1. Correct the following equation so that it makes sense – you can add numbers and operators to it.
Challenge: Make the equation make sense by re-arranging the digits – you cannot add anything new!
How quickly can you find out what is unusual about this  paragraph? It looks so ordinary that you would think that nothing was wrong with it at all and, in fact, nothing is. But  it is unusual. Why? If you study it and think about it you may  find out, but I am not going to assist you in any way.
79 = 24

2. This week: area, perimeter, volume
Convert units of measure and calculate the area, perimeter and volume of common shapes
Find perimeters and areas of 2D shapes, including triangles, parallelograms and trapeziums
Name units of measure for area, perimeter and volume
Calculate volume and surface area of common 3D shapes
Circle vocabulary and formula used to find the circumference and area of a circle
Solve missing number area, perimeter and volume problems
Use reverse methods to calculate missing values

3. Metric
Imperial
Length
Weight
Capacity

4. Converting between km/h and m/s
Convert 100km/h to m/s
Convert 6km/h to m/s
Convert 450m/s to km/h.
Convert 705m/s to km/h.
km/h -> m/s:
x 1000
÷ 3600
72 km/h in m/s:
72 x 1000 = 72,000
72,000 ÷ 3600 = 20 m/s
m/s -> km/h:
÷ 1000
x 3600
100 m/s in km/h:
100 ÷ 1000 = 0.1
0.1 x 3600 = 360 km/h

5. Metric Conversions: cm3 and mm3=
10mm
1cm
VOLUME = 1,000mm3
VOLUME = 1cm3
10mm
1cm
10mm
1cm
x 1,000
cm3
mm3
÷ 1,000

6. Metric Conversions: m3 and cm3=
100cm 1m
VOLUME = 1,000,000cm3
VOLUME = 1m3
100cm 1m
100cm 1m
x 1,000,000 m3
cm3
÷ 1,000,000

7. Perimeter, area and volume
1cm cm cm3
Distance around the outside of a 2D shape
Space inside a 2D shape
Space inside a 3D shape

8. Perimeter and Area 3cm 5cm 5+3+5+3 = 16cm 5 x 3 = 15cm²
Perimeter is the length around the outside of a shape. Area is the space inside a shape.
3cm
5cm
The rectangle has a perimeter of:
The rectangle has an area of:
= 16cm
5 x 3 = 15cm²

9. Calculate the perimeter and area of this rectangle…
4cm
6cm
Perimeter =
Area =
20cm
24cm²

10. Rectangle: Area = length × width 𝑨=𝒍𝒘
Formulae to remember:
Triangle:
Area = base × height ÷ 2
𝑨= 𝟏 𝟐 𝒃𝒉
Rectangle: Area = length × width 𝑨=𝒍𝒘
Find the area and perimeter of this rectangle:
Area = 8 × 6
Area = 48cm²
Perimeter =
Perimeter = 28cm
Find the area and perimeter of this triangle:
Area = 5 × 12 ÷ 2
Area = 60cm² ÷ 2
Area = 30cm²
Perimeter =
Perimeter = 30cm
13cm
6cm
5cm
8cm
12cm

11. Exam Questions Answer: 35cm² Answer: Area = 88cm² Perimeter = 38cm 7cm
Find the area of this triangle:
Question 2
Find the perimeter and area of this rectangle:
7cm
11cm
10cm
Answer: 35cm²
8cm
Answer:
Area = 88cm²
Perimeter = 38cm

12. Formulae to remember: Trapezium:
Area = (Half the sum of parallel sides) × height
𝑨= 𝒂+𝒃 𝟐 ×𝒉
Parallelogram: Area = base × vertical height 𝑨=𝒃𝒉
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

13. Exam Questions Answer: 96cm² Answer: 70cm² 12cm 10cm 8cm 9cm 7cm 11cm
Find the area of this parallelogram:
12cm
10cm
8cm
Answer: 96cm²
Question 2
Find the area of this trapezium:
9cm
7cm
11cm
Answer: 70cm²

14. Find the missing lengths
?cm
6cm
Area = 48cm²
7cm
Area = 21cm²
8cm
?cm
6cm
8cm
?cm
5cm
Area = 32cm²
Area = 28cm²
Height =
4cm
9cm
Height = 4cm

15. 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
Find the height of this cuboid:
280cm³ = 10 × 7 × h
h = 280 ÷ (10 × 7)
h = 4cm
Find the volume of this cuboid:
Volume = 3 × 5 × 4
Volume = 60cm³
Volume = 280cm³
3cm
7cm
4cm
10cm
5cm

