Task Teacher Guide
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In This Task…
Students will determine the number of green bean seeds planted per pot.
Intentionality…
In this task, students will determine the total number of beans to sow per pot. In this context, the number of pots is known, and the quota per pot (the rate) is unknown. Students will likely fair share the total quantity of beans amongst the 7 pots in order to determine the number of beans in every pot. This context is partitive in nature. It can be represented by division. It can also be represented by multiplication with a variable in the place of the quota (or rate). Some of the big ideas that may emerge through this task include:
- There are two types of division;
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;
- The dividend from any division sentence can be decomposed into smaller parts to allow for friendlier division by the divisor. This strategy is known as partial quotients. (i.e.: 85 ÷ 5 = 45 ÷ 5 + 40 ÷ 5 = 9 + 8 = 17);
- Division is the inverse operation of multiplication;
- Variables are used to represent changing or unknown quantities;
- When solving an equation where the coefficient of the unknown variable is not equal to 1, division is required to determine the value of the unknown variable and the context of the problem determines which type of division is required.
Spark
What Do You Notice? What Do You Wonder?
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Estimation: Prompt
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Estimation: Reveal
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Sense Making
Crafting A Productive Struggle: Prompt
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During Moves
While Students Are Productively Struggling…
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Student Approach #1: Concrete Fair Sharing with Counting
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Student Approach #2: Array Using Repeated Addition
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Student Approach #3: Open-Array Using Partial-Products and Revealing Partial-Quotients
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Next Moves
Consolidation: Making Connections
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Reveal
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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.
Download Editable/Printable Handout
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Resources and Downloads
Lesson Tip Sheet
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Printable Handout
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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.
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Consolidation Prompt #1
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Consolidation Prompt #2
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Download Editable/Printable Handout
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