Understanding Functional Skills Maths level 1 Workbook 8 - Converting units of measure EQL SOLUTIONS
INTRODUCTION TO THE MATHEMATICS FUNCTIONAL SKILLS QUALIFICATION AT LEVEL 1 In order to meet the assessment criteria for mathematics at level 1 you will be required to demonstrate your ability to represent, analyse and interpret, using number, geometry and statistics plus a selection of other skills in the coverage and range within functional contexts. Represent Analyse Interpret This means that you will need to: Understand practical problems in familiar and unfamiliar situations. Identify and obtain the necessary information to tackle the problem. Select mathematics in an organised way to find solutions. This means that you will need to: Apply mathematics to find solutions to straightforward practical problems for different purposes. Use appropriate checking procedures at each stage. This means that you will need to: Interpret and communicate solutions to practical problems; drawing simple conclusions and giving explanations. Functional Skills in mathematics at level 1 has 14 areas of coverage and range : Understand and use whole numbers and understand negative numbers in practical contexts Add, subtract, multiply and divide whole numbers using a range of strategies Understand and use equivalences between common fractions, decimals and percentages Add and subtract decimals up to two decimal places Solve simple problems involving ratio, where one number is a multiple of the other Use simple formulae expressed in words for one-or two-step operations Solve problems requiring calculation, with common measures, including money, time, length, weight, capacity and temperature Convert units of measure in the same system Work out areas and perimeters in practical situations Construct geometric diagrams models and shapes Extract and interpret information from tables, diagrams, charts and graphs Collect and record discrete data and organise and represent information in different ways Find mean and range Use data to assess the likelihood of an outcome Page 2
You will be given 1 1/2 hours to complete the test, in which there will be a total of 40 possible marks to achieve. The 40 marks will be broken down into different tasks or a series of questions. Over 75% of the questions will require open-response answers. Open response assessment is defined as: Task-based assessment based on real-life contexts that require learners to apply their skills, knowledge and understanding in order to resolve problem/s or produce effective outcome/s Presenting purposeful tasks and problems, embedded in realistic scenarios but does not prescribe the processes or the methods by which the learner responds Instead of choosing from answers given to you, with this type of question you will need to show the process you have used to obtain your final answer. It is very important to read the question carefully. The way the question is worded will give you valuable clues about how you should answer it. Please note - Calculators are provided for use during the test. Top Tip After each question in your test the maximum number of marks you can obtain through your answer will be displayed. This should give you a clue about how much detail you are expected to show. It is a good idea to try to complete a question, even if you are unsure that you have the correct answer, as you may be awarded some marks for the method you have shown. Page 3
Please find below a selection of very useful websites that can provide additional support resources in Maths. Please take the time to study and review these. http://www.bbc.co.uk/skillswise/maths Click on a topic you are interested in and you will see the different types of materials or activities that are there to help you with that topic. For each topic, you will find fact sheets, worksheets, quizzes and games. Job skills related resources also available. http://www.skillsworkshop.org/numeracy A good site with adult literacy and numeracy activities including more than 1500 free Functional Skills and Skills for Life resources. http://rwp.excellencegateway.org.uk/interactive%20materials/ These are interactive literacy and numeracy practice materials, designed to supplement teaching. The practice material is generic and has been set in everyday recognisable settings. http://www.braingames.org.uk/brain_games_main/flash.aspx Interactive quizzes that allows you to develop both English and maths skills. Even has a facility to be used on a mobile device. Page 4
CONVERTING BETWEEN POUNDS AND PENCE There are 100 pence in one pound. Money can be written as, for example, 5.50, which means five pounds and fifty pence. The decimal point separates the pounds from the pence. In some cases you will see money written as 550p. This is the same amount but there is no decimal point. You should not write money as 5.50p using both and p. The cost of petrol is written in pence. The cost of unleaded petrol in this photo is 117.9p. If this were written in pounds it would be given as 1.17 and 9/10. But since we can t have 9/10 of a penny it would be rounded up to 1.18. 50p in pounds would be written 0.50. 5p in pounds would be written 0.05. Page 5
