A&A 6

Page 1

A&A

Maths English through Maths

6 HM Hison Josi Adu-mfum


PREISSMURPHY A&A

Education Group

PO Box 1529, Corvallis, OR, USA 97339 info@preissmurphy.com Text © HM Hison Josi adu-mfum PREISS MURPHY and PREISS MURPHY SCHOOL PUBLISHERS are trademarks of Preiss Murphy A&A Education Group. Database rights Preiss Murphy A&A Education Group (maker). First published 2019 2019 2020 2021 2022 2023 ISBN 978-9-95737-645-1

No unauthorized copying Report all violations immediately, in confidence, to the Publisher. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, without the prior permission in writing of Preiss Murphy A&A Education Group, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Inquiries concerning reproduction outside the scope of the above should be sent to the ELT Rights Department, Preiss Murphy A&A Education Group, at the address above. It is not permitted to circulate this book in any other binding or cover and you must impose this same condition on any acquirer.

ANY PERSON VIOLATING THESE COPYRIGHT RESTRICTIONS WILL BE PROSECUTED TO THE MAXIMUM EXTENT OF THE LAW AND MAY BE LIABLE FOR DAMAGES.

Requests for permission to make copies of any part of the work should be addressed to school permissions and copyrights at Preiss Murphy A&A Education Group. If you have received these materials as examination copies free of charge, Preiss Murphy A&A Education Group retains title to the materials, and they may not be resold. Resale of examination copies is strictly prohibited and is illegal. Possession of this publication in print format does not entitle users to convert this publication, or any portion of it, into electronic format.

Contents

6A Integers, Patterns and Estimating Numbers Expanded Notation Place Value Patterns Rounding and Estimating Integers Integer Subtracting Regrouping With Two-Digit Addition Regrouping With Three-Digit Addition Regrouping With Subtraction

5 6 7 8 9 10 11 12 13 14

6B Multiplication and Division Multiplying by a Two-Digit Number Regrouping With Three-Digit Multiplication Three-Digit Multiplication Three-Digit Multiplication With Regrouping Tens Power Quotients With Zeros Division Problems Three-Digit Divisor ‘X-ing’ Out Zeros Dividing Decimals Number Facts Word Problems Multiplication or Division? What Sign Is It? Signs Order of Operations Operation Two Ways About It! Let’s Get Tricky!

15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 31 32 33 34

6C Geometric Finished with this book? Save it to reread in the future or pass it along to a friend, classroom, library, or business with a waiting room. If it’s too worn to be read anymore, please recycle it.

Figures Perimeter Area Volume Angles Find the Angle! Quadrilaterals 3D Shapes Review

35 36 37 38 39 40 41 42 43


Contents

6A 6A Numbers

A place value is the value of where a digit is located in a number. The numbers to the left of the decimal point are whole numbers. The numbers to the right of the decimal point are parts of a whole number.

6D Fractions and Decimals

Shaded Fractions Greatest Common Factor Simplifying Fractions Mixed Numbers and Improper Fractions Decimals and Fractions Fraction Addition Fraction Subtraction Fraction Multiplication Equivalent Fractions Ratios Decimals Adding and Subtracting Decimals Multiplying Decimals Percentages Data

48 49 50 51 52 53 54 55 56 57 58 59 60 61 62

6E Units of Measurements

Length (Customary Units) Length (Metric Units) Weight (Customary Units) Units of Capacity Capacity (Metric Units) Thermometers and Temperatures Not Enough or Too Much?

