Math Investigations

Help with Opening PDF Files

Chapter 17

Part 1: For the problem in the Teacher's Edition, page 442

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

Ask the following questions to guide the students in solving the problem.

  • How can we find out what percent of the total music sales is accounted for in the table on page 442? (Add all the percents given in the table.)
  • What percent of the total music sales is accounted for in the table? (63%)
  • How can we find out what percent of the total music sales is not accounted for in the table? (Subtract 63% from 100%.)
  • What percent of the total music sales are not accounted for in the table? (37%)
  • What might the missing data be if there are at least three music categories missing? [Sample Answer: Bluegrass: 6% (3/50 of the total sales); Folk Music: 10% (1/10 of the total sales); Jazz: 11% (11/100 of the total sales); All other categories: 10% (1/10 of the total sales)]

Answer:
Of the total music sales, 37% are not accounted for. Answers will vary for the question about the missing data. See the question above for a sample answer.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 1 on percent as a ratio.

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

Doing the Investigation

The students may need help developing a strategy for solving these problems. You might want to fill in the chart for Colonial Blue with the whole class.

One way to get the information for the Colonial Blue chart is to first find the total number of quarts in the mixture. If two quarts make up 5% of the mixture, then 100% would be 2 × 20, or 40 quarts. The amount of blue in the mixture is 80% of 40 quarts, or 32 quarts. The amount of white in the mixture is 15% of 40 quarts, or 6 quarts.

Another way to get the information for the Colonial Blue chart is to figure that to find the amount of white you could divide 15% by 5% to find out what to multiply 2 quarts by. 15% ÷ 5% is 3, and 3 × 2 quarts is 6 quarts. So the amount of white in the mixture is 6 quarts. To find the amount of blue in the mixture, divide 80% by 5%. 80% ÷ 5% is 16, and 16 × 2 is 32 quarts. So the amount of blue in the mixture is 32 quarts.

Discuss these strategies and any other strategies the students suggest to help them get started doing the investigation.

Answers:

Colonial Blue

Blue: 80% Purple: 5% White: 15%
32 quarts 2 quarts 6 quarts

Brick Red

Orange: 5% Red: 85% Brown: 10%
2 quarts 34 quarts 4 quarts

Bright Yellow

Yellow: 90% Orange: 5% White: 5%
54 quarts 3 quarts 3 quarts

Student Report

The letter back to Enrique Smith gives the students an opportunity to show what they have done and how they did it, thus communicating about mathematics.


Houghton Mifflin Math Grade 6