Catrina wants to know how many football cards she has collected.
She has filled up five pages of her scrapbook and on each page there are four cards.
Can you show how you would find out? You might draw a picture or do some jottings or...
When you have had tried something yourself, click below to take a look at what some other children did:
I drew a number line to help:
I used counters instead of football cards. I made an array:
I drew a picture:
I thought a double number line would help me work out the answer:
What is the same about the four ways? What is different?
How does each way compare with what you did?
Which one do you prefer and why?
Why do this problem?
is designed to deepen children's understanding about multiplication. By offering different representations of multiplication in this task, learners' mathematical curiosity will be aroused. This will provide the motivation to compare the representations with each other and with their own. The
process of comparison will enable children to discover the underlying structure of multiplication.
Introduce the task simply as stated without saying anything more at this stage. Do your best to remain silent and give learners two minutes of thinking time on their own, then time to work in pairs. Emphasise that you are not expecting a complete solution at this stage necessarily, but the aim is to think about ways of working that will help them reach a solution. (Try to
accommodate any equipment requests as best you can!)
You can then reveal the four different representations in turn. The order does not matter particularly, but you could choose one to start with that you have seen quite a few pairs adopting, if applicable. After showing each one, give pairs time to look at it carefully and compare it with their own representation. What is the same? What is different? You may want to
invite a couple of pairs to share their thoughts with the whole group before moving on to the next representation.
Once the class has seen all four representations, invite them to compare all the different ways, including their own. You might find it useful to give out copies of this sheet
, which has all four representations on it. In the plenary, draw out the similarities and differences (which may also involve sharing other representations that
pairs have created themselves), and ask the children which they prefer and why. There is unlikely to be a consensus so it is important that individuals can explain what it is about that particular representation that they found useful.
Tell me about your drawing/jottings/...
What is the same about these two representations? What is different?
What do they all have in common?
You could ask the youngsters to produce a similar question themselves. Then questions could be swapped and children asked to use one of the representations that they did not use originally to solve this new task.
Encourage children working in pairs to talk the problem aloud with each other.