Math Investigations

Help with Opening PDF Files

Chapter 7

Part 1: For the problem in the Teacher's Edition, page 148

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

Have students do research to find the thickness of a quarter or tell them that the thickness of a quarter is 1.75 millimeters (mm).

Help the students develop a plan to answer the two questions.

To find the approximate value of a stack of quarters 2 meters (m) high, you need to divide 2 m by 1.75 mm, to find the number of quarters in the stack and then multiply by $0.25. To divide 2 m by 1.75 mm, convert 2 m to mm by multiplying 2 by 1000 (2000). Then divide 2000 by 1.75 (about 1143). Multiply 1143 by $0.25. The answer is about $286.

To find the height of a stack of quarters that is worth $100, you need to divide $100 by $0.25 to find the number of quarters in $100 and then multiply the answer by 1.75 mm to find the height of the stack. $100 divided by $0.25 is 400. 400 multiplied by 1.75 mm is 700 mm. The answer is about 700mm or 70 centimeters (cm) or 0.7 m.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 2 on multiplying decimals.

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 to work on the investigation.

Doing the Investigation

The different dinner/desert combinations and their cost are:
Roast Beef/Apple Pie: $21.50
Roast Beef/Chocolate Cake: $20.00
Chicken/Apple Pie: $17.00
Chicken/Chocolate Cake: $15.50
Salmon/Apple Pie: $20.25
Salmon/Chocolate Cake: $18.75

The cost of each dinner/desert combination for five people is:
Roast Beef/Apple Pie: $21.50 × 5 = $107.50
Roast Beef/Chocolate Cake: $20.00 × 5 = $100.00
Chicken/Apple Pie: $17.00 × 5 = $85.00
Chicken/Chocolate Cake: $15.50 × 5 = $77.50
Salmon/Apple Pie: $20.25 × 5 = $101.25
Salmon/Chocolate Cake: $18.75 × 5 = $93.75

Student Report

The student report gives students an opportunity to show what they have done.

Houghton Mifflin Math Grade 6