1. Measures

2. Metric Conversions - LENGTH
Functional Skills Mathematics - Measurements
Metric Conversions - LENGTH
Examples:
Convert 3m to cm
3 x 100 = 300cm
Convert 5.7km to m
5.7 x 1000 = 5700m
Convert 3.6km to cm
3.6 x 1000 = 3600m
3600 x 100 = cm
x 1000
x 100
x 10 km m cm mm
÷ 1000
÷ 100
÷ 10

3. Metric Conversions – WEIGHT/MASS
Examples:
Convert 5g to mg
5 x 1000 = 5000mg
Convert 2.9kg to g
2.9 x 1000 = 2900m
Convert 7.6 tonnes to mg
7.6 x 1000 = 7600Kg
7600 x 1000 = g
x 1000 = mg
x 1000
x 1000
x 1000 g mg
Tonne kg
÷ 1000
÷ 1000
÷ 1000

4. Metric Conversions - CAPACITY
Examples:
Convert 9l to cl
9 x 100 = 900cl
Convert 90ml to cl
90 ÷ 10 = 9cl
Convert 15300ml to l
15300 ÷ 10 = 1530cl
1530 ÷ 100 = 15.3l
x 100
x 10 ml l cl
÷ 100
÷ 10

5. Metric to Imperial Conversions
You need to know how to convert the following:
Metric
Imperial
8km
5 miles
2.5cm
1 inch
4.5 litres
1 gallon
1 kg
2.2 pounds

6. Converting km/h to m/s And converting m/s to km/h

8. Converting km/h to m/s

9. Converting m/s to km/h

10. Your Turn Convert 100km/h to m/s Convert 6km/h to m/s
Convert 450m/s to km/h.
Convert 705m/s to km/h.

11. Perimeter, area and volume

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

13. 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

14. Have a go at some: Question 1 Question 2
Find the area of this triangle:
Find the perimeter and area of this rectangle:
11cm
8cm
7cm
10cm

15. 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

16. 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

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

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

19. 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.

20. 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!

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

22. Two questions to have a go at:
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
6cm
0.5m
5cm
0.5m 1m

23. Circles

24. Radius, Diameter and Circumference

25. Lines

26. Slices

27. 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.)

28. 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.)

29. 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

30. 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

31. Find the circumference and area of this circle
Question 1
Find the circumference and area of this circle
9cm

32. Find the circumference and area of this circle
Question 2
Find the circumference and area of this circle
6 cm

33. 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

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

35. 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

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

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

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

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

40. Surface area

41. 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

42. 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

43. 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

44. Surface Area
Calculate the Surface Area of the cube and cuboids shown below:
15cm
7cm
3cm
EXTENSION:
8cm
9cm
6cm
12cm
5cm

45. Your turn! Calculate the surface area of the following shapes. 5cm 9cm

46. 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)

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