Students will perform a simple probability experiment involving repeatedly spinning a spinner to first predict and then determine which player should win the game by placing the most of their coloured cubes on the game board.

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 has a very low floor, but extremely high ceiling by introducing the idea of simple one event probability experiments valid for primary grades or as a warm-up/purposeful practice for middle grades. Then, you can continue building up from this simple one event probability experiment to more challenging scenarios.

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

• We can make predictions about the outcomes of simple 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 simple 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 the full video walk-thru of this task:

Show students this video:

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 a circle with two sections.
• I notice this is a fair spinner because both sections are of equal area.
• I wonder if we will be playing a game?
• I wonder which colour will win?
• I notice a lot of red and blue cubes on the table.
• 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:

So we then challenge the students with the question:

Which colour do you predict will win?

*Note that in this version of the game, the colour cube that appears most on the game board wins.

Challenge students to make a prediction and share with their elbow partners and ensure they attempt convincing them as to why they believe their estimate is reasonable.

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

Let’s craft a productive struggle in order to fuel sense making by using the same rules of the game (most cubes of a colour on the board wins) with different spinners:

Watch This: Video of Spinner #4

Using the same rules to the previous game, except use this unfair spinner (1/4 blue, 3/4 red):

Prompt:

Which colour do you predict to win and how many of each colour will be on the board?

Allow students time to discuss and convince their neighbours. Encourage them to come up with justification that supports their reasoning.

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After students have had the opportunity to discuss their solution strategies with their partners/groups, solution strategies have been selected, sequenced, and shared to the group for the teacher to make connections with, you can share the second reveal video:

Extend this task using the same rules from the original game, but using two different spinners.

Extend #1: Spinner #7 – SPARK

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Extend #1: Spinner 7 – REVEAL

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Extend #2: Spinner 2 – SPARK

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Extend #2: Spinner 2 – REVEAL

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