What are our lucky numbers?
We began by discussing if we had a lucky number and what they were. Diverse numbers were shared and the children passionately explained why they considered their number to be lucky. As hoped, a few of us said 7 was their lucky number.
I asked if they had heard about 7 being lucky and most had. Did we know why?
No one knew the mathematical reason, but some great theories were shared:
- I think it might be because people often win on 7 and so history has taught people that it is lucky.
- It rhymes with heaven so maybe that is the connection.
- Could it have something to do with there being 7 days a week?
- Oh! Ladybirds have 7 spots! Since ladybirds are considered lucky maybe that's why 7 is lucky!
- Maybe most people like the look of 7? They like how it is written.
- But is it really lucky?
And then the magical comment appeared:
- But look at our central idea: 'Instead of luck, mathematicians think of probability' That means in maths 7 isn't really lucky. Some people might think it is, but it can't be. It's just an ordinary number like every other number.
I love it when the children draw upon our central idea in discussions. It shows me they understand our big picture reason for our activities and it also indicates to me that it must be a pretty good central idea since they are accessing it easily without being forced to think of it.
Investigating the Probability:
We then played this game called First Out Wins:
° Each player puts 11 counters on the any numbers on their strip. They can put as many counters as they like on any numbers. When that player rolls 2 dice, they can take ONE counter off the number rolled. The winner is the player who removes all their counters first.
It's a perfect game to firstly assess which students already know the probability when rolling 2 dice and it's also a great way for children to discover and later apply the maths involved (when they play the game again after the investigation).
The student playing the top strip of numbers doesn't seem to understand the probability when rolling 2 dice.
The student below seems to have a better understanding.
Neither of these students seemed to have an understanding yet.
The student playing below based their counters on favourite numbers or birth date numbers etc.
After playing the game a few times, we discussed strategies we were using and what we were noticing. Were some numbers being rolled more than others?
- 7, 8 and 9 seem to be rolled more than others.
- Same with us. Why is that?!?!?
- I couldn't ever roll 11.
- I needed to roll 2 for such a long time.
Do some numbers have a higher probability than others?
It was time to find out.
We brainstormed different ways we could record the possible outcomes when rolling 2 dice and gave them a try.
From these we made the discovery that rolling a 7 has a higher probability of winning than the other numbers!!!
That's why people think 7 is lucky!!!!
When we tried the game again to test out our new understanding our strategies had greatly changed:
We knew which numbers had higher probabilities to win.
This one below really made me laugh. Perhaps the top player was believing in the probability of number 7 a bit too much? ;)
Google Doc Link: FIRST OUT WINS game
On post its, we a had a few minutes to write and then share what today's activity had helped us to understand about probability. We shared these with our table partners and a few shared with us their new understandings. We also discussed how successful our new strategies were when we played the game again after our investigation.
When they walking out to lunch, I overheard the following:
- My lucky number used to be 12, but now I'm changing it to 7.
To which the other student responded:
- It doesn't make it lucky, it's maths!