Math Investigations

Help with Opening PDF Files

Chapter 5

Part 1: For the problem in the Teacher's Edition, page 108

Provide students with the Problem Worksheet (PDF file)

Discuss how to make a circle graph with your students. Show them how you can easily divide a circle into halves and then into fourths. If you divide each fourth in half you have a circle that is divided into eighths. Students can use these circles to create their circle graphs.

For example, the tiger sleeps 16 hours, which is a little more than 5/8 of a day. If the students color five of the eighths, and just a little bit more, on their circle graph, they will have shown the amount of time a tiger sleeps each day.

Students can use this same technique to create circle graphs to show how much time the animals are asleep and how much time the animals are awake.

As you look at students' answers, look to see that their answers are reasonable.

Answers:

Gerbil: circle graph with one 195 degree sector shaded and labeled Time Asleep and the rest of the circle labeled Time Awake Koala: circle graph with one 300 degree sector shaded and labeled Time Asleep and the rest of the circle labeled Time Awake
Opossum: circle graph with one 285 degree sector shaded and labeled Time Asleep and the rest of the circle labeled Time Awake Squirrel: circle graph with one 225 degree sector shaded and labeled Time Asleep and the rest of the circle labeled Time Awake
Tiger: circle graph with one 240 degree sector shaded and labeled Time Asleep and the rest of the circle labeled Time Awake  

Students: Answers will vary but most should show about one-third of the graph labeled “Time Asleep” and two-thirds labeled “Time Awake”.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 6 on function tables.

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

As you watch students doing the investigation, ask them to explain how they are filling in the tables.

Answers:
Dog Food Needed Each Day
Rule: cups of food = (number of dogs) × 3

Number of Dogs Cups of Food
1 3
2 6
3 9
4 12
5 15
6 18
7 21
8 24
9 27

Cost to Board Dog
Rule: cost in dollars = (number of days) × 12

Number of Days Cost
1 $12
2 $24
3 $36
4 $48
5 $60
6 $72
7 $84

Student Report

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

Extending the Investigation

Have students create a rule for a function table. Have them trade function tables so that they can complete each other's function tables.


Houghton Mifflin Math Grade 4