How Do You Do It?

'How Do You Do It?' printed from https://nrich.maths.org/

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How Do You Do It?

This problem is designed to be done in a group. So, ideally, you need to find three or four other people to work with you.

Firstly, take some time to work on your own to find the answers to these calculations, without writing anything down. (Although it would be good to write down the answer itself so you don't forget it.)

$19 \times 24$
$198 + 997$
Half of $57.6$
$3841 - 665.3$
$5.2 \div 4$
$101 \times 16 \times 4$

Now, join together with the other people in your group and focus on the first question.

Do you all agree on the answer?
Give EVERYONE in the group time to explain how they worked it out.
As a group, decide whose method you think is most efficient and why.

Do the same for each of the six questions: give everyone the chance to explain their own method and then choose the most efficient for that calculation.

For the final bit of the challenge, you will need a set of these cards - one set for the group. Each card has another calculation on it. As a group, decide on the most efficient method for each of the cards.
What did you decide and why?

Why do this problem?

This problem is designed for use in a group and it could easily take a couple of lessons. It offers opportunities for learners to discuss their own mental calculation strategies and to make decisions about the effectiveness and efficiency of different strategies in different contexts. The notes below assume that pupils have worked in groups before and, in particular, that they are good at listening carefully to each other.

Possible approach

This activity will work best if children are in groups of four or five.

Begin by explaining to the whole class that you are going to ask them some questions and you would like them to work out the answers in their heads on their own. (You could allow them to make jottings, but discourage them from writing out calculations.) Once they have come to an answer, ask them to write it down, for example on a mini-whiteboard. Suggest that it would be helpful if they tried to remember how they worked out the answer as the methods will be the focus of the group work later. Ask each of the following in turn, giving everyone enough time to work on the answer. It might be helpful to write them up on the board as you say each one.

$19 \times 24$
$198 + 997$
Half of $57.6$
$3841 - 665.3$
$5.2 \div 4$
$101 \times 16 \times 4$

Next introduce learners to the group task. Ask them to consider the first calculation and compare answers. It is very possible that they won't agree but in many ways this is a good thing! Explain to them that you would like them to decide what the right answer is by sharing the ways they worked it out. Emphasise that you would like everyone in the group to have a turn at explaining their own method. Once the group has decided on the answer, the second part of the task is to decide which method they think is most efficient. They can then repeat this process for each of the above calculations.

Once the group has completed this, give them a set of these cards. The challenge now is to work out the answers to this new set of calculations, but working together. The questions on the cards are similar in some ways to the questions initially given, so the idea would be for children to notice the similarities. Encourage them, therefore, to use a method that they have identified as efficient in the first part of the task. It would be good to give each group an A3 sheet of paper (or even bigger) to record the methods that they choose for the calculations on the cards. The posters they create can form the basis of a whole-class discussion in the plenary, comparing their chosen methods, and will make an informative display.

Key questions

How will you agree on the answer to this one?

How did you work out the answer to this one?

Has everyone in the group explained their method?

Which method do you think is most efficient? Why?

Possible extension

Some children will enjoy creating their own calculations which they believe could be solved using a particular method.

Possible support

Some learners will benefit from being 'given permission' to jot down steps in their mental calculations. You may wish some to only focus on the methods they would use, rather than actually performing the calculations themselves.