63 64 65 66 67 68 69

6F Graphs

Data Graphs Tables Pie Graphs Plot Graphs Venn Diagrams Probability Review

Integers, Patterns and Estimating

70 71 72 73 74 75 76

Example: millions

hundred thousands

5

9

ten thousands

thousands

hundreds

tens

ones

tenths

hundredths

2

1

7

9

3

5

7

whole numbers decimal point Write out the words as numbers. 1 . five million, three hundred thousand, four hundred and fifteen _____________________________________________________________ 2. six million, one thousand and eighty-six _____________________________________________________________ 3. three million, three hundred thousand and seven _____________________________________________________________ 4. eight million, nine hundred and seventy five thousand and nine hundred and forty-nine _____________________________________________________________ 5. two hundred thousand, four hundred and sixty-five and three-tenths _____________________________________________________________ Circle the correct number for each place value. 1. millions 3, 6 52, 1 8 7 2. hundreds

5, 6 7 8, 90 1

3. thousands

6, 9 1 2, 1 1 5. 2 7

4. hundredths

1 3 6, 6 3 1 .9 8

5. hundred thousands

4 68, 0 1 2. 1 2

6. tens

1, 2 3 5, 7 9 0.8 5

7. tenths

4, 4 5 4, 3 5 4.8 9

55


6A Expanded Notation Expanded notation is writing the value of each digit in a number. The sum of each digit is shown multiplied by its matching place value.

6A Place Value Solve each problem. Colour the boxes that match one of the answers below. Colour each box the same colour as the answer's bubble.

Example: seven million, six hundred and fifty thousand, two hundred and eighteen 7,6 5 50,218 0,2 18 = 7 x 1 ,,000,000 000,000 + 6 x 100, 000 + 5 x 10, 000 + 2 x 100 + 1 0 x 1 + 8 x 1

1,7 5 9 657 + 48

75 1,9 0 7 + 783

918 69 + 3,5 7 9

9,6 3 1 9, 9 1 8 46 +

4, 9 7 8 843 + 46

8 7,9 8 7 + 5 69

1,5 3 2 567 + 55

5,4 3 4 4,9 3 4 + 1 14

9,4 3 4 582 + 4 69

97 367 + 6, 1 4 6

5 50 35 + 2,9 7 8

852 31 + 1 46

2 06 46 + 7, 8 9 6

18 6, 5 2 3 + 9, 4 6 5

5,6 8 7 979 + 9,4 3 6

789 191 + 2,6 9 8

6,9 9 6 26 + 96

34 63 + 1,0 0 3

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

3 05 3,4 7 9 + 949

Write each number in expanded notation form. 1 . 9, 673, 4 2 1

_______________________________________________

___________________________________________________________ 2.4, 53 3, 2 1 0

_______________________________________________

___________________________________________________________ 3.6, 9 1 4,7 1 4

_______________________________________________

___________________________________________________________ 4.3, 456,1 2 3

_______________________________________________

___________________________________________________________ Write as numbers. 1. 5 x 1,000,000 + 3 x 100,000 + 2 x 10,000 + 5 x 1,000 + 6 x 100 + 3 x 10 + 5 x 1 ________________________________________________________________ 2. 2 x 1,000,000 + 9 x 100,000 + 4 x 10,000 + 9 x 1,000 + 7 x 100 + 1 x 10 + 4 x 1

1,1 0 0

________________________________________________________________

1 6,0 06

3. 3 x 1,000,000 + 5 x 100,000 + 3 x 10,000 + 3 x 1,000 + 3 x 100 + 3 x 10 + 3 x 1 ________________________________________________________________ 4. 6 x 1,000,000 + 0 x 100,000 + 0 x 10,000 + 1 x 1,000 + 8 x 100 + 5 x 10 + 6 x 1 ________________________________________________________________

66

2,1 5 4

10,4 8 5

4,7 3 3

3 ,5 63 5,8 67

1 0,4 8 2

2 ,76 5

77


6A Patterns

6A Rounding and Estimating

Patterns are things that are arranged following a rule or rules.

Example:

Find the missing number and state the pattern used.

