#MondayMaths and the rolling square

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.

Rolling square example

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.