A&A
Maths English through Maths
4 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 978-9-95737-511-9
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Contents
4A Rounding, Angles and Graphing Place Value Place Value: Expanded Notation and Standard Form Rounding: Tens Rounding: Hundreds and Thousands Rounding Time Problems Geometry: Polygons Angles Probability Ratios Finding Ordered Pairs on Graphs Graphs
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4B Adding, Subtracting and Estimating
Addition Adding Larger Numbers Subtraction Subtraction: Regrouping Addition and Subtraction Estimating 4C Multi-Digit Multiplication and Division Multiplication and Division Fact Factory Multiplication Multiplication: Two-Digit Numbers Times Two-Digit Numbers Multiplication: Three-Digit Numbers Division Division Facts Two-Digit Quotients Division Facts Division: Checking the Answers Division Facts Division: Checking the Answers Averaging Guess the Sign! Review
18 20 21 22 23 24 25 26 27 30 31 32 33 34 35 36 37 38 39 40 41
Contents
4A 4A Place Value
4D Measurements
Centimetres and Millimetres Find the Fractions of an Inch Find the Nearest
1 2
Inch
Measurements: Foot, Yard and Mile Metric Measurements: Centimetre,Metre and Kilometre Units of Length Perimeter Measurements: Perimeter and Area Volume Measurements: Ounce, Pound and Ton Metric Measurements: Gram and Kilogram
46 47 48 49 50 51 52 53 54 56 57
4E Fractions
Fractions Fractions: Addition Fractions Fractions: Subtraction Reducing Fractions Adding Mixed Numbers Fractions: Probability Fractions to Decimals Decimals
58 60 61 62 63 64 65 66 68
4F Money for Real!
Money Clothing Shop Multiplying Money Money Maths Too Much Information Perplexing Problems Review
Rounding, Angles and Graphing
69 71 72 73 74 75 76
Look at each number. Write the place value for the red digit in the blank. Place value is the actual value of a digit, or numeral, depending on where it is in a number. For example, in 2,34 1 ,69 0 , '2' has the place value of millions, '3' is hundred thousands, '4 ' is ten thousands, '1 ' is thousands, '6 ' is hundreds, '9 ' is tens and '0' is ones. 54 ,231 ___________ hundreds place 6 9 2,340 ___________ place 7,39 8 ___________ place 44 ,08 7 ___________ place 5,674 ,339 ___________ place 8 82,1 7 5 ___________ place 34 ,76 2 ___________ place 1 2 7,8 6 3 ___________ place 7,9 8 9 ,02 4 ___________ place 34 7,8 1 1 ___________ place Write the correct number. 1 ,9 42 3,385 101,694 5 24,665
is in the ones place is in the thousands place is in the ten thousands place is in the hundreds place
2,25 0,45 6
is in the tens place
8 ,734 ,022
is in the hundred thousands place
6, 8 8 8,5 3 1
is in the millions place
55
4A Place Value Read each place value description. Write the number. 1. Six is in the hundreds place, 5 is in the ones place, 8 is in the thousands place, 7 is in the millions place, 0 is in the tens place, 1 is in the ten thousands place and 9 is in the hundred thousands place. ______________________________________________ 2. Five is in the tens place, 3 is in the hundred thousands place, 2 is in
4A Place Value: Expanded Notation and Standard Form Write each number in standard form and as expanded notation.
Example: thousands hundreds
6
3
tens
ones
5
7
______________________________________________
thousands hundreds
4
2
tens
ones
5
9
3. One is in the ten thousands places, 2 is in the tens place, 8 is in the hundreds place, 9 is in the millions and ones places, 5 is in the hundred thousands place and 4 is in the thousands place. ______________________________________________ 4. Six is in the thousands and millions places, 0 is in the ten thousands place, 3 is in the tens place, 8 is in the hundred thousands place, 4 is in the ones place and 5 is in the hundreds place. ____________________________________________ 5. Seven is in the tens place, 0 is in the hundred thousands place, 6 is in the ones place, 2 is in the millions place, 4 is in the thousands place, 8 is in the hundreds place and 3 is in the ten thousands place.
