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Where Can We Visit?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

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Arithmagons

Can you find the values at the vertices when you know the values on the edges?

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Babylon Numbers

Can you make a hypothesis to explain these ancient numbers?

Gr8 Coach

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Why do this problem?

This problem provides children with an opportunity to make hypotheses and refine them in light of new evidence. It also requires them to devise systematic ways of working and recording their findings.

Possible approach

In order for children to get the most out of this activity, it would be good for them to have direct access to the interactivity, so perhaps pairs could share a computer.

Set the scene for the class and introduce the interactivity, entering any values so that learners see how it works. (Ticking the "Skip animation" box will speed up the process once they have seen a few time trials and races.) Invite pairs to talk about how they would approach the task and then share ideas amongst the whole group. At this stage, you could say very little and encourage them to make a start.

After some time, bring the group together to report on progress so far. At this point, ask them how they are keeping track of what they have tried - there might be some effective strategies that you can draw attention to - and invite some learners to describe what they are doing. Pupils might suggest that you split the task up so that different pairs are investigating different combinations of values.

A plenary could focus on explanations of how children know they have found the optimum regime. Listen out for an awareness of altering values based on the information gathered from testing and the use of a system to ensure no possible "winning" combinations could have been overlooked.

Key questions

What happens if you lower the value of one input?
What happens if you make that same input larger?
What could you try next?
How will you keep track of what you have tried?

Possible extension

Reaction Timer would be a nice follow-up activity to this problem.

Possible support

The task could be broken down for some children by eliminating one variable. For example, they could find out what the best regime is if the rowers have only got time to do 20 minutes of circuits a day.