Functional Skills Mathematics

Transcription

1 Functional Skills Mathematics Level 1 Learning Resource Units of Measure MSS1/L1.4 MSS1/L1.5 MSS1/L1.6 MSS1/L1.7

2 Excellence in skills development Contents Length MSS1/L1.4 Pages 3-6 MSS1/L1.6 MSS1/L1.7 Capacity MSS1/L1.4 Pages 7-9 MSS1/L1.6 MSS1/L1.7 Weight MSS1/L1.4 Pages MSS1/L1.6 MSS1/L1.7 Temperature MSS1/L1.4 Pages Distance MSS1/L1.5 Pages West Nottinghamshire College 2

3 Information Length mm = millimetre cm = centimetre m = metre km = kilometre 10 mm = 1 cm 100 cm = 1 m 1000 m = 1 km To convert mm to cm, divide by 10. To convert cm to mm, multiply by 10. To convert cm to m, divide by 100. To convert m to cm, multiply by 100. To convert m to km, divide by To convert km to m, multiply by A millimetre is approximately the thickness of your nail. It is the smallest measurement most people use. A centimetre is approximately the width of your little finger. Examples You can write lengths using decimals, e.g., this nail measures 35 mm or 3 cm 5 mm. This is the same as 3.5 cm. 0 mm cm To add and subtract lengths, all the measurements must be in the same units, i.e. all centimetres or all metres. e.g. To add 3.2 cm and 125 mm a) Convert to centimetres: 3.2 cm cm = 15.7 cm b) To convert to millimetres multiply by cm 10 = 157 mm West Nottinghamshire College 3

4 Exercise 1 Length Graph paper is necessary for this exercise. 1) On a strip of graph paper, draw a line 10 cm long and mark it off in cm a) How many small squares are there to each cm? b) How long is each small square? c) Mark these measurements on your line, measuring from 0. at 6 mm at 2 cm 3 mm at 4 cm 7 mm at 7 cm 1 mm at 9 cm 5 mm 2) Are these measurements sensible? a) A pen is 30 mm Yes/No b) A 1p coin is 2 cm Yes/No c) A safety pin is 1 m Yes/No 3) a) Estimate the length and width of a sheet of paper in cm. Measure the length and width of that same sheet of paper. b) Give your answer in cm. c) Give your answer in mm. West Nottinghamshire College 4

5 Exercise 2 Length Conversion Table From To Operation Amount mm cm 10 cm m 100 m km 1000 cm mm 10 m cm 100 km m 1000 mm m 1000 m mm ) Convert the following into cm. a) 25 mm b) 176 mm c) 3 mm d) 3721 mm 2) Convert the following into m. a) cm b) 190 cm c) 1759 cm d) 81 cm 3) Convert the following into km. a) 3620 m b) 927 m c) 1362 m d) 25 m 4) Convert the following into m. a) 2000 mm b) 1200 cm c) 5 km d) mm 5) Convert the following into cm. a) 20 m b) 15 m c) 2 km (Hint: first convert to m.) West Nottinghamshire College 5

6 Exercise 3 Length 1) You need to calculate how much ribbon is needed to decorate the hall which measures 13 m 29 cm by 10 m 15 cm. HALL Width 10 m 15 Length 13 m 29 cm a) Write 13 m 29 cm as a decimal fraction, using metres, then multiply by 2 or add twice. b) Write 10 m 15 cm as a decimal fraction, using metres, then multiply by 2 or add twice. c) Add the answers of (a) and (b) and express the result as a decimal fraction of a kilometre. 2) Add these measurements, giving your answer in mm: a) 90 cm + 50 mm cm b) 150 mm + 29 cm cm 3) Add these measurements, giving your answer in cm: a) 5 m cm + 87 cm b) 8.5 cm m + 34 cm 4) Subtract these measurements, giving your answer in mm: a) 58 cm 25 mm b) 3.4 m 600 mm West Nottinghamshire College 6

