Math Investigations

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Chapter 3

Part 1: Home and School Investigation

Send the Letter to Family (PDF file) home with each child. Once each child has brought in a stuffed animal or a picture, have the children group these into categories such as teddy bears, pandas, dogs, and so on. Create a label for each category and place the labels in a row on the floor. Have the children put the animals and pictures in the appropriate line above each category. Discuss the graph the children have made by asking questions such as the following. Make sure that animals are lined up neatly in rows.

  • Which kind of animal do we have the most of?
  • Which kind of animal do we have the fewest of?

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 6 on making a graph.


  • Investigator Worksheet (PDF file) for each group of two children
  • for each pair, a paper bag with two objects in it (Objects must be exactly the same in every way except for color. For example, a blue connecting cube and a yellow connecting cube can be used.)
  • crayons

Introducing the Investigation

Introduce the investigation by showing students a paper bag and putting the two different-colored objects in the bag. Ask a volunteer to choose an object from the bag without peeking. Before the volunteer chooses the object, ask the children to guess what color he or she will pick. Draw a two-column bar graph (similar to the one on the Investigator Worksheet) on the board and record the color of the object that the volunteer chose. Return the object to the bag and ask for another volunteer. Again have the children guess what color the volunteer will draw. Do this a few more times, recording the color each time.

Doing the Investigation

Give each group of two children the Investigator Worksheet, the paper bag with the two objects in it, and crayons. Tell the children to use the crayons to record the color of the objects in their bag in the circles at the bottom of the graph on the Investigator Worksheet. Then tell them to choose an object out of the bag (without peeking) 10 times and record the result each time by coloring a square on the graph. Remind them to put the object back in the bag each time.

When the students are finished, use the following questions for discussion:

  • Did you get more of one color or did you get the same amount of each color? If you got more of one color, were the numbers of each color pretty close to each other or very far apart?
  • Suppose you wanted to have a bag where you would choose yellow most of the time. What would you put in the bag? Lead children to see that you will get yellow more often if there are more yellow objects in the bag than any other color.

Extending the Investigation

  • Have children put a different number of each color object in the bag and record the results. For example, they might put two yellow cubes and one blue cube in the bag.

Houghton Mifflin Math Grade K