Functional Mathematics
Problem solving with decimals
Underpins the following coverage & range statements
Level 1
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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
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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 Mathematics
Problem solving with decimals
When using this resource teachers should
assess and reinforce the L1-2 skill standards:
Level 1
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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
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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 Mathematics
Problem 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 Solving
Show 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 Solving
Show 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
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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 measures
Show all your working out – you can use a calculator
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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?
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
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%
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?
2) 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?
1)
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
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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.
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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
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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?
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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)
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(a) 500cm
(b) 3cm (c) 27cm
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(a) 210mm (b) 3150mm
(c) 46mm
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(a) 5m (b) 3000m
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80mm
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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)
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Hire Purchase £600 + ( 24 x £116) = £3384. So the cost of using credit = £384
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Credit price of drilling machine = £400 + (24 x £170) = £4480.00 Difference = £4480.00 - £3999.99
= £480.01
Gas Bills (Level 2)
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£11.50 + (210 x £0.406) = £96.76
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£10.50 + (220 x £0.39)= £96.30. Budget account estimate 3 x £35 = £105. So account will be in
credit by £8.70