Expanding Investigations
The everyday item below may seem simplistic, but it can offer a rich source of investigation inspiration.
This mind map contains a few ideas for how this could be explored in class. Click on the dot beside each sub-heading for more. You may find the tool itself useful for designing your own investigations too.
Fermi Questions and other Investigation Ideas
Here are a few more ideas for inspiration.
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Other great resources for inspiring investigation

Take students on a guided tour through a virtual museum of mathematics.
Note: Sadly this link no longer connects to the resource. If you know of the new address for the Matrix Maths Museum please share it via the blog page.
Note: Sadly this link no longer connects to the resource. If you know of the new address for the Matrix Maths Museum please share it via the blog page.

Encourage students to explore the maths in the world around them.
My thanks go to the fantastic teachers I met at the 2014 NWPD evening for sharing this final resource.
Videos for classroom discussion
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Interested in more videos like those above? Try Vi Hart's Youtube Channel here.
Visit the Research page for more ideas