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.

Parshat Mishpatim: Percents of the harvest

In this week's parsha, we read "מְלֵאָתְךָ֥ וְדִמְעֲךָ֖ לֹ֣א תְאַחֵ֑ר" - "Thou shalt not delay to offer of the fulness of thy harvest." (Shmot 22:28; quotes by Sefaria.) This is not a pasuk that gets a lot of attention. Quite by accident, I have found it to be instrumental in teaching percents to 6th graders.

Students who don't "get" other aspects of math often "get" percents. They have gone shopping with their parents, they know what a 30% off sale is, and come into class at the beginning of our percents unit knowing what percents are. The key is to grab and hold their attention.

I begin my percents unit with an activity that is designed to figure out if students can calculate percents of different wholes while building an understanding that if the whole changes, the part will change accordingly. Essentially, when x>y, p% of x>p% of y. This has halachic implications, based on the pasuk I quoted above.

The pasuk in this week's parsha is brought as the source for the prohibition of separating Trumot and Maasrot (tithes) out of order. Rabbi Jack Abramowitz explains in The Taryag Companion, "The tithes are a percentage of the whole, a percentage of the remainder, etc. Going out of order invariably leads to errors in one’s calculations."

I designed an activity based on one we did when I was in school, where we imagine a scenario with 10,000 bushels of wheat. Presuming Trumah is 1/50th of the harvest (it can range from 1/40th-1/60th, but 1/50 is 2% and easy to calculate), how many bushels of wheat will the Kohen, the Levi and the Ani get? (In years 3 and 6, of course.)

If we do the math right, Joe Kohen, Yoni Levi and Shani Ani get 180, 980 and 882 bushels respectively. If we change the order and give one person before his or her turn, the ones who come later may not get what they rightfully deserve. Check out the worksheet here and the answer key here.




Kids like the exploration style of this lesson and usually find calculating bushels of wheat to be novel. (After all, we don't do this every day.) This lesson goes over well, year after year.

I always tell my students about the Taryag concept: everyone agrees there are 613 core mitzvot but not everyone agrees what counts as a mitzvah. This law is not the law of Maaser and Terumah itself, it is a supplemental law about how to do the mitzvah itself, which teaches means that each of these laws is really two Biblical laws (or more!) Tithes might not be such a popular topic of conversation, but when the Rabbis double count a law, they do so to show us values and priorities - Maaser teaches us about the responsibility we have for other people in the community, and our law teaches us how important it is to be precise in our financial dealings with other people.

Updated 2/1/16 at 12:24pm to correct an error in the answer key.