1. MATHS
Week 10
More Measures

2. Starter!
You’ve heard of elf on a shelf – can you work out these maths rhymes?

4. What did we do last week?

5. Metric Conversion Quiz
10 quick questions on metric conversion
Write numbers 1 – 10 on a piece of paper and get ready ……….

6. There are 1000 of these in a kilogram
There are 100 of these in a metre
How many millilitres are there in a litre?
There are 1000 of these in a Tonne
There are 10 of these in a centimetre
There are 1000 metres in a ……..?
How many millilitres are there in 1 centilitre?
There are 1000 of these in a litre
There are 1000 of these in a metre
How many centilitres are there in a litre?

7. There are 1000 of these in a kilogram grams
There are 100 of these in a metre centimetre
How many millilitres are there in a litre? 1000
There are 1000 of these in a Tonne kilograms
There are 10 of these in a centimetre millimetres
There are 1000 metres in a ……..? kilometre
How many millilitres are there in 1 centilitre? 10
There are 1000 of these in a litre millilitres
There are 1000 of these in a metre millimetres
How many centilitres are there in a litre? 100

8. What are we going to do this week?
Recap Converting Metric Measures
Recap Converting Imperial to Metric
Perimeter, area and volume

9. Perimeter, area and volume

10. What are perimeter and area?
Perimeter is the length around the outside of a shape. Area is the space inside a shape.

11. Example The rectangle has a perimeter of: 5 + 3 + 5 + 3 = 16cm
The rectangle has a area of: 5 + 5 + 5 =
15cm²
Take note of the units! 5 × 3 =
15cm²

12. Find the perimeter and area of this rectangle:
20cm
24cm²

13. The formulae to remember:
Rectangle: Area = length × width 𝐴=𝑙𝑤 Triangle: Area = base × height ÷ 2 𝐴= 1 2 𝑏ℎ Remember that the height is at right angles to the base!

14. Two examples: Example 1 Example 2
Find the area and perimeter of this rectangle: Area = 8 × 6 Area = 48cm² Perimeter = Perimeter = 28cm
Find the area of this triangle: Area = 5 × 12 ÷ 2 Area = 60cm² ÷ 2 Area = 30cm²
13cm
6cm
5cm
8cm
12cm

15. Have a go at some: Answer: Area = 88cm² Answer: 35cm² Perimeter = 38cm
Question 1
Question 2
Find the area of this triangle:
Find the perimeter and area of this rectangle:
11cm
8cm
7cm
10cm
Answer:
Area = 88cm²
Perimeter = 38cm
Answer: 35cm²

16. The formulae:
Parallelogram: Area = base × vertical height 𝐴=𝑏ℎ Trapezium: Area = (Half the sum of parallel sides) × height 𝐴= 𝑎+𝑏 2 ×ℎ

17. Two examples Example 1 Example 2
Find the area of this parallelogram: Area = 7 × 5 Area = 35cm²
Find the area of this trapezium: Area = ×5 Area = 30cm²
4cm
5cm
6cm
5cm
7cm
8cm

18. Have a go at a couple of questions:
Find the area of this parallelogram:
Find the area of this trapezium:
12cm
9cm
10cm
8cm
7cm
11cm
Answer: 96cm²
Answer: 70cm²

19. Area – Working Backwards
Now you can find the area of shapes, can you find a length having been given the area?

20. Formulae Reminder:
Rectangle: 𝐴=𝑙𝑤 Triangle: 𝐴= 1 2 𝑏ℎ Parallelogram: 𝐴=𝑏ℎ Trapezium: 𝐴= 𝑎+𝑏 2 ×ℎ

21. Find the missing lengths:
None of these are drawn to scale
?cm
6cm
Area = 48cm²
7cm
Area = 21cm²
8cm
?cm
6cm
8cm
?cm
5cm
Area = 32cm²
Area = 28cm²
9cm
Height = ?
4cm
Height = 4cm

22. How to calculate the volume of a cuboid:
A cuboid is a prism, which means that it has the same cross-section all the way through. Find the area of the cross-section then multiply by the length. Volume = Height × Width × Length 𝑉=ℎ𝑤𝑙 This is how you calculate the volume of all prisms.

23. Find the volume of this cuboid: Volume = 3 × 5 × 4 Volume = 60cm³
An example:
Find the volume of this cuboid: Volume = 3 × 5 × 4 Volume = 60cm³
3cm
4cm
5cm
Take note of the units!

