This approach takes standard textbook or practice questions and requires learners to think beyond the question and its answer – they have to focus on the context of the question and investigate that. This kind of activity is about making sense of situations and representing them, as well as processing and using mathematics.
After learners have answered the original question, they could be asked ‘What other questions could be asked about this situation?’. These ideas can be collated and discussed by the group before being answered. Alternatively, specific questions could be asked first and then followed by the further question.
Question 1
It takes 1.75 metres of denim to make a pair of jeans. Denim costs £3.50 per metre.
(a) How much will the material for the jeans cost?
(b) If the price of denim rises by 5%, how much will the material cost?
What other questions could you ask about this situation?
• If the denim can only be bought in an exact number of metres, how much extra will you pay for the denim you do not use?
• How many pairs would you need to make to ensure that there is no wastage of denim?
• What is inflation at the moment? What would happen if you used that figure instead of 5%?
• How much discount would you need to get the price back to where it was before the price increase?
• What would the discount need to be if the increase was 10%, or 20%?
• Can you generalise from these examples?
• The actual price of the jeans is double the cost of the denim because of trimmings, labour and profit. How much will the maker charge for the jeans?
• Would you ever choose to have jeans especially made for you? If so, why, and if not, why not?
• How do you decide where to buy your jeans?
Question 2
Jenny goes shopping and buys two CDs priced at £6.99 each and three T-shirts costing a total of £13.50. She took £40 with her into town. How much change will she have from her purchases?
What other questions could you ask about this situation?
• How much was each T-shirt? How do you know? Give some examples of possible prices.
• Is she likely to come home with all her change?
• How did she get home?
• What else might she spend her money on?
• Estimate her other expenditure.
• What would you spend the money on if you took £40 into town on Saturday?
Question 3
The monthly charge for a mobile phone is £25. This includes 300 minutes of free calls. After that there is a charge of 5p per minute. Calculate the cost of using the phone for 540 minutes in one month.
What other questions could you ask about this situation?
• What other information would you want to know about the charges for this phone before you decide to buy it?
• What difference is it likely to make to the bill if calls after 6.00 pm are only 3p per minute?
• What is the method of payment of your mobile phone? (If you have not got a phone, ask a friend about theirs.)
• Would you consider changing to the phone in the question? Explain your reason.
• Why do some people have ‘pay as you go’ but others have a monthly rental?
Question 4
Claire wants to record four programmes on a video tape that is three hours long. The lengths of the programmes that she wants to record are 30 minutes, 45 minutes, 50 minutes and 40 minutes. How much time will she have left on her tape when she has recorded them?
What other questions could you ask about this situation?
• What do you think the programmes are?
• How much of the time do you think is adverts?
• If Claire started watching the video at 6.00 pm when will she finish watching?
• What time do you think she will finish if she uses fast-forward when the adverts are on?
• What programmes would you like to record this week? How long will they last altogether?
Even ‘simple’ questions from an exercise can be developed into more complex problems.
Question 6
Calculate 20 + 16 × 5
Ask learners to create a story or scenario that this calculation might represent. Once the story has been created the questions that can be asked about the context are limitless. Any sort of calculation problem can be used in this way (eg 34 × 1.05, or 4500 × 3 + 2510 × 2).
Question 1 could be adapted to other contexts by changing the focus of the activity from buying material for a pair of jeans to, for example, ordering ingredients to make a recipe in a catering context, as shown in the
following adaptation.
Question 1
Catering
To make 50 bread rolls takes 1.6 kg of strong white flour, which costs £1.95 per kilogram.
(a) How much will the flour cost?
(b) If the price of flour rises by 5%, how much will the flour cost?
The other questions can also be adapted to the new context, for example in the catering context, as follows.
• If the flour can only be bought in an exact number of kilograms, how much extra will you pay for the flour you do not use?
• How many bread rolls would you need to bake so that there is no wastage of flour?
• What is inflation at the moment? What would happen if you used that figure instead of 5%?
• How much discount would you need to get the price back to where it was before the price increase?
• What would the discount need to be if the increase was 10%, or 20%?
• Can you generalise from these figures?
After learners have answered the original question, they could be asked ‘What other questions could be asked about this situation?’. These ideas can be collated and discussed by the group before being answered. Alternatively, specific questions could be asked first and then followed by the further question.
Question 1
It takes 1.75 metres of denim to make a pair of jeans. Denim costs £3.50 per metre.
(a) How much will the material for the jeans cost?
(b) If the price of denim rises by 5%, how much will the material cost?
What other questions could you ask about this situation?
• If the denim can only be bought in an exact number of metres, how much extra will you pay for the denim you do not use?
• How many pairs would you need to make to ensure that there is no wastage of denim?
• What is inflation at the moment? What would happen if you used that figure instead of 5%?
• How much discount would you need to get the price back to where it was before the price increase?
• What would the discount need to be if the increase was 10%, or 20%?
• Can you generalise from these examples?
• The actual price of the jeans is double the cost of the denim because of trimmings, labour and profit. How much will the maker charge for the jeans?
• Would you ever choose to have jeans especially made for you? If so, why, and if not, why not?
• How do you decide where to buy your jeans?
Question 2
Jenny goes shopping and buys two CDs priced at £6.99 each and three T-shirts costing a total of £13.50. She took £40 with her into town. How much change will she have from her purchases?
What other questions could you ask about this situation?
• How much was each T-shirt? How do you know? Give some examples of possible prices.
• Is she likely to come home with all her change?
• How did she get home?
• What else might she spend her money on?
• Estimate her other expenditure.
