Blog: Vicki Robinson, Communications Officer

# #MondayMaths and the rolling square

Posted: 15/08/16

**It’s often easier to grasp mathematical concepts or problems in a real life situation. So for this week’s puzzle, let’s imagine you’re moving house – which involves shifting a lot of heavy boxes. It turns out it’s much easier to roll them (apart from those marked fragile!)**

This week’s #MondayMaths problem is quite tricky, so puzzle-solvers will need to get their growth mindset hat on. We suggest finding a friend to help you tackle this one – it’s a great opportunity to talk about the maths.

This problem could be used in your Year 10 when studying loci in Spring 2 of our mastery curriculum. This gives students an opportunity to build on the skills developed when studying transformations as part of 2-D geometry towards the end of Year 9.

You can start by asking students to visualise the transformation of a square as it rotates around various vertices along a line – or effectively, rolled along the line. As the square is rolled to the right, the vertex labelled ‘C’ will trace out a path and we’re trying to calculate its length.

**Visualising movement**

The key to cracking this problem is spotting that C will trace out an arc whenever the square is rotated about a pivot.

Students should be able to demonstrate that C is moving along the circumference of a circle and work out:

- The radius of that circle
- What fraction of the full circumference each arc traces

It’s important to spot that, for one rotation, C is the pivot point and so does not trace a path.

The final rotation is the trickiest part of the problem, as the radius of the arc that C traces is less obvious. Students will have to use Pythagoras’ theorem (also introduced towards the end of Year 9) to find the exact radius.

**Using manipulatives**

A square pattern block could help puzzle-solvers visualise the problem. A pair of compasses or dynamic geometry software can also be used to trace the path.

**As always, answers will be posted on Thursday morning on Twitter. We’d love to hear how you get on with this week’s brain-teaser.**