An interactive whiteboard resource that gives you a complete lesson activity for teaching about approaching problems systematically.  The problem presented here is an updated version of one first presented by H.E. Dudeney in the early 20th Century.

The IWB resource presents a reaction test.  The test is successfully passed if 4 circles are lit up and they form the shape of a square.  The resource will join up the circles if the square is formed. The resource is really only intended to engage the students in the problem.  It is used best if the students come up and try and achieve a succesful square by pressing the red button.  When the first student achieves one tell the class that the next square must not be of the same type as the one previously done.  Or if a student misses an intended circle ask if it is possible to still form a square.

Here are 2 examples of two possible scoring formations:

You can see that both layouts form a square.

Once the students understand the ways to find a scoring layout set them the challenge of finding how many different ways there are to achieve a scoring layout using 4 circle targets.  This works best if in the first instance you let the students come up with their own methods.  In the pdf for this resource there is a blank target to be printed for the students to use.  Most students will try colour coding and find that it is hard to work clearly.  The next step is to introduce them to working systematically using a table.  The pdf includes a tabular layout to allow the students to easily work through all of the different combinations and come up with the final number.  You can print this or the children can create their own.

Once the students believe they have worked systematically and are confident they have got the final total you can press solve on the resource to cycle through all of the solutions with a count to help you keep track.

I’ve found this lesson very effective in allowing the students to see how much easier a task is if laid out in an appropriate manner and worked through systematically.  Download the pdf for further notes.  Please feedback on any problems or ways that you have used the resource in the comments section below.