Expanded Notation 6 ,000 + 300 + 5 0 + 7
the millions place, 0 is in the ones and ten thousands places, 7 is in the hundreds place and 9 is in the thousands place.
Standard Form 6 , 35 7
Standard Form Expanded Notation
ten thousands thousands hundreds
7
7
8
tens
ones
4
3
Standard Form Expanded Notation ten hundred thousands thousands thousands hundreds
9
2
5
tens
ones
7
4
3
Standard Form Expanded Notation
________________________________________________ Colour the tens place red, the ten thousands place green, the hundreds place yellow, the ones place blue, the millions place purple, the hundred thousands place black and the thousands place brown.
Write the expanded notation. 630,1 8 8 75 2 3,362 ,5 1 2
66
77
4A Rounding: Tens
4A Rounding: Hundreds and Thousands
Round each number to the nearest ten.
Round these numbers to the nearest hundred.
When rounding a number to the nearest ten, look at the key digit in the ones place. If the ones digit is 5 or more, round up to the nearest ten. If the ones digit is 4 or less, round down to the nearest ten.
22
32 3
478
46 134
69
57 1 3 57 36
75
53 28 6 44
29 17 58
24
99 73
12 52
88
39
Example: Round 78 4 to the nearest hundred. The key digit is 8. It is more than 5, so round up. Answer: 8 0 0
Round 534 to the nearest hundred. The key digit is 3. It is less than 5, so round down. Answer: 5 0 0 426
233
1 08
111
8 62
5 72
793
65 4
956
Round these numbers to the nearest thousand. When rounding to the nearest thousand, look at the key digit in the hundreds place. If the hundreds digit is 5 or more, round up to the nearest thousand. If the hundreds digit is 4 or less, round down to the nearest thousand.
81
33
When rounding to the nearest hundred, look at the key digit in the tens place. If the tens digit is 5 or more, round up to the nearest hundred. If the tens digit is 4 or less, round down to the nearest hundred.
67
Example: Round 6 ,843 to the nearest thousand. The key digit is 8. It is more than 5, so round up. Answer: 7,0 0 0
Round 2,29 7 to the nearest thousand. The key digit is 2. It is less than 4, so round down. Answer: 2,0 0 0
5,7 04
6, 1 2 4
557
77 7
2, 5 1 8
3,2 73
3 ,9 1 1
3, 058
87,6 44
99
4A Rounding
4A Time Problems
Round these numbers to the nearest ten.
26 51
66
43
35
19
38 49
Draw the hands on the clocks to show the starting time and the ending time. Then write the answer to the question.
1 The bike race started at 1 :4 5 p.m. and lasted 3 hours and 20 minutes. What time did the race end?
Round these numbers to the nearest hundred.
315
3 93
20 7
156
722
4 56
1 57
8 42
259
181
664
73 1
Round these numbers to the nearest thousand. 1 , 429
2, 8 8 8
3 , 523
5, 1 78
3, 6 0 7
2, 8 1 2
9 , 599
4 , 58 3
3,9 4 0
5, 300
9 , 7 46
1,9 0 1
Round these numbers to the nearest ten thousand.
10 10
4 8 , 736
25, 6 7 8
3 1 ,6 4 1
82, 5 7 3
36 , 3 1 2
1 0 , 4 32
5 5, 804
7 6 , 4 24
2 The 3 60 -mile boat race started at 9 :3 0 a.m. and lasted 2 hours and 45 minutes. What time did the race end?
3 The train left Waterloo at 6 :3 0 a.m. and arrived in Basingstoke at 11 :5 5 a.m. How long did the trip take?
4 Linda walked in the 14 -mile Charity Walk. She started at 1 1 :3 0 a.m. and finished at 5 :20 p.m. How long did she walk?
5 The steakpie cook-off started at 9 :0 0 a.m. All the pies were cooked by 3 :25 p.m. How long did it take to cook them?
6 The steakpie judging began at 5 :3 0 p.m. After 3 hours and 15 minutes the pies had all been eaten. At what time did the pie judging finish? _________________________________
11 11
4A Geometry: Polygons
4A Angles
A polygon is a closed shape with three or more sides.
