## Lesson: Range and Mode Developing the Concept

Once students feel comfortable analyzing bar graphs, pictographs, and tally charts, they are ready to learn about two special numbers that summarize data. Introduce two vocabulary terms: mode and range.

Materials: one sticker for each student

Preparation: none

Prerequisite Skills and Concepts: Students should have basic counting skills and be familiar with time lengths in hours. Students should be able to interpret data.

Draw the grid for a bar graph on the board. At equal intervals, write the following categories: 0 hours, about 1 hour, about 2 hours, about 3 hours, and about 4 hours.

• Say: You know that graphs and tally charts display a lot of data. Sometimes we need to summarize that data into just a few numbers. Today we will learn about two special numbers that can help us describe data shown in a bar graph, line plot, or tally.
Write the words mode and range on the board.
• Ask: Who enjoys watching television? I'd like you to think about the amount of time you spent last night watching television. Now look at the categories shown in the graph written on the board. Decide which category best describes your television watching: 0 hours, about 1 hour, about 2 hours, about 3 hours, or about 4 hours.
As students decide their category, distribute one sticker to each child.
• Say: As you go to the board, put your sticker above the category that best describes the amount of time you spent watching television last night.
Allow 1 or 2 students at a time to place their stickers on the board. Urge students to build bars as for a bar graph. Continue until all students have placed their stickers on the board. Do not allow overlapping of the stickers.
• Ask: Wow! Look at the bar graph we made! Can you find the most popular amount of time for watching television? How can you tell?
Students should realize that the tallest bar represents the most popular amount of television watching time.
• Say: The most popular answer is called the mode. In this graph, the mode is the most popular amount of time spent watching television last night. It means that amount of time occurs more than any other time.
Have students review the word mode in relationship to the graph on the board.
• Ask: Study our graph again. What is the shortest amount of time that someone watched television? (check the graph) What is the longest amount of time that someone watched television? (check the graph)
Emphasize that at least one student must be in the category for it to count. If at least one student did not watch any television, then the shortest amount of time is 0 hours. If at least one student watched about 4 hours of television, then the longest amount of time is about 4 hours.
• Say: Now subtract those two amounts of time. Your answer is called the range. It describes the spread of time intervals from the shortest to the longest.
Have students review the word range in relationship to the graph on the board. Then redistribute the stickers in the graph.
• Ask: Suppose this new bar graph shows the results from the fourth grade. What is the mode? Is it different from our class? What is the range? How do you know?
Students should analyze the new graph and apply the meanings of the vocabulary terms.

Wrap-Up and Assessment Hints
Display a line plot that shows the number of pets in ten families. Have students find the mode and the range of the data. Remind them to subtract to find the range. Discover how they found the mode and range. Be sure to encourage students to use number sense in finding their answers as they analyze the graph.