1. To find the surface area of a cuboid
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2. Find the surface area of the cuboids
10 cm
3.5 cm 3 ?
1 cm
1 cm
3.6 cm
3cm ?
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5cm

3. Learning Objective Draw the position of shapes on
a coordinate grid after rotations
and translations.
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4. This shape has moved 4 places to the right, and 2 places up.
Translation 10
Translation: Translation means moving a shape to a new location. Watch these examples: 9 8
This shape has moved 4 places to the right, and 2 places up. 7 6 5 4 3 2
Congruent Shapes 1
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5. When a shape is translated the image is congruent to the original.
Translations
When a shape is translated the image is congruent to the original.
The orientations of the original shape and its image are the same.
An inverse translation maps the image that has been translated back onto the original object.
What is the inverse of a translation 7 units to the left and 3 units down?
The inverse is an equal move in the opposite direction.
That is, 7 units right and 3 units up.
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6. 10 9
This shape will be translated 6 places to the right, and 2 places down. What will it look like? 8 7 6 5 4 3 2 1
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7. This shape will be translated 2 places to the right, and 4 places up.10 9 8 7
This shape will be translated 2 places to the right, and 4 places up. 6 5 4 3 2 1
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8. 10 9
6 squares left, and 1 square down. 8 7 6
What has this shape been translated by? 5 4 3 2 1
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9. Describing translations
When we describe a translation we always give the movement left or right first followed by the movement up or down.
We can describe translations using vectors.
For example, the vector describes a translation 3 right and 4 down. –4 3
As with coordinates, positive numbers indicate movements up or to the right and negative numbers are used for movements down or to the left.
Compare a translation given as an angle and a distance to using bearings. For example, an object could be translated through 5cm on a bearing of 125º.
A different way of describing a translation is to give the direction as an angle and the distance as a length.
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10. Translations on a coordinate gridy
A(5, 7)
The vertices of a triangle lie on the points A(5, 7), B(3, 2) and C(–2, 6).
C(–2, 6) 7 6 5 4 3 2
B(3, 2)
Translate the shape 3 squares left and 8 squares down. Label each point in the image. 1 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 x –1
A’(2, –1) –2
C’(–5, –2) –3
Point out that when we translate shapes on a coordinate grid we can find the coordinates of the vertices of the image shape by adding to the original’s x-coordinates the size of the translation to the right (or subtracting the size of a translation to the left); and adding to the original’s y-coordinates the size of the translation up (or subtracting the size of a translation down). –4
What do you notice about each point and its image? –5 –6
B’(0, –6) –7
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11. Translations on a coordinate gridy
The coordinates of vertex A of this shape are (–4, –2). 7 6 5 4 3
When the shape is translated the coordinates of vertex A’ are (3, 2). 2
A’(3, 2) 1 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 x –1 –2
A(–4, –2)
What translation will map the shape onto its image? –3
Tell pupils that we can work this out by subtracting the coordinate of the original shape from the coordinate of the image.
The difference between the x-coordinates is 7 (3 – –4) and the difference between the y-coordinates is 4 (2 – –2). The required translation is therefore 7 right and 4 up. –4 –5 –6 –7
7 right
4 up
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12. Translations on a coordinate grid1 2 3 4 5 6 –2 –3 –4 –5 –6 –7 –1 y x 7
The coordinates of vertex A of this shape are (3, –4).
When the shape is translated the coordinates of vertex A’ are(–3, 3).
A’(–3, 3)
What translation will map the shape onto its image?
The difference between the x-coordinates is –6 (–3 – 3) and the difference between the y-coordinates is 7 (3 – –4). The required translation is therefore 6 left and 7 up.
If required this slide can be copied and modified to produce more examples. To change the shapes, go to View/toolbars/drawing to open the drawing toolbar. Select the shape and using the drawing toolbar, click on draw/edit points to drag the points to different positions. Edit the new coordinates as necessary.
A(3, –4)
6 left
7 up
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13. Translation golf
In this game pupils are required to estimate the required translation to move the ball to the hole. The length of one unit is shown in the top right-hand corner.
To translate the ball to the left or down, a negative number must be used.
Challenge pupils to get the ball into the hole in as few moves as possible.
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14. Look at the DENOMINATORS. What are the MULTIPLES?
Look at the DENOMINATORS. What are the MULTIPLES?
9: 9, 18, 27, 36, 45, 54, …
12: 12, 24, 36, 48, 60, …
6: 6, 12, 18, 24, 30, 36, 48, …
4: 4, 8, 12, 16, 20, 24, 28, 32, 36,…
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15. 2/4
3/5
6/10
1/2
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16. 3/6
7/8
3/4
4/4
2/3
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17. Learning Objective Draw the position of shapes on
a coordinate grid after rotations
and translations.
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18. Rotational Symmetry A complete turn (360°) 90° Rotation Clockwise
Centre of Rotation
180° Rotation Clockwise
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270° Rotation Clockwise

19. Centre of Rotation
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20. We are going to rotate this rectangle 90° clockwise.
Centre of Rotation
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21. Rotate 90° Anti-Clockwise
Rotate 90° Clockwise
Rotate 90° Anti-Clockwise
Rotate 90° Anti-Clockwise
Rotate 180° Clockwise
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Click on each shape to reveal the answer

