Task Teacher Guide

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Students will perform a simple probability experiment involving repeatedly spinning two spinners to first predict and then determine which player should win the game.

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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.

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Watch the full video walk-thru of this task:

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Spark

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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:

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Sense Making

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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.

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During Moves

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[accordion-item title=”Student Approach #1:”]

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[accordion-item title=”Student Approach #2:”]

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[accordion-item title=”Student Approach #3:”]

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After Moves

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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.

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Extend #1: PROMPT

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Extend #2: SPARK

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Extend #2: REVEAL

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Extend #2: REVEAL 2

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Extend #3: SPARK

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Extend #3: REVEAL

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Extend #3: REVEAL 2

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We suggest collecting this reflection as an additional opportunity to engage in the formative assessment process to inform next steps for individual students as well as how the whole class will proceed.

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Explore The Entire Unit of Study

This Make Math Moments Task was designed to spark curiosity for a multi-day unit of study with built in purposeful practice, and extensions to elicit and emerge mathematical models and strategies.

Click the links at the top of this task to head to the other related lessons created for this unit of study.