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Solve Multiplicative Comparison

Problems

Grade 4: Unit 9: Lesson 7

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Lesson Purpose

The purpose of this lesson is for students to solve problems involving multiplicative comparison.

Lesson Narrative

This lesson allows students to solve problems that involve multiplicative comparisons in the

context of cost of living. Students are presented with different cost information and asked to make

comparisons in different ways. For instance, they may be given the cost in one country and told that

the cost in a second country is “9 times as much”, and asked to find the dollar cost in the second

country. They may be given the costs in two countries and then asked to compare the costs using a

comparison statement that uses multiplication. Students also reason about how many of an item

could be purchased in a country given a certain dollar amount (for example, how many months of

rent in Ghana can one afford with $2,000?).

The work requires students to use several operations and to consider estimates where the

operations would go beyond grade level (MP1, MP2). In many questions, it is not important that

students find exact products, quotients, or answers. The emphasis is on reasoning flexibly about

relative sizes of quantities and solving problems multiplicatively.

If students need additional support with the concepts in this lesson, refer back to Unit 5, Sections

A and C in the curriculum materials.

Learning Goals

• Use the four operations to solve word problems involving multiplicative comparison.

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Let’s solve real-world multiplicative comparison problems.

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Notice and Wonder: Two Cities

Warm Up

The purpose of this warm-up is to elicit observations about differences in costs of living in different

parts of the United States. It prepares students to look for and make sense of multiplicative

comparisons later in the lesson. It also helps elicit what students know about how the different

costs may be different depending on where you live.

Students may notice and wonder many things about the data in the table and both additive and

multiplicative comparisons are likely to come up. Some students may note that an item costs “some

dollars more” in San Francisco than in Fort Wayne, while others may say it costs “some number of

times as much” based on the quantities or their estimation of the quantities. In the synthesis, focus

student discussion on additive and multiplicative comparison.

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What do you notice? What do you wonder?

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Let’s Talk About!

How could you compare the cost for renting an apartment in San Francisco to the cost in Fort Wayne? How could you use multiplication to compare the costs?

The prices of the things you need to live, like food, clothing, and shelter, are called the cost of living. The cost of living can be very different depending on where in the world you live. Today we are going to compare the cost of living in different places around the world.

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The Most and Least Expensive

Activity 1

MLR8: Discussion Supports

This activity prompts students to use multiplicative comparison to determine the cost of different

living expenses in Bermuda and in India. Students use these costs to interpret and solve a multi-

step problem. The multi-step problem can be solved in more than one way. Students might use

multiplication or division. They may also choose to estimate rather than perform each calculation.

Encourage students to use the Three Reads routine as needed to solve problems.

When finding the missing prices in the table, students also have an opportunity to reason about

how to find a value that is 2.5 times as much. Students are not expected to multiply whole numbers

by decimals in grade 4, but may use their understanding of decimal notation and decimal fractions

to estimate the cost by doubling the price in India and adding half the price or by reasoning that 2.5

is close to 3.

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Launch

Groups of 2

• “We saw one example of how the same items can vary a lot in cost depending on where you

live in the United States. Let’s look at the costs of some other things in two different

countries—one known to be very expensive and the other known to be inexpensive.”

Student Work Time

• 5 minutes: independent work time on the first question

• Monitor for students who use the multiplication or division algorithm, draw diagrams, write

equations, or use estimation to find the missing values.

• Pause for a discussion. Select students to share their responses and reasoning for finding the

costs in the table.

• Highlight that to find the missing cost in Bermuda, we can multiply the cost in India by the

number in the middle column, and to find the cost in India, we divide the cost in Bermuda by

the number in the middle column.

• 4 minutes: independent work time on the second question

• 4 minutes: partner discussion

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b. In India, rent for a 1-bedroom apartment outside of a city center costs about $76 per month. A similar apartment in Bermuda costs 23 times as much.

Utilities (electric, gas, water, and heating) for a small apartment costs about $27 in India and 7

times as much in Bermuda.

If a person earns $2,000 per month, can they afford to pay rent and utilities in Bermuda?

Launch

Groups of 2

• “We saw one example of how the same items can vary a lot in cost depending on where you

live in the United States. Let’s look at the costs of some other things in two different

countries—one known to be very expensive and the other known to be inexpensive.”

Student Work Time

• 5 minutes: independent work time on the first question

• Monitor for students who use the multiplication or division algorithm, draw diagrams, write

equations, or use estimation to find the missing values.

• Pause for a discussion. Select students to share their responses and reasoning for finding the

costs in the table.

• Highlight that to find the missing cost in Bermuda, we can multiply the cost in India by the

number in the middle column, and to find the cost in India, we divide the cost in Bermuda by

the number in the middle column.

• 4 minutes: independent work time on the second question

• 4 minutes: partner discussion

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Let’s Talk About!

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The Cost of Living

Activity 2

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Launch

• Groups of 2

• “Have you ever traveled to another place far away? Do you know a friend or family member

who has?”

• Share responses.

• “In this activity, you will compare the typical cost for things in the United States to the same

costs in Ghana.”

Student Work Time

• 4 minutes: independent work time on the first question

• 2 minutes: partner discussion

• Monitor for the different ways students make estimates, for example, whether they:

◦ opt to multiply or divide

◦ use exact or rounded numbers

◦ round before computing or compute before rounding

• Pause for a brief discussion. Select students to share their responses and reasoning for finding

the costs in the table.

• 4 minutes: independent work time on the second question

• 2 minutes: partner discussion

• Monitor for different strategies students use to find how many months of rent the family could

afford in each country, including strategies based on estimation.

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Suppose a family has $3,000 for housing and wants a 1-bedroom apartment outside of a city center.

With that amount of money, how many months of rent can they afford in:

a. the United States? Explain or show your reasoning.

b. Ghana? Explain or show your reasoning.

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Lesson Synthesis

Today we compared the cost of living in several countries.

What are the different ways you compared the prices and the cost of living between two different

places in the activities today?

When would it be important to compare the cost of living in one place compared to another?

What questions do you have about cost of living that you would like to learn more about?

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Restaurant Budget

Cool-Down

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Cool-Down: Restaurant Budget

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