Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
Arrange the shapes in a line so that you change either colour or
shape in the next piece along. Can you find several ways to start
with a blue triangle and end with a red circle?
Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?
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
In this activity, the computer 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.
Click on 'Start' and the computer will tell you the total number of spots its rectangle uses.
In the left-hand 'test' grid, click on a spot to see whether it is part of the computer's rectangle. If it is part of the rectangle, the spot will turn yellow. If it isn't part of the rectangle, the spot will turn blue.
Once you think you know where the computer's rectangle is, you can create it on the 'decide here' grid. Clicking 'Reveal' will show whether you are correct.
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 computer's rectangle.
Clip 1: 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: We then introduced the class to the interactivity. 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: In this clip, we encourage the children to find the rectangle more quickly and this time it contains six plugs.
Clip 5: 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: 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!