Understanding Functional Skills Maths level 2

Transcription

1 Understanding Functional Skills Maths level 2 Workbook 8 - Use, convert and calculate using metric and, where appropriate, imperial measures

2 INTRODUCTION TO THE MATHEMATICS FUNCTIONAL SKILLS QUALIFICATION AT LEVEL 2 In order to meet the assessment criteria for mathematics at level 2 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 routine and non routine problems in familiar and unfamiliar contexts and situations. Identify the situation or problems and identify the necessary mathematical methods needed to solve them. Choose from a range of mathematics to find solutions. This means that you will need to: Apply a range of mathematics to find solutions. Use appropriate checking procedures and evaluate their effectiveness at each stage. This means that you will need to: Interpret and communicate solutions to multi-stage practical problems in familiar and unfamiliar contexts and situations. Draw conclusions and provide mathematical justifications. Functional Skills in mathematics at level 2 has 12 areas of coverage and range : Understand and use positive and negative numbers of any size in practical contexts Carry out calculations with numbers of any size in practical contexts Understand, use and calculate ratio and proportion including problems involving scale Understand and use equivalences between fractions, decimals and percentages Understand and use simple formulae and equations involving one- or two-step operations Recognise and use 2D representations of 3D objects Find area, perimeter and volume of common shapes Use, convert and calculate using metric and, where appropriate, imperial measures. Collect and represent discrete and continuous data, using information and communication technology (ICT) where appropriate Use and interpret statistical measures, tables and diagrams for discrete and continuous data, using information and communication technology (ICT) where appropriate Use statistical methods to investigate situations Use probability to assess the likelihood of an outcome Page 2

3 You will be required to sit a formal test in order to assess your skills. 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 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

4 Please find below a selection of very useful websites that can provide additional support resources in English. Please take the time to study and review these. 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. A good site with adult literacy and numeracy activities including more than 1500 free Functional Skills and Skills for Life resources. 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. 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

5 USE, CONVERT AND CALCULATE USING METRIC AND, WHERE APPROPRIATE, IMPERIAL MEASURES Converting: conversion between metric units MSS1/L1.2, MSS1/L1.3, MSS1/L2.1 MSS1/L2.2, MSS1/L2.3, N1/L2.4 MSS1/L2.5 MSS1/L2.4 The metric system is based on tens, hundreds and thousands. To convert from one unit to another you need to multiply or divide by 10, 100 or You should know the following conversions to change from one metric unit to another: Length Weight Capacity/Volume 10 mm = 1cm 1,000 mg = 1g 100 cl = 1 litre 100 cm = 1m 1,000 g = 1kg 1,000 ml = 1 litre 1,000 mm = 1m 1,000 kg = 1 tonne 1,000 cm 3 = 1 litre 1,000 m = 1km 1,000 litres = 1m 3 Example 1: 1 litre of water weighs 1 kilogram. What does 100 millilitres of water weigh? If 1 litre of water weighs 1kg, then 1,000 ml weighs 1,000g, so that 100ml weighs 100g. Answer: 100 g Example 2: The length of a standard safety barrier on UK motorways is 30 metres. How many standard safety barriers are needed on a 10 kilometre stretch of motorway? 10km = 10 1,000m = 10,000m. The number of barriers needed is 10, = barriers is not enough Answer: 334 barriers

6 Example 3: A measuring jug contains 500 millilitres of water. Stones for a fish tank are added and the measuring jug then reads 875 millilitres. What is the volume of stones for the fish tank? = 375ml 1000 cm 3 = 1 litre = 1,000ml So 375 ml = 375cm 3 Answer: 375cm 3 Top Tip: Converting between metric To convert from large units to small units, multiply (x) To convert from small units to large units, divide ( ) Page 6

