3-Act Task: The Doubling Die

Standard

CCSS.MATH.CONTENT.7.SP.C.5 – Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Act 1

What do you notice? What do you wonder?

Act 2

Faces of the Doubling Die

What is the probability of rolling a multiple of 2?

What is the probability of rolling a multiple of 16?

What is the probability of rolling multiples of 4, 8, 32 or 64?

Place the probabilities on the number line below:

Act 3

Use your completed number line to describe how likely each roll is to occur.

Sequel

If you rolled the die a second time, what would the probability of each be?

4 thoughts on “3-Act Task: The Doubling Die”

1. Stats is a tough one to pin down in the first act for sure. I’m not sure students will naturally go where you want them to with your intended question, mainly because it might be the first time they’ve seen this game/dice. Would this idea work with another game that students might be more familiar with? Not sure.
I really like the modeling of probability on a number line but is there any way we can make it more open to different representations? As the task appears now, it seems scripted and I’m just wondering how to take away that feeling.
Hope this doesn’t seem too harsh because I really like the idea Andrew.

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• Thank you Graham for bringing a critical lens to this task. One of the aspects of your pedagogy that I admire is your commitment to student-centered learning.

That said, one of the my favorite characteristics of 3-acts is that the teacher presents a scenario that elicits a question from the students where math can be useful to answer. With the video here there’s a seemingly clear question…what will it land on? Probability can help us answer that question! “It will most likely land on ____!”

Another important aspect of 3-act tasks that I feel is important and often overlooked is the role of the teacher. Here, once probability is introduced as a way to help us answer the question the model of the number line is introduced to help students organize their thinking. I agree that other models can be utilized, but the number line model is the clearest visual representation of the standard listed.

Also since differentiation is important to me as a special educator, I thought the number line representation could lead to some cool equivalent fraction conversations, if the teacher identified that as appropriate work for some students. There are also pathways into discussions about multiples and factors, if a teacher identified the need for students to work on that as well.

Thanks again for the feedback! I’d love to mine ideas to open it up to multiple representations!

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2. Hey Andrew,

I definitely like Act 1 because it’s intriguing, and I want to know what number it landed on. The students may be interested in that as well so I think it would be cool to have an Act 3 video showing the result.

Since it’s the same probability for each number by itself to be rolled, what if your Act 2 information focused on the numbers that were not the answer? I think you could get the kids into the scenarios you’re looking for while still having the intrigue of figuring out the Act 3 result. It could almost be like a treasure hunt where kids have clues about what numbers are not the answer, and they could work through the different clues using the number line strategies you envision.

I love your ability and passion to create a safe, inviting environment for every student. I’m following you big time because I see a lot of flaws in my approaches. Keep up the great work!

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3. Hey Andrew,
Sorry for the late reply. I really like the first act. It’s so simple and quick – and it leads to the question, “What will it land on?” Math and probability can answer that – Perfect! The number line is great as a model for probability and can even be scaffolded for students by replacing 0 and 1 with “not likely” and “very likely.”
My only suggestion is to make some kind of connection between the act 1 video and the “need to know information in act 2.” Why do I want to know the chances of rolling a multiple of 2? Maybe a close up of the die before you roll it, showing all sides? That may make it less “scripted” as Graham mentioned above.
I do like that you’re using probability in a 3-act! Hope these suggestions are helpful.

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