Math Background

Lesson: Graphing Data
Developing the Concept

Your children have now learned how to create tally charts and picture graphs. While these are good ways to represent and compare data, they are not the only ways. Children will now learn another way to represent data by learning how to create and read bar graphs.

Materials: The posterboard Shirt Color tally chart and picture graph from the Introducing the Concept Lesson; a posterboard bar graph showing the shirt color data from the Introducing the Concept Lesson; a blank overhead transparency of Learning Tool 20 from the Learning Tools Folder; one copy of Learning Tool 20 for each child; crayons

Preparation: Make an overhead transparency of Learning Tool 20 and one copy for each child. Create a bar graph on posterboard showing the data from the shirt-color survey from the Introducing the Concept lesson. Tape the Shirt Color tally chart to the chalkboard.

Prerequisite Skills and Concepts: Children should know how to collect data on a tally chart and how to transfer it to a picture graph.

Begin by reviewing tally marks by using the Shirt Color tally chart from the previous lesson. Ask the children which shirt color group has [3] people in it. Repeat, using numbers from the other shirt-color groups on the tally chart.

  • Ask: Last time, we learned how to collect information by using a tally chart. Who can tell how we displayed that data?
    Children should say with a picture graph. Tape the Shirt Color picture graph to the board, next to the tally chart. Review what each picture stands for.
  • Ask: Today we are going to learn about a new kind of graph called a bar graph. A bar graph is like a picture graph, because it shows us how many are in each group. The difference between a picture graph and a bar graph is how the information is shown. If a picture graph uses pictures to show us how many, what do you think a bar graph uses to show us how many?
    Help children realize that bars are used to show how many. Tape the Shirt Color bar graph to the chalkboard, next to the picture graph.
    Shirt Color bar graph
  • Ask: How did we find the number in each group on the picture graph?
    Children may explain that they counted the number of pictures in each group.
  • Say: If we want to find how many are in a group using a bar graph, we can count the number of colored boxes for that group. Let's count the boxes for (Color C) together.
    Point to each box in the row for shirt color C as the children count aloud.
  • Ask: Now look at the picture graph. Is the number of people with (Color C) shirts the same as the number of people with that color on the bar graph? (yes) If each picture on the picture graph stands for one person, what does one box (frame one box with your thumb and pointer finger) on a bar graph stand for? (one person) What do you notice about the number below where the bar ends for (Color C)?
    Children should say that it is the same as the number of boxes that they just counted.
  • Say: Bar graphs use both bars and numbers to show how many are in each group. Instead of having to count all the boxes, we can just look at the number below where the bar ends to find how many.
  • Ask: How many people have (Color A) shirts?
    Answers will vary but should match the information from the graph.
    Have children tell you the number of people in each of the other groups by reading the bar graph. Model following the line from the end of the bar down to the number. Reinforce that the numbers are the same as those on the picture graph.
  • Ask: Which is easier to read, the bar graph or the picture graph?
    Answers will vary. Point out that the picture graph is easy to read because all you need to do is count the number of pictures. Emphasize that you can read the bar graph quickly by looking at the numbers instead of counting.

    Remove all three pieces of posterboard from the board.

  • Say: Now we are going to learn how to make a bar graph. We will start by collecting data on a tally chart. Let's talk about our favorite animals. I need to know four of your favorite animals.
    Accept four responses from children and write them on the board in a tally chart. Choose a child to come up and record the tally marks for each animal. Have children raise their hands to vote for an animal.
  • Say: Now we are going to make a bar graph from this tally chart. I am going to pass out a blank bar graph so each of you can make one along with me.
    Give each child a copy of the blank bar graph. Discuss how bar graphs can be horizontal or vertical and still show the same information. Relate this to adding horizontally or vertically. Tell children that the graph they are about to make will be vertical.
  • Say: We will start the bar graph together, and then you can finish it on your own. First, we need to write in the names of the four animals. I will write them on my graph on the overhead, and you can copy them onto yours.
    Write the names of the animals on the overhead transparency of the blank bar graph.
  • Ask: Who can tell us how we will record the information on this graph?
    Children should say that for each tally mark on the chart, they will need to color in one box on the bar graph.
  • Ask: How many boxes should I color in for (Animal A)?
    Answers will vary. Color in the appropriate number of boxes on the overhead.
  • Say: Look at the number where the bar ends to check that you have colored in the correct number of boxes. You can finish coloring boxes for the last 3 animals on your own. Remember to color one box for each tally and to check the numbers to make sure you've colored the correct number of boxes.
    Circulate around the room to check children's progress and comprehension.
  • Ask: Let's look at our graphs. Which animal was chosen by the most people? (Answers will vary.) How can you tell?
    Children may say it is because that bar is the longest.
  • Ask: Which animal was chosen by the fewest people?
    (Answers will vary.) How were you able to tell?
    Children may say it is because that bar is the shortest.
  • Ask: Did any animals get the same number of votes? (Answers will vary.) How can you tell?
    Answers will vary. If some animals got the same number of votes, the bars will be the same length.

    Continue asking questions such as

    How many more votes did (Animal C) get than (Animal A)?
    Which animal got [2] votes more than (Animal B)?
    Which got fewer votes, (Animal A) or (Animal B)?
  • Ask: How are bar graphs and picture graphs alike?
    Children may suggest that they can both be made from tally charts, they both show information, they both show how many things, and they both make it easier to compare information.
  • Ask: How are bar graphs and picture graphs different?
    Bar graphs use bars and numbers to show information; picture graphs use pictures to show information. With a picture graph you need to count each time to find how many, but with a bar graph you can just look at the bars and numbers.

Wrap-Up and Assessment Hints
To check children's understanding of the different ways of representing data, have them do a simple survey. First, they should formulate a question. Then have them create a tally chart and survey ten classmates. Have children use the data in their tally chart to create a picture graph or bar graph to show the results of their survey. Children can present their graphs to the class. Allow them to ask the class two or three simple questions about their graphs.


Houghton Mifflin Math Grade 1