3D Shape Families
•	Quadrilaterals all have 4 sides (square, rectangle, rhombus, parallelogram, trapezium).
•	Prisms are like an elongated shape or a cylinder with edges, such as a hexagonal prism with hexagons on each end.
•	Pyramids all have a base with the sides meeting at one point, such as a square-based pyramid or an octagonal-based pyramid.
•	Polygons are 2D shapes that usually end in ‘-agon’, such as octagon or nonagon.
•	Polyhedrons are 3D shapes that usually end in ‘-hedron’, such as octahedron or dodecahedron.

Prime Numbers

Square Numbers

Only divisible by itself and 1.
Remember:  1 is not a prime number

A number multiplied by itself produces a square number.
The opposite of a square number is a square root.
√

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Triangles
Equilateral	Right-Angled
All sides and		Includes one angles equal.	right angle (90°)

Isosceles	Scalene
Two sides equal	No sides equal. in length.

×

1

2

3

4

5

6

7

8

9

10

11

12

1

1

2

3

4

5

6

7

8

9

10

11

12

2

2

4

6

8

10

12

14

16

18

20

22

24

3

3

6

9

12

15

18

21

24

27

30

33

36

4

4

8

12

16

20

24

28

32

36

40

44

48

5

5

10

15

20

25

30

35

40

45

50

55

60

6

6

12

18

24

30

36

42

48

54

60

66

72

7

7

14

21

28

35

42

49

56

63

70

77

84

8

8

16

24

32

40

48

56

64

72

80

88

96

9

9

18

27

36

45

54

63

72

81

90

99

108

10

10

20

30

40

50

60

70

80

90

100

110

120

11

11

22

33

44

55

66

77

88

110

110

121

132

12

12

24

36

48

60

72

84

96

120

120

132

144

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

Column Calculations
Commonly used for addition and subtraction. Some tips to remember:
•	Always work from right to left.
•	Don’t forget to add on any numbers you carry over to the next column.
•	For subtractions the largest number is always on the top and it is always ‘top take away bottom’ as you work through.

12 and 24 Hour Clock

Metric Measurements
Distance

Volume

Weight

Time

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Converting Units
‘Kilo’ means thousand and ‘milli’ means a thousandth

Metric Distance

Metric Volume

Imperial and Metric

Metric Weight

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From

To

Method

kg

g

× 1000

g

kg

÷ 1000

From

To

Method

miles

km

× 1.6

km

miles

÷ 1.6

From

To

Method

l

ml

× 1000

ml

l

÷ 1000

From

To

Method

cm

m

÷ 100

cm

mm

× 10

m

km

÷ 1000

km

m

× 1000

Unit

Symbol

Equivalent

Hour

H/h

= 60mins

Minute

mins

= 60secs

Seconds

secs

= 1000ms

Unit

Symbol

Equivalent

Tonne

t

= 1000kg

Kilogram

kg

= 1000g

Gram

g

= 1000mg

Milligram

mg

Unit

Symbol

Equivalent

Kilolitre

kl

= 1000l

Litre

l

= 100cl

Centilitre

cl

= 10ml

Millilitre

ml

Unit

Symbol

Equivalent

Kilometre

km

= 1000m

Metre

m

= 100cm

Centimetre

cm

= 10mm

Millimetre

mm

12 Hour Clock

24 Hour Clock

12pm

12:00

1pm

13:00

2pm

14:00

3pm

15:00

4pm

16:00

5pm

17:00

6pm

18:00

7pm

19:00

8pm

20:00

9pm

21:00

10pm

22:00

11pm

23:00

12 Hour Clock

24 Hour Clock

12 midnight

00:00

1am

01:00

2am

02:00

3am

03:00

4am

04:00

5am

05:00

6am

06:00

7am

07:00

8am

08:00

9am

09:00

10am

10:00

11am

11:00

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Angles
•	Inside angles of a triangle = 180°
•	Inside angles of a quadrilateral = 360°
•	A straight line = 180°
•	A full circle = 360°
•	Opposite angles on crossing lines are equal, for example:

130°
      			50°				50°
     130°

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Coordinates

The x axis goes across/horizontal The y axis goes up/vertical
•	Coordinates are written (x,y)
•	The first number moves horizontally
•	The second number moves vertically
•	A useful tip is “along the corridor and up the stairs” (although
the stairs may be down if you have negative numbers!).