22. To work out the square and square root of numbers.
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23. Learning Objective
To find the next number in a sequence, including decimal and Fraction sequences.
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24. What about guess the rule?
Look at these number sequences carefully can you guess the next 2 numbers?
What about guess the rule?
+10 30 40 50 60 70 80 +3 17 20 23 26 29 32 -7 48 41 34 27 20 13
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25. Can you work out the missing numbers in each of these sequences?
+25 50 75
100
125
150
175
+20 30 50 70 90
110
130 -5
196
191
181
176
171
186
-10
306
296
286
276
266
256
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26. Now try these sequences – think carefully and guess the last number!
+1, +2,
+3 … 1 2 4 7 11 16
double 3 6 12 24 96 48
+ 1.5
0.5 2
3.5 5
6.5 8 -3 7 4 1 -2 -5 -8
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27. Now try these sequences – think carefully and guess the last number!
+ 1/3
2 1/3
2 2/3 3
3 2/3
+ 2 2/3 2
2 2/3
3 1/3 4
4 2/3
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28. See if you can find out something about Fibonacci!
This is a really famous number sequence which was discovered by an Italian mathematician a long time ago.
It is called the Fibonacci sequence and can be seen in many natural things like pine cones and sunflowers!!!
etc…
Can you see how it is made? What will the next number be?
34!
See if you can find out something about Fibonacci!
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29. Fibonacci’s number pattern can also be seen elsewhere in nature:
with the rabbit population
with snail shells
with the bones in your fingers
with pine cones
with the stars in the solar system
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30. For these sequences I have done 2 maths functions!
Guess my rule!
For these sequences I have done 2 maths functions! 3 7 15 31 63
127
x2 +1
x2 -1 2 3 5 9 17 33
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31. 24 42 28 1 2 3 1
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32. Learning Objective
To use functions machines to recognise number sequences.
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33. Single machines
INPUT
OUTPUT
PROCESSOR
Imagine that we have a robot to help us make patterns. 1 6 2 7 5 10
+ 5

34. Single machines
INPUT
OUTPUT
PROCESSOR
Imagine that we have a robot to help us make patterns 17 10 20 13 25 18
− 7

35. Single machines
INPUT
OUTPUT
PROCESSOR
Imagine that we have a robot to help us make patterns 3 12 6 24 12 48
× 4

36. Single machines
INPUT
OUTPUT
PROCESSOR
Imagine that we have a robot to help us make patterns 12 4 33 11 27 9
÷ 3

37. Exercises 1 + 2 × 7 - 7 ÷ 6 × 4 ÷ 9 Here are single number machines
What is the output since we know the input? a 1 3 d 11 77
+ 2
× 7 3 5 9 63 5 7 7 49 b 9 2 e 12 2
- 7
÷ 6 13 6 36 6 29 22 66 11 c 3 12 f 18 2
× 4
÷ 9 7 28 54 6 9 36 81 9

38. Exercises 2 + 9 × 9 - 11 ÷ 7 × 8 ÷ 11 Here are single number machines.
What is the output since we know the input? a 1 10 d 6 54
+ 9
× 9 3 12 4 36 5 14 9 81 b 11 e 21 3
- 11
÷ 7 24 13 49 7 36 25 63 9 c 4 32 f 11 1
× 8
÷ 11 7 56 33 3 9 72 66 6

39. Inverse machines
Can we calculate the input since we know the output?
INPUT
INVERSE
PROCESSOR
OUTPUT 6 12 8 14 17 23
− 6
+ 6
+ 6

40. Inverse machines
Can we calculate the input since we know the output?
INPUT
INVERSE
PROCESSOR
OUTPUT 40 32 23 15 15 7
+ 8
− 8
− 8

41. Inverse machines
Can we calculate the input since we know the output?
INPUT
INVERSE
PROCESSOR
OUTPUT 6 30 9 45 11 55
÷ 5
× 5
× 5

42. Inverse machines
Can we calculate the input since we know the output?
INPUT
INVERSE
PROCESSOR
OUTPUT 12 3 20 5 48 12
× 4
÷ 4
÷ 4

43. Exercises 3 + 3 × 12 - 6 ÷ 13 × 6 ÷ 15 Here are single number machines
What is the input since we know the output? a 4 7 d 5 60
+ 3
× 12 8 11 2 24 31 34 6 72 b 12 6 e 39 3
- 6
÷ 13 14 8 65 5 18 12 91 7 c 7 42 f 30 2
× 6
÷ 15 11 66 75 5 12 72
105 7

44. Exercises 4
Here are single number machines
What is the input since we know the output? a 6 19 d 2 28
+ 13
× 14 3 16 4 56 12 25 6 84 b 22 5 e 32 2
- 17
÷ 16 26 9 80 5 28 11
112 7 c 3 45 f 76 4
× 15
÷ 19 9
135 38 2 11
165
114 6

