Task Teacher Guide

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Students will investigate the theoretical probability of a name being drawn for a prize. Students will express the theoretical probability on a number line from 0-1 and as a percentage.

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In this task, similar to Day 1, students will observe two names being placed into a container. However, in today’s context, the names are being considered for a draw. The name selected from the container will win a prize. Students will represent the theoretical probability that one of Luca’s ballots will be drawn. This task will allow students to develop a deeper understanding of big ideas, including the following:

• A part of a whole represented as a percentage is a part-whole ratio whose whole is 100;
• A percentage is one of infinitely many equivalent part-whole ratios in a ratio relationship;
• A percentage can be used to scale in tandem and reveal an infinite number of equivalent ratios in a ratio relationship;
• Partitive division can be used to divide a percentage by 100 percent to reveal a rate for the proportional relationship;
• Theoretical probability is a method to express the likelihood that something will occur when the probability of occurrence is known;
• The probability that an event will occur can be expressed on a continuum from 0 (impossible) to 1 (certain) or as a percentage out of 100.

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Spark

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Show students the following video where two names are being written on two separate pieces of paper before being placed in the container.

Ask students to engage in a notice and wonder protocol. ANYTHING and EVERYTHING that comes to mind is fair game.

Write down all of the noticing and wondering from your students.

For example:

• I notice the same container that we saw a couple days ago when we had the vote between Eli and Sonya.
• I notice a stack of paper.
• I see names being written on the stack of paper similar to the other day.
• The names are Ali and Luca.
• Is this another vote?
• Could this be a draw?
• And so on…

Take time to acknowledge the noticing and wondering your students have engaged in and try to answer any that you can address right away without revealing information that will rob students of the opportunity to think later in the lesson.

For example:

• Yes, this is a similar container to the one used the other day.
• No, this isn’t a vote today. This is actually a draw.
• There are only two people being entered in this draw and their names are Ali and Luca as you all mentioned.

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Show the following video:

Ask the following questions:

Whose name is more likely to be drawn for the prize?

How can you describe the likelihood that each name will be drawn?

This discussion will create an opportunity to introduce the idea of theoretical probability. The likelihood of an event occurring when all of the possible outcomes are known. The probability can be represented on a number line from 0 (impossible) to 1 (certain). It can also be represented as a fraction, or as a percentage. 100% meaning that the outcome is certain.

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Sense Making

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Share the following prompt:

Luca has his name on 33 ballots in the draw.
He is three times more likely to have his name drawn than Ali.

What is the probability (likelihood) that Luca’s name will be drawn based on the total number of tickets in the container?

Encourage students to work through this problem without the use of a calculator. Prompt students to create a convincing argument by highlighting their strategy and modelling their thinking.

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During Moves

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[accordion-item title=”Student Approach #1: Concrete Set Model and a Fraction”]

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[accordion-item title=”Student Approach #2: Stacked Bar Model and a Percentage”]

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[accordion-item title=”Student Approach #3: Symbolic with a Percentage and Equivalence”]

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Next Moves

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After students are finished sharing what they noticed from their exploration, share what really happened by showing the following video and/or image:

Screenshot of the final frame can be seen below:

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Provide students an opportunity to reflect on their learning by offering this consolidation prompt to be completed independently.

Consolidation Prompt #1:

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Consolidation Prompt #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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Resources and Downloads

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.