Triangle in a Square

This task is best done with at least one other person so you can talk through your ideas with someone else.

In the interactivity below, you can click through a series of mathematical statements made by Badger.

When each statement is revealed, your challenge is to decide whether or not it is true and why.
Talk to someone else about your thinking. Mathematicians don't like to take your word for it, they like to see a watertight chain of reasoning that covers all possibilities. Has Badger provided that?

If you are happy with a statement, you can click on 'OK' and the next statement is shown.

If you click on 'Pause' you have an opportunity to see some other children's thinking, which might help you form your own mathematical argument. Clicking on any of the examples of children's thinking will reveal Badger's response.

We would love to hear about your reasoning at each step. Can you use what you know about number and calculations to put together a watertight chain of reasoning that would convince a mathematician?

And perhaps you could create your own series of statements like this which includes some reasoning which isn't quite right? If you send us your statements, you may see them appear as an interactive task on NRICH!