45. A Broken Processor
INPUT
OUTPUT
??????????
Imagine that the processor has broken!!!!! 5 10 10 15 25 30
???
+ 5

46. A Broken Processor
INPUT
OUTPUT
???????????
Imagine that the processor has broken!!!!! 17 9 21 13 25 17
???
− 8

47. A Broken Processor
INPUT
OUTPUT
??????????
Imagine that the processor has broken!!!!! 3 21 6 42 7 49
???
× 7

48. A Broken Processor
INPUT
OUTPUT
??????????
Imagine that the processor has broken!!!!! 81 9 18 2 36 4
???
÷ 9

49. Exercises 5 + 8 × 11 - 5 ÷ 10 × 6 ÷ 17 Here are single number machines
What is the action since we know what the input and output are? a 1 9 d 3 33
+ 8
× 11 3 11 7 77 5 13 10
110 b 10 5 e 10 1
- 5
÷ 10 41 36 30 3 88 83
120 12 c 4 24 f 34 2
× 6
÷ 17 7 42
102 6 9 54 51 3

50. Exercises 6 + 4 × 8 - 7 ÷ 3 × 5 ÷ 7 Here are single number machines
What is the action since we know what the input and output are? a 5 9 d 3 24
+ 4
× 8 11 15 7 56 23 27 10 80 b 15 8 e 39 13
- 7
÷ 3 42 35 66 22 88 81
120 40 c 4 20 f 42 6
× 5
÷ 7 7 35 63 9 9 45 77 11

51. Double vision 4 12 13 7 21 22 8 24 25 × 3 + 1 Machine 1 Machine 2
Imagine that we have two robots to help us make patterns
The output of machine 1 is input to machine 2 4 12 13 7 21 22 8 24 25
× 3
+ 1
Machine 1
Machine 2

52. Double vision 4 16 11 3 12 7 11 44 39 × 4 − 5 Machine 1 Machine 2
Imagine that we have two robots to help us make patterns
The output of machine 1 is input to machine 2 4 16 11 3 12 7 11 44 39
× 4
− 5
Machine 1
Machine 2

53. Exercises 7 × 5 + 6 × 7 - 11 × 6 - 5 Here are two stage machines
What is the output since we know the input? a 2 16
× 5
+ 6 4 26 8 46 b 5 24
× 7
- 11 10 59 7 38 c 6 31
× 6
- 5 3 13 1 1

54. Exercises 8 ÷ 2 + 2 ÷ 5 - 5 ÷ 7 + 6 Here are two stage machines
What is the output since we know the input? a 6 5
÷ 2
+ 2 8 6 10 7 b 45 4
÷ 5
- 5 55 6 75 10 c 42 12
÷ 7
+ 6 21 9 35 11

55. 30 56 52 1 2 3 1 1
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56. Learning Objective
To know to find and extend number sequences and patterns
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57. Number Patterns - Matches
Gareth uses matches to produce hexagon patterns
Draw a rough draft
of the next two patterns.
Pattern 1
Pattern2
Pattern 3

58. Number Patterns - Matches
Gareth uses matches to produce hexagon patterns
Pattern 4
Pattern 5

59. Number Patterns - Matches
Gareth uses matches to produce hexagon patterns 1. 2. 3. 4. 5.
Pattern Number 1 2 3 4 5 6 7 8 9 10
Number of matches 6 11 16 21 26 31 36 41 46 51 +5 +5 +5 +5 +5 +5 +5 +5 +5

60. Number Patterns – Counters
Sion uses counters to produce coloured patterns
Draw a rough draft
of the next two patterns.
Pattern 1
Pattern 2
Pattern 3

61. Number Patterns – Counters
Sion uses counters to produce coloured patterns.
Pattern 4
Pattern 5

62. Number Patterns – Counters
Sion uses counters to produce number patterns
Complete the table below, what is the pattern?
Red 1 2 3 4 5 6 7 8 9 10
Green 4 7 10 13 16 19 22 25 28 31 +3 +3 +3 +3 +3 +3 +3 +3 +3

63. Beginning to Use Algebra
It is easy enough to discover how many need to be added every time. What about the following pattern?
What rules need to be used to calculate the number of matches since we know the pattern number?
Think about the DOUBLE Robots!!
Pattern Number 1 2 3 4 5 6 7 8 9 10
Number of matches 6 11 16 21 26 31 36 41 46 51 1 6
× 5
+ 1 2 11 3 16

64. Beginning to Use Algebra
It is easy enough to discover how many need to be added every time. What about the following pattern?
What rules need to be used to calculate the number of green counters since we know the number of red counters?
Think about the double Robots again.
Red 1 2 3 4 5 6 7 8 9 10
Green 4 7 10 13 16 19 22 25 28 31 1 4
× 3
+ 1 2 7 3 10

65. Other Number Patterns Consider the following pattern using squares..
The name of the above sequence is SQUARE NUMBERS
5 × 5
4 × 4
3 × 3
2 × 2
1 × 1 1 4 9 16 25 +3 +5 +7 +9

66. Other Number Patterns Consider the following pattern using dots.
The name of the above sequence is TRIANGLE NUMBERS 1 3 6 10 15 +2 +3 +4 +5