Task Teacher Guide
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In This Task…
Today students will explore a composed unit ratio from a recipe with three distinct units. Based on the available quantity of, they will have to reveal the corresponding quantities for the others by determining a rate through partitive division, or a scale factor through quotative division.
Intentionality…
In this task, students will determine how much of each ingredient they will need to make an Alrnold Palmer drink. The spark in today’s task will attempt to encourage students to leverage their understanding of composed unit ratios to either reveal rates through partitive division or a scale factor through quotative division.
Some of the big ideas that may emerge through today’s tasks include:
- There are two types of ratios; composed unit and multiplicative comparison;
- A composed unit is often (not always) a ratio with two distinct units;
- A composed unit can be scaled in tandem;
- Equivalent ratios are derived from the same rate;
- When you divide a composed unit through partitive division, you reveal a rate;
- Quotative division is applied when trying to determine a scale factor between two quantities/measures of the same unit (i.e. rice and rice, water and water);
- When you invert the dividend and the divisor in a quotative division sentence, the quotient (the revealed scale) has a reciprocal relationship (i.e., 4 1 = 4 and 1 4 = ¼ )
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: Partitioning a Volume Model
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Student Approach #2: Revealing a Rate on a Stacked Number Line
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Student Approach #3: Using Multiplicative Comparison and a Bar Model
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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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Resources and Downloads
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Printable Handout
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Consolidation Prompt #1
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Consolidation Prompt #2
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