Thursday, 23 April 2015

Compound Area and the order of operations.

A colleague of mine reminded me today about an old idea that I must confess I had forgotten about. I believe it was 'originally' in the Standards Unit (I say originally as I am sure they got the idea from somewhere!), the idea of compound area and the order of operations. This led me to create the diagram below:
On its own it isn't much, but I very much like the two questions with it:

1. How many of these calculations give the area of the shape?
- 3 x 5 + 2 x 4 [this one does]
- 3(5 + 2) + 2 [this one does]
- 5 x 2 x 4 x 3
- 4 x 7 - 5 [this one does]
- 5 + 2 x 3 + 2
- 5 x 5 - 2 [this one does]
- 5 x 7 - 3 x 4 [this one does]
- 3 x (5 + 4) - 4 [this one does]

2. Can you explain how each one of the correct calculations is found from the shape (you may need to rearrange the two rectangles to see some of them). [I am leaving this one for you to answer for yourselves].

I really like this activity. In terms of applying linked areas or maths and being able to communicate their understanding (ears prick up for those working on the new GCSE and the KS3 curriculum) it links diagrams with explanations and it also gives pupils a discussion focus around the different calculations. These sort of activities are very easy to design and can be extended nicely into the formation and equivalence of algebraic expressions when pupils have developed their mathematics a little bit. You can adapt the questions, remove the links, or change the shapes slightly to provide differentiation if you need to.