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Contents Number 1 Whole numbers 1
1
2 Whole numbers 2
9
3 Decimals 1
13
4 Decimals 2
17
5 Fractions
21
6 Percentages
25
7 Ratio and proportion
29
8 Addition and subtraction 1
33
9 Addition and subtraction 2
37
10 Addition and subtraction 3
45
11 Multiplication and division 1
49
12 Multiplication and division 2
57
13 Multiplication and division 3
65
Geometry 14 2D shape, including symmetry
73
15 3D shape
77
16 Angles
81
17 Position and movement
85
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Measure 18 Length
93
19 Mass
97
20 Capacity
101
21 Time
105
22 Area and perimeter
109
Handling data 23 Handling data
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Unit
1
Lesson 1: Counting on and back (1)
Whole numbers 1
Key words
• step • sequence • count on • count back
• Count on and back in steps of equal size
Discover
Number
Workbook page 2
Counting forwards and backwards in steps helps you understand the pattern and sequence of number.
137
+
4
+
+
4
4
Learn You can use a number line to explore forwards and backwards counting sequences. You can start at any point on the line and count on or back in whole numbers or decimals. Count forward in 1s 0
1
2
3
4
5
6
7
8
Count backwards in 2s 9 10 11 12 13 14 15 16 17 18 19 20
Example Count back from 43 in steps of 3. Is 28 in this sequence?
22
25
28
31
34
37
40
43
Put your finger on 43 and count back in 3s: 43, 40, 37, 34, 31, 28, 25, 22....yes, 28 is part of this sequence. 1
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Unit
1
Whole numbers 1
Workbook page 4
Lesson 2: Number sequences Number
• Describe number sequences and find the rule
Discover
Key words
• step • rule • sequence • value • term • common d ifference
The black keys on the piano are arranged in a sequence, 3, 2, 3, 2 … .
Learn A sequence is an ordered list of numbers called terms. Each term has a value. Every sequence has a rule. Once you know the rule, you can work out the next term in the sequence. A sequence is enclosed within curly brackets.
Use a comma to separate each term.
1st term
{ 2 , 4 , 6 , 8 , 10 , 12 , … } The three dots mean the sequence continues.
3rd term
2nd term
Example There are eight terms in this sequence. 2
9 +7
16 +7
23 +7
30 +7
37 +7
44 +7
51 +7
The values in the sequence are {2, 9, 16, 23, …} The rule is ‘add 7’. 2
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Unit
Workbook page 6
Lesson 3: Place value (1)
1
Whole numbers 1
• place value • digit • hundred th ousands • ten thousa nds
• Know what each digit represents in a five- or six-digit number
Discover
Place value helps you understand the value of a digit in a number.
Number
Key words
21 409 g or 21 940 g
Learn The value of a digit depends on its place, or position, in the number. Each place has a value of 10 times the place to its right.
Example
tens
units
× 10
hundreds
× 10
thousands
× 10
ten thousands
× 10
hundred thousands
Value of 3 digit: 300 000 (three hundred thousands)
× 10
3
0
7
4
8
2
Value of 0 digit: 0 (zero ten thousands)
Value of 7 digit: 7000 (seven thousands) 3
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Unit
1
Whole numbers 1
Workbook page 8
Lesson 4: Place value (2)
Key words
Number
• place value • digit • partition
• Use place value to partition any number up to one million
Discover Knowing the value of each of the digits in a number is very important, because adding and subtracting often need you to exchange one value for another.
tens
units
tens
units
30
4
20
14
34 can be expressed as 2 tens (20) and 14 units.
Learn To exchange one value for another it is important to know how to split a number into thousands, hundreds, tens and units. This 6-digit number has been partitioned into its separate place values. 634 129 = 600 000 + 30 000 + 4000 + 100 + 20 + 9
Example Arrow cards can be used to show how numbers can be split into separate place values, then recombined. 438 129 = 400 000 + 30 000 + 8000 + 100 + 20 + 9 4 0 3 0 8 1 0 0 2 0 9
4 0 0 0 0 0 3 0 0 0 0 1 0 0
8 0 0 0 2 0
9
4
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Unit
1
Lesson 5: Multiplying and dividing by 10 or 100
Whole numbers 1
Key words
• place value • multiply • divide
• Multiply and divide whole numbers by 10 or 100
Discover
Number
Workbook page 10
Multiplying and dividing by 10 or 100 can help you to convert metric measurements and find percentages.
×10
×100
mm
cm
÷10
m
÷100
Learn Multiply by 10: Move all digits one place value to the left. Multiply by 100: Move all digits two place values to the left.
