Task Teacher Guide
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In This Purposeful Practice…
Students will explore equivalent ratios, reveal rates through partitive division and scale factors through quotative division.
Intentionality…
The purpose of the Day 4 activities is to reinforce key concepts from Days 1 to 3. Students will engage in a math talk and will have an opportunity to complete independent purposeful practice. The math talk and purposeful practice serve to develop a deeper understanding of the following big ideas.
- 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 ,1 4 = ¼ ).
Math Talk
Overview of the Problem String
In today’s visual math talk, we will be presenting the following quotative division sentences one at a time. Since we are dividing quantities of the same unit, the type of division is quotative and the resulting quotient will represent a scale factor. Encourage the use of an area, volume or linear model to justify each equation.
$60 ÷ $30
$30 ÷ $60
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Consider leveraging the following visual math talk prompt videos to understand how to facilitate this math talk using a stacked bar model as well as to provide students with an engaging set of visual prompts.
Problem #1
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Problem #2
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Problem #3
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Problem #4
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Problem #5
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Problem #6
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Purposeful Practice
While Students Are Practicing…
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Questions: Ratios and Rates
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Problem #1
Problem #2
Problem #3
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Problem #4
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Problem #5
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Problem #6
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1. Model and solve…
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2. Calista is baking…
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3. Consider the…
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4. Complete the…
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5. Logan says that…
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