In the time before the mathematical idea of randomness was discovered, people thought that everything that happened was part of the will of supernatural beings. So have things changed?

To get an idea of how this interactivity works, set the grid size to 10 rows and 10 columns, and the size of each trial to 10.

Click on "Randomise" a few times. Can you work out what is happening?

Clear the grid so that the red squares disappear.

Now click in the "Keep previous trials" box, still with the grid size at 10 by 10 and the size of each trial at 10.
This time, click "Randomise" exactly ten times. What happens? Is this what you expected?

Clear the grid once more and try the same thing again, clicking "Randomise" exactly ten times with the "Keep previous trials" box ticked.

Can you explain what you think is happening? You may want to repeat this several more times to test your ideas.

Clear the grid again and this time click on the "Toggle Shape Type" button. You'll see a shape appear on the grid. Make sure the "Keep previous trials" box is ticked again.

How many times do you think you'll have to click on "Randomise" in order for all the small squares you can see to be coloured red?
Try it and find out. How close were you?
Try the same thing again. Were you closer this time? Why do you think that was?

Once all the small squares you can see are red, how many small squares hidden by the shape would you expect to be white still?
Remove the shape and see whether you were right.

How would your estimate for the number of white squares left depend on the size of the shape?
You could choose some different shapes to try out your ideas.

This interactivity can be used to help estimate the area of a shape. Can you explain how?

Why do this problem?

This problem will help children explore and understand the concept of randomness. The interactivity will provoke much discussion, prompting learners to offer conjectures and justifications. The final part of the problem also brings in ideas related to ratio and proportion.

Possible approach

Share the interactivity with the whole class on an interactive whiteboard or project it onto an ordinary screen. Without saying anything, click on "Randomise" a few times, as suggested in the problem. Give children a minute on their own to think about how they would explain what this button does, then give them the chance to talk to a partner. Share ideas amongst the whole group and try to
come to a consensus.

Again, without talking, go on to the next part of the problem, giving them a chance to explain what they think might be happening. At some stage, somone will notice the small numbers written in some of the red squares, so you can discuss what they might mean and how this helps them to understand the interactivity.

You may want to continue in a similar way, or if you have access to a computer suite, children could use the interactivity directly. Make time for learners to offer conjectures about what might happen at each stage and encourage justification of them. The final part of the problem could be a follow-on lesson in itself.

Key questions

Can you describe what is happening when I press "Randomise"?

Why does it take more than ten clicks to make all the squares red?

Can you explain why you think that?

Possible extension

Children can explore the full scope of the interactivity in more detail, for example by investigating how the accuracy of their estimations of an area might be affected by the trial size.

Possible support

Some children will find it much easier to engage with this interactivity if they have a chance to manipulate it themselves.