Correct the following equation so that it makes sense – you can add numbers and operators to it. Challenge: Make the equation make sense by re-arranging the digits – you cannot add anything new! How quickly can you find out what is unusual about this  paragraph? It looks so ordinary that you would think that nothing was wrong with it at all and, in fact, nothing is. But  it is unusual. Why? If you study it and think about it you may  find out, but I am not going to assist you in any way. 79 = 24

This week: area, perimeter, volume Convert units of measure and calculate the area, perimeter and volume of common shapes Find perimeters and areas of 2D shapes, including triangles, parallelograms and trapeziums Name units of measure for area, perimeter and volume Calculate volume and surface area of common 3D shapes Circle vocabulary and formula used to find the circumference and area of a circle Solve missing number area, perimeter and volume problems Use reverse methods to calculate missing values

Metric Imperial Length Weight Capacity

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, area and volume 1cm 1cm2 1cm3 Distance around the outside of a 2D shape Space inside a 2D shape Space inside a 3D shape

Perimeter and Area 3cm 5cm 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. 3cm 5cm 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… 4cm 6cm Perimeter = Area = 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 height of this cuboid: 280cm³ = 10 × 7 × h h = 280 ÷ (10 × 7) h = 4cm Find the volume of this cuboid: Volume = 3 × 5 × 4 Volume = 60cm³ Volume = 280cm³ 3cm 7cm 4cm 10cm 5cm

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

Volume of Prisms Volume = Area of cross section x depth 11cm Volume = Area of cross section x depth Area of cross section = (11 x 8) ÷ 2 = 44cm2 9cm 8cm 20cm Volume = 44 x 20 = 880cm3 11cm 7mm 7mm 105m3 5cm 343mm3 80cm3 6m 5m 2cm 7m 8cm 7mm 6m

Cylinder What is the volume of this cylinder? Volume = r2h

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

Cones If Pringles came in a cone, which was the same height and diameter as the tall tube, it would contain one third of the calories. Why? Pringles A third of the calories

Cones Slant height (l) Example: find the volume of this cone Volume =

Pyramids Volume = 1/3 x base area x height Find the volume of this pyramid Volume = 1/3 x base area x height

Spheres 4/3π of the volume of a cube-shaped container. Find the volume of a sphere whose diameter is 15 cm 4/3π of the volume of a cube-shaped container. Volume =

Surface Area Surface area is the total area of the outside of a 3D object Each face is the same – a square. Area A = 5 x 5 = 25cm2 Total Surface Area = 6 x 25 = 150cm2 5cm A 5cm 5cm

A B C Surface Area 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

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

Word Problems A length of copper piping is in the shape of a triangular prism. The triangle on it’s end is a right angle, 9mm by 4mm by 10mm. The piece of pipe is 18cm long. What is the surface area of the pipe? Area of Triangles = (9 x 4) ÷ 2 = 18mm2 = 18 x 2 = 36mm2 10mm Front Rectangle = 180 x 10 = 1800mm2 9mm 180mm 4mm Back Rectangle = 180 x 9 = 1620mm2 Base Rectangle = 180 x 4 = 720mm2 Total Surface Area = 36 + 1800 + 1620 + 720 = 4176mm2

Surface Area SA = 294cm2 SA = 378cm2 SA = 270cm2 Calculate the Surface Area of the cube and cuboids shown below: SA = 294cm2 SA = 378cm2 7cm 15cm 3cm EXTENSION: SA = 270cm2 9cm 8cm 6cm 12cm 5cm

Surface Area of a Cone, Sphere & Cylinder SA = π rl SA =4 π r2 Cylinder r h SA = Curved surface area + Top + Bottom h 2 π r Curved area = = 2 π rh SA = 2 π rh + 2 π r2

Circumference Circumference = π × diameter circumference diameter

Examples Circumference = π × diameter Circumference: = π × 4 4cm = 12·57cm (2 d.p.) 8cm Circumference: = π × 16 = 50·27cm (2 d.p.)

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

Example Area = π × radius × radius Area 7cm = π × 7 × 7 = π × 7 × 7 = 153·94cm² (2 d.p.) area 10cm Area = π × 5 × 5 = 78·54cm² (2 d.p.)

Find the circumference and area of this circle: Exam Question 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: Exam Question 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 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