Functional Maths: Questioning with a focus on the context

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 5

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 (e.g. 34 × 1.05, or 4500 × 3 + 2510 × 2).

‘Asking Questions’ is taken from chapter 2 of Teaching and learning functional mathematics, written by Susan Wall to support the pilot for functional mathematics.

Article by NCETM

tim

tim

Tim is a multidisciplinary developer.