7 Conversion between metric and imperial units Some imperial units are still used in the UK. For example, distances on road signs are given in miles and drinks can be measured in pints. You should be familiar with some of the more common imperial units and the connection between them. Length Weight Capacity/Volume 12 inches = 1 foot 16 ounces = 1 pound 1 pint = 20 fluid ounces 3 feet = 1 yard 14 pounds = 1 stone 8 pints = 1 gallon 1,760 yards = 1 mile 160 stone = 1 tonne It is useful to remember some of the approximate connections between metric and imperial units to give you an idea of the relative size. For example: One yard is a little less than one metre Two pounds is a little less than one kilogram Two pints is a little more than one litre The table shows some conversions between metric and imperial units which are usually used in test questions. Length Weight Capacity/Volume 1 inch = 2.5cm 1 ounce = 25g 1 litre = 1.75 pints 1 foot = 30cm 1kg = 2.2 pounds 1 gallon = 4.5 litres 1 m = 39 inches 8 km = 5 miles (Please note that you will NOT be expected to remember these, as the conversion formula will always be shown within a test question). Page 7

8 Example 1: Jessica is 5 feet 4 inches tall. What is her height in metres? Using the table: 1 foot = 30cm so 5 feet = 5 30 = 150cm 1 inch is 2.5cm so 4 inches = = 10cm Total height = = 160cm = 1.6 metres Answer: 1.6 metres Example 2: A supermarket sells milk in 6 pint containers. What is 6 pints in litres? Using the table: 1 litre = 1 ³ ₄ pints = 1.75 pints As every 1.75 pints is 1 litre, the calculation is = litres. The answer should be given to an appropriate degree of accuracy. As 1 litre = 1,000 millilitres, to write to the nearest millilitre you need 3 places of decimals, which is litres, or 3 litres 429 millilitres. Answer: litres Top Tip: Converting between metric and imperial Decide which of fraction, decimal or percentage form is most suitable to use in calculations. Page 8

9 Conversion factors You can convert between units by using a conversion factor. A conversion factor is a number by which you multiply or divide measures to change them to another unit. Example 1: Convert 2.55 hours to hours and minutes hours = 2 hours hours The conversion factor to change a fraction or decimal fraction of an hour to minutes is = (0.5 60) + ( ) = = 33 minutes Answer: 2 hours 33 minutes Top Tip: 2.55 hours is not the same as 2 hours 55 minutes as there are 60 minutes in an hour. Example 2: A car travels at a speed of 60 mph. Approximately what is 60 mph in km per hour? From the table on the previous page, 5 miles = 8 kilometres so 1 mile = 8/5 kilometres = 1.6 kilometres The conversion factor from miles to kilometres is mph = = 96 km per hour Answer: 96 km per hour Top Tip: Check your answer makes sense. 1 mile is longer than 1 kilometre so the answer must be more than 60km per hour. Page 9

10 Example 3: A tennis player weighs 60kg. What is her weight, in stones and pounds? 1 kilogram is approximately 2.2 pounds and 14 pounds = 1 stone. First, change kilograms to pounds by multiplying by = (60 2) + (60 0.2) = = 132 pounds 14 pounds = 1 stone so 140 pounds = 10 stones 132 pounds = 10 stones 8 pounds = 9 stones 6 pounds Answer: 9 stones 6 pounds Example 4: A car uses an average of 47 miles per gallon. How much is this in kilometres per litre? Use the conversion factors 1 gallon = 4.5 litres and 1 mile = 1.6 kilometres 47 miles per gallon = 47 miles per 4.5 litres = 47 miles per litre 4.5 This is miles per litre As 1 mile = 1.6km the calculation is = Answer: 16.7km per litre (to 1 d.p.) Page 10

