Understanding Functional Skills Maths level 1 Workbook 7 - Measures 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
Measurement symbols cm 2 cm 3 Centimetres squared Centimetres cubed Kg Kilograms g Grams lbs Pound in weight oz Ounces mm Millimetres cm Centimetres mtrs Metres OR m Metres km Kilometres ml Millilitres (used for measurements of fluid) ltrs Litres (used for measurements of fluid) How to understand metric/imperial information Length 1 centimetre (cm) = 10mm 1 metre (m) = 100cm 1 kilometre (km) = 1,000m Volume and Capacity 1 litres (l) = 1,000ml = 0.0353oz Weight 1,000 mg = 1g = 0.0353oz 1kg = 1,000g = 2.2046lb Page 5
ADDING AND SUBTRACTING MONEY N1/ L1.3, MSS1/ L1.1 To add or subtract money values you must: Write down the money using two decimal places - the digits to the right of the decimal point are pence, full pounds to the left Make sure the decimal points line up beneath each other in the correct place If there are no pence in one of the columns, add a zero after the decimal point to indicate 0p Start your calculation from the right From the right, the columns represent single digits at far right, then multiples of 10, then multiples of 100 (in this case 100p or 1) When the number in one column goes over its limit, move this extra amount into the next column Write it down in the correct column so that you don t forget to include it Example 1: Adding Money Liz bought a newspaper for 50p, a drink for 1.05 and a sandwich for 2.25. How much did she spend altogether? Pound Pence 0. 5 0 + 1. 0 5 + 2. 2 5 3. 8 0 Total of all columns added together Page 6
Example 2: Subtracting Money A power tool costs 42.95 on special offer in store A, and 65.75 in store B. How much money do you save by buying it from store A? Larger value at the top (store B). Pound Pence 6 5. 7 5-4 2. 9 5 2 2. 8 0 Detract the smaller value (store A). The saving is the difference between the two. Page 7
DIVIDING MONEY N1/ L1.3, MSS1/ L1.1 Write down the money using two decimal places - the digits to the right of the decimal point are pence, full pounds to the left Make sure the decimal points line up beneath each other in the correct place Perform the division on each column in turn Start your calculation from the left You can also use the traditional division method. Example 1: Five pens cost 3.85. How much does one cost? Pound Pence 3 5 5p 5 3. 8 5 5 6 0 1 6 + 1 7 7 80p 5 Total 77p each Dividing decimals can sometimes give you a long string of numbers. In this case, work as far as three decimal places and then round the second place up or down. If the last figure is five or more, round up. If it is less than five, round down. Page 8
Example 2: Jimmy paid 70 for six tickets at a special offer price. His five friends shared the cost with him. How much did each ticket cost? The actual figure has an infinitely recurring six at the end. Pound Pence 7 0. 0 0. 6 1 1. 6 6 6 6 1 1. 6 7 Stop at three decimal places and round up to the nearest pence. Because the third decimal place is a six, round up. The cost is 11.67 to the nearest penny. Page 9
MULTIPLYING MONEY N1/ L1.3, MSS1/ L1.1 Write down the money using two decimal places - the digits to the right of the decimal point are pence, full pounds to the left Carry out the multiplication ignoring the decimal point and starting from the right When multiplying by a number greater than 10, break the number down and multiply the money separately by the multiples of 10 and any smaller digits (e.g. to multiply something by 23, multiply it by 3, then 10, then 10: 3 + 10 + 10 = 23) Put a decimal point into your answer so that it has two decimal places to return it back to a monetary value Example: Dan bought 12 MP3 tracks at 1.35 each. What was the total cost? Pound Pence 1.35 2 1.35 10 1. 3 5 1 2 2 7 0 + 1 3 5 0 1 6. 2 0 Remove the decimal point at this stage. Add the decimal point back in to denote pounds and pence. Page 10
HOW TO UNDERSTAND 12- AND 24-HOUR TIMES MSS1/ L1.2, MSS1/ L2.2 Look at the time on this digital clock. This is displayed in the 24-hour format. We can tell it s evening, but how do we know what the hour is? The clock says 20 hours and 27 minutes. To change this time to the 12-hour clock take away 12 from the hours. 20-12 = 8 So we know that it s something past 8 at night. The number after the colon (:) gives us the minutes, so it s 27 minutes past 8. So 20:27 is the same as 8:27 p.m. In the 24-hour clock the hours keep on going up from 12 to 13, then 14 and so on. In the 12-hour clock they go from 11 to 12 then start again at back from 1, 2, 3 and so on. 12 HOUR CLOCK 24 HOUR CLOCK 12 HOUR CLOCK 24 HOUR CLOCK 12 a.m. (midnight) 00:00 12 p.m. (noon) 12:00 1 a.m. 01:00 1 p.m. 13:00 2 a.m. 02:00 2 p.m. 14:00 3 a.m. 03:00 3 p.m. 15:00 4 a.m. 04:00 4 p.m. 16:00 5 a.m. 05:00 5 p.m. 17:00 6 a.m. 06:00 6 p.m. (evening) 18:00 7 a.m. 07:00 7 p.m. 19:00 8 a.m. (morning) 08:00 8 p.m. 20:00 9 a.m. 09:00 9 p.m. 21:00 10 a.m. 10:00 10 p.m. (night) 22:00 11 a.m. 11:00 11 p.m. 23:00 Page 11
