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Here are some questions about Jola's birthday party.
How would you represent them using:
- other ways?
Jola has 24 cupcakes to share equally between 3 plates for her birthday party.
How many cakes will go on each plate?
There are 8 children coming to the party (including Jola). They are all going to the cinema.
How many cars will they need to take them there? Each car can take 4 children and a driver.
Jola is going to give everyone some chocolate eggs to take home at the end of the party. They fit into egg boxes which hold 6 eggs each. Will 50 eggs be enough for each of the 8 party guests to have a box of eggs?
At first glance this looks like any collection of word problems about division. However each different scenario draws attention to a different way of thinking about the idea of division:
You might like to take a look at this article which explores different ways of thinking about division.
Whilst the children are working on each question, the teacher can observe just how they are considering it, and this may be somewhat different from the taught approach. Given the opportunity, children often have their own ways of working.
In each case it would be possible to use a range of representations of the situation to help solve the problem and children should be encouraged to explain how they have tackled the problem and arrived at their solution using different resources to help them. Look and listen carefully to hear how they make sense of the question and develop a strategy for solving it.
Talk to the children about how different people do things in different ways and explain that this activity is all about that - it's important that the children don't presume that there is one way and one way only to see the calculation.
Working within a pair or small group and tackling one problem at a time can help children to focus more deeply on one task rather than racing through them. You could suggest that they think and talk about what they are going to do before they actually begin.
They may decide to enact with objects or make a picture and just record the answer. Or use these as a prompt to transfer the problem to a calculation which they would record horizontally. Whichever, your observations will allow you to reflect on the children's confidence, language and understanding and possibly what misconceptions they hold.
Tell me how you are working this out.
What do you think of _____'s way of doing this?
How did you know what to do first?
Is the way you've done this one different from the way you have done the others?
Ask the pupils to create stories that involve calculations for their partners to do.
Give the pupils a written form of a division question eg $18 ÷ ? = 3$ and challenge them to create a story around it.
Ask the children to create their own division problems based on stories about sharing, grouping, 'undoing' multiplication or successive subtraction. Additional links to other division problems can be found in this article.
Some pupils will benefit from working with some small toys/dolls so that they can enact the situation before being able to think about the calculation, for example the children could use Lego figures to show the children at the party and counters for the cakes with circles of paper as plates. The physical act of moving objects in different ways while enacting the story can often help less confident children to work out how to think about the division in an appropriate way that makes sense to them.
There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?