I started the topic of Probability with my Year 10 students yesterday and I was so happy with how the lesson ran and how engaged the students were, so I thought I’d share.

These kids didn’t see probability at all last year, so even though they’re a really strong group of mathematicians, I wasn’t confident with how much they remembered.

We started of by drawing mind maps of everything they could think of to do with probability – individually at first and then as a class on the whiteboard. Most of them were pretty blank. We ended up with words like chance, predictability, certain, impossible, likely, unlikely, 50/50. A few students also wrote that probability can be written as fractions, decimals and percentages so we had a chat about the probability number line.

Rather than start off with relative frequency calculations, I really wanted to get these kids thinking about the broader concepts in probability. I read out the statements below and as a class we talked about whether or not we agreed with it and, more importantly, *why*.

- There are 26 letters in the English alphabet. Therefore the chance that someone’s name starts with the letter X is 1 in 26.
- There are only 2 possible outcomes in a game of tennis – winning or losing. Therefore I have an even chance of wining a game.
- I have flipped a coin 4 times and each time it has landed on tails. Therefore it is almost certain the next toss will be a tail.

These started some really great conversations about whether the outcomes were equally likely, whether events were independent of previous outcomes, etc. Now that their minds were warmed up and thinking about probability, I handed out these sheets for students to complete in pairs. I didn’t work through the whole activity as it’s described – instead I printed “Are They Correct?” and “Card Set: True, False or Unsure?” back to back and had students write a sentence about each statement.

After a while we came back as a class and spoke about a few of the statements that had caused a bit of debate or that identified an important concept.

To finish off the lesson we had a look at this problem from nrich. I had students stand around the edge of the room with a piece of paper and a pen. I asked them to write down a number between 1 and 225 and not let anyone else see it. Then I asked them what they thought the probability was that at least two people had chosen the same number. The general consensus was that since they had 225 numbers to choose from it was pretty unlikely. Then I had them read out their numbers one by one. The first time we did this there was laughter and playful mocking of the students who had the same numbers and it was largely written off as a coincidence. We repeated this about 5 more times with new numbers and every time there was a minimum of 2 people with the same number. It was beautiful watching my student’s faces as they became really curious about what was happening.

Next lesson we’re going to dive into the maths that explains why they were so likely to pick the same numbers.