Problem Solving Skills – How much is a tin of tomatoes?

Image from the Sainsbury's website, I hope they are pleased to get some free advertising :)

Ever since I went to school. the format for a “normal” Maths lesson has been the same:

  1. Teach a new method
  2. Show the class some examples
  3. Give them a set of similar problems to try.

Just at the moment I’m exploring an alternative approach

  1. Think about ONE interesting* problem to give the pupils
  2. Give it to them, and see what they come up with, being open to them experiencing a dose of “I can’t do it” and “I’m stuck”

The definition of *interesting is a big challenge of course, and will rest on how well you know your pupils. Today I picked food because it is an area of common interest between me and one of my pupils. I gave her a problem which I would classify as a “backwards” problem – I was asking her to discover the price of a tin of tomatoes, given some clues.

Click Here to see the printable Tomato Puzzle

Isosceles Triangle Numbers

9 is an isosceles triangle number
9 is an isosceles triangle number
16 is a square number
16 is a square number
The next person produced this answer, which means the number 16 went on the Isosceles Triangle list as well.
16 is an isosceles triangle number

A bit more experimentation, and we realised a couple of things – it was easy to play around with this investigation on 1cm squared paper, and it let us try find some MUCH bigger isosceles triangle numbers. We also noticed that the bottom row of counters has to contain an ODD number or the triangle won’t come to a point at the top.

We also found some bigger square numbers, and both lists got quite a bit longer.

Then, we noticed something about the lists…. try it. What do you notice? Why??