Probability Gambling (Age 7)

The Activities

1. Topic: Logic, Problem Solving: Book: More Stories to Solve by Shannon. This is a book of 15 short stories with surprise endings you can try to figure out. The kids really loved this, and begged to do more stories.  We read 5 stories, and were able to solve 4 of them by discussing them together.

2. Topic: Logic. We played Logic Links again. This time I had printed out sheets with the formations needed for the harder puzzles.

A solved logic puzzle.

3. Topic: Probability. Probability race: each kid gets two dice, rolls them, adds them up and colors in the corresponding number on the chart. The first number to get rolled 5 times wins the race.

How did it go?

School is back in session now, so we had all 5 kids. It was a really fun circle with lots of excited contributors, and even some hard thinking.

This time we did puzzles with nine clues.  The first puzzle was easy enough that everyone solved it with few problems.  The second puzzle was harder, and eventually one kid stumbled across the correct arrangement, and the kids used her paper as reference.  This game works pretty well with a large group, though it can be frustrating for the kids who don’t happen to get the solution first.

Probability Race

These kids did a bunch of probability races in past years, but at first only my daughter remembered the activity.  As soon as I explained the rules, they started speeding through the races. The kids are MUCH faster now at rolling, adding, and marking their charts.  Again, all the kids enjoyed my commentary about how 7, 8, and 9 are tied on Kid X’s paper, etc.

After we finished around 8 races, we stopped and reviewed the winners.  7 won four times, 3 once, 6 twice, and 9 once.  I asked the kids what number they would pick if they could win a dollar for guessing right.  Most kids said 7.

I asked why 7 had won so many times, and a girl suggested that there are more ways to get 7 than any other number.  She counted up “1+6”, “2+5”, “3+4” to get 7.  Then she figured out there were 3 ways to get 6 also: “1+5”, “2+4”, “3+3”.

At this point I got a piece of paper, and wrote die A and die B at the top, and we made a chart of possible ways to get 7 based on various rolls of die A and B.  We found 6 ways.  In contrast there were only 5 ways to get 6.  The kids were pretty interested in figuring out how many ways to get various number.

One kid said she thought “3+4” and “4+3” should count as the same.  I said that they were different because they were on different dice, but she asked how we could tell the dice apart.  Next time, we should use dice of two different colors.

While we were figuring out the ways to roll 5, I asked what if die A rolls a 6? What does die B need to be to add up to 5?  At this point, one of the kids said that negative numbers are not allowed at her school.  I said no? And she said they never do problems like 5 – 6 at school.  I asked everyone if negative numbers are allowed at Math Circle?  They all said “Yes!”.  I asked, “Can we roll a negative 1 on a die?”, and we all agreed no.

Finally, I let the kids pick 3 numbers. If one of those numbers wins the race, they get a prize from our prize box.  They quickly (and wisely) picked 6, 7, and 8. We had a very dramatic race, ending with 6 winning everything, and lots of cheering.  We picked prizes, and circle was over.