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Volume www.mathsrevision.com S4 Counting Volume cubes Volume of a cuboid Liquid Volume Scales Weight and Scales Using Weights 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Starter Questions S4 www.mathsrevision.com 1. Find 20% of 650 2. Round to 1 decimalplace (a) 172.66 (b) 2.78 3. I got paid £364 for 7 days work. What is my daily rate of pay. 4. 21-Jul-15 July 21, 2015 Tuesday, 1 of 210 7 Compiled Created by Mr. byLafferty Mr. Lafferty Maths Dept. @www.mathsrevision.com 2 Volumes by Counting Cubes www.mathsrevision.com S4 Learning Intention 1. To understand the term volume in terms of counting cubes. Success Criteria 1. To know what volume means. 2. Work out volumes using 3 1cm cubes. 3. Answer to contain appropriate units. 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Volume & Weight S4 www.mathsrevision.com Volume is the amount of space a 3D - shape takes up Grain of salt 1mm2 21-Jul-15 A dice 1cm2 Compiled by Mr. Lafferty Maths Dept. 4 Wheelie bins 1m2 Volume & Weight S4 www.mathsrevision.com Weight is measured in grams, Kilograms and Tonnes A cubic centimetre of water weights exactly 1g A litre of water weights exactly 1 kg A cubic metre of water weighs exactly 1 Tonne 1g 21-Jul-15 1kg Compiled by Mr. Lafferty Maths Dept. 1Tonne Volume & Weight S4 www.mathsrevision.com What unit of volume should you use to measure (a) Packet of cereal cm3 (b) A diamond mm3 (c) A warehouse m3 (d) A raindrop mm3 (e) The water in a swimming pool m3 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Volume & Weight S4 www.mathsrevision.com What unit of weight should you use to measure (a) A person kg (b) A yacht Tonnes (c) A cup of water g (d) A load of timber Tonnes (e) A feather g 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Volumes by Counting Cubes S4 www.mathsrevision.com Volume is the amount of space a 3D - shape takes up 1cm 1cm One Unit of Volume is the “CUBIC CENTIMETRE” = 1 centimetre cube = 1 cm³ 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Volumes by Counting Cubes www.mathsrevision.com S4 This shape is made up of 1 centimetre cubes placed next to each other. What is its volume in cm³ 1cm 1cm 1cm = 3 centimetre cubes = 3 cm³ 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Volumes by Counting Cubes S4 www.mathsrevision.com What is its volume in cm³ of these shapes. 3 5 cm 3 5 cm 21-Jul-15 3 6 cm Compiled by Mr. Lafferty Maths Dept. Volumes by Counting Cubes S4 www.mathsrevision.com One unit of Volume is the “CUBIC CENTIMETRE” 3cm 4cm Volume = 24 centimetre cube = 24 cm³ 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Volumes by Counting Cubes www.mathsrevision.com S4 Now try Ex 2.1 Ch4 (page 57) 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Starter Questions S4 www.mathsrevision.com 1. Find 25% of 640 2. Round to 1 decimalplace (a) 163.82 (b) 72.38 3. I got paid £54 for 9 hours work. What is my hourly rate of pay. 4. 21-Jul-15 July 21, 2015 Tuesday, 1 of 450 9 Compiled Created by Mr. byLafferty Mr. Lafferty Maths Dept. @www.mathsrevision.com 13 Volume of a cuboid www.mathsrevision.com S4 Learning Intention 1. To understand how to calculate the volume of cuboid. Success Criteria 1. To know the formula. 2. Use formula correctly. 3. Show working and appropriate units. 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Volume of a cuboid S4 18 cubes fit the base. 4cm 6cm 3cm = 1 centimetre cube = 1 cm³ 4 layers of 18 cubes = 4 x 18 = 72 centimetre cubes = 72 cm³ 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. A short cut ! S4 height 4cm Area of rectangle 6cm 3cm breadth length Volume = 6 x 3 x 4 = 72 cm³ Volume = length x breadth x height 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Example 1 Working Volume = l x b x h 27cm V = 18 x 5 x 27 V = 2430 cm³ Heilander’s Porridge Oats 18 cm 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Example 2 S4 Working Volume = l x b x h V=2x2x2 V = 8 cm³ 2cm 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Volume of a cuboid www.mathsrevision.com S4 Now try Ex 3.1 & 3.2 Ch4 (page 58) 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Starter Questions S4 www.mathsrevision.com 1. Find 50% of 95 2. find the time difference between 08.30 and 16.39 3. What is the better deal 3 bars of soap for 99p or 4 bars of £1.40 4. 21-Jul-15 July 21, 2015 Tuesday, 1 of 240 5 Compiled Created by Mr. byLafferty Mr. Lafferty Maths Dept. @www.mathsrevision.com 20 Liquid Volume www.mathsrevision.com S4 Learning Intention 1. To understand the term liquid volume using millilitres and litres. Success Criteria 1. To know the term liquid volume. 2. Work out volumes using ml and litres. 3. Answer to contain appropriate units. 