# Poly Plug Rectangles

*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.*

*could*the rectangle be? How do you know?

*can't*the rectangle be? How do you know?

Thank you to everybody who sent us their ideas about how to find the monkey's rectangle. You can see some videos of children working on this task in our Early Years Children's Thinking section.

Sion from Twyford School in England sent in this strategy:

Well done, Sion - I agree that this strategy will always work!

I wonder if there's a way that Sion could change this strategy to use fewer test spots?

Louis from Prospect House School in England sent in this picture of the grid:

Thank you for sending in this picture, Louis. Can you see where the rectangle will be? The rectangle in this grid is actually a special type of rectangle - what other name do we have for rectangles like this one?

If we didn't have the monkey's clue about how many plugs are used in the rectangle, could we still work out exactly where the rectangle will be using Louis's test spots? Why or why not?

We thought you might also like to see these sketches, drawn by a member of the NRICH team as he was working on a new interactivity for this task:

What might he be thinking?

If you would like to get in touch with us about how you approached this task, please email us with your ideas.

**Why do this problem?**

### Possible approach

*This problem featured in an NRICH video in June 2020.*

**Version 1**

**Version 2**

### Key questions

### Possible extension

Learners could play a version of the game in pairs which allows diagonal rectangles too.

### Possible support

### Annotated videos

*With thanks to Class Two children and teachers at Bourn Primary School.*

**Clip 1 (above):** We gave the children some time to play with the Poly Plugs as these were new to them. Not all used them to make patterns within the grid but almost everything was mathematical! There was a lot of noise, most of it productive, and our feeling was that if we hadn't given them this time, they would not have been so focused later on.

**Picture 2:**Having given them time to play freely, we then suggested they make any pattern or picture they like using just six plugs. We used this child's pattern to draw out the properties of a rectangle.

**Clip 3 (above):** We then introduced the class to the interactivity. *(The interactiivty has since been updated so looks a little different now.)* We made the mistake of using a rectangle of four plugs, rather than building on the work they'd just done using six plugs to make a rectangle. You can see the difference in their reactions in this
clip and clip 4 which does use six plugs. We re-wrote these teachers' notes after this experience.

**Clip 4 (above):** In this clip, we encourage the children to find the rectangle more quickly and this time it contains six plugs.

**Clip 5(above):** We were keen that the children should share their thinking. It was interesting, but unsurprising, that they were disappointed when a plug turned blue.

**Clip 6 (above):** In this clip, we confronted their keenness to choose only positive examples, trying to help them to see that a blue plug could give them far more information than a yellow one. We're not sure we won though!