Week 10 Perimeter, area and volume (including circles) Functional MATHS Week 10 Perimeter, area and volume (including circles)

What are the arrows for A to M pointing to? Today’s starter… What are the arrows for A to M pointing to? A B C D E F G H I J K L M

Units and measures What did we do last week? Estimate, measure and compare length, capacity and weight Convert between metric units Convert between metric and imperial units (L2) Solve problems requiring calculation with temperature, time and money

Units and measures Recap

What units do we measure the following in? Length Weight Capacity (volume)

Metric Conversions - LENGTH Functional Skills Mathematics - Measurements Metric Conversions - LENGTH

How many metres to London? Units of Distance 1km = 1000 m 1 m = 100 cm 1 cm = 10 mm Use these relationships to help you work out the following problems: London 5 km How many metres to London? 5 000 m Km to m

0.95 km Units of Distance 1km = 1000 m 1 m = 100 cm 1 cm = 10 mm Use these relationships to help you work out the following problems: How many km to Berlin? Centre 950 m 0.95 km

Units of Distance 2.15 m length 215 cm 0.9 m width = 90 cm 1km = 1000 m 1 m = 100 cm 1 cm = 10 mm Use these relationships to help you work out the following problems: Find the length and width of the pool table in cm. 2.15 m length 215 cm 0.9 m width = 90 cm

Units of Distance height = 7650 mm width = 3040 mm 1km = 1000 m 1 m = 100 cm 1 cm = 10 mm Use these relationships to help you work out the following problems: Find the height and width of the tower in mm. height = 7650 mm 7.65 m width = 3040 mm 3.04 m

Metric Conversions - Weight Functional Skills Mathematics - Measurements Metric Conversions - Weight

Units of weight This German shepherd puppy weighs 5.4kg. What is this in grams? 5.4 x 1000 = 5400 grams

Metric Conversions – Capacity (volume) Functional Skills Mathematics - Measurements Metric Conversions – Capacity (volume)

Units of capacity (volume) The liquid in this jug is filled to 300ml. 300 / 1000 = 0.3 litres What’s this in litres?

Write these down and work them out… You need to be able to convert distances between mm, cm, m, km 50cm = m 3000m = km 500mm = cm 6.5m = cm 1.5m = mm 0.5 3 50 650 1500

Task: Organising the new office How many filing cabinets are you able to fit along the wall with the desk? How much space is there left along the wall

Put your name on it please before handing in! Directed Study

What are we going to do today? Perimeter, area and volume Use metric units in everyday situations Work out areas and perimeters in practical situations Find the area, perimeter and volume of common shapes (including circles) Please write your SMART target on the top of your blue feedback form …

Perimeter

Perimeter 15 m 5 m 5 m 15 m Perimeter = 15 m + 5 m + 15 m + 5 m = 40 m The perimeter of a shape is the distance around the outside. Rectangles 15 m 5 m 5 m Length Width 15 m Perimeter = 15 m + 5 m + 15 m + 5 m = 40 m

Example 4 cm 7 cm Essential working Perimeter = 4 + 7 + 4 + 7 = 22 cm Perimeter = 8 + 14 = 22 cm Perimeter = 2 x 11 = 22 cm Perimeter = 2 x 4 + 2 x 7 = 22 cm Discuss these different ways of showing your method. Can you think of any others?

Find the perimeter of each rectangular shape below. 1 2 3 4 5 8½ cm 5½ cm 90 feet 50 feet 210 cm 90 cm Not to scale. 280 ft 300 m 600 cm = ? 320 m 28 cm

Find the perimeter of the shapes below. 5 cm Find the perimeter of the shapes below. Regular Pentagon Regular Hexagon Regular Quadrilateral 6 cm 7 cm Irregular Quadrilateral 3 mm 4 mm 6 mm 9 mm 7 mm 10 mm Irregular Pentagon Diagrams not to scale Square P= 4 x 5 = 20 cm P= 5 x 6 = 30 cm P= 6 x 7 = 42 cm P= 3 + 3 + 4 + 6 = 16 mm P= 3 + 10 + 3 + 7 + 9 = 32 mm

Perimeter of Compound Shapes Diagrams Not to scale Perimeter = ? 1m 3m 4m 4 m + 4 m + 7 m + 3m + 3m + 1m + = 22m

Perimeter of Compound Shapes Not to scale Perimeter = ? 5 m 4 m 2 m + 2 m + 5 m + 4 m + 2 m + 2 m + 5 m + 8 m = 30 m

Area

18 cm2 AREA 6 cm 3 cm 1 cm2 Area = 6 cm x 3 cm = 18 cm2 Remember: The perimeter of a shape is a measure of distance around the outside. The area of a shape is a measure of the surface/space contained within its perimeter. Area is measured in units2 Units of distance mm cm m km inches feet yards miles Units of area mm2 cm2 m2 km2 inches2 feet2 yards2 miles2 1 cm 1 cm2 6 cm 3 cm Metric Imperial 18 cm2 Area = 6 cm x 3 cm = 18 cm2

