Math Background

Lesson: Graphing Data
Introducing the Concept

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Your children have had experience in sorting items by like attributes and in gathering data through class surveys. They will now use these skills to collect data and learn to create a picture graph.

Materials: 2 large pieces of posterboard, one for a tally chart and one for a picture graph; one blank shirt outline for each child; crayons

Preparation: On one piece of posterboard, create a blank tally chart with four rows and three columns. Glue or tape one blank shirt in each row of the left column as shown.

Shirt Color bar graph

Draw a blank picture graph on the second piece of posterboard with 4 equal-sized rows and 2 columns. The left column should be the width of one blank shirt outline. Glue or tape one blank shirt in each row of this column. The right column should be wide enough to fit several blank shirts as shown.

Shirt Color bar graph

Copy a blank shirt outline for each child. Use the Shirt Outline Template (PDF file).

Prerequisite Skills and Background: Children should know how to sort and classify items by like attributes.

  • Ask: We have sorted items by color, by size, and by shape. Today we are going to sort the class by shirt color. What are some different shirt colors?
    Responses will vary and may include blue, white, pink, green, red, and yellow. Select 4 children with different shirt colors.
  • Say: Here are the four colors by which we will sort the class.
    Say each child's name and the shirt color that the child represents. You may wish to explain to children that shirts with more than one color should be sorted by the predominant color. Write the name of each color on the chalkboard and have the appropriate child stand in front of it.
  • Say: You have one minute to look at each person's shirt. Decide who has a shirt closest in color to yours. It's OK if your shirts are not exactly the same color as that person's shirt. Then sit down and remember which color group you belong to.
    Give the children time to select their groups. Then have them raise their hands to show which group they belong to.
    Ask the children how many more are in one group than another. Lead them to see that they need to raise their hands again to answer.
  • Ask: I want to ask you several questions about the number of people in each group. How can you find the answers without having to raise your hands over and over?
    Elicit that you should write down the number of people in each group.
  • Say: We can organize our information and show the number of people in each group by making a tally chart. For each person in a group, we'll make one tally. (Draw a tally on the chalkboard.)
    Tape the posterboard tally chart to the chalkboard. Label each row and quickly color each blank shirt, placing the largest group first. Say the name of the largest group and ask children who are in that group to raise their hands. Make a tally mark for each child.
  • Say: What does each tally stand for? (one person) What is different about the tally mark for the fifth person? (It is slanted.) What is the pattern? (Every fifth tally is slanted.)
    If your largest group does not have at least five people, model this for the children so they can see how five is shown with tally marks.
  • Ask: When you write tally marks, the first four are straight up and down. The fifth one is slanted across the first four, as if it is holding them together. This pattern repeats over and over. How many people does each group of tallies represent? (Frame a group of 5 tallies with your fingers.)
    The children should answer “five.” Ask several questions about the number in each group and the relationships among the groups.
  • Ask: I have another way that we can show this same information. It's called a picture graph. What do you think a picture graph uses to show information?
    Elicit that a picture graph uses pictures to show how many are in each group. Show children the blank picture graph.
  • Say: This is a picture graph. Each one of you will color a shirt like this (point to a blank shirt on the graph) and then place it in the correct color row.
    Tape the posterboard picture graph to the chalkboard next to the tally chart. Label each row and quickly color each blank shirt. Make sure the groups are in the same order as they were on the tally chart. Explain to children what colors to use for each group.
    Give each child a blank shirt and allow each child time to color it. Then call each group up one at a time and have that group tape its shirts to the appropriate row on the picture graph.
  • Ask: How can we find the number of children in each group by using the picture graph?
    Children may say that we can count the number of shirts in a row to find the number of children in that group.
  • Ask: How many are there in the (Color A) group on the picture graph? (Answers will vary.) How many are there on the tally chart?
    Answers will vary, but should be the numbers in each group and should be the same for both the picture graph and the tally chart. Repeat for each color.
  • Ask: One tally on the tally chart and one picture on the picture graph each stand for one person. Now look at the picture graph. Which group has the most pictures in it? (Answers will vary.) How can you tell which one has the most people in it?
    Children should recognize that the row with the most pictures in it has the most people in it.
  • Ask: Which group has the least? (Answers will vary.) How can you tell which one has the least?
    Children should recognize that the row with the fewest pictures has the least number of people in it. Ask children several questions comparing different groups. For example, how many more people have blue shirts than yellow shirts?
  • Ask: How are tally charts and picture graphs alike?
    Elicit that they both help you to organize information so that it is easier to understand. Both show you how many are in a group and make it easier to compare groups.
  • Ask: How are tally charts and picture graphs different?
    Children should recognize that picture graphs use pictures to show their information and that tally charts use tally marks. They may mention that tally charts show numbers in groups of five.

    Continue asking the children questions about the picture graph, including how many are in two groups combined and how many more or less are in one group than another.

Houghton Mifflin Math Grade 1