Measures

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 = 360000cm x 1000 x 100 x 10 km m cm mm ÷ 1000 ÷ 100 ÷ 10

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 = 7600000g 7600000 x 1000 = 7600000000mg x 1000 x 1000 x 1000 g mg Tonne kg ÷ 1000 ÷ 1000 ÷ 1000

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

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

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

Converting km/h to m/s

Converting m/s to km/h

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.

Perimeter, area and volume

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

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

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

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

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

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

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

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.

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!

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

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

Circles

Radius, Diameter and Circumference

Lines

Slices

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.)

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.)

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

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

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

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

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

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

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

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

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

Volume of a Cylinder Diameter 40cm Height 25cm

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

Surface area

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 = (45 + 27 + 15) x 2 = 174cm2 B C A 5cm 3cm 9cm

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

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 = (88 + 55 + 40) x 2 = 183 x 2 = 366cm2 C B 11cm A 5cm 8cm

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

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

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)

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