× and ÷ by 10, 100 or 1000

× move all digits to the left
÷ move all digits to the right

×10 move all digits	÷ 10 move all digits
1 place to the left	1 place to the right
× 100 move all digits	÷ 100 move all digits 2 places to the left	2 places to the right
× 1000 move all digits	÷ 1000 move all digits
3 places to the left	3 places to the right

Multiplication Shortcuts
× 20 = double it then × 10
× 30 = × 3 then × 10
× 4 = double, then double again
× 8 = double, double and double again.
× 15 = × 10, half it, then add both together.
× 50 = × 100, then half it.

	

You use fractions all the time without thinking, like when you get 8/10 a spelling test. There are 10 equal marks
available and you’ve got 8 of them.

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Finding Any Percentage

Once you know that to find 1% is the same as dividing by 100, you can then multiply that by whatever percent you want!
For example 17% is 17 lots of 1%
So you will need to ÷ 100, then × 17.
There are quick ways of finding some percentage such as 10% = ÷ 10, but even this long method would work the answer out correctly.

Finding Quick Percentages

Find 1% = ÷ 100
Find 10% = ÷ 10
Find 20% = ÷ 5
50% = ÷ 2
25% = ÷ 4
75% = ÷ 4, then × 3

Comparing Fractions

Sometimes you will need to compare or calculate using fractions. The easiest way to compare them is to change them to a common denominator (same bottom number).
Do this by multiplying or dividing with the rule: do the same to the top as you do to the bottom.

So 5/12, 5/6 and 3/4 can all be made into 12ths by multiplying the 5 and the 6 by 2 and also the 3 and the 4 by 3 giving: 5/12, 10/12, 9/12

What is a Fraction?

The top number is called the numerator and tells you
¾ how many pieces you have out of the possible pieces. The bottom number is called the denominator and
tells you how many equal pieces something is cut into.

Dividing Fractions
1.	Flip the second fraction over. 
2.	Multiply the two top numbers together to get a new top number.

3.	Multiply the two bottom numbers together to get a new bottom number.

Example : 3/5 ÷ 2/7

1.	Flip the fraction over so it becomes 3/5 x 7/2

2.	Multiply the two top numbers together = 3 x 7 = 21

3.	Multiply the two bottom numbers together 5 x 2 = 10

So the answer is 21/10 which you can simplify to 2 1/10

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Multiplying Fractions

4.	Multiply the two top numbers together to get a new top number.
5.	Multiply the two bottom numbers together to get a new bottom number.

Example: 3/5 x 4/6 

4.	Multiply the top two numbers together = 3 x 4 = 12

5.	Multiply the two bottom numbers together = 5 x 6 = 30

So the answer is 12/30 which you can simplify to 6/15, 4/10 or 2/5

Subtracting Fractions

6.	Change them to a common denominator.
7.	Subtract the top numbers only and keep the same denominator.

Example: 3/4 - 4/6 

6.	Change both fractions to 12ths  = 9/12 -8/12 

7.	Subtract the top numbers only and keep the bottom number: 9 - 8 = 1

So the answer is 1/12

Adding Fractions

8.	Change them to a common denominator.
9.	Add the top numbers only and keep the same denominator.

Example: 3/4 + 4/6 

8.	Change both fractions to 12ths  = 9/12 +8/12 

9.	Add the top numbers only and keep the bottom number: 9 + 8 = 17

So the answer is 17/12 or simplified to 1 5/12

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Times Table Square

Fractions, Decimals and %

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Fraction

Decimal

Percentage %

1
100

0.01

1%

1
10

0.1

10%

1
5

0.2

20%

1
2

0.5

50%

1
4

0.25

25%

3
4

0.75

75%

×

2

3

4

5

6

7

8

9

10

2

4

6

8

10

12

14

16

18

20

3

6

9

12

15

18

21

24

27

30

4

8

12

16

20

24

28

32

36

40

5

10

15

20

25

30

35

40

45

50

6

12

18

24

30

36

42

48

54

60

7

14

21

28

35

42

49

56

63

70

8

16

24

32

40

48

56

64

72

80

9

18

27

36

45

54

63

72

81

90

10

20

30

40

50

60

70

80

90

100

Decimals
A good tip with decimals is to think of them as money.
For example: 1.2 + 3.4
could be thought of as: £1.20 +
£3.40 giving an answer of £4.60 and it seems much easier.
Just don’t forget to make it back into a plain decimal in
the end.
So £4.60 would be 4.6

Roman Numerals

I = 1	VI = 6	L = 50
II = 2	VII = 7	D = 500
III = 3	VIII = 8	M = 1000
IV = 4	IX = 9	M = 1 million
V = 5	X = 10

A line over any letter makes it 1000 times bigger.