MATHS Week 10 More Measures

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

What did we do last week?

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

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?

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

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

Perimeter, area and volume

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 Answer: 240cm³ Answer: 0.2m or 20cm

Circles

Parts of a Circle Centre

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

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

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

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

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

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

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

Parts of a Circle Arc (part of the circumference)

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

Parts of a Circle Semicircle (half a circle)

What is this? Radius

What is this? Semicircle

What is this? Centre

What is this? Diameter

What is this? Chord

What is this? Sector

What is this? Circumference

What is this? Segment

What is this? Tangent

What is this? Diameter

What is this? Sector

What is this? Semicircle

What is this? Segment

What is this? Chord

What is this? Tangent

What is this? Arc

Learn these words (meanings & spellings)

Radius, Diameter and Circumference

Lines

Slices

Circumference circumference Circumference = π × diameter diameter

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.)

Area Area = π × radius × radius = π × radius2 radius area

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 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.)

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.)

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 π x 20 x 20 x 25 =

Volume of a Cylinder π x 8 x 8 x 35 = 7037.17cm3 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 SA = 294cm2 SA = 378cm2 SA = 270cm2 Calculate the Surface Area of the cube and cuboids shown below: SA = 294cm2 SA = 378cm2 15cm 7cm 3cm EXTENSION: 8cm SA = 270cm2 9cm 6cm 12cm 5cm

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

Your turn! SA = 120cm2 SA = 216cm2 SA = 88m2 Calculate the surface area of the following shapes. 5cm 9cm SA = 120cm2 14m 3cm 6cm SA = 216cm2 4cm 1m 2m SA = 88m2

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? Circumference = π x 16 = 50.27cm 50.27 x 35 = 1759.45cm2 Area of circle = π x 8 x 8 = 201.06cm2 x 2 = 402.12 1759.45 + 402.12 = 2161.57cm2 Radius = 8cm Length = 35cm

Complete the Volume & Surface area worksheet

Answers 48cm3 88cm2

Answers 75.4cm3 100.53cm2

Answers 300cm3 360cm2

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

Directed Study

Metric and imperial units cross-number