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Why do this problem?
offers a situation that is not too complex to understand and yet opens out many possible explorations. It would be a good chance to focus on the different ways children have represented their solutions.
You could present the problem orally to the class, rather like telling a story. Ask them how many branches there would be by the end of the second week. You could then invite them to talk in pairs about the number of branches at the end of the third week. Giving learners mini-whiteboards might help at this stage. How did they work out the answer? Having got this far, leave them to work
on the problem in their pairs.
In the plenary, you could draw attention to the different ways of representing the problem you have seen. Some children may have drawn pictures of the plant, others may have just drawn lines. There may be some children who have simply noted down numbers. Invite several pairs to talk about their own representation and then you could have a group discussion about the advantages of each
You may want to make a note of the numbers of branches at the end of each week and to ask the children what they notice. Can they explain why this pattern occurs? Could they predict how many branches there would be after seven weeks (if there weren't any flowers) without drawing a picture?
How many branches will there be after three weeks? Four weeks ...?
How will you keep track of the number of branches?
What kinds of things have you noticed?
Once children have solved the problem as it stands, the activity may be opened out and extended. For example:
1. If the plant branches in twos each year and we look at the units figure for a few years' growth we see year by year that the number of flowers [2 4 8 16 32 64 as in the problem] is:
2 4 8 6 2 4 ...
You can ask the pupils to see what they notice about the pattern.
2. Then you can pretend that the plant branches in different ways, maybe in 3s, 4s, 5s etc. For example the fours and fives units would look like:
The pupils can then be asked to explore what the patterns show and look at others for 6s 7s etc.
Further extension ideas are described on this sheet
You may want to talk to individual pupils about what is happening to the plant at each stage so they understand the context better.