Lesson 10

The warm-up prepares students for the next info gap activity by first asking them to brainstorm what information they would need to know to solve an equivalent ratio problem. Next, the teacher demonstrate asking students to share what they want to know and why they want to know it before giving them the information.

Give students 2 minutes of quiet think time.

Demonstrate asking students the questions they will use in the Info Gap in the next activity. Ask them, “What specific information do you need?” As students pose questions, write them down and ask, “Why do you need that information?”

When students explain why they need the information, provide it to them. After sharing each piece of information, ask the class whether they have enough information to solve the problem. When they think they do, give them 2 minutes to solve the problem and then have them share their strategies.

• The red car is traveling faster than the blue car.
• One car is traveling 5 miles per hour faster than the other car.
• The slower car is traveling at 60 miles per hour.
• The blue car is traveling at 60 miles per hour.
• The faster car is traveling at 65 miles per hour.
• The red car is traveling as 65 miles per hour.
• Both cars entered the highway at the same location.
• Both cars are traveling in the same direction.

In this info gap activity, students solve problems involving equivalent ratios. If students use a table, it may take different forms. Some students may produce a table that has many rows that require repeated multiplication. Others may create a more abbreviated table and use more efficient multipliers. Though some approaches may be more direct or efficient than others, it is important for students to choose their own method for solving them, and to explain their method so that their partner can understand (MP3).

The info gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve it. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need (MP6).

Here is the text of the cards for reference and planning:

Problem Card 1

Jada mixes milk and cocoa powder to make hot chocolate. She wants to use all the cocoa powder she has left. How much milk should Jada use?

Data Card 1

• One batch of Jada’s recipe calls for 3 cups of milk.
• One batch of Jada’s recipe calls for 2 tablespoons of cocoa powder.
• Jada has 2 gallons of milk left.
• Jada has 9 tablespoons of cocoa powder left.
• There are 16 cups in 1 gallon.

Problem Card 2

Noah needs to peel a lot of potatoes before a dinner party. He has already peeled some potatoes. If he keeps peeling at the same rate, will he finish all the potatoes in time?

Data Card 2

• Noah has already been peeling potatoes for 10 minutes.
• Noah has already peeled 8 potatoes.
• Noah needs to peel 60 more potatoes.
• Noah needs to be finished peeling potatoes in 1 hour and 10 minutes.
• There are 60 minutes in 1 hour.

Arrange students in groups of 2. In each group, distribute a problem card to one student and a data card to the other student.

Students may misinterpret the meaning of the numbers or associate quantities incorrectly and multiply 8 by 6 (because \(10 \boldcdot 6\) is 60). Encourage them to organize the given information in a table or a double number line.

Select one student to explain each distinct approach. Highlight how multiplicative reasoning and using the table are similar or different in each case.

When all approaches have been discussed, ask students: “When might it be helpful to first find the amount that corresponds to 1 unit of one quantity and scale that amount up to any value we want?” Encourage students to refer to all examples seen in this lesson so far.

This activity provides an opportunity for additional practice in solving equivalent ratio problems. Monitor for students solving the problems in different ways.

Give students 4 minutes of quiet work time and then have them discuss their solutions with a partner. 

Select students to present their solutions. Sequence solutions with diagrams first and then tables. Make sure students see connections between the different representations and ways of solving the problems.