Task Teacher Guide

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Students will explore modelling both types of division (partitive and quotative).

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The purpose of the Day 2 activities is to reinforce key concepts from Day 1. 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 also begin investigating finding a percent of a quantity through the relationship between percents, fractions and partitioning. The math talk and purposeful practice serve to develop a deeper understanding of the following big ideas.

• 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.

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Math Talk

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Part 1: 

Present the contexts below one at a time. Consider leveraging the context from day 1 in that there are many different tourist attractions in Niagara Falls, Ontario which is why the following contexts arise.

Encourage students to use a mathematical model to represent the situation and solve. If the array is not a model used by any students, find an opportunity to highlight this tool by using it to model the thinking of a student as you highlight their approach and strategy regardless of whether they chose to use the array model to represent their thinking.

$120 was used to purchase 8 tickets. What was the cost of each ticket?

$120 was used to purchase tickets at a cost of $16 per ticket. How many tickets were purchased?

The roller coaster has a maximum capacity of 160 riders. If there are 8 passenger cars, how many passengers does each car hold?

The roller coaster has a maximum capacity of 160 riders. If each passenger car can hold 8 passengers, how many cars are there?

Part 2: 

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Purposeful Practice

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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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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.