Task Teacher Guide

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Students will explore the relationship between multiplication and division and will solve problems involving multiplying a whole number by a decimal. 

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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 be tasked with applying a partial product strategy to multiply a whole number by a decimal.

The math talk and purposeful practice serve to develop a deeper understanding of the following big ideas and should be completed without the help of a calculator. 

• Multiplication and division are related.
• There are two types of division.
• 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).
• Partial products, made possible by the distributive property, allows one or both of the factors to be decomposed in order to simplify a multiplication sentence.

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Math Talk

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Part 1: 

Present the expressions below one at a time. Consider leveraging the context of the Whirlpool Aero Car.

For example, in the first problem of the string, consider stating that there were 10 trips of 16 passengers.

In the fourth problem of the string, state that there were 192 passengers divided by 16 passengers per car in order to give students a quotative division context which lends itself to partial products and/or partial quotients.

Encourage students to use a mathematical model to represent the situation and solve. If the area model 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.

10 x 16
2 x 16
12 x 16
192 ÷ 16
20 x 24
19 x 24
456 ÷ 24

If you are unsure how to model the problems in this string using the area model, revisit the consolidation from Whirlpool Aero Car [Day 1] and view the silent solution animation.

Part 2: 

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Purposeful Practice

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Allow students the opportunity to engage in purposeful practice without the use of a calculator to promote their fluency and flexibility with these concepts and to model their thinking:

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.