7 Information Capacity ml = millilitre cl = centilitre l = litre 1000 ml = 1 litre 100 cl = 1 litre To convert ml to litres, divide by To convert cl to litres, divide by 100. To convert litres to ml, multiply by To convert litres to cl, multiply by 100. Capacity is the amount that something will hold. Liquid is measured in millilitres, centilitres, and litres. Examples You can write capacity using decimals, e.g., this bottle of liquid is 1250 ml or 1 litre 250 ml. This is the same as 1.25 litres. To add and subtract capacity, all the measurements must be in the same units, i.e. all millilitres or all litres. e.g. To add 400 ml and 1.4 litres a) Convert to millilitres: 400 ml ml = 1800 ml b) To convert to litres divide by ml by 1000 = 1.8 litres West Nottinghamshire College 7

8 Exercise 4 Capacity A 500 ml measuring jug is necessary for this exercise. 1) a) If the jug is half full, how many ml does it contain? b) Write/express that as a decimal fraction of a litre. c) 1 How many ml are there if the jug is full? 4 d) Write/express that as a decimal fraction of a litre. 2) Estimate the divisions on the scale. a) b) c) e) f) a) b) c) d) e) f) 3) You are having a party. You need 10 bottles of red wine, each containing 750 ml. a) Write 750 ml as a decimal fraction of a litre. b) Multiply 750 ml by 10 and write the answer as a decimal fraction, using litres. You buy a further 6 bottles of white wine, each containing 750 ml. c) How many millilitres of white wine do you buy? d) How many ml of wine do you buy in total? e) How many litres do you buy in total? West Nottinghamshire College 8

9 Exercise 5 Capacity From To Operation Amount ml l 1000 l ml 1000 cl l 100 l cl 100 1) Convert these millilitres (ml) to litres. a) 1000 ml b) 5276 ml c) 232 ml d) ml e) 8 ml 2) Put these bottles in order of size, starting with the smallest capacity. 165 ml 1.22 litres 1250 ml 1.8 litres 3) Convert these litres to centilitres a) 2 litres b) 1.8 litres c) 7.25 litres West Nottinghamshire College 9

10 Information Weight g = gram kg = kilogram 1000 g = 1 kg To convert g to kg, divide by To convert kg to g, multiply by A bag of sugar weighs 1 kg. Examples You can write weights in decimals, e.g., this box weighs 6250 grams or 6 kg 250 grams. This is the same as 6.25 kg. To add and subtract weights, all the measurements must be in the same units, i.e., all grams or all kilograms. e.g. To add 420 g and 1.25 kg a) Convert to grams: = 1670 b) To convert to kilograms, divide by = 1.67 kg West Nottinghamshire College 10

11 Exercise 6 Weight A set of kitchen and bathroom scales plus various items for weighing are necessary for this exercise. 1) Weigh the following in grams (g) using a set of kitchen scales. Weight grams a) a book b) a calculator c) a tin of baked beans or something similar 2) Write/express the weight of these items in kilograms (kg). Weight kilograms a) a book b) a calculator c) a tin of baked beans or something similar 3) Estimate the following weights in kilograms (kg). Weight kilograms a) your weight b) a chair c) a basket of laundry 4) Now check your answers using a set of bathroom scales. Write/express the weight of these items in grams (g). Weight grams a) your weight b) a chair c) a basket of laundry West Nottinghamshire College

12 Exercise 7 Weight From To Operation Amount g kg 1000 kg g ) Convert these grams to kilograms. a) 3892 g b) 500 g c) 120 g d) 10 g 2) Convert these kilograms to grams. a) 6 kg b) 18 kg c) kg d) kg 3) Write these weights in kilograms and grams. a) 9500 g kg g b) 4750 g kg g c) 6250 g kg g d) 2500 g kg g 4) Write the weights shown by each arrow (in kg). b) a) c) d) 5) Following on from the previous question. What is the difference, in weight, between: a) 4a) and 4b) b) 4b) and 4d) c) 4a) and 4c) d) 4c) and 4d) West Nottinghamshire College 12

