Chanukah: Experimental vs. Theoretical Probability Dreidl Game

Everyone says "probability" when they hear you played dreidl in math class. I was surprised to wake up Wednesday morning and find I did not have an "Intro to Probability" with dreidls worksheet in my archive. So I made one.

I decided to dig into experimental probability. The main part of the lesson involves the students playing dreidl and recording the results of all spins for their group. I deemphasized the "winning" aspect of it by having them play with poker chips.

Having three groups of students provided wonderful variability in the data. It was fascinating to see how one group had a low yield of gimmels while another had a high yield. This gets into the heart of randomness and variability, and I ended up taking more time than I expected to discuss it.

I reinforced equivalent fractions and estimation by asking students to identify which results were close to 25% (which I arbitrarily defined as 20% to 30%) and which were not. We had two groups with results mostly not near 25% for each possible outcome and one group with really well distributed rolls. 

In class, I only had time to add up the totals for the gimmel column, and we ended up with a grand total of 19 gimmels in 79 class rolls, about 24% and very close to 1/4. 

If I add up the totals for the others, I get: 

(5+4+8)/79 for nun, which is 17/79 (a bit less than 22%); 

27/79 for hey which is a bit more than a third, 

and 16/79 which is about 20%.

So even though in small groups we had varied data, when we added them up the data came closer to the expected 1/4. 

We barely had time on day 1 to talk about multiple events. The next day would be to cover how to find multiple events using a tree diagram and a table (pictured below).

The answer key makes clear that my handout needs more space for a tree diagram. I like tree diagrams because they allow us to compute the probability of 3 or more events. (A table limits you to two.) That way we can ask awesome questions like "What is the probability of getting AT LEAST one gimmel on 3 spins?" 

Teaching them about 'at least' versus 'exactly' is a great extension for strong students.

The tree and table take us to the fundamental counting principle, which is what allows us to multiply the probabilities. Next we would do dependent events, but I don't have dreidl examples for those. 

This lesson is really a rough draft. It went really well; the hardest part was getting the kids to read the directions! Tips, feedback and suggestions always welcome.