'Ethical' number challenges and investigations with money
Numeracy doesn't have to be morally neutral. The What if Learning project suggests that a Christian understanding of life can make a positive difference to teaching and learning. Teachers of all faiths and beliefs have found this approach helpful when considering how their subjects might contribute to a child's Spiritual, Moral, Social and Cultural education. But how could Numeracy investigations about money show the values of faith, hope and love? Here are some possibilities you might want to adapt to suit the needs of your pupils. All provide challenging Numeracy investigations into working with money - and add an ethical dilemma for discussion during the plenary part of the lesson. For more examples of problems on the theme of hope and love, buy a copy of our teaching resource Valuing Money (BRF, 2015).
Here's a useful tip: before setting a problem - solving task for your pupils, try doing it yourself for five minutes without looking at the answers. It's fascinating to notice which key bits of knowledge or skills are dredged up from our own memories when we tackle problems like this - and it can illuminate the difficulties (or useful steps) for our pupils as well.
Faith makes us sure of what we hope for and gives us proof of what we cannot see.
Hebrews 11:1 (CEV)
'If you had faith no larger than a mustard seed, you could tell this mountain to move from here to there. And it would. Everything would be possible for you.'
Matthew 17:20 (CEV)
Faith is a hypothesis, an experiment of trust that uses a smaller bit of information to draw conclusions about something greater - then tests them. All mathematical investigations involving 'trial - and - improve' methods exercise faith by using strategies that have worked before and might work again - or need improving! Before we make a purchase, faith also asks questions such as:
- Do I trust what's been offered?
- Does it fit with what I already know?
- Will it be worth it?
- Will I check my change afterwards?
Paula wants to buy a new laptop and needs £150. The website of a loans company offers an 'easy' loan of £150 to be paid back at £5.00 a day (including interest) over 36 days.
- How much extra will the laptop cost if Paula takes out the loan?
- Do you think this is worth it?
- What could go wrong if Paula doesn't keep up with the repayments?
Answer: 36 x £5.00 = £180.00. Paula is paying £30.00 extra, an interest rate of 20%. That's a bit steep - and if she doesn't keep up with the repayments, it'll be a lot more, because the interest on the unpaid amount might become much higher. Alternatively, if she saves £150 over 36 days, she'll be £30.00 better off when she buys the laptop. (Which would you prefer to do, and why?)
Alvin is interested in finding out more about the human body. A weekly magazine is being advertised on TV. Over 52 weeks, the magazines build up to make a medical encyclopedia, and each magazine comes with a plastic body part for building up a model of the human body. The first magazine costs £2.99, and after that they cost £5.99 each. Two large binders (holding the magazines together) will cost another £9.99 each.
- Calculate the final cost of the complete encyclopedia and model.
- Do you think it's worth it?
- Do you think Alvin could buy the completed items cheaper elsewhere?
Answer: £2.99 + (£5.99 x 51) (£9.99 x 2) =
£2.99 £305.49 £19.98 = £328.46
Note: How many people work out the total cost of this kind of magazine offer before signing up for it? Medical encyclopedias can be bought very cheaply in discount bookshops, often with medical models attached! Nearly all these TV - advertised weekly - instalment purchase schemes are incredibly expensive. If someone likes building model kits, they should go to a model hobby shop.
Show a menu from a local restaurant or takeaway that offers discounts for customers who buy the set meals instead of individual items. Pick one set meal, and work out the savings if customers did this instead of buying the individual items.
- Is it worth it?
- Would you actually end up spending more, because it encourages you to have more items? Does that matter?
Develop this investigation further by planning the best possible value meal for four people, costing £40.00 in total.
Note: all answers depend on the local prices. Discuss why a restaurant or takeaway might offer these deals. Are they able to offer these particular dishes more cheaply because the ingredients are cheaper - and if so, does that matter?
Most children need to drink about a litre of water a day in some form, and bottled water costs about £1.50 a litre.
- If Barak only drank bottled water, how much would that cost him per week?
- How much would it cost for a month (four weeks)?
- How much would it cost for a year (52 weeks)?
- How much would it cost for five years?
- Barak could drink water from the tap much more cheaply. Why do you think some people prefer buying bottled water?
- Do you think bottled water is worth all the extra packaging and cost? Why?
Answer: £1.50 x 7 = £10.50
£10.50 x 4= £42.00
£10.50 x 52 = £546.00
£546.00 x 5= £2730.00
Note: That's an awful lot to pay for bottled water, which is usually taken straight from the local water supply providing local tap water - or even worse, might be transported internationally! Concerns about the taste of local tap water (which may be hard or soft) or added chemicals such as fluoride (to harden teeth) may be genuine - but are they worth the extra expense?
It's always important to check your change when shopping - but do you know how to count up quickly like old - fashioned shop assistants? Suppose you pay one pound for an item costing 65p. The shop assistant might repay you like this, counting up from 65p by first giving you the 5p ('That's 70p...'), then 10p ('... 80...'), 10p ('... 90...') and 10p ('... one pound!') You should then be holding 35p.
In 10 seconds or quicker (working with a partner and some plastic coins), use this method to work out the right change if you handed over a £1.00 coin to buy:
- a comic at 75p
- a magazine at 85p
- a bag of sweets at 55p.
Encourage pupils to try a few more, then to develop this challenge with a partner. Set them three different prices to see how fast they can work out the change for a £2.00 coin. Which mental maths techniques work best?
Note: Afterwards, it's worth discussing how confident we might be at challenging an adult shop assistant's maths if we think they've got it wrong. But we are always advised to check our change before leaving a shop. So what's the best way to dispute our change without starting an argument?
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