Identify whether angles are right, acute or obtuse. An angle is the point where two line segments meet.
A triangle has 3 sides.
A rectangle has 4 sides.
A hexagon has 6 sides.
When two lines meet at 9 0°, they form a right angle.
A square has 4 equal sides.
A pentagon has 5 sides.
Look and identify the polygons below.
An octagon has 8 sides.
When two lines meet at less than 9 0°, they form an acute angle.
When two lines meet at more than 90°, they form an obtuse angle.
To measure an angle, use a protractor. Place the protractor at the bottom edge of the angle, and then align it in the centre to measure the angle. Identify whether angles are right, acute or obtuse.
right angle
acute angle
obtuse angle.
Look at these shapes and write the name of the angle that has been circled.
12 12
13 13
4A Probability Solve the problems. Probability shows how likely something is to happen. It can be written as a ratio or a fraction. When written as a ratio, such as 4:8, this means 4 is how many times something particular is likely to happen and 8 is the total amount of possibilities. The probability of picking a queen from a pack of cards is 4:5 2 because there are 5 2 cards in a pack and it only contains 4 queen cards. Look at this coloured square with 16 parts and answer the following questions below. 1. What is the probability of choosing a red square? _______________________________________
4A Ratios Look at each set of boxes and answer the questions using the figure on the right. A ratio shows the sizes of two or more numbers when compared to each other. For example, if there were 5 boys and 7 girls in a class, we would say the ratio of boys to girls is 5:7. We could also say that the ratio of girls to boys is 7:5. ratio of orange to red ratio of green to blue ratio of red to green
____________ ____________ ____________
ratio of red to yellow ratio of green to red ratio of yellow to blue
____________ ____________ ____________
ratio of red to yellow ratio of green to red ratio of yellow to blue
____________ ____________ ____________
ratio of red to orange ratio of purple to green ratio of blue to yellow
____________ ____________ ____________
2. What is the probability of choosing a green square? _______________________________________
3. Which coloured square has the lowest probability? Write the ratio. _______________________________________ 4. A box has 6 bananas, 3 apples, 1 2 strawberries and 7 peaches. What is the possibility of taking? a. a banana? _____________________ b. a strawberry? ___________________ c. an apple or a peach? ___________________
14 14
15 15
4A Finding Ordered Pairs on Graphs
4A Graphs
Write the ordered pair for the following shapes. Identify the shapes and its colour located at the following points. The first one has been done. Graphs and grids can be used to find where an object is.
Answer the questions by reading the graphs. A graph is a picture that shows data or information about numbers. How many books did the shop sell in August? ___________________________
Example: Look at the objects on the graph. The blue star is located at point (2,4) on the graph. To find the ordered pairs for the blue star on the graph, follow the line from the blue star downwards to the bottom of the graph first, which is ‘2’ (the first number). Then follow the line from the blue star to the left of the graph until you get to ‘4’ (the second number). ( 2,4 ) _________ red triangle _________ green star
blue star
_________
purple star _________ brown star _________ blue triangle _________ 10 ( 6,8 ) ____________ red star
9 8
200
( 6,2 ) ____________
6
( 1,9 ) ____________
5
150 125 100
In which month did they sell the least books? ___________________________
75 50 25 0 May
June
July
August September
Pens Sold by Days of The Week 90
How many books did the shop sell over all 5 months? ___________________________ How many pens did the store sell on Tuesday and Friday? ___________________________
75 60
4
( 6,6 ) ____________
3 ( 9,5 ) ____________
2
On what days did the shop sell the least pens? ___________________________
45 30 15
1
0 0
16 16
In which month did the shop sell the most books? How many did they sell? ___________________________
175
( 4,7 ) ____________
7
Books Sold by Month
1
2
3
4
5
6
7
8
9
10
M
T
W
TH
F
S
SU
What is the difference between the number of pens sold on Friday and Sunday? ___________________________
17 17