11 CALCULATING USING MEASURES Calculating using MONEY or CURRENCY: Currency conversion Banks, Post Offices and travel agencies and some building societies sell foreign currencies. They charge for this service, it is called commission. They will buy foreign money from you at a lower rate than when they sell it to you to pay for the cost of doing the business for you. Pounds to Euros To change from one currency to another you need to know the exchange rate for that day. On 24/08/02 the pound ( ) to euro ( ) exchange rate was 1 = 1.59 (or 1 and 59 cents). Convert from to like this. Check your calculation by dividing by = 1 x 1.59 = = 1 2 = 2 x 1.59 = = 2 3 = 3 x 1.59 = = 3 So multiply the number of pounds ( ) by the exchange rate. Euros to Pounds On the euro ( ) to pound ( ) exchange rate was: 1 = 0.63 Convert from to like this. Check your calculation by dividing by = 1 x 0.63 = = 1 2 = 2 x 0.63 = = 2 3 = 3 x 0.63 = = 3 So multiply the numbers of Euros ( ) by the exchange rate. The box shows the exchange rate for one pound ( 1). This indicates that: You have to give the bank 1.74 for every 1 they give you. The bank will give you only 1.59 for every 1 you give them. Page 11 We buy Exchange Rates Euros we sell

12 Calculating using Time You need to know the units for time and the connections between them: 60 seconds = 1 minute 7 days = 1 week 60 minutes = 1 hour 52 weeks = 1 year 24 hours = 1 day 12 months = 1 year 1 month has between 28 and 31 days 365 days = 1 year (366 in a leap year) In the 24-hour clock the day runs from midnight to midnight and is divided into 24 hours, numbered from 0 to 23. Such as: = 5.25pm (17 12 = 5) Example 1: A train leaves Manchester at 09:45 and arrives in London at 12:06. How long does the train take to get from Manchester to London? 09:45 to 11:45 is 2 hours. 11:45 to 12:00 is 15 minutes. 12:00 to 12:06 is 6 minutes. Total time = 2 hours + 15 minutes + 6 minutes = 2 hours 21 minutes Answer: 2 hours 21 minutes Page 12

13 Example 2: A boy is 9 years 2 months old. His sister is 2 years 5 months younger. How old is his sister? You need to subtract 2 years 5 months from 9 years 2 months First subtract 2 years to give 7 years 2 months Then subtract 2 months to give 7 years. (5 = 2 + 3) Finally, subtract the remaining 3 months to give 6 years 9 months Answer: 6 years 9 months Page 13

14 CALCULATING USING MEASURES Length is the measurement of something from one end to the other. You measure length all the time. Example The width of your bedroom is 2m The distance from your house to the train station is 3km The thickness of some loft insulation is 370mm The length of your pencil is 14cm When measuring lengths you can use a ruler or tape measure. Here s an example of reading length from a ruler: 0cm When we look at a ruler the centimetres are marked, but there are unmarked divisions in between. These divisions divide each cm into ten parts Each division is equal to 1mm because 10mm = 1cm The arrow reaches the 7cm mark You will need to know the metric units for length and the connections between them. 10mm = 1cm 100cm = 1m 1,000m = 1km Page 14

15 CALCULATING USING WEIGHT Weight is a measure of the mass of an object. You will need to know the metric units for weight and the connections between them mg = 1 g 1000 g = 1 kg 1000 kg = 1 tonne Weight - The measurement of how heavy something is: Milligram/mg - Unit for measuring very small weights, such as the content of vitamins or tablets (mg is the abbreviation for milligram). A milligram is a thousandth of a gram. Gram/g - Unit for measuring small weights, such as in cooking (g is the abbreviation for gram). A gram is a thousandth of a kilogram. Kilogram/kilo/kg - Unit for measuring large weights - for example a person (kilo and kg are abbreviations for kilogram). Tonne/t - Unit for measuring very large weights, such as a lorry. Measuring instrument - You use measuring instruments to measure weight. Kitchen scales and bathroom scales are types of measuring instruments. Scale - All measuring instruments have a scale. You read off a scale to find the weight of objects. Division - The individual markers on scales. For example kitchen scales may show up to 5kg and will be divided into marked 500g and unmarked 100g divisions. Page 15

16 CALCULATING USING CAPACITY/VOLUME (MSS1/L1.4) We use the term capacity when talking about the measure of how much space there is available to hold something. For example the capacity of: A jug A teacup or mug A food container A petrol tank Capacity is the amount a container can hold. But what about volume? This is something slightly different. Here s an example: This jug has a capacity of 250ml. The volume of milk in the jug is 175ml. The volume of milk needed to fill the jug is 250ml. Can you see the difference? The volume is how much milk is in the jug. Volume is a measure of the space taken up by something. The metric units for capacity are: litres (l), centilitres (cl) millilitres (ml) Centilitre means one hundredth of a litre. Millilitre means one thousandth of a litre. There are 100 centilitres in 1 litre. There are 1,000 millilitres in 1 litre. You measure capacity by reading from scales, such as the scales on the milk jug above. Page 16

