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
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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