Spin To Win! [Game 3] - Make Math Moments Academy

Task Teacher Guide

Be sure to read the teacher guide prior to running the task. When you’re ready to run the task, use the tabs at the top of the page to navigate through the lesson.

In This Task…

Intentionality…

As is true for any task, the intentionality or learning objective can vary depending on what mathematical thinking you are hoping to elicit.

This task is a continuation from the previous two versions [game 1 and game 2] and promotes a very low floor, but extremely high ceiling by introducing the idea of simple one event probability experiments in game 1 and game 2 that can be used in primary grades or as a warm-up/purposeful practice for middle grades. Now, in game 3, we have built up our understanding and confidence of simple one event probability experiments to probability experiments with two independent events.

Some of the big ideas we will explore through this lesson include:

We can make predictions about the outcomes of probability experiments by thinking of the ratio of successful outcomes to total outcomes as a composed unit and scaling to reveal other equivalent ratios in that proproportional relationship;
We can make predictions about the outcomes of probability experiments by revealing the rate of successful outcomes per trial by partitively dividing the number of successful outcomes possible by the total number of outcomes possible and using the rate to multiply by the number of trials; and,
As the number of trials in an experiment increase, the outcomes in that experiment will get closer to the outcomes expected theoretically.

Watch Full Video Walk-Thru

Spark

Show students this image:

Ask students to engage in a notice and wonder protocol. ANYTHING and EVERYTHING that comes to mind is fair game. Here’s some of the “everything and anything” students noticed and wondered on chart paper:

I notice two spinners with two sections.
I notice the spinners both have red and blue sections.
I notice one spinner is fair, the other is not.
I wonder if you get to choose which spinner to use in this game?
I wonder if you must get the same colour on both spinners in order to put that colour on the game board?
Will we be playing this game in this class?
And many others…

Take some time to acknowledge the noticing and wondering your students have engaged in and try to answer any that you might be able to address right away.

Show this video and ask students if they have any more noticings and wonderings:

Sense Making

Crafting a Productive Struggle

So we then challenge the students with the question:

How many red do you expect will be on the board?
How many blue do you expect will be on the board?
How many black do you expect will be on the board?
How do you know?

Note that in this version of the game, the colour cube (red or blue) that appears most on the game board wins.

Have students turn and talk with their neighbours to come up with an estimate for how many red and how many blue [and black] you should expect to see once the game board is full. If necessary, clarify when each colour was used.

During Moves

While Students Are Productively Struggling…

Student Approach #1:

Student Approach #2:

Student Approach #3:

Student Approach #4:

After Moves

Consolidation

Reveal

After allowing students to share their thinking with partners and then with the whole group, we can share what really happened with this video.

Consider showing this second reveal video to help students visualize the results better and fuel sense making:

Revisit the student responses.

Why did the experimental probability (results in the video as well as in the many experiments conducted in class) not match the theoretical probability?

Have students discuss their thinking and what they would change if they did the task again.

Return to the notcing and wondering you recorded from the SPARK and EXPLORE sections, and answer any questions that have not been answered.