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Summer School - Day One - Jelly Beans

Proportional reasoning is a huge part of Apprenticeship and Workplace (A&W) Math 10. this basic mathematical tool can be used to solve problems ranging from sale price and taxes to measurement and trigonometry. I think understanding ratios and proportions is crucial to success in this course.
I started my first summer school class with a jar of jelly beans. I asked my students if they had any questions. The obvious first response was "How many jelly beans are there?" The next obvious question (after much prodding) was "How many yellow ones are there?" I then asked the students to randomly guess how many jelly beans there were. The guesses ranged from 60 up to 668. Then I had them work in small groups to come up with a more accurate estimate using mathematical reasoning.
**What was good**
- Students were engaged... sort of. It is the first day of summer school and I'm sure they would rather be anywhere than math class counting jelly beans. But the sight of candy perked them up a bit.
- Two groups came up with the idea of comparing the volume of the jar with the volume of a jelly bean. This proportional reasoning is exactly what I was trying to get at. So the activity accomplished what I had intended.
- It was messy. The jar was not an exact cube. Jelly beans are not the same shape. There is empty space in the jar. All this provides a real world context where the answer is not as simple as it might appear in the first place. I like that.

__What was not__
- Although students were (somewhat) engaged in the problem, there was little discussion or sharing with each other. I think this was poor timing on my part. I wanted to introduce the concept of proportional reasoning in a way that made intuitive sense to the students. But they probably were not in the correct frame of mind to tackle this type of activity on the first day of summer school.
- Students did not know how to calculate the volume of a cube-shaped jar. This is not a criticism of the students' knowledge. It is a criticism of my teaching for not providing the necessary tools for success in solving the problem. I failed to access prior knowledge or determine deficiencies before-hand.
- I am not sure how effective it was overall in helping students grasp the concepts of ratios and proportions. They could clearly see a relationship between the volume of the jar and the volume of the jelly bean. They could clearly see the relationship between the number of one colour and the number of another colour (a good extension activity). But I did not feel like they really understood to the extent that they can transfer the jelly bean concepts to other problem-solving contexts.

I also realize that I only loosely followed Dan Meyer's 3 acts for mathematical story telling. It may be more effective if I create 3 acts more closely aligned to Dan's ideas and give students more time to wrestle with the problem in act 2. But, I think I have the beginning of a good idea. I may create a video of this activity that follows the 3 acts. Even if I don't use the video, the process of creating it will help me think through the learning process more carefully.
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