900 3 00 100 Divide each number by 3 to get the next number. The answer is 1 00. Write the missing number in each sequence. State the rule that was used. 1 . 7, 2 1, 6 3 , _______

___________________________________

2 . 3, 6, 9, 1 2 , _______

___________________________________

3 . 7, 1 2, 1 6 , 1 9 , _______

___________________________________

4 . 1 5, 3 0, 6 0, _______

___________________________________

Solve the pattern in the first two grids. Use the same pattern to complete the last grid. 36

6

6

64

16

4

2

1

2

16

8

2

18

6

3

4

2

2

27

To round a number is to make a number simpler, but keeping it close to its original value. We round off numbers to the nearest ten, hundred, thousand and so on. Follow these steps: 1 ) Decide what place value you want to round off to. 2) Increase by one if the next digit is 5 or more. 3) Leave it the same if the next digit is less than 5. We can then calculate approximately with the rounded numbers. This is called estimating.

Example:

7 6 9 rounded to the nearest hundred is 8 0 0. 7 2 3 rounded to the nearest hundred is 7 0 0. 3 6, 8 4 1 rounded to the nearest thousand is 3 7,0 0 0. 3 6, 4 9 3 rounded to the nearest thousand is 36,0 0 0.

Example:

A toy car that costs €9.3 9 and a teddy bear that cost €1 1. 2 9 total about €20. 70 (€ 9.4 0 plus €1 1. 3 0 ).

Round and estimate to find the answers. Show your work. 1 . Steve is having a birthday party and wants to fill 2 1 jugs from a 1 0 0 litre tank of water. Around how many litres should he pour into each jug?

3 3

9

This is a Pascal triangle. Find the pattern to fill in the bottom row. 1 1 2 1 1 3 3 1 1 4 6 4 1 1 __ __ __ __ 1 These are Sierpinski triangles. How many green triangles will be in the next triangle in the pattern?

2 . Walter played 4 3 minutes every day for 7 days. Around how long did he play for? 3 . About how much does this lunch cost? slice of pizza €2.5 9

side salad €1. 4 9

drink €1.4 5

4 . One car at the lot weighs 2,963 pounds and the other weighs 3, 3 9 3 pounds. Around how much heavier is the second car than the first car?

88

99


6A Integers

6A Integer Subtracting

An integer is a whole number with no fractional part. These include counting numbers ( 1, 2, 3), 0 and negative numbers (-1, -2, -3 ). Opposite integers are two integers that are the same distance from 0 in different directions (+2, -2). A pair of positive and negative integers are called opposite integers.

- 10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 negative numbers

Example:

(+7) - (- 8) = (+7) + (+8) = + 1 5 (+4) - (+3) = (+4) + (-3) = + 1 (- 9 ) - (- 1 2) = (- 9 ) + (+ 1 2) = +3 (+5) - (+ 8) = (+5 ) + (-8) = - 3

0

1

2 3

origin

4 5 6 7

8 9 10

positive numbers

Complete. 1 . Write each problem as an integer. a. positive 9 = ________

b . losing â‚Ź1,0 0 0 = ________

c . 1 1 degrees below 0 = ________

d . gaining 3 0 pounds = ________

2 . Write the opposite integer. a. positive 6 9 = ________ b. negative 3 0 = ________ c . 1 5 degrees below 0 = ________ d. losing a basketball game by 3 5 points = ________ 3 . Write integers to express each idea. a. a kite string is 5 inches too short = ________ b. winning a football game by 1 point = ________ c . a table that is 7 inches too long = ________ d. a present that has 5 fewer items than it should = ________

10 10

When subtracting a negative integer, change it into a positive and add. When subtracting a positive integer, change it into a negative and add.