CONVERTING FROM HOURS TO MINUTES To convert from hours to minutes we first need to remember that there are 60 minutes in every hour. Example: Take a look at these car parking prices. Daily Tariff Up to 2 Hours - 2.60 Up to 4 Hours - 3.40 Up to 6 Hours - 4.80 Up to 8 Hours - 6.00 Up to 12 Hours - 9.00 Up to 24 Hours - 15.00 How many minutes would you get for 3.40? Looking at the table, 3.40 pays for 4 hours. To change hours into minutes multiply by 60. Each hour has 60 minutes; this means that you get 4 lots of 60. 4 x 60 = 240 minutes. There are 240 minutes in 4 hours Therefore you would get 240 minutes for 3.40. Page 6
CONVERTING FROM MINUTES TO HOURS Time is sometimes given in minutes rather than hours and minutes. For example: Film title Star Wars Episode 1: The Phantom Menace 3D The Artist Running time 132 minutes 100 minutes The Woman in Black 95 minutes Big Miracle 107 minutes There are 95 minutes of viewing in The Woman in Black. Is the film longer than an hour? Is it more than 2 hours? There are 60 minutes in one hour. Two hours would be 2 x 60 = 120 minutes. So 95 minutes is more than an hour but less than 2 hours. In fact if you subtract 60 from 95 you get 35 minutes. So the film is 1 hour 35 minutes long. For Star Wars Episode 1, find out how many times 60 divides into the 132 minutes. 132 60 = 2 (with 12 minutes left over). So you get 2 hours and 12 minutes of viewing. You could use a number line that goes up in multiples of 60 to help: Hours 1 2 3 4 5 Minutes 60 120 180 240 300 Page 7
HOW TO CALCULATE CONVERSIONS BETWEEN CENTIMETRES AND METRES MSS1/ L1.4, MSS1/ L1.7, MSS1/ L2.3, MSS1/ L2.5 There are 100 centimetres in 1 metre. To convert from metres to centimetres MULTIPLY by 100. To convert from centimetres to metres DIVIDE by 100. Example 1: Example 2: Convert 2.5 metres into centimetres. Solution: Convert 360cm into metres. Solution: 2.5m = 2.5 100cm = 250cm 360cm = 360 100m = 3.6m (the point has moved two places to the left) Conversions between grams and kilograms There are 1,000 grams in 1 kilogram. To convert from kilograms to grams MULTIPLY by 1,000. To convert from grams to kilograms DIVIDE by 1,000. Example: Convert 5.5 kilograms into grams. Solution: 5.5kg = 5 1,000g = 5,500g (the point has moved three places to the right) Page 8
Conversion between litres and millilitres There are 1,000 millilitres in 1 litre. To convert from millilitres to litres MULTIPLY by 1,000. To convert from litres to millilitres DIVIDE by 1,000. Example: Convert 5.5 litres into millilitres. Solution: 5.5 l = 5.5 1,000ml = 5,500ml (the point has moved three places to the right). Page 9
QUESTIONS The Akram Family 1. The Akram family go into the zoo gift shop Here is a list of some of the things on sale in the gift shop. Big Cats pen set - 3.75 Dolphin pen set - 3.75 Postcard - 60p Big Cats poster - 3.25 Dolphins poster - 3.25 Mrs Akram says she will buy some things for Jason and Laxmi. Jason chooses the Big Cats pen set. Laxmi chooses the Dolphin s poster and the postcard Mrs Akram pays with a 10 note. How much change should Mrs Akram get? Use the box below to show clearly how you get your answer. Page 10
Recording TV Programmes 2. Tim wants to record four TV programmes while he is on holiday. Day Programme Starts Finishes Thursday Top Gear 8pm 9pm Friday Mad Men 10.50pm 11.40pm Saturday Casualty 8.10pm 9pm Sunday The Bourne Identity 8pm 10.20pm There is only 5 1/2 hours of recording time left on Tim s recorder. Is there enough recording time left for all four TV programmes? Use the box below to show clearly how you get your answer. Page 11
Rob s Jobs 3. Here is a list of jobs Rob has to do on Monday. The time for each job includes Rob s travelling time. Mrs Andrews Double oven Morning (2 hours) Mr Long Hob and fan Afternoon (1 1/2 hours) Betty Grey Single oven Morning or afternoon (1 1/2 hours) Sam Bell Barbeque Morning or afternoon (1 1/2 hours) Rob wants to: Start work at 9am Finish work by 5pm Have at least 30 minutes for his lunch break Rob needs to plan the order he will do the jobs He needs to know the time he will start each job. Make a time plan for rob for Monday. Show your time plan in the box below. Page 12
Boomerang Ride 4. Toni is 138cm tall. BOOMERANG RIDE To go on the Boomerang Ride you must be at least 1.4m tall Is Toni tall enough to go on the Boomerang ride? Use the box below to show clearly how you get your answer. Page 13
Eggs 5. Monty keeps the eggs in a tray. The tray is 633mm wide. He wants to put the tray in a space 0.7m wide. Is the space wide enough for the tray? Use the box below to show clearly how you get your answer. Page 14
Rabbits 6. The rabbits need a space to run in the garden. Cathy needs to put wire fencing around this space. The diagram shows a plan of Cathy s garden. Space for rabbits Diagram not accurately drawn 170cm 80cm Cathy s garden Cathy does not need to put wire fencing where the wall is. How many metres of wire fencing does Cathy need? Use the box below to show clearly how you get your answer. Page 15
