Poly Plug Rectangles

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

 

This activity has been inspired by Doug Williams' Poly Plug resource.  You can find out more details, including how to order sets of Poly Plug, on the Mathematics Centre website.  However, you do not need sets of Poly Plug to have a go at this activity - please see below and take a look at the Teachers' Notes.

 

In this activity, the monkey secretly makes a rectangle using equal rows of spots on the $5$ by $5$ grid.

The aim is for you to find the rectangle by testing spots on the interactivity below.

Once you think you know where the monkey's rectangle is, click the 'Ready' button.  

Which spot is a good one to test first?  Why?

If you had to use as few test spots as possible, how would that change the way you play?

Are there some total numbers of spots that are easier than others?

We would love to hear about the strategies you use for finding the monkey's rectangle.

 

You may be interested in the other problems in our Jaunts into Geometry Feature.

This problem featured in an NRICH video in June 2020.