READING 24-HOUR TIMES MSS1/ L1.2, MSS1/ L1.3, MSS1/ L2.2 Example: What is 17:42 in the 12-hour clock? Again start by taking 12 from the hours. 17-12 = 5 So 17:42 is the same as 5:42 p.m. which is 42 minutes past five in the evening. It s useful to know this time as so many minutes to six as well, so how do we work out the minutes before six? Take the minutes away from 60, as there are 60 minutes in one hour. 60-42 = 18 It s 18 minutes to 6 in the evening. There are 18 minutes to go until 6 pm. This is the same time in the 24-hour clock. 10 9 8 11 7 12 1 2 3 6 5 4 Page 12
Look at the opening hours for this shop. OPENING HOURS Monday Tuesday Wednesday Thursday Friday 8.45 8.45 8.45 8.45 8.45 18.00 18.00 18.00 18.00 18.00 What time does it close during the week? What about Saturday and Sunday? Monday to Friday it closes at 18:00 which is 6:00 p.m. On Saturday it s 17:30 which is 5:30 p.m. On Sunday it closes at 16:30 which is 4:30 p.m. Saturday Sunday 9.00 10.30 17.30 16.30 What about converting a time into the 24-hour system? For example what is 3:36 p.m. in the 24-hour clock? This time is p.m. so add 12 hours onto the hours (the number in front of the point). 3 + 12 = 15 So, 3:36 p.m. will be 15:36 in the 24-hour clock. Page 13
MEASURING LENGTHS KEY WORDS (MSS1/L1.4) Length - The measurement of something from one end to the other. Words like width, distance, height, diameter and thickness also involve finding a length. Millimetre/ mm - Unit for measuring tiny lengths - for example, the thickness of cardboard. One thousandth of a metre (mm is the abbreviation). Centimetre/cm - Unit for measuring small lengths - for example, the length of a pencil. One hundredth of a metre (cm is the abbreviation). Kilometre /km - Unit for measuring longer lengths - for example, distances. It means one thousand metres (km is the abbreviation). Measuring instrument - You use measuring instruments to measure length. Tape measure, ruler and trundle wheel are types of measuring instrument. Scale - All measuring instruments have a scale. You read off the markers on a scale to find the length of objects. Division - The individual markers on scales. For example, a 30-cm ruler will be divided into marked centimetre and unmarked millimetre divisions. Top Tip Millimetre (mm) - milli means one thousandth. So a millimetre is one thousandth of a metre Centimetre (cm) - centi means one hundredth. So a centimetre is one hundredth of a metre Kilometre (km)- kilo means one thousand. So a kilometre is one thousand metres Page 14
MEASURING LENGTHS Length is the measurement of something from one end to the other. You measure length all the time. Examples: 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 1 2 3 4 5 6 7 8 9 10 11 12 When we look at a ruler the cm are marked, but there are unmarked divisions in-between. These divisions divide each cm into ten parts Each division is equal to 1mm because 10 mm = 1cm The arrow reaches the 7cm mark Page 15
USING DISTANCE TABLES (MSS1/L1.5) 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 230 249 Hull 212 230 60 Leeds 191 210 122 69 Preston 224 243 38 24 96 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. 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. Page 16
WEIGHT KEY WORDS (MSS1/L1.4) 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 (t is the abbreviation for tonne). A tonne is 1000kg. 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. Top Tip Milligram (mg) - milli means one thousandth. So a milligram is one thousandth of a gram Kilogram (kg) - kilo means one thousand. So a kilogram is one thousand grams Page 17
READING SCALES TO MEASURE WEIGHT (MSS1/L1.4) When you re measuring weight you use scales - for example, kitchen or bathroom scales. Digital weight scales are easy to use, but when you use other scales you have to read them more carefully. The pointer on the kitchen scales is between two divisions: 0 g and 500 g. There are four main divisions between these two values. Each main division is 100 g. The pointer is four divisions from zero (0). So the object on the scales weighs 400 g. Top Tip Before you weigh items on mechanical scales, make sure the pointer is at zero. Page 18
CAPACITY AND 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 250 ml. The volume of milk in the jug is 175 ml. The volume of milk needed to fill the jug is 250 ml. 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 1000 millilitres in 1 litre. You measure capacity by reading from scales, such as the scales on the milk jug above Page 19
