11/28/17 Functions, Volume, and Optimization

I felt pretty good with the lessons that I did the past two days, so I thought I’d share what I’m doing in my classes. Because a lot of my students (who are future teachers) believe that math is one of their weaker subjects, I try my best to include fun, yet rich mathematical tasks so my students see that math is not scary, but rather, attainable and enjoyable.

Math 10A: What’s my Rule?

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In Math 10A, we are learning about functions, so I decided to have each group think of a rule, and other students would do a gallery walk and can only give 4 inputs, in which the docent would give the 4 outputs. Then, the students have to guess their rule. There was a lot of laughter shared. Surprisingly (or not so surprisingly), just getting students out of their chairs makes activities much more exciting.

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Math 10B: Finding volume

Power Solids are amazing. I had students make a conjecture of how many square pyramids fit into a square prism of the same base and height. A lot guessed 2 or 4, but hardly anyone said 3. After pouring rice from one solid to another, they found that 3 square pyramids fit into a square prism. We did the same for cones and cylinders, and triangular pyramids and triangular prisms with the same base and height, then we generalized to obtain the volume formulas. Discovering formulas is one of my favorite activities to do. I often see epiphanies and if you’re a teacher, you know that that is one of the best feelings ever.

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Math 100: Optimization

Alright, now this one is just fun. We did this in the 5 E’s style where I pretended that I was their boss at Coca-Cola and they are my interns. I want them to tell me which way to pack 12 cans of soda is more efficient in terms of space. This involved knowing the area of a rectangle, a circle, Pythagorean Theorem, and percentages. After we determined which model was the best, I then extended the problem to 20 cans and asked if the result would be the same.

One of my students commented that she loved this because it brings in a lot of prior knowledge. She said she never saw a clever way of using the Pythagorean Theorem but now she has.

I also love this because I can finally talk about limits. What if we had 1,000,000 cans? Does the space occupied by the cans tend to 100% if we keep increasing the amount of cans?

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Bonus:

Lastly, in office hours, I had a couple students talk to me about either Ditch that Homework by Alice Keeler and Matt Miller or Mathematical Mindsets by Jo Boaler. I LOVE students who take education seriously and are preparing themselves NOW. What surprises me about a lot of students is that they just take classes for the units, but it’s those students who really say “What can I take from this into my future classroom?” that makes teaching effortless.