Lesson 6

This warm-up prepares students for the Info Gap activity that follows. First, students brainstorm what information they would need to know to solve a problem that involves constant speed. Then, the teacher demonstrates the process of asking a student why they need a specific piece of information before sharing it with them, in preparation for students following this procedure with their partner in the next activity.

Give students 1 minutes of quiet think time to brainstorm what information they would need to know to solve the problem, followed by a whole-class discussion demonstrating the procedure for the Info Gap activity.

Ask students:

• "What specific information do you need?" 
• "Why do you need that information?"

Share each piece of information with the class after a student specifically asks for it (and explains why they need to know it).

• The race is 10,000 meters long.
• The race started at 9:15 a.m.
• In 1 minute, the person ran \(156\frac{1}{4}\) meters.
• An equation relating distance and time is given by \(d = 156\frac{1}{4} \boldcdot t\) where \(d\) represents distance in meters and \(t\) represents time in minutes.
• It takes 32 minutes for the person to run 5,000 meters.
• The person runs at a pace of 6.4 minutes per kilometer (or 1,000 meters).

After you share each piece of information, ask the class whether they have enough information to be able 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 person should finish the race at 10:19 a.m.)

Tell students that they will be working in groups of two in the next activity and that they will be using the same procedure that you just demonstrated to solve a problem.

In this info gap activity, students write equations for several proportional relationships given in the contexts of a bike ride and steady rainfall. They use the equations to make predictions.

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:

Invite students to share their equations and predictions. Record their equations displayed for all to see. Ask them to explain how they determined the constant of proportionality as well as why it made sense to represent the situation with a proportional relationship.

In this activity students compute rates to decide which job applicant is working the fastest checking online comments. They compare rates and total number of comments checked, then see that using rates is the more useful information in this situation. 

Keep students in the same groups of 2.

Ask students which job applicant should get the job and why. If time permits, consider using MLR 1 (Stronger and Clearer Each Time).