Task Teacher Guide
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In This Purposeful Practice…
Students will explore modelling both types of division (partitive and quotative) and determine a percent of a whole number.
Intentionality…
The purpose of the Day 4 math talk and purposeful practice is to reinforce key concepts from Days 1-3. Students will engage in a string of related problems through a math talk and will have an opportunity to complete independent purposeful practice.
They will find a percent of a whole number and begin making connections to multiplying by a fraction. Today, you will notice and name the two types of division, partitive and quotative.
- Multiplication and division are related.
- There are two types of division.
- Partitive division reveals a rate.
- Quotative (or measured) division reveals the numbers of parts when the rate is known.
- 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)
- Percents and fractions are related.
- A percent of a quantity can be found through partitioning.
- Multiplying by a percent is the same as multiplying by an equivalent fraction.
Math Talk
Related String of Problems
Part 1:Â
Remind students of the context from the previous day where safety restrictions called for allowing only 40% of the 600 passenger maximum capacity per boat. Today, we will be determining how many passengers would be allowed on a boat with a maximum capacity of 150 at various safety restriction percentages.
While we will acknowledge and honour the approaches of all students to show we value their strategies and mathematical models of their choosing, we will plan to emerge a linear model to represent the varying student strategies.
10% of 150
5% of 150
50% 150
60% of 150
65% of 150
Continue exploring the connection between finding a percent of a number, division and multiplying by a fraction.
Part 2:Â
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Purposeful Practice
While Students Are Practicing…
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Questions: Partitive & Quotative Division and Finding a Percent of a Quantity
Question #1:
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Question #2:
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Question #3:
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Question #4:
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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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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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Determine…
10% of 150
…
5% of 150
…
50% 150
…
60% of 150
…
65% of 150
Brainstorm…
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1. Consider the model below…
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2. Layla has been…
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3. Nia purchased…
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4. Amir will be…
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Download Editable/Printable Handout
Become a member to access purposeful practice to display via your projector/TV, download the PDF to upload to your LMS and/or print for students to have a physical copy