VOLUME MSS1/ L1.10, MSS1/ L2.9 Volume is how much space a solid object takes up or holds. Volume is calculated by: depth x width x length (height). Volume is represented in cubed units such as cubic centimetres (cm³) or cubic metres (m³). The imperial system uses units such as cubic feet (ft³). A solid such as a cube or a cuboid is three-dimensional (3D). That simply means that you need three measurements in order to work out its volume: depth, width and height. Example: 2cm In this cubed shape: Volume = length width depth 3cm 3cm 2cm 2cm = 12cm 3 The volume of the shape = 12cm 3 2cm Warning: The width, depth and length must be in the same units. For example you cannot mix metres and centimetres. Page 20
TEMPERATURE (MSS1/L1.4) 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. C = degrees Celsius F = degrees Fahrenheit 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. Page 21
READING SCALES WITH UNMARKED DIVISIONS (MSS1/L1.4 N1/L1.2) Some thermometers have scales with both marked and unmarked divisions. You must first make sure what each small division represents. Thermometer A is marked in 10s. The unmarked division between each pair of marked ones is the halfway value (-5, 5, 15 ), so the reading is closest to the 15ºC division. A. Thermometer B is marked in 5s, 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. B. Page 22
QUESTIONS Job Advert 1. Pete is Rob s brother. Pete wants a job. Rob says... Come work for me. Work from Monday to friday. I will pay you 45 a day. Pete sees his job advert in the local paper. Cleaner wanted Mon-Fri 30 hours per week- 7.30 per hour. Tel: 01234 456789 Pete wants to earn as much money as possible. Which job pays the most money? Use the box below to show clearly how you get your answer. Page 23
Gardener 2. Mabintou asks a gardener to do some work in her garden. The gardener charges 11.50 per hour. One week the gardener works for a total of 7 hours. How much money does Mabintou pay the gardener? Use the box below to show clearly how you get your answer. Page 24
Furniture 3. Owain has a cane seat. The cane seat is broken. Owain finds this information about the cost of repairing the seat from two different companies. Foster s Furniture Repair of cane seat: 1.70 per drill hole Jack s Repairs Ltd Repair of cane seat: 75 There are 48 drill holes in Owain s Cane seat. Which company is cheaper? Use the box below to show clearly how you get your answer. Page 25
Music Festival 4. Anka has a ticket for a music festival in a park in London. She will travel by train from Andover to London. Andover 08.35 09.04 09.38 10.04 10.38 Whitchurch 08.43 09.12-10.12 - Woking 9.19 09.51 10.17 10.51 11.17 London 9.51 10.19 10.49 11.19 11.49 Anka needs to arrive at the station in London by 11.00am. She wants to leave home 30 minutes before the train leaves Andover. Anka starts a time plan. Complete the time plan for Anka showing the latest train she could catch. Time Plan Leave home at... Train leaves Andover at... Train arrives in London at... Page 26
Free Range Egg Farm 5. Monty has a free range egg farm. He makes deliveries of eggs to restaurants and hotels. monty will make deliveries to the Central Hotel, the Baine Restaurant and the Deepa Restaurant. Central Hotel Braine Restaurant Deepa Restaurant Farm Monty will begin his deliveries from the farm. He will return to the farm when he has finished all his deliveries. The table shows the usual time to travel between the farm, the restaurants and the hotel. Farm (F) 10 minutes Central Hotel (C) 10 minutes 15 minutes Baine Restaurant (B) 10 minutes 10 minutes 20 minutes Deepa Restaurant (D) Page 27
Monty needs to plan the route for his deliveries. Find a route for Monty that takes the shortest time. You may write on the diagram on the previous page. Use the box below to show clearly how you get your answer. Page 28
Driving to Town 6. Owain needs to drive to these towns to buy things for his lounge. Bellside 15 miles 19 miles Owains house 13 miles Ainsley 25miles 15 miles 23 miles Diagram NOT accurately drawn Callen Owain is going to leave his home in the morning, He will drive to all three towns and then return home. Find the shortest route for Owain. Use the box below to show clearly how you get your answer. Page 29
Luggage 7. Tim wants to take his case as hand luggage. The weight of each piece of hand luggage must be less than 10 kilograms. Tim s scales show the weight in stones and pounds. He finds this rule to change stones and pounds into kilograms. To find the number of kilograms: Multiply the number of stones by 14 Add on the number of pounds Write down the result Divide the result by 2.2 Tim s case has a weight of 1 stone and 10 pounds. Can Tim take his case as hand luggage? Use the box below to show clearly how you get your answer. Page 30
