Math Background

Lesson: Graphing Data
Introducing the Concept

Your children have experience in gathering data through class surveys. They will now expand this skill to learn to collect and compare data in tables and pictographs.

Materials: 2 pieces of chart paper, 2 large pieces of posterboard for pictographs, one blank circle outline for each child, crayons

Preparation: On each piece of chart paper, make a blank tally chart with four rows and two columns. On each piece of posterboard, draw a blank pictograph with four equal-sized rows and two columns. For each child provide a cut-out circle that will fit on a row of the pictograph.

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

  • Ask: Today we are going to compare the hair color of the boys and the girls in our class. What color hair do the children in this class have?
    Responses will vary and may include black, blond, red, and brown. Select 4 children with different-colored hair.
  • Say: Here are the four categories we will use to sort the entire class.
    Say each child's name and the hair color that that child represents. Write the name of each color group on the board and have the appropriate child stand in front of it.
  • Say: You have one minute to look at each person's hair. Decide who has hair closest in color to yours. Then sit down and remember which group you belong to.
    Give children time to select their group. Then have them raise their hands by gender to show to which group they belong. (For example, say Raise your hand if you are a girl with brown hair, and so on.)
  • Ask: How many more boys than girls have (Color A) hair?
    Lead the children to see that they will need to raise their hands again to find the answer.
  • Ask: I want to ask you several questions like this. How can you find the answers without having to raise your hands over and over?
    Elicit that you could write down the number of boys and girls in each group.
  • Say: We can organize our information and show the number of boys and girls in each group by making two tally charts. For each girl or boy in a group, we'll make one tally. (Draw a tally on the board.)
    Tape the blank tally charts on the board. Label one chart Girls' Hair Color and the other Boys' Hair Color. Write the four colors in the left column of each chart. Then have the children raise their hands by gender to show to which gender group they belong. Make a tally mark for each child.
Girls' Hair Color 
Hair Color  Tally Marks  Number 
     
     
     
     

 

Boys' Hair Color 
Hair Color  Tally Marks  Number 
     
     
     
     
  • Ask: 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 that they can see how five is shown with tally marks.
  • Say: 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.
    Ask the children how many are in each group to ensure that they understand how to count the tallies.
  • Ask: How many more boys than girls have (Color A) hair?
    (Answers will vary.) Ask children several questions comparing the data in the two tables. Questions may include
How many boys/girls are there in all?
How many children have (Color B) hair?
How many boys/girls have (Color C) hair?
How many more girls than boys have (Color D) hair?

  • Ask: I have another way that we can show this information. It's called a pictograph. What do you think a pictograph uses to show information?
    Elicit that pictographs use pictures to show how many are in each group.
Boys' Hair Color
Hair Color
Black  
Blond  
Red  
Brown  

Each circle icon stands for 1 person.

Girls' Hair Color
Hair Color
Black  
Blond  
Red  
Brown  

Each circle icon stands for 1 person.

  • Say: These are pictographs. Each one of you will color a circle the same color as your hair and then place it in the correct row.
    Remove the tally charts and tape the posterboard pictographs to the board. Label one graph Girls' Hair Color and the other Boys' Hair Color. Write the name of each color in the left column of each graph. Give each child a blank circle and review the colors to use for each group.

    Allow the children time to color. Then call each group up one at a time and have each group tape its circles to the appropriate row on the appropriate graph, according to gender. Set aside the Boys' graph so that the children are all looking at the Girls' graph.

  • Ask: How can we find the number of girls in each color group by using the pictograph?
    Children may say that since each circle stands for one girl they could count the number of circles in a row to find the number of girls in that group.
  • Ask: Which group has the most? (Answers will vary.) How can you tell which one has the most?
    Children may recognize that the row with the most circles represents the most girls.
  • Ask: Which group has the least? (Answers will vary.) How can you tell which one has the least?
    Children may recognize that the row with the fewest circles represents the least number of girls. Ask children several questions comparing different groups. Questions may include
    How many girls have (Color B) hair?
    Do more girls have (Color A) or (Color C) hair?
    How many girls have either (Color D) or (Color C) hair?

    Remove half the circles from the Boys' chart. If there is an odd number, include the teacher in the survey. At the bottom of the chart, write the key: “Each (tape up a blank circle) stands for 2 people.”

  • Ask: How many girls does each circle stand for on this pictograph? (Point to the Girls' graph.)
    The children may say that one picture stands for one girl. Write a key at the bottom of the Girls' graph that says, “Each [circle symbol] stands for 1 person.”
  • Say: This is called a key. The key tells you how many each picture stands for. When you read a pictograph, always start with the key.
    Remove the Girls' graph. Put the Boys' graph back up on the board.
  • Say: In the Girls' pictograph, one picture stood for one person. Look at the graph for the boys. I have changed it a little. Let's read the key together.
    Have the class read the key aloud.
  • Ask: How can we find the number of boys in each group?
    Elicit that we can count by twos to find the number in each group.
  • Ask: Which group has the most? (Answers will vary.) Do you have to count the pictures to tell which one has the most?
    Children may say that they need to find the row with the most pictures to find the group with the most.
  • Ask: Which group has the least? (Answers will vary.) Do you have to count the pictures to tell which one has the least?
    Children may say that they just need to find the row with the fewest pictures to find the group with the least.

    Ask the children several questions comparing different groups. Questions should be similar to those asked about the Girls' graph.


Houghton Mifflin Math Grade 2