24. Another example, working backwards:
Find the height of this cuboid: 280cm³ = 10 × 7 × h h = 280 ÷ (10 × 7) h = 4cm
Volume = 280cm³
7cm
10cm

25. Two questions to have a go at:
Find the volume of this cuboid:
8cm
6cm
5cm
Answer: 240cm³

26. Circles

27. Parts of a Circle
Centre

28. Parts of a Circle
Diameter (must go through the centre)

29. Parts of a Circle
Radius (half a diameter – from the outside to the centre)

30. d = 2r or r = d/2 Radius and Diameter
The radius is half of the diameter OR
The diameter is double the radius
d = 2r or r = d/2

31. Parts of a Circle
Sector (like a slice of pizza)

32. Parts of a Circle
Chord (a line that crosses the circle but not through the centre)

33. Parts of a Circle
Segment (looks a bit like an orange segment)

34. Parts of a Circle
Circumference (the perimeter of the circle)

35. Parts of a Circle
Arc (part of the circumference)

36. Parts of a Circle
Tangent (a line that touches the circle at a single point on the circumference

37. Parts of a Circle
Semicircle (half a circle)

38. What is this?
Radius

39. What is this?
Semicircle

40. What is this?
Centre

41. What is this?
Diameter

42. What is this?
Chord

43. What is this?
Sector

44. What is this?
Circumference

45. What is this?
Segment

46. What is this?
Tangent

47. What is this?
Diameter

48. What is this?
Sector

49. What is this?
Semicircle

50. What is this?
Segment

51. What is this?
Chord

52. What is this?
Tangent

53. What is this?
Arc

54. Learn these words (meanings & spellings)

55. Radius, Diameter and Circumference

56. Lines

57. Slices

58. Circumference
circumference
Circumference =
π × diameter
diameter

59. Example 1 Circumference = π × diameter Circumference = π × 4
Find the circumference of this circle
circumference
Circumference
= π × diameter
4cm
Circumference
= π × 4
= 12·57cm (2 d.p.)

60. Example 2 Circumference = π × diameter Circumference = π × 16
Find the circumference of this circle
circumference
Circumference
= π × diameter
8cm
Circumference
= π × 16
= 50·27cm (2 d.p.)

61. Area
Area
= π × radius × radius
= π × radius2
radius
area

62. Example 1 Area = π × radius × radius Area = π × 7 × 7
Find the area of this circle
Area
= π × radius × radius
7cm
Area
= π × 7 × 7
= 153·94cm² (2 d.p.)
area

63. Example 2 Area = π × radius × radius Area = π × 5 × 5
Find the area of this circle
Area
= π × radius × radius
10cm
Area
= π × 5 × 5
= 78·54cm² (2 d.p.)
area

64. Find the circumference and area of this circle
Question 1
Find the circumference and area of this circle
Circumference = π × diameter
Circumference = π × 9
= 28·27cm (2 d.p.)
9cm
Area = π × radius × radius
Area = π × 4·5 × 4·5
= 63·62cm² (2 d.p.)

65. Find the circumference and area of this circle
Question 2
Find the circumference and area of this circle
Circumference = π × diameter
Circumference = π × 12
= 37·70cm (2 d.p.)
6 cm
Area = π × radius × radius
Area = π × 6 x 6
= 113·10cm² (2 d.p.)

66. What is a prism?
A prism is a 3D shape that has the same cross-section all the way through. For example:
Triangular Prism
Hexagonal Prism
Cylinder

67. Calculating the volume of a prism:
Find the area of the cross-section then multiply by the length. Volume = Area of cross-section × length

68. Find the volume of this cylinder: Volume = 𝜋× 3 2 ×8 Volume = 226.2cm³
Two examples
Example 1
Example 2
Find the volume of this cylinder: Volume = 𝜋× 3 2 ×8 Volume = 226.2cm³
If the volume of this prism is 360cm³ and it is 9cm long, what is the area of the cross-section? Area of cross-section = 360 ÷ 9 Area of cross-section = 40cm²
3cm
8cm

69. Find the volume of this triangular prism:
Have a go:
Question 1
Find the volume of this triangular prism:
9cm
12cm
8cm
Answer: 432cm³

70. Volume of a cylinder
Area of circle (Πr2) x height

71. Volume of a Cylinder
Diameter 40cm
Height 25cm

72. Volume of a Cylinder
Radius = 8cm
Length = 35cm

73. Surface area

74. Surface Area
Surface area is the total area of the outside of a 3D object
Area A = 5 x 9
= 45cm2
Area B = 9 x 3
= 27cm2
Area C = 3 x 5
= 15cm2
Total Surface Area = ( ) x 2
= 174cm2 B C A
5cm
3cm
9cm

75. A Surface Area Each face is the same – a square. Area A = 5 x 5
= 25cm2
Total Surface Area = 6 x 25
= 150cm2
5cm A
5cm
5cm

76. C B A Surface Area Area A = 8 x 11 = 88cm2 Area B = 5 x 11 = 55cm2
Area C = 5 x 8
= 40cm2
TOTAL SURFACE AREA
= ( ) x 2
= 183 x 2
= 366cm2 C B
11cm A
5cm
8cm

77. Surface Area of a Cylinder
Can you see a cylinder is actually a rectangle with two small circles?
Surface Area of a Cylinder =
Area of rectangle +
(Area of circle x 2)

78. How can I work out the area of the rectangle?

79. Surface Area of a Cylinder?
Radius = 8cm
Length = 35cm

80. Complete the Volume & Surface area worksheet

81. Answers

82. Answers

83. Answers

84. TOPIC TEST
You have 20 minutes to individually complete the AQA Topic Test

92. Moodle

93. Directed Study

94. Metric and imperial units cross-number