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Functional Mathematics Problem solving with decimals
Underpins the following coverage & range statementsLevel 1► add and subtract decimals up to two decimal places► convert units of measure in the same system ► solve problems requiring calculation, with common measures, including
money, time, length, weight, capacity & temperature ► extract and interpret information from tables, diagrams, charts and graphs ► understand and use equivalences between common fractions, decimals
and percentages Level 2► carry out calculations with numbers of any size in practical contexts, to a
given number of decimal places
Kindly contributed to www.skillsworkshop.org by Elizabeth Adeyemi, South Thames College
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Functional MathematicsProblem solving with decimals
Kindly contributed to www.skillsworkshop.org by Elizabeth Adeyemi, South Thames College
Level 1► understand practical problems in familiar and unfamiliar contexts and situations, some of which
are non-routine ► apply mathematics in an organised way to find solutions to straightforward practical problems
for different purposes interpret and communicate solutions to practical problems, drawing simple conclusions and giving explanations
► identify and obtain necessary information to tackle the problem ► use appropriate checking procedures at each stage ► select mathematics in an organised way to find solutions Level 2► understand routine and non-routine problems in familiar and unfamiliar contexts and situations► apply a range of mathematics to find solutions► interpret and communicate solutions to multistage practical problems in familiar and unfamiliar
contexts and situations ► identify the situation or problems and identify the mathematical methods needed to solve them ► use appropriate checking procedures and evaluate their effectiveness at each stage► draw conclusions and provide mathematical justifications► choose from a range of mathematics to find solutions
When using this resource teachers should assess and reinforce the L1-2 skill standards:
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Aims: Use efficient and accurate methods to solve contextualised problems involving money/decimals
Learning outcomes:By the end of the lesson ALL learners will be able to:Read, write and understand decimals up to two decimal places in practical contexts. (as: common measures to one decimal place, e.g. 1.5m; money in decimal notation)
► carry out simple calculations involving money.► identify the correct mathematical procedures needed to solve problems
Some learners will be able to (differentiated outcomes for more able learners within the group):► carryout the calculations efficiently and accurately.►Calculate cost of credit on loans and hire purchase.
Functional MathematicsProblem solving with decimals
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Money Problem SolvingShow all your working out – you can use a calculator
1) 4030 people go to a football match. Each ticket costs $4.25.What is the total cost of all the tickets?
2) A person earns $345 per month. What is his annual salary?
3) You pay $558.72 in tax per year. How much do you pay per month in tax?
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4) Arnis pays $58.50 per week in rent. How much does he pay per year?
5) Sale items were advertised at half price of normal prices. What did it cost in a sale to buy a blouse, skirt and jeans if the normal prices were $17.60, $19.40 and $14.40 respectively?
Money Problem SolvingShow all your working out – you can use a calculator
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Choosing a savings accountTASK 1
What things would you take into consideration when opening an account?Rate the following in order of importance to you: 1 most important to 12 least important
► Friendly staff► Close to where you live► Good rates of interest► Recommended by a friend► Has cash machines► Low bank charges► Nice carpets► A well known company► Good adverts► Informative staff► Easy to understand literature► Short queues
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► Convert the following to centimetres:(a) 5 metres (b) 30 millimetres (c) 270 millimetres
► Convert the following to millimetres:(a) 21cm (b) 315 cm (c) 4.6 cm
► Convert the following to metres:(a) 500cm (b) 3km
► You are fitting kitchen cabinets. The gap for the last cabinet is 80cm. The sizes of the cabinets are shown in millimetres. Which size should you look for?
► Thirty children in a class each need 20 cm of string for a project. How many metres of string will they use all together?
Metric measuresShow all your working out – you can use a calculator
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Different accounts have different interest rates. The more money you have – the better the interest rate. You also get better rates if you tie up your money for set periods.
TASK 2Which account/s might you choose if:a) you had $200 and needed instant access to your moneyb) you had $5000 and needed instant access to your moneyc) you didn't need instant access and had $750
Newtown Building SocietyInstant Access Account Up to $500 4.5%$500+ 4.45%$2000+ 5.5%
Chrome & Leather BankInstant Access AccountUp to $5000 4.03%$5000+ 4.45%$10000+ 6.2%
Northford Building Society60 Day AccountUp to $500 5.67%$500+ 5.75%$2000+ 6.30%
E-Turnip BankOnline AccountMin $500 6.75%$1000 + 7.23%$2500+ 7.50%
Choosing a savings account
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Wages
► A man earns a basic $180 a week, plus $45 in overtime. He pays $26.80 in tax, $5.75 in national insurance, and his pension contribution is $5 for every $100 on his basic pay. What is his net pay for the week?
► A woman’s basic rate is $6.20 an hour but for weekend working she gets double time. In one week she works 50 hours, of which 12 were at the weekend. How much did he earn that week?
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Bank loans………
1) A man sees a new car priced at $5000. The car dealer asks for ¼ deposit and then 24 monthly instalment of $192. Her bank offers her a loan of $5000 for 24 monthly payments of $235. Which overall payment is cheaper and by how much?
2) A motorbike is on offer at $480 cash but with a special offer of 1/5 deposit and 24 monthly payments of $17. A man asks the bank and they offer a loan of $480 with 24 monthly payments of $22. Which overall payment is cheaper and by how much?
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Cost of Credit► A second hand car is offered at $3000 cash or by a
deposit of 1/5 of the cash price plus 24 monthly payments of $116. Find the hire purchase price and calculate cost of credit.
► A new drilling machine is on offer at $3999.99 but it can be bought by a deposit $400 and then 24 monthly payment of $170. What is the difference between the cash price and the credit price?
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Gas Bills
► 210 therms of gas were used in a quarter when the price per therm was 40.6c With the standing charge at $11.50 how much was the gas bill?
► A gas budget account is estimated at $35 per month. In the first quarter 220 therms are used at 39.0c a therm and the standing charge is $10.50. Is the account in credit or not at the end of first quarter and by how much?
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AnswersMoney problem solving (Level 1)1) £17127.50 2) £4140 3) £46.56 4) £3042 5) £25.70Metric measures (Level 1)► (a) 500cm (b) 3cm (c) 27cm► (a) 210mm (b) 3150mm (c) 46mm► (a) 5m (b) 3000m► 80mm ► 6m string6m stringChoosing a savings account (Level 1)Task 1) student choice. Task 2) a) Newtown, b) Newtown, c) E-Turnip.Task 1) student choice. Task 2) a) Newtown, b) Newtown, c) E-Turnip.Wages (level 1)1) £225 - (26.80+5.75+9) =2) (38 x £6.20) + (12 x 12.40) =Bank Loans (Level 2)1) Dealer : £1250 + (24 x £192) =£5858. Bank: 24 x £235 = £5640 so the bank is cheaper by £2182) Special offer: £96 + (24 x £17) = £504. Bank: 24 x £22 = £528 so special offer is cheaper by £24Cost of credit (Level 2)► Hire Purchase £600 + ( 24 x £116) = £3384. So the cost of using credit = £384► Credit price of drilling machine = £400 + (24 x £170) = £4480.00 Difference = £4480.00 -
£3999.99 = £480.01Gas Bills (Level 2)► £11.50 + (210 x £0.406) = £96.76► £10.50 + (220 x £0.39)= £96.30. Budget account estimate 3 x £35 = £105. So account will be in
credit by £8.70