Find the area of each rectangular shapes below. 100 m 50 m 120 m 40 m 1 2 3 4 5 8½ cm 5½ cm 90 feet 50 feet 210 cm 90 cm Not to scale. 4500 ft2 5 000 m2 18 900 cm2 4 800 m2 46.75 cm2

Area of Compound Shapes Diagrams Not to scale Area of Compound Shapes 16 m2 9 m2 Area = 4 x 4 + 3 x 3 = 16 + 9 = 25 m2

6 cm 2 cm 8 cm 12 cm 4 cm 6 cm 2 cm 8 cm 12 cm 4 cm 8 cm2 12 cm2 16 cm2 24 cm2 2 cm 8 cm2 12 cm2 2 cm Area = 24 + 8 + 8 = 40 cm2 Area = 16 + 12 + 12 = 40 cm2

Area of Compound Shapes Not to scale 16 m2 ? 6 m2 3 m 20 m2 ? 4 m Area = 16 + 20 + 6 = 42 m2

Perimeter and Area Exercise New Flat: Perimeter and Area Exercise Plan of flat Plan of garden

Volume

Front face 20 cm2 2D Volume of a Cuboid 3D 4 cm 5 cm Remember: the area of a shape is a measure of the surface/space contained within its perimeter. 2D Volume of a Cuboid The volume of a shape is a measure of the space contained within its faces/boundary. 3D 1 cm 1 cm3 1 cm2 1 cm Units of area mm2 cm2 m2 km2 inches2 feet2 yards2 miles2 Metric Imperial Units of volume mm3 cm3 m3 km3 inches3 feet3 yards3 miles3 Metric Imperial 4 cm Front face 20 cm2 5 cm

20 cm3 40 cm3 60 cm3 2D 3D Volume Volume of a Cuboid 5 cm 4 cm 3 cm Remember the area of a shape is a measure of the surface/space contained within its perimeter. Units of area mm2 cm2 m2 km2 inches2 feet2 yards2 miles2 Metric Imperial 1 cm2 1 cm The volume of a shape is a measure of the space contained within its boundary. Units of volume mm3 cm3 m3 km3 inches3 feet3 yards3 miles3 1 cm3 5 cm 4 cm 20 cm3 40 cm3 60 cm3 3 cm Volume = 4 cm x 5 cm x 3 cm = 60 cm3

Volume of a Cuboid 9.6 mm 5 mm 2.3 mm Find the volume of the following cuboids (to 1 dp) Diagrams not to scale. 12 cm 8.1 cm 1.3 cm 3.1 cm 1 2 3 Volume = 2.3 x 9.6 x 5 = 110.4 mm3 Volume = 3.1 x 3.1 x 3.1 = 29.8 cm3 Volume = 1.3 x 12 x 8.1 = 126.4 cm3

Volume of Objects 6 cm 3 cm 21 cm 13 cm 1.1 m 1.3 m 1.8 m Volume = 3 cm x 13 cm x 21 cm = 819 cm3 Volume = 63 = 216 cm3 Volume = 1.3 m x 1.8 m x 1.1m = 2.574m3

Volume of Compound Shapes 8 cm 12 cm 5 cm 2 cm 3 cm Not to scale Volume = 5 x 2 x 8= 80 cm3 80 cm3 512 cm3 288 cm3 Volume = 83 = 512 cm3 Volume = 12 x 3 x 8= 288 cm3 Volume = 512 + 288 + 80 = 880 cm3

Volume problems worksheet

Volume problems worksheet

Volume problems worksheet

Circles Circumference Area

circumference. radius. The distance all the way round the outside of a circle is called the circumference. Radius From the centre of the circle to the circumference is called the radius.

diameter diameter A line which passes through the centre of a circle and touches the circumference twice is called a diameter diameter

r = ½ D D = 2r The radius is half of the diameter radius radius

Pi to the first 1000 decimal places is:- Even with all these decimal places - pi still works out to be a bit more than 3

Area of a circle =  x the radius squared A =  r 2

Circumference of a circle =  x the diameter C =  D

Circumference and area of a semi circle?? Just half it! ÷ by 2

The circumference of a Circle C =  D Find the circumference of the following circles. 1 2 8 cm 18.7 cm C =  D C =  x 16 C = 50.3 cm (1 dp) C =  D C =  x 18.7 C = 58.8 cm (1 dp)

The Area of a Circle A = r2 1 2 Find the area of the following circles. 1 2 8 cm 9.5 cm A = r2 A =  x 82 A = 201.1 cm2 (1 dp) A = r2 A =  x 9.52 A = 283.6 cm2 (1 dp)

A = r2 Find the area of the clock face and radar screen. 12 cm 60 cm A =  x 122 A = 452.4 cm2 (1 dp) A = r2 A =  x 302 A = 2827 cm2 (nearest cm2)

The Area of a Circle A = r2 1 2 Find the area of the following semi-circles. 1 2 8 cm 9.5 cm A = ½r2 = ½ x  x 42 = 25.1 cm2 (1 dp) A = ½r2 = ½ x  x 4.752 = 35.4 cm2 (1 dp)

Directed Study

Please complete and bring back next week…. Level 1 Level 2