17 CALCULATING USING DISTANCE Most road atlases include a distance chart, which gives distances between the main towns. This can be very useful when you re planning a journey if you don t have satellite navigation. You take figures from the chart rather than having to take measurements. If your town or village is not in the chart you use the figures given for a nearby town. Here s part of a chart giving distances in miles. Bristol 42 Cardiff Hull Leeds Preston York Example 1 Sam wants to find the distance between Bristol and Preston. She looks for the number where the Bristol column meets the row for Preston. The arrow shows that the distance is 191 miles. Answer: 191 miles Example 2 Zak is travelling from Cardiff to Leeds and then on to York. He wants to know how long the journey will be. Zak looks for the number in the Cardiff column where it meets the Leeds row, which is 230 miles. Then he looks for the number in the Leeds column where it meets the York row, which is 24 miles. So his total journey will be 230 miles + 24 miles, so a total of 254 miles. Answer: 254 miles Page 17

18 To convert between metric and imperial distances there are 2 recognised formulas: To convert kilometres into miles: divide by 8 and multiply by 5 To convert miles into kilometres: multiply by 8 and divide by 5 Top Tip: 1 kilometre = ⁵ ₈ of a mile 1 mile = 1.6km Don t worry of you cannot remember these 2 formulas as in the actual test they will be displayed for you to then calculate. Page 18

19 CALCULATING USING TEMPERATURE Temperature is measured in degrees using a thermometer. Temperature is usually recorded in degrees Celsius, although degrees Fahrenheit are still sometimes used. Many thermometers show temperatures in Celsius and Fahrenheit. You can use comparison scales to compare and convert between Celsius and Fahrenheit. C = degrees Celsius F = degrees Farenheit 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. If we look at the thermometer we can see that the red line comes to the 20 C mark. This would normally be said as 20 degrees. A temperature of above zero is a positive temperature. A temperature of less than zero is a negative or minus temperature reading. To convert Celsius (Centigrade) to Fahrenheit, multiply the Celsius temperature reading by ⁹ ₅, and then add 32. C x ⁹ ₅ + 32 = F To convert Fahrenheit to Celsius, subtract 32 from the Fahrenheit temperature, and then multiply by ⁵ ₉. (F - 32) x ⁵ ₉ = C Again, don t worry of you cannot remember these 2 formulas as in the actual test they will be displayed for you to then calculate.

20 READING SCALES WITH UNMARKED DIVISIONS Some thermometers have scales with both marked and unmarked divisions. You must first make sure what each small division represents. A. Thermometer A is marked in 10 s. The unmarked division between each pair of marked ones is the halfway value (-5, 5, 15 ), so the reading is closest to the 15 o C division. B. Thermometer B is marked in 5 s, with 4 unmarked divisions between each pair of marked ones. This means that the unmarked divisions are each 1 degree apart. The reading is 2 degrees below the 0 o C mark, so the temperature is -2 o C. Page 20

21 QUESTIONS Measurements 1. Kim uses this recipe to make cakes to sell at the fair. Kim already to make between 50 and 60 cakes. Kim already has these quantities. Ingredients for 12 cakes Self raising flour 175g Self raising flour 1kg Margarine 110g Margarine 600g Caster sugar 110g Caster sugar 750g Eggs 2 Eggs 12 Does Kim have enough of each ingredient to make between 50 and 60 cakes? Use the box below to show clearly how you get your answer. Page 21