Example HTh TTh
2
2 5
Divide by 10: Divide by 100:
Th 2 5 3
H 5 3 8
T 3 8 0
U 8 0 0
× 10 × 100
Move all digits one place value to the right. Move all digits two place values to the right.
Example HTh TTh
Th 7
H 5 7
T 0 5 7
U 0 0 5
÷ 10 ÷ 100 5
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Unit
1
Whole numbers 1
Workbook page 12
Lesson 6: Rounding
Key words
Number
• round • rounding d igit • nearest 10 • nearest 10 0 • nearest 10 00
• Round 4-digit numbers to the nearest 10, 100 or 1000
Discover The exact number of fans at a football match was 56 327, but the newspaper says there were 56 330. They have rounded the number to the nearest 10.
Match Report
Attendance: 56 330
Learn
To round If the digit is: a number, • 5 or greater, round up look at the digit to the right of the place • less than 5, the whole number position you are remains the same. rounding to. Include place holder zeros as needed.
Example Round 3862 to the nearest hundred. 3862 is between 3800 and 3900. 3862 3800
3900
Look at the number to right of the 8, which is 6. 6 is greater than 5, so round up to 3900. Replace the rest of the digits with placeholder zeros. 6
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Unit
Workbook page 14
1
Whole numbers 1
Lesson 7: Comparing and ordering • Use the > and < signs to order and compare numbers up to a million
Discover Place value can help you to put large numbers in order. The diameter of Earth, Uranus and Neptune can be put in order by looking at the ten thousands place.
Number
Key words
• place value • digit • thousands • hundreds • tens • units
Earth 12 756 km < Neptune 49 528 km < Uranus 51 118 km.
Venus Mercury
Mars Earth
Uranus Jupiter
Neptune
Saturn
Learn
We can compare whole numbers with the same number of digits.
• Compare digits in each place position, starting on the left. • If the left-most digit is the same, compare digits in the next place to right. • When two numbers have different digits in the same place, the number containing the larger digit is the larger number.
Example HTh TTh
4 3 4
Th
H
T
U
5 7 7
1 8 3
3 9 5
7 8 2
47 352 > 45 137 > 37 898
37 898 is the smallest number; then comparing the next digit (thousand place) 47 352 is the larger number. 7
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Unit
1
Whole numbers 1
Workbook page 16
Lesson 8: Odds, evens and multiples (1) Number
• Recognise odd and even numbers and multiples of 5, 10, 25, 50 and 100
Discover
Key words
• odd • even • multiple
The door numbers on the blue doors are multiples of 25 but not 50.
125
175
150
110
Learn Numbers with 00, 25, 50 or 75 in the tens and units positions are multiples of 25. Numbers with 00 or 50 in the tens and units positions are multiples of 50. Numbers which end in 1, 3, 5, 7 or 9 are odd numbers. 50
25 00
multiples of 25
50
00
multiples of 50
75
Example Which of the following numbers are multiples of 25 but not 50: 200, 650, 2275, 4300, 6625? Multiples of both 25 and 50 have 00 or 50 in the tens and unit positions. Multiples of 50 but not 25 have 25 or 75 in the tens and unit positions. So, only 2275 and 6625 are multiples of 25 but not 50. 8
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2
Unit
Workbook page 18
Lesson 1: Whole numbers
°C
We use negative numbers to describe a value on a scale that goes below zero. The temperature on this thermometer reads −5 °C.
• negative n umber • positive nu mber • step • sequence • count on • count back
Number
Key words
• Describe and continue number sequences, including negative numbers
Discover
Whole numbers 2
30
20
10
0
–5°C –10
How do temperature and money both use negative numbers?
Learn Positive numbers are greater than zero. Negative numbers are less than zero.
–10
–6
–2
0
2
6
10
Count back from 10 in steps of 4. Is −4 in this sequence? Place your finger on 10 and count back in 4s to check. 9
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2
Unit
Whole numbers 2
Workbook page 20
Number
Lesson 2: Positive and negative numbers
Key words
• negative n umber • positive nu mber • order • thermomete r • temperature • degrees Ce lsius (°C)
• Order and compare negative and positive numbers on a number line and temperature scale
Discover In golf, the player with the lowest score wins. Sometimes it can be a negative score. Position Name Score 1st Jason –5 Day 2nd Jordan –3 Spieth 3rd Rory –1 McIlroy 2 4th Bubba Watson 4 5th Louis Oothuizen
Learn Writing numbers on a number line makes it easier to order positive and negative numbers. Numbers on the left are smaller than numbers on the right. Numbers on the right are greater than numbers on the left.
Example –14
–3
–15 –14 –13 –12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1
2 0
1
2
8 3
4
5
6
7
8
9
10
Placing numbers on the number line shows that: −14 < −3 < 2 < 8 10
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