Category: visual maths

Association of Teachers of Mathematics – Singapore Branch meeting

Last year we set up a branch of the Association of Teachers of Mathematics (ATM) in Singapore. The ATM is a UK professional organisation and I used to go to their meetings in the UK and in Hong Kong.

Last year, one of my colleagues in the Infant school decided to set up an ATM branch in Singapore. (Setting up a branch is free and astoundingly easy.) So far the ATM branch has met four times with about 50 teachers each time.

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We had a meeting this week and it was brilliant to meet both primary and secondary colleagues from around Singapore to talk about maths teaching ideas. And eat cakes and fruit drink wine!

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The theme for our meeting was shape and geometry teaching ideas. One good idea that was shared in the Secondary teachers chat was a gift-wrapped sphere with a note that said, “This Secret Santa present is yours if you can estimate its volume to within 50 cm2.” I made an estimate (without a calculator) but apparently I was 52 cm2 off the correct answer! Doh. I never did find out what was in that package.

I shared an idea for teaching about the surface area of a sphere using an orange that you unpeel. It’s described on this wonderful blog by William Emeny. (His blog’s name is eerily similar to my own!)

If you work in Singapore, please come along to our next meeting! We meet once a term (three times a year) and email invites are sent out.

If you don’t live in Singapore, consider joining a professional group near you. I highly recommend it for meeting new friends, hearing about other schools, and sharing ideas.

Animal Algebra: General Terms of Sequences

Use linking cubes and make these three animals.

algebra animals

Ask students to discuss:

  • How do they see these animals growing?
  • What does the next animal look like? How many cubes will be needed for its {head/body/front leg/hind leg}?

Using these answers, bring students to see the general term for the number of cubes used. I’ve used this picture to help:

animal-expanded

Now do a similar exercise using growing L-shapes, growing T-shapes, growing Z-shapes, growing animals of their creation.

I have used this lesson countless times and it continues to be a favourite. I like that general terms are introduced without the method of making a table of values. I want to avoid reducing geometric sequences to a meaningless sequence of numbers.

Excellent similar ideas are found at visualpatterns.org and this nrich problem about cable bundles. (The nrich problem has sample student work, making it good for teacher workshops, as well.)

Does anyone know where this idea is from? It’s not original to me and the second image in this post is a screenshot from a long lost book. I have also seen that Colin Foster had an idea like this in his (amazingly free) book, Instant Maths Ideas for Key Stage 3 Teachers: Number and Algebra.

a mathematics lesson that worked

Update:

Thanks to Colin, I think the original idea is from Paul Andrews’ book, Linking Cubes and the Learning of Mathematics. It’s available for sale from the ATM and I highly recommend it. (I have just bought a new copy.)