Use linking cubes and make these three 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:

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*.

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.)

I think I first came across this idea from Paul Andrews – see his book available here https://www.atm.org.uk/shop/linking-cubes-and-the-learning-of-mathematics/act016

Jo Boaler writes about it in “What’s Math Got To Do With It?”