Chance and fairness

We're looking at chance and fairness in maths in Y4 this week. Here's some of what we've been up to in 4G.

We've been spinning these spinners - lots of times, to see whether the spinners are fair.

Here's all our results, and some of our thoughts about  them:

All in all, we were fairly sure the numbers we were getting were just random, luck, chance.

So how could we make it unfair? We decided to add a weight onto a number. We added some Blue Tak to number 5.

 Here's the results we all got:

All but one of us thought we got so many 5s because the spinner was not fair.

We plotted the results on a chart, like this:

The next day, we turned to dice. There's just been an ancient dice discovered in China:

The ancient Chinese dice, with its net on the right

Tibo suggested that we should try and make this one. Perhaps we will...
But for now, we looked at a couple of other nets:

What do you notice about this last one?

So, we put the nets together... tomorrow we will roll them. What do you think we will see?

--------------------???--------------------

The next day...

Once we had put the nets together, we felt more sure of how the dice were going to behave. We made some predictions. About this one:

Sure enough, this one seemed to land on all colours equally:

And about this one:

We noticed that the squares were bigger than the other shapes. The square is 9 little squares, and Felix and others saw that the other shape would be 8 little squares:

 But the difference in size wasn't big enough to explain what we found:

This was the sort of results all of us with this dice were getting!

We wondered why. We think it's because of the way the dice balances and tips. When it's on the square, it doesn't move easily.

But on the other shape, it's just about to tip over.

We looked again at that ancient Chinese dice. We like the idea of trying it out. We're not sure if it's fair, whether all the sides have the same chance of being landed on:

What do you think? Is it more likely that the dice will land on squares? Or on hexagons? Or are they equally likely?