Floors 7. Tony needs some new floors in his house. He is going to make a concrete floor in the kitchen. Tony needs 850kg of cement to make the concrete. The graph shows the amount of sand he needs for different amounts of cement. 1,000kg = 1 tonne How many tonnes of sand does tony need for 850kg of cement? Use the box below to show your answer. Page 16
Six Bottles 8. Rob buys oven cleaner in 5 litre containers. He pours the oven cleaner into 750ml spray bottles. Oven cleaner 5 litres Oven cleaner 750ml How many spray bottles can Rob fill up completely from the 5 litre container? Page 17
ANSWERS The Akram Family 1 In this question you will need to add and subtract with money and convert between pounds and pence. First you will need to add up the total cost of the items purchased. 3.75 + 3.25 + 60p ( 0.60) = 7.60 If Mrs Akram pays with a 10 note you will then need to subtract the total cost of the items bought from this amount. 10.00-7.60 = 2.40 Mrs Akram will therefore get 2.40 in change. 2. Recording TV Programmes In this question you will need to add and convert units of time. The first thing you will need to do is to calculate the length in time of each programme that Tim wants to record. Top Gear = 1 hour Mad Men = 50 Minutes Casualty = 50 minutes The Bourne Identity = 2 hours 20 minutes If we add the lengths of the programme together we will then be able to identify whether Tim has enough time left on his recorder. The easiest way to do this is to convert all the times into minutes. Top Gear Mad Men Casualty The Bourne Identity = Total minutes 1 hour = 60 minutes 50 minutes 50 minutes 2 hours 20 minutes = 140 minutes 300 minutes Page 18
We can now convert this total back into hours and minutes by dividing by 60. 300 60 = 5 Therefore Tim has 5 hours of TV to record. Tim has 5 1/2 hours of recording left on his recorder. Therefore Tim DOES have enough recording time left to record all 4 programmes. Tim would have 30 minutes left over. Robs Job s 3. In this question you will need to convert between hours and minutes. Your time plan should clearly show the start time as 09:00 and should be accurate in the length of time taken for each job. Your time plan could look something like this: TIME JOB CLIENT TIME NEEDED 09:00 Start work Double oven Mrs Andrews 2 hours 11:00 Single oven Betty Grey 1.5 hours 12:30 Lunch Lunch 0.5 hours 13:00 Barbeque Sam Bell 1.5 hours 14:30 Hob and fan Mr Lang 1.5 hours 16:00 Finish work -- -- Boomerang Ride 4. In this question you will need to convert between units of length. Toni is 138cm tall. To find out if Toni is tall enough to go on the Boomerang ride we need to convert her height into metres. To do this we need to divide her height by 100. 138 100 = 1.38 Therefore Toni s height is 1.38 metres. The Boomerang ride has a minimum height requirement of 1.4 metres. Therefore Toni is NOT tall enough to go on the Boomerang ride. She is 2cm too small. Page 19
Eggs 5. In this question you will need to convert between units of length. Monty s tray is 633mm wide. To find out if the space is wide enough for the tray we need to convert this length into cm. To do this we divide by 10 (1cm = 10mm) 633 10 = 63.3cm The space is 0.7 m wide. To find out if the space is wide enough for the tray we need to convert this length into cm. To do this we multiply by 100 (1m = 100cm) 0.7 x 100 = 70cm The space is 70cm wide. Monty needed a width of 63.3cm. Therefore the space IS wide enough for the tray. There will be 6.cm of extra width. Rabbits 6. In this question you will need to convert units of length. The first step is to add the relevant lengths of the space for the rabbits. 170 170 + 80 420 Cathy needs 420cm of fencing. However the question asks for the fencing in metres. To convert from cm to metres we need to divide by 100 (1m = 100cm) 420 100 = 4.2 Cathy needs 4.2 metres of wire fencing. Page 20
Floors 7. In this question you will need to convert between units of weight. The first step is to accurately read from the graph in kg s. According to the graph for 850 kg of cement Tony will need 2600 kg s of sand. The question asks for the weight of sand in tonnes. To convert from kg to tonnes you need to divide by 1000 (1000kg = 1 tonne) 2600 1000 = 2.6 Therefore Tony will need 2.6 tonnes of sand. Six Bottles 8. In this question you will need to convert between units of capacity. To find out how many of the 750ml bottles Rob can fill, we need to convert the capacity of the oven cleaner into ml. To do this we need to multiply by 1000 (1 litre = 1000ml) 5 x 1000 = 5000 Therefore 5 litres = 5000ml We can now divide this figure by the capacity of a spray bottle, to find out how many Rob can fill. 5000 75 = 6.6666666 The question asks how many bottles Rob can COMPLETELY fill. Therefore Rob can fill 6 bottles.
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Understanding Functional Skills AON WB8 Converting units of measure L1 V3