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Liquid Volume www.mathsrevision.com S4 A cube with volume 1cm³ holds exact 1 millilitre of liquid. A volume of 1000 ml = 1 litre. Liquids are measured in ml and litres These jugs have different scales. How do we work out how much liquid in a jug? 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Liquid Volume S4 www.mathsrevision.com How much liquid in the jug ? Litres Count the number of small divisions 2 1litre 5 = 1000ml Each division is worth 1 1 litre ÷ 5 = 1000ml ÷ 5 = 200ml 0 200ml x 4 = 800ml 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Liquid Volume S4 www.mathsrevision.com How much liquid in the jug ? Litres 2 1 Count the number of small divisions 1litre 5 = 1000ml Each division is worth 1 litre ÷ 5 = 1000ml ÷ 5 = 200ml 200ml x 7 = 1400ml or 1.4 litres 0 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Liquid Volume S4 www.mathsrevision.com How much liquid in the jug ? ( Careful different scale) Litres 2 1 0 Count the number of small divisions 1litre 4 = 1000ml Each division is worth 1 litre ÷ 4 = 1000ml ÷ 4 = 250ml 250ml x 7 = 1750ml or 1.75 litres 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Liquid Volume www.mathsrevision.com S4 Now try Ex 4.1 Ch4 (page 61) 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com S4 Q1. Convert to 24hr clock Q2. Round to 1 decimal place 103.525 Q3. How many minutes in 6 hours Q4. Find the time difference between 5.12am and 2.34pm 21-Jul-15 8.15am Compiled by Mr. Lafferty Maths Dept. 10.02pm Weight & Scales www.mathsrevision.com S4 Learning Intention 1. To explain how to read scales for weighs and how to convert from grams to kilograms and vice versa. 21-Jul-15 Success Criteria 1. To be able to read scales. 2. Be able to convert from grams to kilograms and vice versa. Compiled by Mr. Lafferty Maths Dept. Weight & Scales www.mathsrevision.com S4 Calculate the weight each arrow is pointing at? 120g 0 100g Count the number of small divisions 5 200g 300g 500g 400g Each division is worth 280g 100 ÷ 5 = 20g 540g 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Weight & Scales www.mathsrevision.com S4 Calculate the weight each arrow is pointing at? 80g 0 200g Count the number of small divisions 5 400g Each division is worth 600g 1kg 800g 200 ÷ 5 = 40g 720g 1kg 20g 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Weight & Scales www.mathsrevision.com S4 Calculate the weight each arrow is pointing at? 80g 0 200g Count the number of small divisions 5 400g Each division is worth 600g 1kg 800g 200 ÷ 5 = 40g 720g 1kg 20g 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Weight & Scales www.mathsrevision.com S4 Kilograms 2kg 1.5kg grams 21-Jul-15 3000g 1500g x 1000 2 x 1000 1.5 x 1000 ÷ 1000 3000 ÷ 1000 1500 ÷ 1000 Compiled by Mr. Lafferty Maths Dept. grams 2000g 1500g Kilograms 3kg 1.5kg Weight & Scales www.mathsrevision.com S4 Now try Ex 5.1 & 6.1 Ch4 (page 63) 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Starter Questions Level E www.mathsrevision.com 1. Find the missing angle 2. 3 cans of juice cost £2.40. How much for 2 cans. 3. 78 10 4. Find 2 numbers that add to 20 and divide to give 1. 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. 40o Weight & Scales www.mathsrevision.com S4 Learning Intention 1. To solve problems involving weight and proportion. Success Criteria 1. To be able to convert between grams and kilograms. 2. Use proportion to solve weight problems. 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Weight & Scales S4 www.mathsrevision.com You need to remember the following. 1000g = 1kg 1000kg = 1 tonne Example : Change 1.7kg to grams 1.7 x 1000 = 1700g 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Weight & Scales S4 www.mathsrevision.com You need to remember the following. 1000g = 1kg 1000kg = 1 tonne Example : Change 3200kg to tonnes 3200 ÷ 1000 = 3.2 tonnes 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Weight & Scales S4 www.mathsrevision.com You need to remember the following. 1000g = 1kg 1000kg = 1 tonne Example : Change 4.5kg to kg and grams 4 kg 500g 21-Jul-15 Compiled by Mr. Lafferty Maths Dept. Using Weight S4 www.mathsrevision.com 4 packets of crisps weigh 100g (a) What is the weight of 1 packet. (b) What is the weight of 6 packets. Answer : (a) Answer : (b) 21-Jul-15 4pkts 100g 1 pkt 100 ÷ 4 = 25g 6 pkts 25 x 6 = Compiled by Mr. Lafferty Maths Dept. 150g 39 Using Weight S4 www.mathsrevision.com 6 teacakes weigh 120g (a) What is the weight of 1 teacake. (b) What is the weight of 10 teacakes. Answer : (a) Answer : (b) 21-Jul-15 6pkts 120g 1 pkt 120 ÷ 6 = 20g 10 pkts 20 x 10 = 200g Compiled by Mr. Lafferty Maths Dept. 40 Weight & Scales www.mathsrevision.com S4 Now try Ex 7.1 & 7.2 Ch4 (page 65) 21-Jul-15 Compiled by Mr. Lafferty Maths Dept.