Math Investigations

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Chapter 12

Part 1: For the problem in the Teacher's Edition, page 300

Provide your students with a copy of the Problem Worksheet (PDF file).

If students need help on this activity, use the following questions to guide them.

  • What is the expression for two times the number of trails that Antonio visited? (2a)
  • What should we do with that expression so that it represents the number of trails that Brian visited? (Subtract five from it.)
  • What is the expression for the number of trails that Brian visited? (2a − 5)

Answer:

2a - 5
Antonio: 6, Brian: 7
Antonio: 7, Brian: 9
Antonio: 8, Brian: 11

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 1 on writing expressions.

Introducing the Investigation

Introduce the investigation by reading aloud the assignment at the top of the first page of the Description of Investigation and Student Report (PDF file), by having one of your students read aloud the assignment, or by having the students read the assignment individually.

Put students in groups of two to four students to work on the investigation.

Doing the Investigation

When students get to the last question, ask the following questions to help guide them.

  • When the number of hours is less than four, do you think it is better to choose Plan A or Plan B? (Plan B)
  • When the number of hours is greater than six, do you think it is better to choose Plan A or Plan B? (Plan A)
  • What number of hours would you like to try to see if we get the same cost for both plans? (Try whatever the students suggest. Since five is greater than four and less than six, five would be a good number of hours to try.)
  • What happens when we use five hours in both the Plan A and the Plan B expressions? (We get $60 either way.)

Answers:

Here are the expressions for each plan.
x is the number of hours of a bike trip.

Plan A:           50 + 2x          

Plan B:           12x          

Cost for Each Plan and Recommendation

Trip L: 2 hours
Plan A: 50 + (2 × 2) = 54 $54
Plan B: 12 × 2 = 24 $24
Plan B is the best choice.

Trip M: 4 hours
Plan A: 50 + (2 × 4) = 58 $58
Plan B: 12 × 4 = 48 $48
Plan B is the best choice.

Trip N: 6 hours
Plan A: 50 + (2 × 6) = 62 $62
Plan B: 12 × 6 = 24 $72
Plan A is the best choice.

Trip O: 8 hours
Plan A: 50 + (2 × 8) = 66 $66
Plan B: 12 × 8 = 24 $96
Plan A is the best choice.

If you take a bike trip of           five           hours it does not matter which plan you choose.

Student Report

The letter back to Susan Chung gives students an opportunity to show the expressions they have written and make recommendations.


Houghton Mifflin Math Grade 6