Functional Mathematics   Problem solving with decimals <ul><li>Underpins the following coverage & range statements </li></...
Functional Mathematics Problem solving with decimals Kindly contributed to  www.skillsworkshop.org  by  Elizabeth Adeyemi,...
<ul><li>Aims:   </li></ul><ul><li>Use efficient and accurate methods to solve contextualised problems involving money/deci...
Money Problem Solving Show all your working out – you can use a calculator <ul><li>1) 4030 people go to a football match. ...
<ul><li>4) Arnis pays $58.50 per week in rent.  </li></ul><ul><li>How much does he pay per year? </li></ul><ul><li>5) Sale...
Choosing a savings account <ul><li>TASK 1 </li></ul><ul><li>What things would you take into consideration when opening an ...
<ul><li>Convert the following to centimetres: </li></ul><ul><li>(a) 5 metres (b) 30 millimetres (c) 270 millimetres </li><...
Different accounts have different interest rates. The more money you have – the better the interest rate. You also get bet...
Wages <ul><li>A man earns a basic $180 a week, plus $45 in overtime. He pays $26.80 in tax, $5.75 in national insurance, a...
Bank loans……… <ul><li>1)  A man sees a new car priced at $5000. The car dealer asks for ¼ deposit and then 24 monthly inst...
Cost of Credit <ul><li>A second hand car is offered at $3000 cash or by a deposit of 1/5 of the cash price plus 24 monthly...
Gas Bills <ul><li>210 therms of gas were used in a quarter when the price per therm was 40.6c With the standing charge at ...
Answers <ul><li>Money problem solving (Level 1) </li></ul><ul><li>1) £17127.50 2) £4140 3) £46.56 4) £3042 5) £25.70 </li>...
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L1l2fmdecimalproblems

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  • Kindly contributed to www.skillsworkshop.org by Elizabeth Adeyemi, South Thames College. Feb 2010
  • L1l2fmdecimalproblems

