This week: measures Convert units of measure and calculate the area, perimeter and volume of common shapes Name common units of measure for weight, length and capacity Calculate perimeter and area of common 2D shapes Convert between Metric units of measure Calculate volume and surface area of common 3D shapes Convert Imperial units of measure to Metric Solve missing number area, perimeter and volume problems

What did we do last week?

Recap Quiz Draw 5 2D shapes Name 3 3D shapes Obtuse angles are between which values? Draw an irregular octagon Draw a regular triangle How many degrees in a right angle? Draw an example of tessellation Draw a net of a cube What is the mathematical name for the shape of a Toblerone? Which 2D shape shares its name with a flying toy?

Units?

Metric Conversions (Length) Functional Skills Mathematics - Measurements Metric Conversions (Length) x 1000 x 100 x 10 cm mm km m ÷ 1000 ÷ 100 ÷ 10 Convert 3.6km to cm 3.6 x 1,000 = 3,600m 3,600 x 100 = 360,000cm Convert 5.7km to m 5.7 x 1,000 = 5,700m Convert 3m to cm 3 x 100 = 300cm

Metric Conversions (Weight) x 1000 x 1000 x 1000 g mg Tonne kg ÷ 1000 ÷ 1000 ÷ 1000 Convert 7.6 tonnes to mg 7.6 x 1,000 = 7,600kg 7600 x 1,000 = 7,600,000g 7,600,000 x 1,000 = 7,600,000,000mg Convert 2.9kg to g 2.9 x 1,000 = 2,900g Convert 5g to mg 5 x 1,000 = 5,000mg

Metric Conversions (Capacity) x 100 x 10 l cl ml 1ml = 1cm3 ÷ 100 ÷ 10 Convert 15,300ml to l 15,300 ÷ 10 = 1,530cl 1,530 ÷ 100 = 15.3l Convert 90ml to cl 90 ÷ 10 = 9cl Convert 9l to cl 9 x 100 = 900cl

Calculate these conversions: 1) 2) 3) 4) 5) 6) 1) 2) 3) 4) 5) 6)

Metric to Imperial Conversions 1 km 0.621 miles 2.54 cm 1 inch 4.5 litres 1 gallon 1 kg 2.2 pounds 1 metre 3.3 feet

This mans nose is 8.8cm long, convert this to inches.

The diameter of this bubble is 20.3 inches, convert this to cm. 20.3 x 2.54 = 51.56 cm

This woman’s legs are 132cm long, convert this to inches.

This man’s mouth is 6.8 inches across, convert this to cm. 6.8 x 2.54 = 17.27 cm

This woman’s waist is 15.2 inches around, convert it to cm. 15.2 x 2.54 = 36.60 cm

This snake is 7.3 m long, convert this to feet. 7.3 x 3.3 = 24.09 feet

Metric and Imperial Measures

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

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

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

Perimeter and Area 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. The rectangle has a perimeter of: The rectangle has an area of: 5+3+5+3 = 16cm 5 x 3 = 15cm²

Calculate the perimeter and area of this rectangle… 20cm 24cm²

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

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

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 = 4+8 2 ×5 Area = 30cm² 4cm 5cm 6cm 5cm 7cm 8cm

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

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

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 volume of this cuboid: Volume = 3 × 5 × 4 Volume = 60cm³ 3cm 4cm 5cm

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

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

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

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

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

What is the value of x? 6

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

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

What is the area of this shape? 12

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