Rewrite each problem first, then solve. -1 2 - (- 9 ) = _________ - 8 + (- 5 ) = _________ 4 - (- 2 ) = _________

1 1 - (- 8 ) = _________ - 1 7 - (- 1 9 ) = _________ - 1 1 - (+ 6 ) = _________

a. In Mexico, the highest temperature was +1 1 3 degrees. The lowest temperature was +7 3 degrees. What is the difference between the two temperatures? ___________________________________ b. At Steven’s apartment one night, the thermometer read +1 degrees. The weather forecast said it was -5 degrees. What is the difference between the two temperatures? ___________________________________ c. What is the difference between a wind chill factor of -19 degrees and a temperature of +7 degrees? ___________________________________ d. During a drought, the lake's water level dropped from 8 feet above normal to 2 1 feet below normal. How many feet did it drop? ___________________________________ e. These are the average temperatures in John’s freezer for three days: -6 , -1 2 and -9 . What is the difference between the highest and lowest temperature? ___________________________________

11 11


6A Regrouping With Two-Digit Addition

6A Regrouping With Three-Digit Addition

Example:

Example: Add the ones.

If needed, regroup.

96 +7 9 5

Add the tens.

1

1

96 + 79 5

96 + 79 1 75

Add the tens.

1

337 + 893 0

Add the hundreds.

1 1

1 1

337 + 893 30

337 + 893 1, 2 3 0

Add. If necessary, regroup.

Add. If necessary, regroup.

12 12

Add the ones.

47 + 38

65 + 39

20 + 35

81 + 67

19 + 18

739 + 605

857 + 983

4 52 + 767

59 + 85

97 +2 7

85 + 26

18 + 81

8 + 47

818 + 209

213 + 510

687 + 777

9 + 69

83 + 98

330 + 787

56 1 + 583

666 + 555

55 + 35

49 + 6

28 + 57

74 + 29

803 + 9 69

487 + 1 87

909 + 4 09

3 05 + 949

559 +71 4

7 00 + 9 69

444 + 888

13 13


6A Regrouping With Subtraction

6B

Example: Regroup the ones column. 2

7,9 3 1 5 - 5,9 86

Multiplication and Division

6B Multiplying by a Two-Digit Number

Subtract the ones. 2

7,9 3 1 5 - 5,9 86 9

Regroup and subtract the tens. 8 12

7,9 3 1 5 - 5,9 86 49

Regroup and subtract the hundreds.

Subtract the thousands.

6 1 8 12

6 1 8 12

7,9 3 1 5 - 5,9 86 949

7,9 3 15 - 5,9 86 1 ,94 9

Example: Multiply by the tens place. Place a 0 in the ones column.

Multiply each digit by the ones place.

3, 5 6 9 32 x 7 1 38 1 07070

3,5 6 9 32 x 7 1 38

Subtract. If necessary, regroup.

Add. 3, 5 6 9 32 x 7 1 38 +1 0 7 0 7 0 1 1 4, 2 0 8

Match column A with column B. 8, 763 - 5,9 5 6

1,9 8 7 - 1 ,79 8

8,9 3 6 - 3,8 5 7

5,8 2 1 - 4 ,9 52

6,3 0 5 - 3 ,3 0 0 A

9,0 3 3 - 7,54 9

2,4 3 8 - 1 ,5 75

5,9 4 3 - 4,76 5

8,3 25 - 4,08 7

9,9 2 6 - 6,7 5 9

1.

1 2x24

a.

9, 4 4 4

2.

409x 1 5

b.

3, 2 6 7

3.

787x 1 2

c.

559

4.

99x3 3

5.

3 33x52

6. 4, 1 7 9 x 8 5

d. 1 4 8, 2 6 0 e.

1,2 2 1

f. 3 5 5, 2 1 5

43x 1 3

g.

288

8. 2,4 7 1 x 6 0

h.

4, 7 6 1

7.

14 14

B

9.

1 1 1 x1 1

i.

1 7, 3 1 6

1 0.

69x69

j.

6, 1 3 5

15 15


Turn static files into dynamic content formats.

Create a flipbook
Issuu converts static files into: digital portfolios, online yearbooks, online catalogs, digital photo albums and more. Sign up and create your flipbook.