Math Background

Lesson: Range and Mode
Introducing the Concept

Last year, students represented and compared data using tally marks. This year, have students focus on making connections between tally marks and visual representations of the data.

Materials: pictograph, tally chart, vertical bar graph, and horizontal bar graph showing the number of students with birthdays in each month of the year

Preparation: Draw the pictograph, tally chart, and bar graphs on a transparency for the overhead projector, or draw them on the board.

Prerequisite Skills and Concepts: Students should have basic counting skills. Students should be able to organize and interpret data.

Display the tally chart, pictograph, and bar graphs for all students to see.

  • Ask: Look at these displays. There is a tally chart, a pictograph, and two bar graphs. What information is displayed?
    Students should realize that the same information is shown on all three displays. Each display shows the number of students who have birthdays in each month of the year.
  • Ask: In which month is your birthday?
    Have several volunteers tell the class in which category they have been counted. Give volunteers time to explain their reasoning.
  • Ask: How many students have birthdays in April? Which display shows the answer best?
    Have volunteers explain their answers. Students should realize that the answer can be found in all displays, either by counting the tallies or by reading the corresponding scale of the graphs. For more reinforcement, repeat the question using different months.
  • Ask: Which month has the least number of birthdays? Which month has the greatest number of birthdays? How do you know?
    Have volunteers explain their answers. Students should realize that the answer can be found in all displays. Emphasize that the heights or lengths of the bars in the bar graphs help to decide the answers, while the number of tallies in the tally chart and line plot gives the same information.
  • Ask: How many more students have birthdays in March than in November? What operation did you use to find the answer?
    Lead students in a step-by-step development of the answer. First, find the number of students having birthdays in March. Second, find the number of students having birthdays in November. Third, subtract the two numbers to find the answer.
  • Ask: How many birthdays are in the first three months of the year? How do you know?
    Have a volunteer explain the steps needed to find the answer. First, find the number of birthdays in January. Second, find the number of birthdays in February. Third, find the number of birthdays in March. Fourth, add the three numbers for the answer.
  • Ask: Are there two or more months that have the same number of birthdays? If so, name the months.
    Have volunteers point out quick ways to find the answer, such as comparing the heights or lengths of the bars in the bar graph.

Houghton Mifflin Math Grade 3