Burning Coal 8. Mr and Mrs Chang want to burn coal in their fireplace. They know: They will burn an average of 2kg of coal per day in winter Coal is solid in 25kg bags Mr and Mrs Chang want to have enough coal to last them till the end of January. At the beginning of November they buy 10 bags of coal. Have Mr and Mrs Chang bought enough bags of coal to last them from the beginning of November to the end of January? Use the box below to show clearly how you get your answer. Page 31
Chilli Recipe 9. Anya makes some chilli to sell at the fair. She has this recipe for chilli. Chilli Serves 6 450g mince 1 onion 1 can tomatoes 1 can kidney beans 2 tbsp tomato puree 1 pinch chilli powder 1 pinch garlic powder Anya s recipe serves 6 people. she is going to make chilli for 30 people. What weight of mince does Anya need? Use the box below to show clearly how you get your answer. Page 32
Growing Potatoes 10. Mabintou wants to grow some potatoes. She will grow the potatoes in large buckets. Mabintou has to fill the buckets with compost. She wants to buy at least 100 litres of compost. Mabintou can buy compost in 3 different sized bags. 2.45 each 30 litre bag 2 for 9.28 60 litre bag 3.19 Buy 3 bags get the 4th bag free 25 litre bag Mabintou wants to pay as little as possible for the compost. How much will Mabintou have to pay for the compost? Page 33
Rob s Holiday 11. Rob did not have a holiday in the Lake District last year. He wants to have a holiday in the Lake District this year. Rob does not earn any money when he is on holiday. The table below shows the amount of money he was paid each month last year. Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec 2100 1520 2350 2450 1450 1500 1580 1930 1890 1670 1850 2500 Rob wants to go on holiday when the temperature is likely to be at least 15 o C. This table shows the average daily temperature in the Lake District for each month. Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec 5 o C 6 o C 9 o C 10 o C 14 o C 16 o C 20 o C 18 o C 16 o C 13 o C 10 o C 8 o C In what month should Rob go on holiday in the Lake District? Explain why you think this. Give your answer and explain it in the box below. Page 34
ANSWERS Job Advert 1. To answer this question you will need to multiply with money. The first task is to find out how much each job will pay in total; per week, so that you can compare the amounts to find out which job pays the most money. Pete s brother Rob says he will pay him 45 a day. The job is Monday to Friday, which is 5 days. To find the total cost per week you need to multiply 45 by 5. 45 x 5 = 225 or 225.00 or 225 pounds The cleaning job pays 7.30 per hour for 30 hours per week. To find the total cost we multiply 7.30 by 30. 7.30 x 30 = 219 or 219.00 or 219 pounds. Now you can compare the two figures. 225 is more than 219. Therefore Rob s job pays the most at 225 Page 35
Gardener 2. For this question you will need to multiply with money The gardener charges 11.50 per hour. The gardener works for 7 hours. To find the total amount Mabintou will need to pay the gardener you will need to multiply the hourly cost by the number of hours the gardener worked. 11.50 x 7 = 80.50 Mabintou will pay the gardener 80.50 or 80 pounds and 50 pence. Furniture 3. For this question you will need to multiply with money and subtract with money. You will need to find the total cost of repairing the seat with each company in order to compare the 2 costs and identify which company is cheaper. Foster s Furniture charge 1.70 per drill hole. Owain needs 48 drill holes. To identify the cost you will need to multiply the cost per drill hole by the number of drill holes required. 1.70 x 48 = 81.60 Jack s repairs charges a set rate of 75 for repairs. To find the difference between the 2 costs we subtract the lowest cost from the highest cost. 81.60-75 is 6.60 Jack s Repairs is therefore cheaper by 6.60 than Foster s Furniture. Page 36
Music Festival 4. For this question you will need to read time and subtract time. The train arriving in London at 10.49 Leaves Andover at 9.38am Andover 08.35 09.04 09.38 10.04 10.38 Whitchurch 08.43 09.12-10.12 - Woking 9.19 09.51 10.17 10.51 11.17 London 9.51 10.19 10.49 11.19 11.49 According to the table the closest to 11.00 am that Anka can arrive in London is 10.49am To complete the time plan you also need to calculate the time that Anka needs to leave home. Anka needs to leave home 30 minutes before the train leaves Andover. 09:38-00:30 09:08 Therefore Anka s time plan should look like this: Time Plan Leave home at 9:08 Train leaves Andover at 9:38 Train arrives in london at 10:49 Page 37
