Solve Multiplicative Comparison Problems

10 min

Narrative

The purpose of this Warm-up is to elicit observations about differences in the cost 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 costs may be different, depending on where a person lives.

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 Activity Synthesis, focus students’ discussion on additive and multiplicative comparison.

Launch

  • Groups of 2
  • Display the table.
Teacher Instructions
  • “What do you notice? What do you wonder?”
  • 1 minute: quiet think time
  • 1 minute: partner discussion
  • Share and record responses.

Student Task

What do you notice? What do you wonder?

2023 prices San Francisco, CA Fort Wayne, IN
population 715,717 269,621
milk (1 gallon) $5.99 $2.79
bread (1 loaf) $4.79 $3.99
gasoline (1 gallon) $6.02 $3.56
movie ticket $17 $10.50
internet connection (1 month) $89 $60
rent for a 3-bedroom apartment in the city center (1 month) $5,000 $1,200
cost of a house $1,380,000 $210,000

Sample Response

Students may notice:
  • The table shows a list of the different costs in two cities.
  • San Francisco has more people than Fort Wayne.
  • Milk costs more than 2 times as much in San Francisco as in Fort Wayne.
  • An apartment is about 4 times as much in San Francisco as in Fort Wayne.
  • A house costs almost 7 times as much in San Francisco.
Students may wonder:
  • Why is everything more expensive in San Francisco?
  • Why is the difference in cost less for some things than for other things?
  • Why is it so much cheaper to buy a house in Fort Wayne than in San Francisco?
Activity Synthesis (Teacher Notes)
  • “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?”
  • As needed, “About how many more times as much is the cost of a house in San Francisco compared to the cost of a house in Fort Wayne?”
  • “The prices of the things you need to live, such as 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 costs of living in different places around the world.”
Standards
Addressing
  • 4.OA.2·Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
  • 4.OA.A.2·Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.<span>See Glossary, Table 2.</span>

20 min

15 min