Functional MathematicsProblem solving with decimals Underpins the following coverage & range statements Level 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
Kindly contributed to www.skillsworkshop.org by Elizabeth Adeyemi, South Thames College Functional MathematicsProblem solving with decimals When using this resource teachers should assess and reinforce the L1-2 skill standards: 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
Functional MathematicsProblem solving with decimals 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.
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?
Money Problem SolvingShow all your working out – you can use a calculator 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?
Choosing a savings account TASK 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
Metric measuresShow all your working out – you can use a calculator • 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?
Choosing a savings account 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 2 Which account/s might you choose if: a) you had £200 and needed instant access to your money b) you had £5000 and needed instant access to your money c) you didn't need instant access and had £750
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?
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?
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?
Gas Bills • 210 therms of gas were used in a quarter when the price per therm was 40.6p. 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 39.0p 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?
Answers Money problem solving (Level 1) 1) £17127.50 2) £4140 3) £46.56 4) £3042 5) £25.70 Metric measures (Level 1) • (a) 500cm (b) 3cm (c) 27cm • (a) 210mm (b) 3150mm (c) 46mm • (a) 5m (b) 3000m • 80mm • 6m string Choosing a savings account (Level 1) 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 £218 2) Special offer: £96 + (24 x £17) = £504. Bank: 24 x £22 = £528 so special offer is cheaper by £24 Cost 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 = £480.01 Gas 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