Frees Range Egg Farm 5. For this question you will need to add time. To find the shortest route for Monty you will need to try a few different routes and compare the results. The route will always start from and end at the farm. E.g. From the farm to: Central 10 mins Deepa 10 mins Central 10 mins Baine 15 mins Central 20 mins Deepa 10 mins Deepa 20 mins Baine 15 mins Baine 20 mins Farm + 15 mins Farm + 10 mins Farm + 10 mins Total 60 mins Total 55 mins Total 50 mins From the calculations above you can see that the shortest route that has been identified is: Farm Central Deepa Baine Farm. This takes 50 minutes Page 38
Driving to Town 6. For this question you will need to add lengths. To find the shortest distance for Owain to travel you will need to try a few different routes and compare the results. The route will always start from and end at Owain s House E.g. from Owain s house to: Ainsey 13 miles Ainsey 13 miles Callan 13 miles Bellside 19 miles Callen 23 miles Bellside 19 miles Callen 25 miles Bellside 25 miles Ainsey 25 miles Owain s house + 15 miles Owain s house + 15 miles Owain s house + 15 miles Total 72 miles Total 76 miles Total 72 miles From the above calculations you can see that there are two routes, both with the equal shortest length. To get the question right you just need to identify one appropriate route. E.g. O A B C O is the shortest route at 72 miles. Top Tip In a question like this it is always worth putting as much information in as possible to your final answer. For example in this question it would be correct to put: The shortest route is O- A B C- O But you would be likely to pick up extra points from the mark scheme by adding in the distance travelled E.g. The shortest route is O- A B C- O at 72 miles. Page 39
Hand Luggage 7. In this question you will need to multiply, add and divide with weight. The weight of the case is 1 stone 10 pounds. To convert into kilograms we need to: Multiply the number of stones by 14. 1 x 14 = 14 Add on the number of pounds 14 + 10 = 24 Divide the result by 2.2 14 2.2 = 10.9 Therefore Tim s case weighs 10.9 kg The weight limit says that each piece of hand luggage must weigh less than 10 kilograms. So the answer to the question is No, Tim cannot take his case as hand luggage. Page 40
Burning Coal 8. For this question you will need to multiply and divide with weight. Your first step will be to identify how much coal the Chang s have bought. The Chang s bought 10 of the 25 kg bags of coal. 10 x 25 = 250 so the Chang s have 250 kg of coal. Next you will need to find out how much this is per day. The changes will be burning coal in November, December and January. Add the number of days in each month to give you a total number of days where the Chang s will be burning coal. November December January Total 30 days 31 days + 31 days 92 days The Chang s will be burning coal for 92 days. If you divide the amount of coal by the number of days it will tell you how much coal the Chang s can burn per day with their 10 bags of coal. 250 92 = 2.71 Therefore the Chang s HAVE bought enough coal to last them for the three months. The Chang s needed 2 kg of coal per day. They have 2.71 kg of coal per day. Page 41
Chilli 9. In this question you will need to multiply weights. Anya is making chilli for 30 people. The recipe serves 6 people. 6 x 5 = 30 So Anya needs 5 times the recipe amount to make enough chilli. 450g x 5 = 2250g This could also be written as 2.25 kg So Anya needs 2250g or 2.25 kg of mince. Growing potatoes 10. In this question you will need to understand weight. First you will need to calculate the number of bags needed. Mabintou needs at least 100 litres of compost. Therefore she would need to buy: 4 of the 30 litre bags Or 2 of the 60 litre bags Or 4 of the 25 litre bags. Secondly you need to calculate the cost of each option. 4 of the 30 litre bags 4 x 2.45 = 9.80 2 of the 60 litre bags 2 for 9.28 4 of the 25 litre bags. Buy 3 get one free, so 3 x 3.19 = 9.57 According to the results, the cheapest option is for Mabintou to buy 2 of the 60 litre bags at 9.28 Therefore Mabintou would spend 9.28 Page 42
Rob s Holiday 11. For this question you will need to understand temperature. Fist you would need to identify the months when Rob earns the LEAST amount of money. These are June and July. Next you would need to identify which months have the HIGHEST temperatures. These are July and August. July meets Rob s criteria for Temperature and Wages Therefore your answer should be: Rob should go on holiday in July because in this month there is an average temperature of 20 o C and it is his second lowest earning month for wages. Page 43
Understanding Functional Skills AON WB7 Measures L1 V3