# A Living Maths Approach to Angles

For our living maths story this week I’d planned to build on what we learned recently about right angles by reading  Sir Cumference and the Great Knight of Angleland. As usual, I think I learned as much as the children – and not just about maths.

### Sir Cumference and the Great Knight of Angleland

The book tells the story of Radius, son of Sir Cumference and Lady Di of Ameter, who sets off on a quest to earn his knighthood. He takes with him a family heirloom – a circular medallion with mysterious numbers around its edge (the book comes with a cardboard copy of the medallion).

During Radius’s quest we discover with him how to use the numbers on the medallion to measure right, acute and obtuse angles. With the medallion’s help, Radius succeeds in navigating a path through the perilous maze to complete his quest.

### Maths Playtime

C(9) actually jumped ahead and read the book while I was working on something else with J(8)*. I came over to find her playing with the “medallion” (protractor). She’d drawn around it and marked 0, 90 and 180 degrees.

We talked about acute and obtuse angles, and I asked her what we might also call the 0 point (“360”.)

Then I pointed to the six o’clock position on the circle and asked how many degrees round that would be, counting clockwise from zero. I left the room to transfer some washing to the dryer – our “maths lesson” wasn’t meant to have started at this point. 😉

A few minutes later she came and found me with the answer – “270 degrees”. I asked how she’d worked it out. Finding out how a student’s minds works is such a valuable part of the mentoring process.

She told me she’d measured a degree with a ruler and found that “this amount” on the protractor [ten degrees] was the same as “that amount” on the ruler [a centimetre]. By working around the circle she’d found the answer. “Then,” she continued, “I realised there was a pattern – you add 90 each time you go round a quarter of the circle.”

I congratulated her on thinking like a mathematician!

If we used a formal curriculum, I’m sure my third grader would have “learned” about acute and obtuse angles by now and maybe even used a protractor to measure them. But what I love about this approach is seeing her sheer joy at figuring it all out for herself.

Hearing her animated explanation of how she’d solved the puzzle showed me without doubt that she really understood the concept. It also gave me valuable insight into her learning process, which is quite different from her brother’s.

If I’d asked J(8) the same question, I’m pretty sure he would have come straight out with the answer “270” – but he wouldn’t have been able to explain how he found it. Not having to “show your workings” when your brain doesn’t consciously do workings is one of the joys of homeschooling for the right-brained visual-spatial learner. Teaching J(8) to “backwards-engineer” and thus extend his thinking process (as well as pass exams, later on) is one of my long-term goals.

A final indication that C(9) took ownership of what she learned was that she decided to make a notebook page about what she’d learned for her maths journal.

*Incidentally, while C(9) was teaching herself about angles, I was helping J(8) understand the steps of long division using Life of Fred (Honey) – at his request.  I love how a living maths mentoring approach means I can help each of my children learn in the way that’s right for them. (Which might be a different way next week – there’s never a dull moment!)

For more hands-on maths ideas, visit the Math Teachers at Play Carnival #63.