Math Investigations

Help with Opening PDF Files

Chapter 7

Part 1: For the activity in the Teacher's Edition, page 174

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

Help students answer the question by asking the following questions:

  • Which colored ball do you think the jar has most of? Why? (Answers will vary. There is a good argument that the jar contains more yellow balls than any other color of ball because a yellow ball was picked more times than any other color.)
  • Which colored ball do you think the jar has the fewest of? Why? (Answers will vary. There is a good argument that the jar contains fewer blue balls than any other color of ball because blue was picked fewer times than any other color.)

There are many reasonable answers to the question of how many of each colored ball is in the jar. Some students might suggest that the numbers are the same as the numbers in the table (four red, seven yellow, three green, two blue). This is a reasonable answer. Look for answers where the greatest number of balls is yellow.

Part 2: Be an Investigator

Materials

  • 100 small red, blue, and white objects or pieces of paper for each group

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.

Working on the Investigation

Some students will be able to figure this out mathematically while others will want to experiment with manipulatives to arrive at the answer. Allow students to work at whatever level they are comfortable.

Answers:
Jar A: 10 red gumballs, 40 blue gumballs
Jar B: 30 blue gumballs, 70 white gumballs
Jar C: 40 white gumballs, 50 red gumballs, 10 blue gumballs

Letter

The letter back to Tanya LaChance gives students an opportunity to communicate about mathematics by writing about what they have done.

Extending the Investigation

After students have carried out the activities in this investigation, you may want to set up the three jars and ask students questions such as the following about them:

  • If you picked a gumball out of Jar A, what color would you be most likely to get? (blue)
  • If you picked a gumball out of Jar B, what color would you be most likely to get? (white)
  • If you picked a gumball out of Jar C, what color would you be most likely to get? (red)
  • If you wanted the greatest chance of picking a white gumball, which jar would you choose? (Jar B)
  • If you wanted the greatest chance of picking a blue gumball, which jar would you choose? (Jar A)

Houghton Mifflin Math Grade 3