Math Background

Lesson: Graphing Data
Developing the Concept

Your children have learned how to create tally charts, compare data in tables and charts, and read pictographs. They will now learn to read and create bar graphs and to find range and mode.

Materials: The chart-paper “Girl's Hair Color” tally chart and both posterboard pictographs from the Introducing the Concept lesson; 2 versions of a bar graph showing the boys' hair-color data from the previous lesson, one with a scale of 1, the other with a scale of 2; a blank overhead transparency of Learning Tool 10 from the Learning Tools Folder; one copy of Learning Tool 10 for each child; crayons

Preparation: Make 2 transparency copies of Learning Tool 10, the Horizontal Bar Graph, and one copy for each child. Leave one transparency blank. Create a bar graph on the other, with the data from the Boys' Hair Color survey. Rewrite the numbers on another copy of Learning Tool 10 (give it a scale of 2) and make a transparency. Create a bar graph with the data from the Boys' Hair Color survey.

Prerequisite Skills and Concepts: Children should know how to collect data on a tally chart, how to compare data in tables and charts, and how to read a pictograph.

  • Ask: Last time we learned how to collect information on a tally chart. Who can tell how we displayed this data?
    Children may say with a pictograph. Tape the Boys' Hair Color pictograph to the board. Read the key and review what each picture stands for.
  • Ask: Today we are going to learn about another kind of graph called a bar graph. A bar graph is like a pictograph, because it shows how many are in each group. The difference between a pictograph and a bar graph is how the information is shown. If a pictograph uses pictures to show how many, what do you think a bar graph uses to show how many?
    Help children realize that bars are used to show how many. Put the Boys' Hair Color bar graph with a scale of one on the overhead.
  • Ask: How did we find the number in each group on the Boys' and Girls' pictographs?
    Children may say that they counted the number of pictures in each group, either by ones or twos, depending upon the key.
  • Say: If we want to find how many are in a group by using a bar graph, we can either count the number of colored boxes for that group or look at the numbers at the bottom of the graph. Let's count the boxes for (Color C) together.
    Point to each box in the row for hair color C as the children count aloud.
  • Ask: Follow my finger down the line. What number is shown here? What do you notice about the number below the end of the bar for (Color C)?
    Children may 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. How many people have (Color A) hair?
    Answers will vary, but the answer should match the information from the graph.

    Have the 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 on the pictograph.

  • Ask: Which is easier to read, the bar graph or the pictograph?
    Answers will vary. Point out that the pictograph 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. Tell children that bar graphs can be horizontal or vertical and still show the same information. Relate this to adding horizontally or vertically.
  • Ask: How many does each box on this bar graph stand for?
    The children may say “one.” Replace the current overhead transparency with the Boy's Hair Color bar graph with a scale of two.
  • Ask: Now look at this bar graph. It shows the same information as the last one. What is different about this graph?
    Elicit that the bars are shorter and that you count the numbers by twos instead of by ones.
  • Ask: So how many does each box stand for on this graph?
    The children should say “two.”
  • Say: This bar graph shows the same information as the last one—you just count by twos instead of by ones.
    Have children find the number in each group on the new bar graph to confirm that the data are the same on both graphs.
  • Say: Now we are going to learn how to make a bar graph. We will make the graph to show the data we collected about the girls' hair color.
    Remove the bar graph from the overhead and replace it with the blank copy of learning Tool 10. Tape the Girls' Hair Color tally chart onto the board. Give each child a blank copy of Learning Tool 10.
  • Say: We will start the bar graph together, and then you will finish it on your own. First, we need to write in the four hair colors. I will write them on my graph, and you can copy them onto yours.
    Write the names of each hair color on the overhead transparency of Learning Tool 10.
  • Ask: We are going to make a graph where each box stands for one person. So how will we put the information in this graph?
    Children may say that for each tally mark on the chart, they will need to color in one box on the graph.
  • Ask: How many boxes should I color in for (Color A)?
    (Answers will vary.) Color in the appropriate number of boxes on the overhead.
  • Say: Look at the number below the bar to check that you have colored in the correct number of boxes. You can finish the last three hair colors on your own. Remember to color one box for each tally and to check with the numbers below to make sure you've colored the right number of boxes.
    Circulate around the room to check children's progress and comprehension.
  • Ask: Let's look at our graphs. Which hair color do most girls have? (Answers will vary.) How can you tell?
    Children should say because that bar is the longest.
  • Say: This is the mode of the data. The mode of any set of data is the category with the greatest number.
  • Ask: Which hair color do the fewest girls have?
    (Answers will vary.) How were you able to tell this? Children should say because that bar is the shortest.
  • Ask: What is the difference between the hair color that the greatest number of girls have and the hair color that the least number of girls have? (Point to the appropriate rows on the chart.)
    Answers will vary.
  • Say: This number is the range. The range of any set of data is the difference between the category with the greatest number and the category with the least number. Let's find the range and mode of the data for the boys.
    Put either of the Boys' bar graphs back on the overhead and find the range and mode.
  • Ask: Last time we learned about pictographs, and this time we learned about bar graphs. How are bar graphs and pictographs alike?
    Children may suggest that they can both be made from tally charts, they both show data, they both show the number of things, and they both make it easier to compare information.
  • Ask: How are bar graphs and pictographs different?
    Bar graphs use bars and numbers to show information, and pictographs use pictures to show information. With a pictograph you need to count each time to find how many, but with a bar graph you can just look at the number.

Wrap-Up and Assessment Hints
To check children's understanding of the different forms of data representation, have them think of a simple survey question. Then have them create a tally chart and survey ten classmates. From their tally chart, have the children create a bar graph to show the results of their survey. Have children present their graph to the class, explaining the range and mode of their data. Allow them to ask the class two or three simple questions about their graphs.


Houghton Mifflin Math Grade 2