13 Exercise 8 Weight 1) Adam is making some bread. Here is the recipe. 15 g sugar 15 g salt 25 g yeast 450 g flour 100 g margarine a) What is the total weight of these ingredients in grams? b) What is this as a decimal fraction of a kilogram? c) Adam wants to make twice the quantity. List the weight of ingredients that he will need (in grams). g sugar g salt g yeast g flour g margarine 2) Four parcels weigh 2.85 kg, kg, 950 g and 1 kg 25 g. What is the total weight in kg? 3) Work out these calculations and give your answer in kilograms. a) 2 kg g b) 4 kg kg c) kg g 4) Find the differences in weight (in kg) between: a) 6 kg and 800 g b) 18 kg 1 kg 200 g c) kg and 3.4 kg 1 5) A shopper buys 5 kg of potatoes, kg of carrots, 300 g of turnips and a bag of 2 mushrooms weighing 220 g. How heavy is the shopping altogether (in kg)? West Nottinghamshire College 13

14 MSS1/L1.4 Information Temperature Temperature is measured in degrees using a thermometer. Many thermometers show temperatures in Celsius and Fahrenheit. You can use comparison scales to compare and convert between Celsius and Fahrenheit. The Celsius scale (written in C) has two reference points which are important to us: 0 C which is the freezing point of water; 100 C which is the boiling point of water. Normal body temperature is 37 C (98.6 F) but may vary by up to 1 C (2 F) throughout the day; it is at its lowest in the early hours of the morning. A high temperature of 40 C (104 F) means you have a fever. Example 32 F Conversion scales 212 F F C 0 C Freezing point 100 C Boiling point C = degrees Celsius F = degrees Fahrenheit West Nottinghamshire College 14

15 MSS1/L1.4 Exercise 9 Temperature 1) The temperature at which water freezes is: a) F b) C 2) The temperature at which water boils is: a) F b) C 3) The weather forecast for tomorrow shows a maximum temperature of 21 C. Is it going to be: a) cold b) warm c) hot 4) What temperature could you expect in January/February? a) 0 C - 10 C b) C - 20 C c) 21 C - 30 C 5) The temperature gauge registers -3 C. Is this: a) mildly cold b) very cold c) quite warm 6) Look at the weather forecast in a newspaper and record the expected temperature for tomorrow. a) C b) F 7) Is it likely to be: a) cold b) warm c) hot West Nottinghamshire College 15

16 MSS1/L1.5 Information Distance In this country distance is measured in miles, but, in mainland Europe, distance is measured in kilometres. 1 kilometre is 8 5 mile. It takes approximately 20 minutes to walk 1 mile. You will often find a distance chart in a road map; this shows an approximate distance between major cities. When you look at a road map, it will often have a scale shown on the front cover. You can use this scale to estimate the distance you will be travelling or the distance between two cities. West Nottinghamshire College 16

17 MSS1/L1.5 Examples Distance Example 1 Distance Chart Aberdeen 514 Cardiff Not genuine Dover Edinburgh Glasgow Hull Leeds To find the distance between the cities, you simply follow the rows and columns until they meet. e.g. Aberdeen Hull is 479 miles. Example 2 Sketch Road Map This is a sketch map using a scale of 1 cm representing 100,000 cm or 1 km. This means that on the map, the road measures 3 cm between Hoptown and Goodwich and this represents 3 km; so it is 3 km from Hoptown to Goodwich. The towns are shown by the dots CROWBRIDGE BROUGHTON CARLTON HOPTOWN SHIPLEY RICHMOND GOODWICH BRADSTOCK SPRINGWOOD CHANDBURY 1cm Scale 1: 100,000 West Nottinghamshire College 17

18 MSS1/L1.5 Exercise 10 Distance Using the grid shown on the previous page, answer the following: 1) How many miles between: a) Aberdeen/Hull b) Cardiff/Glasgow c) Aberdeen/Edinburgh d) Dover/Leeds 2) Find the nearest city to where you live on the grid. a) What is the city called? How far is it from this city to: b) Edinburgh c) Leeds d) Exeter 3) Draw a line to match each journey time shown on the left with an approximate distance. 1 hour by train 4 miles 10 minutes walking 50 miles 1 hour by car 1 mile 2 2 hour walking 85 miles 4) In order to complete this exercise you will need a road map which includes a distance chart. Using a map locate your nearest town or village. The scale tells you what every inch/cm on the map represents. a) How far is it to the next nearest town? b) How far to the nearest city? West Nottinghamshire College 18