22 Length 2. Nita has to buy a birthday present for her brother. She finds some belts in a shop. The boxes below show some information about the belts. The lengths of the belts are given in inches. Not all the brands give the same names to the lengths. Petrol 35 Small 32 Medium 34 Large 36 Rafe 30 Small 32 Medium 36 Large 38 Ex large 42 Dinosaur Small 32 Medium 34 Large 36 Chief 45 Small 30 Medium 32 Large 34 Ex large 36 Jerry 25 Small 32 Medium 36 Large 40 Ex large 44 Norman 30 Small 30 Medium 32 Large 34 Ex large 36 Page 22

23 Nita knows the belt must be at least 90cm long. Nita wants to spend less than 40. Nita does not want to buy a Large belt or an Extra Large belt Use 1 inch = 2.54cm Which belt should Nita buy for her brother s birthday? Use the box below to show clearly how you get your answer. Page 23

24 Volume 3a. Fraser is going to drive his car to Lyon in France. He needs to drive to Dover to get on a ferry. Fraser wants to know if he has enough fuel to drive from his home to Dover. His car fuel tank has a capacity of 70 litres. The fuel tank is a quarter full. Use: 1 gallon = 4.55 litres How many gallons of fuel are there in the fuel tank? Use the box below to show clearly how you get your answer. 3b. Fraser knows that his car uses about 1 gallon of fuel every 40 miles. The distance from Fraser s home to Fraser s home to Dover is 200 miles. Does Fraser have enough fuel in his fuel tank to drive from his home to Dover? Use the box below to show clearly how you get your answer. Page 24

25 Time 4. Fraser is going to cycle a route around Lyon. He knows that without rests, the route takes 8 hours 50 minutes total cycling time. Fraser needs to stop for a rest after every 3 to 3¹ ₂ hours of cycling time. His rest periods are 45 minutes. Fraser needs to finish the cycling route by 18:40. He wants to start cycling the route as late as possible. a. What time should Fraser start cycling? Use the box below to show clearly how you get your answer. Page 25

26 Money 5a. Susan sells some drinks to a passenger on a plane. The drinks cost a total of 18. The passenger wants to pay for the drinks in dollars ($). The passenger pays with 2 x $20 dollar notes. Susan uses 1 = $1.64 How much change must Susan give the passenger? Use the box below to show clearly how you get your answer. 5b. Show a check for part (a). Write your check in the box below. Page 26

27 Distance 6. Canal boats go through locks to get up to a higher level and to get down to a lower level. Jerry plans a route for Tuesday. He knows that: A canal boat travels a maximum distance of 4 miles in one hour It takes an average of 15 minutes for a canal boat to go through a lock The route Jerry plans for Tuesday Is 20 miles long Has 14 locks Jerry only wants to travel for a maximum of 8 hours on Tuesday. Will Jerry be able to travel this route in less that 8 hours? Use the box below to show clearly how you get your answer. Page 27

28 Temperature 7. The recipe states that the oven must be set at 350 o F. The oven used in the competition shows temperature in o C. C = 5 (F - 32) 9 C = Temperature in o C F = Temperature in o F Rikka sets the oven at 200 o C. Is this the right temperature? Show why you think this. Use the box below to show clearly how you get your answer. Page 28

29 ANSWERS Measurements 1. In this question you need to show an understanding of how to calculate measure using weight. You will be expected to show that you identified that to scale up from the original recipe for 12 cakes you need to (using the larger maximum figure of 60 cakes) MULTIPLY each ingredient by 5. As 12 x 5 = 60 To do this: Ingredient Weight for 12 cakes Scale up to bake for 60 cakes New weight for 60 cakes Self-raising flour 175g x 5 875g Margarine 110g x 5 550g Caster sugar 110g x 5 550g Eggs 2 x 5 10 From this you will be expected to identify if this is within the quantities already held by Kim: Ingredient New weight for 60 cakes Weight currently held by Kim Is this enough to make the 60 cakes? Self-raising flour 875g 1kg YES Margarine 550g 600g YES Caster sugar 550g 750g YES Eggs YES Answer: Therefore overall Kim does have enough ingredients to make at least 60 cakes as required. There are a possible 4 marks for this question if you complete the calculation close to the example above you will gain full marks however marks will be lost if it is not totally accurate or clear to the marker. 1 mark is simply given for attempting to convert the ingredients x 5 to meet the amount required for 60 cakes. Page 29

