Task Teacher Guide

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Students will model multiplication and division contexts involving positive and negative integers in order to solve.

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In this task, students will represent and solve a quotative division context involving a negative dividend and positive divisor. They will determine how to fairly share the task of digging to find a fossil amongst the members of the team. Some of the big ideas revealed in today’s lesson include:  

• Partitive division is when the total quota is known (the dividend), and the number of parts or groups (the divisor) is known;
• Partitive division reveals a rate;
• In partitive division, the dividend and the divisor often have different units;
• A negative number divided by a positive number has a quotient that is negative.

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Spark

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Show students the following video:

Then, ask students:

What do you notice?
What do you wonder?

Give students 60 seconds (or more) to do a rapid write on a piece of paper.

Replaying the video can be helpful here.

Then, ask students to share with their neighbours for another 60 seconds.

Finally, allow students to share with the entire group.

Some of the noticing and wondering that came up in a class recently included:

• I notice dirt
• I notice a bone.
• I notice a scale that counts by 5.
• I notice the bone is at -55 feet.
• I wonder how long it will take to dig up that bone.
• I wonder if one person is digging.

At this point, you can answer any notices and wonders that you can cross off the list right away. Confirm for students that the dinosaur fossil is located -55 feet below ground level.

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Sense Making

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[accordion-item title=”Crafting A Productive Struggle: Prompt”]

Since you have already taken some time to set the context for this problem and student curiosity is already sparked, we have them in a perfect spot to help push their thinking further and fuel sense making.

Share the following prompt.

A team of five is planning to dig for this dinosaur fossil. They want to share the work equally amongst all members of the team. How many feet should each person dig?
Write an equation to represent this scenario.

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During Moves

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[accordion-item title=”While Students Are Productively Struggling…”]

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

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

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[accordion-item title=”Student Approach #3: Using the Inverse Operation”]

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Next Moves

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[accordion-item title=”Consolidation: Making Connections”]

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[accordion-item title=”Reveal”]

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[accordion-item title=”Reflect”]

Provide students an opportunity to reflect on their learning by offering these consolidation prompts 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.