    1. 1. Functional Mathematics Problem solving with decimals <ul><li>Underpins the following coverage & range statements </li></ul><ul><li>Level 1 </li></ul><ul><li>add and subtract decimals up to two decimal places </li></ul><ul><li>convert units of measure in the same system </li></ul><ul><li>solve problems requiring calculation, with common measures, including money, time, length, weight, capacity & temperature </li></ul><ul><li>extract and interpret information from tables, diagrams, charts and graphs </li></ul><ul><li>understand and use equivalences between common fractions, decimals and percentages </li></ul><ul><li>Level 2 </li></ul><ul><li>carry out calculations with numbers of any size in practical contexts, to a given number of decimal places </li></ul>Kindly contributed to www.skillsworkshop.org by Elizabeth Adeyemi, South Thames College
    2. 2. Functional Mathematics Problem solving with decimals Kindly contributed to www.skillsworkshop.org by Elizabeth Adeyemi, South Thames College <ul><li>Level 1 </li></ul><ul><li>understand practical problems in familiar and unfamiliar contexts and situations, some of which are non-routine </li></ul><ul><li>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 </li></ul><ul><li>identify and obtain necessary information to tackle the problem </li></ul><ul><li>use appropriate checking procedures at each stage </li></ul><ul><li>select mathematics in an organised way to find solutions </li></ul><ul><li>Level 2 </li></ul><ul><li>understand routine and non-routine problems in familiar and unfamiliar contexts and situations </li></ul><ul><li>apply a range of mathematics to find solutions </li></ul><ul><li>interpret and communicate solutions to multistage practical problems in familiar and unfamiliar contexts and situations </li></ul><ul><li>identify the situation or problems and identify the mathematical methods needed to solve them </li></ul><ul><li>use appropriate checking procedures and evaluate their effectiveness at each stage </li></ul><ul><li>draw conclusions and provide mathematical justifications </li></ul><ul><li>choose from a range of mathematics to find solutions </li></ul>When using this resource teachers should assess and reinforce the L1-2 skill standards:
    3. 3. <ul><li>Aims: </li></ul><ul><li>Use efficient and accurate methods to solve contextualised problems involving money/decimals </li></ul><ul><li>Learning outcomes: </li></ul><ul><li>By the end of the lesson ALL learners will be able to: </li></ul><ul><li>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) </li></ul><ul><li>carry out simple calculations involving money. </li></ul><ul><li>identify the correct mathematical procedures needed to solve problems </li></ul><ul><li>Some learners will be able to (differentiated outcomes for more able learners within the group): </li></ul><ul><li>carryout the calculations efficiently and accurately. </li></ul><ul><li>Calculate cost of credit on loans and hire purchase. </li></ul>Functional Mathematics Problem solving with decimals
    4. 4. Money Problem Solving Show all your working out – you can use a calculator <ul><li>1) 4030 people go to a football match. Each ticket costs $4.25. </li></ul><ul><li>What is the total cost of all the tickets? </li></ul><ul><li>2) A person earns $345 per month. </li></ul><ul><li>What is his annual salary? </li></ul><ul><li>3) You pay $558.72 in tax per year. </li></ul><ul><li>How much do you pay per month in tax? </li></ul>
    5. 5. <ul><li>4) Arnis pays $58.50 per week in rent. </li></ul><ul><li>How much does he pay per year? </li></ul><ul><li>5) Sale items were advertised at half price of normal prices. </li></ul><ul><li>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? </li></ul>Money Problem Solving Show all your working out – you can use a calculator
    6. 6. Choosing a savings account <ul><li>TASK 1 </li></ul><ul><li>What things would you take into consideration when opening an account? </li></ul><ul><li>Rate the following in order of importance to you: 1 most important to 12 least important </li></ul><ul><li>Friendly staff </li></ul><ul><li>Close to where you live </li></ul><ul><li>Good rates of interest </li></ul><ul><li>Recommended by a friend </li></ul><ul><li>Has cash machines </li></ul><ul><li>Low bank charges </li></ul><ul><li>Nice carpets </li></ul><ul><li>A well known company </li></ul><ul><li>Good adverts </li></ul><ul><li>Informative staff </li></ul><ul><li>Easy to understand literature </li></ul><ul><li>Short queues </li></ul>
    7. 7. <ul><li>Convert the following to centimetres: </li></ul><ul><li>(a) 5 metres (b) 30 millimetres (c) 270 millimetres </li></ul><ul><li>Convert the following to millimetres: </li></ul><ul><li>(a) 21cm (b) 315 cm (c) 4.6 cm </li></ul><ul><li>Convert the following to metres: </li></ul><ul><li>(a) 500cm (b) 3km </li></ul><ul><li>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? </li></ul><ul><li>Thirty children in a class each need 20 cm of string for a project. How many metres of string will they use all together? </li></ul>Metric measures Show all your working out – you can use a calculator
    8. 8. 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. <ul><li>TASK 2 </li></ul><ul><li>Which account/s might you choose if: </li></ul><ul><li>a) you had $200 and needed instant access to your money </li></ul><ul><li>b) you had $5000 and needed instant access to your money </li></ul><ul><li>c) you didn't need instant access and had $750 </li></ul>Choosing a savings account Newtown Building Society Instant Access Account Up to $500 4.5% $500+ 4.45% $2000+ 5.5% Chrome & Leather Bank Instant Access Account Up to $5000 4.03% $5000+ 4.45% $10000+ 6.2% Northford Building Society 60 Day Account Up to $500 5.67% $500+ 5.75% $2000+ 6.30% E-Turnip Bank Online Account Min $500 6.75% $1000 + 7.23% $2500+ 7.50%
    9. 9. Wages <ul><li>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? </li></ul><ul><li>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? </li></ul>
    10. 10. Bank loans……… <ul><li>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? </li></ul><ul><li>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? </li></ul>
    11. 11. Cost of Credit <ul><li>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. </li></ul><ul><li>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? </li></ul>
    12. 12. Gas Bills <ul><li>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? </li></ul><ul><li>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? </li></ul>
    13. 13. Answers <ul><li>Money problem solving (Level 1) </li></ul><ul><li>1) £17127.50 2) £4140 3) £46.56 4) £3042 5) £25.70 </li></ul><ul><li>Metric measures (Level 1) </li></ul><ul><li>(a) 500cm (b) 3cm (c) 27cm </li></ul><ul><li>(a) 210mm (b) 3150mm (c) 46mm </li></ul><ul><li>(a) 5m (b) 3000m </li></ul><ul><li>80mm </li></ul><ul><li>6m string </li></ul><ul><li>Choosing a savings account (Level 1) </li></ul><ul><li>Task 1) student choice. Task 2) a) Newtown, b) Newtown, c) E-Turnip. </li></ul><ul><li>Wages (level 1) </li></ul><ul><li>1) £225 - (26.80+5.75+9) = </li></ul><ul><li>2) (38 x £6.20) + (12 x 12.40) = </li></ul><ul><li>Bank Loans (Level 2) </li></ul><ul><li>1) Dealer : £1250 + (24 x £192) =£5858. Bank: 24 x £235 = £5640 so the bank is cheaper by £218 </li></ul><ul><li>2) Special offer: £96 + (24 x £17) = £504. Bank: 24 x £22 = £528 so special offer is cheaper by £24 </li></ul><ul><li>Cost of credit (Level 2) </li></ul><ul><li>Hire Purchase £600 + ( 24 x £116) = £3384. So the cost of using credit = £384 </li></ul><ul><li>Credit price of drilling machine = £400 + (24 x £170) = £4480.00 Difference = £4480.00 - £3999.99 = £480.01 </li></ul><ul><li>Gas Bills (Level 2) </li></ul><ul><li>£11.50 + (210 x £0.406) = £96.76 </li></ul><ul><li>£10.50 + (220 x £0.39)= £96.30. Budget account estimate 3 x £35 = £105. So account will be in credit by £8.70 </li></ul>

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