A Living Maths Approach to Angles

Sir Cumference and the Great Knight of Angleland - living maths

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).

“What are these numbers around the edge of the medallion?” Radius asks. “No one knows,” Lady Di answered, “but may it bring you courage on your journey.”

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.

living maths - measuring angles

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!

living maths - measuring angles

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.

living maths - measuring angles
C(9)’s notebook page (she went a bit heavy on the glue, oops)

*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.

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10 thoughts on “A Living Maths Approach to Angles

  1. Love this! You write fantastic posts. I need to get my behind into gear and actually do some living and exciting maths. My children wanna come to your school!!

  2. What wonderful examples of how your children learn! The process is very similar to how maths happens in our home too. It’s interesting to note how C9 figured out the angles by herself, and how J8 is able to have the answer straightaway but not yet able to describe step-by-step workings. In many ways, I recognise their thinking process as being very similar to Tiger’s. As you’ve said, it’s really valuable that we can support our children’s unique ways of learning in the homeschool environment. Another wonderful post, Lucinda!

    1. Thank you so much, Hwee! It’s funny, when I came across C with the protractor I was reminded of your recent post about Tiger with the set square (I think it was?)!

  3. Your creative math post are very inspiring. I love the way your daughter arrived at the answer of 270 degrees and was able to explain her method. It very good to relate this to a clock.

    We have this book at home and I’m embarrassed to admit that I haven’t yet read it with the kids. Now that summer is here we should have more time for creative activities. If they go well I hope to continue into the school year.

    Thank you

    1. Thanks, Julie. I must admit I still don’t fully understand C(9)’s method (why did she need the ruler?!), but I understand that it worked for her! 😀 Enjoy your creative summer. We’re doing English terms so we’re working up til mid-July. Then again we’re off to Norway tomorrow so I can’t complain!

  4. Lucinda,

    That looks like a wonderful book. Lady Di of Ameter. I love that!

    A few months ago I suddenly got curious, wondering what exactly my girls knew about angles. I asked them if they knew the special names for the various sized angles and Sophie replied, “Acute angles, right angles, straight angles and obese angles.” Well, nearly! Don’t you love obese angles? I think that name is rather appropriate and I can see why she came up with it!

    1. Hello Sue, Lovely to see you here!

      Obese angles – I love it! I think I shall find myself calling them that. And I think you know from Sophie’s word choice that she definitely does understand what an obtuse angle is!

  5. I love that this approach is natural and meaningful to her.

    I wish we had homeschooled from the beginning and my girls’ foundation was more like this.

    1. Thanks, Theresa. Yes I wish we had done maths like this from the start. But I guess all we can do is jump in right where we are! 🙂

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