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First lesson with year 7 and 8 – Caterpillars

September 10, 2017

It’s been ages since I’ve blogged. You know what it’s like! Anyway, I intend to do some more so, here goes!


What do you do in your first lesson with year 7? Rules? Expectations? I certainly do mention those things but usually, I like to do some maths and the investigation I choose is Caterpillars. I’ll explain it first then discuss why I like it.

What is ‘Caterpillars’?

Caterpillars have three simple rules:

  • Stop when you get to 1
  • Even numbers – halve them
  • Odd numbers – add one

and that’s it. I demonstrate with 14 like this:


and then just say things like “I wonder if you can get a caterpillar as long as mine”, “Can anyone get one longer? or shorter?”. Then I let them try some of their own recommending (strongly) that their starting number is under 100.

After a short while, I ask people to make comments on what they’ve noticed and it’s often:

  • They end 4,2,1
  • They all get to 1
  • Odds are better than evens

Amongst other things. This is a project that will comfortably take the first lesson.

So, why do I like it?

The actual operations are very straight forward as they are just halving and adding one. This investigation quickly show you who your weaker students are as they struggle to halve.

The project introduces a clear set of rules to follow. Which students bother to check whether the number is odd/even and which simply alternate the rules?

Who ignores the suggestion to start under 100? Why have they done that? It’s a great chance to tackle the misconception that picking higher numbers shows that you’re cleverer.

What numbers do they start with? Are they being remotely systematic in their choices?

Who can articulate a conjecture clearly? Who can do it concisely?

There’s frequently a chance when someone’s conjecture is contradicted by someone else and we get a chance to discuss how to handle this. The conjecture is wrong now, but it wasn’t at the time. Such a crucial way to show that someone has learnt something is that they’ve found something that doesn’t work!

Also in this project, you’ll eventually end up discussing whether decimals are odd or even. Is 5.2 even? What if it was? How do you know a number is even/odd? There’s a lot to discuss here and you will uncover misunderstanding about what odd and even means.

Someone might choose a negative number, presenting you with an early chance to think about adding one to a negative. A student may well choose zero and the infinity discussion to follow is always a nice moment!

Finally, I like that the longest caterpillar is fairly surprising. I won’t spoil it here but I honestly think this project starts the year with an air of curiosity and a chance to show determination while telling a lot about the students in front of you.

Let me know what your starting lessons are in the comments!

From → Maths

  1. Jill Day permalink

    We started Year 7s with Craig Barton’s Rich Task number 8: ‘Diffy’. Same reasons: simple arithmetic, see who can formulate a conjecture and test it. Also showed up who can or can’t follow several steps across a grid of numbers. It has competitive potential with ‘biggest diffy’. I think I might try Caterpillars as an investigation later in the term.

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