Student engagement is a funny thing.

On twitter I’ve been pretty critical about using extrinsic rewards to increase student engagement.

Today was our 100th day of school (as calculated by our students!) To celebrate we made 100 piece trail mix. Our trail mix included: cheerios, chex, raisins, and M&Ms. Candy! Talk about extrinsic student engagement! Before we dove in to the rewards food, I gave my class the following problem:

We have 4 ingredients to make trail mix. How many different combinations of ingredients can we have if our trail mix only has 100 total pieces?

The students persisted through their work on this word problem, until they arrived at various solutions based on their calculations and personal taste. For instance, one student is allergic to nuts and could only eat the cheerios and raisins, so that impacted his work on the problem. The students worked diligently and happily ate the trail mix once they had arrived at a reasonable solution.

However, after class I channeled Graham Fletcher and Dan Meyer to try to make this mathematical experience a more rich one for the students. So, here is a preview of the 3-act task we will be doing tomorrow in class…

Act 1

What do you notice?

What do you wonder?

Act 2

Act 3

Sequel

What are other reasonable amounts of Cheerios, Chex, and M&Ms for this trail mix?

How many possible solutions are there?

The reward here is intrinsic. Students are motivated and engaged by using math to solve a problem they themselves have developed. Also here’s an applicable standard, if that’s your thing.

## 6 thoughts on “3-act Task: Trail Mix”

1. Andrew, I love this task. It has so many possibilities. I’m going to try this one out…I think it would work well in grades 2 and/or 3.
After the initial notice and wonder after the act 1 video, I think the question of how many pieces are in the bag will arise, and that’s what I’ll use as the focus question. For act 2, the information they’ll need is in the picture you’ve provided for act 2: the cheerios, M & Ms, and chex lined up in those arrays. They’ll need to come up with a way to count them (I see some nice multiplicative thinking coming into play here), and then add the 1 raisin. The act 2 picture then can be used in act 3 as the reveal.
For the sequel, the kids can come up with different combinations of raisins, M & Ms, Cheerios, and chex to equal 100. They could even choose one to “market”, and provide an explanation as to why they’ve chosen that combination.

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• I love the open-endedness of this task! There are a lot of reasonable good guesses based on the information they have. Joe, I like you idea of “marketing” their idea– explain why your model is a good guess. What if you also did a partial reveal? Like Act 3a. After students have created an initial model, you could have them count out one of the ingredients, like all of the Chex cereal. Students could then decide how they might revise their models, given this new information. Did they include too many Chex cereals? Too few? If there are only 8 Chex, but we said there were 13… What do we think those extra 5 pieces are?

Thanks for sharing!

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2. Very cool! Besides how very articulate you were when opening the baggie at the start, I felt my curiosity rising as I thought about your activity from today and what students might be thinking when they see your Act 1 video tomorrow. My guess is many will “believe” there is 100 pieces based on today’s work, but others might try to challenge that thinking. Interested to hear how it turns out!

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3. This could extend itself up through Grade 6 as a percent/decimal problem, simplification of fractions as well as factors and multiples.
Looks like a yummy trail mix very M & M based 🙂

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4. I would like to follow you.
My email is ratman34@msn.com.

Please add me to a mail list if you send out questions.

Mark Chubb just spoke about you at the OAME math conference.

Cheers,
Paul

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