Consecutive sums/Consecutive sums activity: Difference between revisions

Here is a diagram to show an example of steps:

This sort of diagram can suggest ways of explaining particular sums. For example, three steps (which can be thought of as summing three consecutive numbers) can then be split up in several different ways.

The first square in the bottom row can be cut off and added to the top row to make a rectangle with height three, showing that this is multiple of 3.

A similar thing happens with multiples of other odd numbers and the middle number is always the important one.

Exploring even numbers of steps is interesting and gives an insight into why making even numbers in this way is more difficult.  

Another way of splitting up the diagram is shown here:

This means that every consecutive sum answer can be considered to be a triangular number plus a rectangle that has the same height as the triangle.