Math Investigations

Help with Opening PDF Files

Chapter 6

Part 1: For the activity in the Teacher's Edition, page 124

Provide your students with a copy of the Activity page (PDF file).

The following example will show you how to work with your students to create a circle graph.

Favorite Vegetable Survey

Carrots: 8 people
Broccoli: 6 people
Peas: 2 people

The students can divide a circle into sixteenths by dividing it into fourths and then dividing each fourth into four equal parts. They color 8/16 of the circle to show how many people chose carrots. They color 6/16 a different color to show how many people chose broccoli. They color 2/16 of the circle to show how many people chose peas.

circle graph divided into 16 equal parts; 6 spotted for broccoli, 8 grey for carrots, and 2  striped for peas.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 3 on multiplying mixed numbers.

Introducing the Investigation

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

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

Doing the Investigation

Make sure that students understand what to multiply each amount by. Since the mix is for four people, they would multiply by two to find the amount of each ingredient needed in a mix for eight people. They would multiply by 3 to find the amount of each ingredient needed for a mix for 12 people.

Answers:

Basic Trail Mix
Ingredient Mix for 4 People Mix for 8 People Mix for 12 People
Peanuts 1/2 cup 1 cup 11/2 cups
Almonds 1/4 cup 1/2 cup 3/4 cup
Raisins 11/2 cup 3 cups 41/2 cups
Deluxe Trail Mix
Ingredient Mix for 4 People Mix for 8 People Mix for 12 People
Almonds 3/4 cups 11/2cups 21/4 cups
Cashews 1/3 cup 2/3 cup 1 cup
Dried Cranberries 11/4 cup 21/2 cups 33/4 cups
Trail Mix with Chocolate
Ingredient Mix for 4 People Mix for 8 People Mix for 12 People
Almonds 1/4 cup 1/2 cup 3/4 cup
Peanuts 11/3 cups 22/3 cups 4 cups
Chocolate Chips 2/3 cup 11/3 cup 2 cups

Student Report

The letter to Ty gives students an opportunity to report on what they have done.

Extending the Investigation

Have students use one of the recipes to make some trail mix for four people and then make it again for eight people. See if it tastes the same. Have them use an example where the math was done incorrectly for a mix for eight people and compare the tastes.


Houghton Mifflin Math Grade 6