30 Length 2. In this question you need to show a deeper understanding of how to calculate measure using length and to apply this process into problem solving. The most logical way is to split the question into 3 areas (of criteria), for example: Criteria 1:The question asks that Nita only want to spend less than 40. Therefore there are 2 brands that are actually over this value: Dinosaur ( 45.99) and also Chief ( 45) so these need to be disregarded. Criteria 2: Next you need to determine what lengths of belt are required The question asks that they must be at least 90cm and also gives the conversion formula from inches into cm as: 1 inch = 2.54cm Therefore you need to calculate each imperial unit of length (inches) into the metric equivalent (cm) for each length included in the question: Imperial measure Conversion factor Metric measure 30 inches x cm 32 inches x cm 34 inches x cm 36 inches x cm 38 inches x cm 40 inches x cm 42 inches x cm Page 30

31 Looking at these calculations it is then straightforward to interpret that the belt must be AT LEAST 36 inches as anything below this is too low as requested by Nita. Criteria 3: The question asks that the belt must not be classed as large or extra large. Therefore you now need to go though each of the 4 available brands to determine if their naming of the 36 inch belt conforms to the constraint of the question: Brand name of belt Name of 36 inch size Is this then appropriate? Petrol Large NO Rafe Medium YES Jerry Medium YES Norman Extra Large NO Answer: So overall there are 2 belts that are available for Nita to purchase: The Rafe belt in the Medium size The Jerry belt in the Medium size There are a possible 3 marks for this question if you complete the calculation close to the example above you will gain full marks however marks will be lost if it is not totally accurate or clear to the marker. 1 mark is simply given for attempting to convert the imperial measures (inches) into metric (cm). Page 31

32 Volume 3. In this question you need to show a deeper understanding of how to calculate measure using volume and to apply this process into problem solving. a) You will be expected to identify that the capacity of the fuel tank is 70 litres but is only ¼ full therefore a calculation is initially required: 70 4 = 17.5 litres of fuel currently in the tank Next you need to convert this figure into gallons, using the formula provided (1 gallon = 4.55 litres) litres 4.55 = gallons Answer: gallons b) You will be expected to identify that the distance to Dover is 200 miles with the car using 1 gallon every 40 miles, therefore you need to calculate how much fuel (in gallons) Fraser requires. To do this: Divide 200 miles by the fuel consumption of 40 miles per gallon = 5 Therefore identifying that Fraser requires 5 gallons of fuel for the journey to Dover Answer: Overall Fraser only has gallons of fuel left in his tank and he requires 5 gallons for the journey to Dover therefore he DOES NOT have enough fuel left in his fuel tank. There are a possible 4 marks for this question if you complete the calculation close to the example above you will gain full marks however marks will be lost if it is not totally accurate or clear to the marker. 1 mark is simply given for attempting to convert the metric measures (litres) into imperial (gallons). Page 32

33 Time 4. In this question you need to show a deeper understanding of how to calculate measure using time and to apply this process into problem solving. The most logical way is to split the question into 3 sections, for example: Step 1: Calculate the number of breaks that Fraser requires. You know that he must stop every 3 to 3 ½ hours. You also are told he wants to do the journey in the least possible time therefore control his breaks so that he has the maximum length of cycling tome of 3 ½ hours: 8 hours 50 minutes 3.5 hours = 2.6, therefore Fraser can complete the journey with only 2 breaks of 45 minutes each = 1 hour and 30 minutes Step 2: Next you will be expected to add this figure (1 hour 30 minutes) onto the existing cycling time of 8 hours and 50 minutes: 1 hour 30 mins + 8 hours 50 mins = 10 hours 20 mins Therefore now identifying that there needs a total journey length of 10 hours and 20 minutes Step 3: Finally you can calculate the latest start time for the journey using 18:40 as the finish time. To do this you need to subtract 10 hours 20 minutes from this: 18:40 10:20 = 08:20 Answer: Overall Fraser needs to start the journey at 08:40 to reach the destination by the desired time of 18:40. Fraser will have only 2 rest breaks in this time. There are a possible 3 marks for this question if you complete the calculation close to the example above you will gain full marks however marks will be lost if it is not totally accurate or clear to the marker. 1 mark is simply given for attempting to calculate the number of rest breaks required. Page 33