• What would you spend the money on if you took £40 into town on Saturday?
Question 3
The monthly charge for a mobile phone is £25. This includes 300 minutes of free calls. After that there is a charge of 5p per minute. Calculate the cost of using the phone for 540 minutes in one month.
What other questions could you ask about this situation?
• What other information would you want to know about the charges for this phone before you decide to buy it?
• What difference is it likely to make to the bill if calls after 6.00 pm are only 3p per minute?
• What is the method of payment of your mobile phone? (If you have not got a phone, ask a friend about theirs.)
• Would you consider changing to the phone in the question? Explain your reason.
• Why do some people have ‘pay as you go’ but others have a monthly rental?
Question 4
Claire wants to record four programmes on a video tape that is three hours long. The lengths of the programmes that she wants to record are 30 minutes, 45 minutes, 50 minutes and 40 minutes. How much time will she have left on her tape when she has recorded them?
What other questions could you ask about this situation?
• What do you think the programmes are?
• How much of the time do you think is adverts?
• If Claire started watching the video at 6.00 pm when will she finish watching?
• What time do you think she will finish if she uses fast-forward when the adverts are on?
• What programmes would you like to record this week? How long will they last altogether?
Even ‘simple’ questions from an exercise can be developed into more complex problems.
Question 6
Calculate 20 + 16 × 5
Ask learners to create a story or scenario that this calculation might represent. Once the story has been created the questions that can be asked about the context are limitless. Any sort of calculation problem can be used in this way (eg 34 × 1.05, or 4500 × 3 + 2510 × 2).
Question 1 could be adapted to other contexts by changing the focus of the activity from buying material for a pair of jeans to, for example, ordering ingredients to make a recipe in a catering context, as shown in the
following adaptation.
Question 1
Catering
To make 50 bread rolls takes 1.6 kg of strong white flour, which costs £1.95 per kilogram.
(a) How much will the flour cost?
(b) If the price of flour rises by 5%, how much will the flour cost?
The other questions can also be adapted to the new context, for example in the catering context, as follows.
• If the flour can only be bought in an exact number of kilograms, how much extra will you pay for the flour you do not use?
• How many bread rolls would you need to bake so that there is no wastage of flour?
• What is inflation at the moment? What would happen if you used that figure instead of 5%?
• How much discount would you need to get the price back to where it was before the price increase?
• What would the discount need to be if the increase was 10%, or 20%?
• Can you generalise from these figures?
• The actual price of the bread rolls is double the cost of the flour because of the yeast, butter and sugar needed and the baker’s profit. How much will the baker charge for the bread rolls?
• Does the type of bread roll make a difference to the cost? Are brown bread rolls more expensive than white bread rolls? If so, why might that be, and if not, why not?
• How do you decide where to buy your bread rolls?
• What other questions could be asked about this situation?
This approach to adapting questions for learners can be applied to many learning and work contexts. Question 2 could be adapted to a social care context, as follows, where care workers in a residential home are often asked to shop for residents.
Question 2
Social care
Jenny goes shopping for Ada, one of the residents, who wants four Lucky Dips at £1 each, a magazine that costs £1.30, two pairs of support tights that cost £6.15 a pair and two boxes of tissues at £0.75 a box. She gives Jenny £20 to buy everything. How much change will Jenny have to give back to Ada?
The further questions would need to be adapted, but could include asking learners to decide how much extra change Jenny would have if the tissues were on special offer at £1.35 for two boxes, or what she could do if the tights had gone up in price by 50p a pair.
This approach can be applied to any problem that has a context relevant to the learners, including problems from other subject areas. Learners could, for example, tackle a problem about population from geography or one about the laws of motion from physics. These problems can be extended in the same way by asking further questions and extending the context.
Learners sometimes struggle to identify what mathematics is needed to solve a particular problem. Ask them to identify the mathematics in a range of everyday events by suggesting questions that could be asked about them. The questions do not have to be answered but creating them and discussing them will encourage learners to decide what mathematics is involved in particular situations. They may be surprised at how much mathematics they can find.
Encourage learners to ask as many different questions as they can and then, as a class or as a small group, write problems that require some or all of these questions to be answered. Learners could also be asked to create a problem about each scenario that does not require any mathematics to answer it. Other learners can then try to identify some relevant mathematical questions that can be asked. Some of the problems may be trivial but it is all part of the process of sorting out whether or not a problem lends itself to mathematics. In this way, learners will get used to ‘looking for the mathematics’ so that, when they are faced with a problem to solve, they will be able to give a sensible decision as to whether it requires mathematics to solve it.
This can be extended by giving learners particular problems that need solving and asking them what, if any, mathematics they need to solve the problem. This is particularly appropriate if problems from other curricular areas are used. Learners can firstly identify all the mathematics that there is in the context of the problem, possibly by considering what questions can be asked, and then decide whether any of it is relevant to tackling that particular problem.
This will encourage learners to think about all the mathematics involved in any problem and whether or not it is appropriate to use mathematics to solve the problem.
The following are examples of scenarios that could be used.
What mathematical questions could be asked about:
• a bus journey to work?
• making a cup of coffee?
• watching a DVD?
• going to watch a football match?
• booking a client for treatment, for example in a beauty salon?
• painting the skirting board of a room?
• planning a holiday?
• today’s weather?
• the London Marathon?
• the moon?
Alternatively, learners could be shown a visual image or information that is relevant to them and asked to ‘look for the mathematics’. The image or information could come from their vocational area, the local environment, or other curricular subjects, for example a map from geography, a graph from chemistry, a source from history, a design from technology or a formula from physics.
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