – 16.41 = $3.59

ii) 40%

b) i) 25%

125% 1 ¼

/100 or /20

15

85% 17

85

0.40 40%

0.30 3/10

3.

2.

4A

Barbara ~ 30/40

Charles ~ 32/40

e) Charles -

Mode = 12 iv) 49/56

5A

Median = 14

f) Mean = 17.6

e) 17

iii) 3/5

ii) 6/30

d) i) 12/21

iv) >

6A

g) 540

ii) 11 9/16 iii)
or < between the following pairs of fractions or decimals to indicate which is greater.

i)

ii)

iii)

d) Place each of the following numbers in order of size – from greatest to least.

e) State the mean, mode and median for the following five numbers.



Mean:



Mode:



Median:

©

30

Number and Operations CC3112

Percentages, Rounding, Ordering, Patterning .................. a) The owner of a local sports store has discounted every item in stock. Calculate the sale price for the following items. ITEM i)

A baseball glove

ii)

A bicycle

iii)

A hockey stick

RETAIL PRICE

DISCOUNT

$60

40%

$640

20%

$135.95

12.5%

SALE PRICE

iv)

b) Round off the following numbers to the nearest tenth. i)

ii)

iii)

c) List the following rational numbers in order from least to greatest (may include fractions and decimals).

d) What fraction is halfway between ______ and ______?

Answer:

e) One number in the following set is not equivalent to the others. Determine which number it is and explain why.

©

31

Number and Operations CC3112

Rounding, Ordering, Patterning, Fractions, Greater Than/Less Than .................. a) Round off the following numbers to the nearest hundredth. i)

ii)

iii)

b) List the following integers in order from least to greatest.

c) What is the number 10 000 before:

d) By which number is the pattern decreasing? ,

,

e) Reduce the following fractions to their simplest forms. i)

ii)

iii)

f) Circle either < or > to indicate which number is larger in each of the following pairs.

i)

©

< >

< >

ii)

32

iii)

< >

Number and Operations CC3112