34 Money 5a. In this question you need to show a deeper understanding of how to calculate measure using money and currency and to apply this process into problem solving. The most logical way is to split the question into 3 sections, for example: Step 1: Firstly it is recommended that you simply show to the marker that you have calculated that the passenger actually gives Susan 2 x $20 dollar notes: 2 x $20 = $40 Step 2: Next you need to convert how much 18 into $: The conversion rate is given for you: 1 = $1.64 Therefore the calculation is: 18 x $1.64 = $29.52 The drinks will cost the passenger $29.52 Step 3: Finally you need to calculate the amount of change to give back to the passenger. To do this simply subtract $29.52 from the $40 handed over to Susan: = $ Answer: Overall Susan needs to return $10.48 back to the passenger as change for the drinks. There are a possible 3 marks for this question if you complete the calculation close to the example above you will gain full marks however marks will be lost if it is not totally accurate or clear to the marker. 1 mark is simply given for attempting to calculate the value of the 2 x $20 notes. b) To show a check for the calculation all that is expected is that you perform a reverse or accuracy check on the final subtraction calculation from part (a) of the question. The opposite (or reverse) of subtraction is addition therefore all you need to show is that you have added up the 2 smaller values from the calculation ($10.48 and $29.52) to hopefully return back to the original larger value ($40.00): mark would be awarded for identifying this accurately = $ 40.00

35 Distance 6. In this question you need to show a deeper understanding of how to calculate measure using time and to apply this process into problem solving. The most logical way is to split the question into main 3 sections, for example: Step 1: It is recommended that you need to calculate the time it takes to travel the 20 miles of the canal route. To do this divide the journey (20 miles) by the speed (4 miles per hour): 20 4 = 5 hours travelling time required Step 2: Next calculate the time it takes to get through the 14 locks. To do this multiply the number of locks (14) by the time it takes for each (15 minutes): 14 x 15 minutes = 3 ½ hours Now add these 2 answers together to identify the total travelling time: 5:00 hours + 3:50 hours = 8:50 hours Which is more appropriately written as 8 ½ hours or 8 hours and 30 minutes. Step 3: Finally you need to come to a logical conclusion with supporting data in your answer. For example: Answer: Jerry will not be able to travel the full distance of 20 miles on the canal boat in the 8 hours planned as I have calculated that it will take him 8 ½ hours to do this. This is 30 minutes too long and if he travels at a speed of 4 miles per hour this will leave him 2 miles short as it will take 30 minutes to complete the last 2 miles of the journey. There are a possible 3 marks for this question if you complete the calculation close to the example above you will gain full marks however marks will be lost if it is not totally accurate or clear to the marker. 1 mark is simply given for attempting to calculate the journey time of 20 miles in 5 hours. Page 35

36 Temperature 7. In this question you need to show a deeper understanding of how to calculate measure using temperature and to apply this process into problem solving using a formula. Using the formula provided in the question you are recommended to convert the 350 F into C and then compare this against the temperature set by Rikka, for example: C= 5 (F-32) 9 C= 5 (350-32) 9 C= 5 x C= C= Therefore by calculating this accurately you identify that the temperature set is actually Centigrade. From this you need to put forward a logical conclusion, such as: Answer: As I have calculated the oven will be set at a temperature of C which unfortunately is below the required temperature of 200 C therefore this is NOT the right temperature. There are a possible 3 marks for this question if you complete the calculation close to the example above you will gain full marks however marks will be lost if it is not totally accurate or clear to the marker. 1 mark is simply given for attempting to calculate the formula. Page 36

37 NOTES: Page 37

38 Understanding Functional Skills AON WB8 Metric and imperial shapes L2 V4