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

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

Example The rectangle has a perimeter of: 5 + 3 + 5 + 3 = 16cm The rectangle has a area of: 5 + 5 + 5 = 15cm² Take note of the units! 5 × 3 = 15cm²

Find the perimeter and area of this rectangle: 20cm 24cm²

The formulae to remember: Rectangle: Area = length × width 𝐴=𝑙𝑤 Triangle: Area = base × height ÷ 2 𝐴= 1 2 𝑏ℎ Remember that the height is at right angles to the base!

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: Answer: Area = 88cm² Answer: 35cm² Perimeter = 38cm Question 1 Question 2 Find the area of this triangle: Find the perimeter and area of this rectangle: 11cm 8cm 7cm 10cm Answer: Area = 88cm² Perimeter = 38cm Answer: 35cm²

The formulae: Parallelogram: Area = base × vertical height 𝐴=𝑏ℎ Trapezium: Area = (Half the sum of parallel sides) × height 𝐴= 𝑎+𝑏 2 ×ℎ

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 Answer: 96cm² Answer: 70cm²

Area – Working Backwards Now you can find the area of shapes, can you find a length having been given the area?

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 6cm Area = 48cm² 7cm Area = 21cm² 8cm ?cm 6cm 8cm ?cm 5cm Area = 32cm² Area = 28cm² 9cm Height = ? 4cm 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: 8cm 6cm 5cm Answer: 240cm³

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

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 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)

How can I work out the area of the rectangle?

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

Complete the Volume & Surface area worksheet

Answers

Answers

Answers

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

Moodle

Directed Study

Metric and imperial units cross-number