Introducing algebra- consecutive numbers addition puzzle

Here’s are really good way of introducing algebra and getting across the idea of what a variable is. The pdf slides that you can use on the interactive white board to run this activity are here.

Start by getting the pupils to draw this diagram in their books:

They then choose a number between 1 and 10 and write this in the top corner of the big triangle. Next they put the next consecutive number in the bottom right corner of the large triangle and the next consecutive number after that in the bottom left corner of the big triangle. If their starting number was 5, there triangle would now look like this:

They then fill in the circles by adding together each of the two corners that each circle is connected to. If the example above were carried on it would look like this:

The middle square is calculated by summing the three circles. Like this:

You can now impress the students by getting them to read out their starting number (at the top of the triangle) and instantly saying “so your middle number must be x” (where x = 6n + 6 if n is the starting number). After the novelty has worn off and they start asking you how you did it you can set the scene for an investigation. Get them to see if they can work out a relationship between the top number and the middle number. Maybe they will make a table of top number vs middle number and see if they can spot a pattern or maybe some of them might start creating word formulas. After a good class discussion of their methods and findings you can introduce the idea of using the variable n for the top number and build up to the following slide showing the relationship:

By taking this approach where they all started off with different numbers but have ended up with a rule linking their starting numbers to their middle numbers hopefully the power of algebra will shine through and also they will start to understand why we use variables.

A massive thanks to Rob S for sharing this with us!

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