16. Find the volume of this cuboid:
Exam Questions
Find the volume of this cuboid:
The tank below contains exactly 100 litres of water. How far up the tank does the water go? (Hint: 1 litre = 1000cm³)
8cm
0.5m
6cm
0.5m
5cm 1m
Answer: 240cm³
Answer: 0.2m or 20cm

17. What is a prism? Hexagonal Prism Cylinder Triangular Prism
A prism is a 3D shape that has the same cross-section all the way through.
Triangular Prism
Hexagonal Prism
Cylinder
Find the area of the cross-section then multiply by the length.
Volume = Area of cross-section × length

18. Volume of Prisms Volume = Area of cross section x depth
11cm
Volume = Area of cross section x depth
Area of cross section
= (11 x 8) ÷ 2 = 44cm2
9cm
8cm
20cm
Volume = 44 x 20 = 880cm3
11cm
7mm
7mm
105m3
5cm
343mm3
80cm3 6m 5m
2cm 7m
8cm
7mm 6m

19. Cylinder
What is the volume of this cylinder?
Volume = r2h

20. Find the volume of this cylinder: Volume = 𝜋× 3 2 ×8 Volume = 226.2cm³
Recap
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

21. Find the volume of this triangular prism:
Exam Questions
Find the volume of this triangular prism:
A circular pond contains 18,850 litres of water. It has a diameter of 4m. How deep is the pond if it is a cylinder? (1 litre = 1000cm³)
9cm
12cm
8cm
Answer: 432cm³
Answer: 1.5m or 150cm

22. Cones
If Pringles came in a cone, which was the same height and diameter as the tall tube, it would contain one third of the calories.
Why?
Pringles
A third
of the
calories

23. Cones
Slant height (l)
Example: find the volume of this cone
Volume =

24. Pyramids Volume = 1/3 x base area x height
Find the volume of this pyramid
Volume = 1/3 x base area x height

25. Spheres 4/3π of the volume of a cube-shaped container.
Find the volume of a sphere whose diameter is 15 cm
4/3π of the volume of a cube-shaped container.
Volume =

26. Surface Area
Surface area is the total area of the outside of a 3D object
Each face is the same – a square.
Area A = 5 x 5 = 25cm2
Total Surface Area = 6 x 25 = 150cm2
5cm A
5cm
5cm

27. A B C Surface Area 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

28. 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

29. Word Problems
A length of copper piping is in the shape of a triangular prism. The triangle on it’s end is a right angle, 9mm by 4mm by 10mm. The piece of pipe is 18cm long. What is the surface area of the pipe?
Area of Triangles = (9 x 4) ÷ 2
= 18mm2
= 18 x 2
= 36mm2
10mm
Front Rectangle = 180 x 10
= 1800mm2
9mm
180mm
4mm
Back Rectangle = 180 x 9
= 1620mm2
Base Rectangle = 180 x 4
= 720mm2
Total Surface Area =
= 4176mm2

30. Surface Area SA = 294cm2 SA = 378cm2 SA = 270cm2
Calculate the Surface Area of the cube and cuboids shown below:
SA = 294cm2
SA = 378cm2
7cm
15cm
3cm
EXTENSION:
SA = 270cm2
9cm
8cm
6cm
12cm
5cm

31. Surface Area of a Cone, Sphere & Cylinder
SA = π rl
SA =4 π r2
Cylinder r h
SA = Curved surface area + Top + Bottom h
2 π r
Curved area =
= 2 π rh
SA = 2 π rh + 2 π r2

33. Circumference
Circumference = π × diameter
circumference
diameter

34. Examples Circumference = π × diameter Circumference: = π × 4 4cm
= 12·57cm (2 d.p.)
8cm
Circumference:
= π × 16
= 50·27cm (2 d.p.)

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

36. Example Area = π × radius × radius Area 7cm = π × 7 × 7
= π × 7 × 7
= 153·94cm² (2 d.p.)
area
10cm
Area
= π × 5 × 5
= 78·54cm² (2 d.p.)

37. Find the circumference and area of this circle:
Exam Question
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.)

38. Find the circumference and area of this circle:
Exam Question
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.)

39. What is the value of x? 6

40. The area of this shape is 20cm2. What is the length, b ?5
4cm
b cm

41. What is the perimeter of this shape?
2.5cm
2.5cm
2 cm 7

42. What is the area of this shape?12

43. 3cm
What is the area of this shape?
4cm 20