## Pitching Cards

• Lesson
3-5
1

Students measure distances using standard and nonstandard units and record their measurement in various tables. Then use descriptive statistics to report the results. In this lesson, students play a game in which they pitch cards and measure the distances traveled.

Give each student a set of five unlined index cards and crayons. Ask them to draw a picture of themselves on the front and to write data about themselves on the back, such as age, grade, and hobbies.

Demonstrate how to pitch the cards from a set distance to the wall, as well as how to measure distances with a meter stick.

Divide the students into small groups. Distribute a copy of the Pitching Cards Activity Sheet to each student.

Guide the students as they take five turns each, recording the distance from the wall to each card pitched. Remind students to try to use the same force when pitching each card, so the results of their experiments will be more accurate. Students should record their data on the table on the Pitching Cards Activity Sheet.

Ask the students to order their distance data from least to greatest.

Demonstrate how to determine the median, or middle, score. Ask students what would happen to the median if we had ordered the data from greatest to least, instead of least to greatest. Students should respond that the median will not change.

Ask students how they will find the range. Students should respond that they can subtract the smallest data value from the largest data value to find the range.

Discuss the completed activity sheets. Ask students to make observations about their tables in question #1. You may wish to pose questions such as:

• Did any of your data values repeat? (For example, did 5 cm appear in your table more than once?)
• Was all of your data close together, or was it spread out?
• Other than a table, what's another way you could record your data? (Students may suggest conducting more trials and then creating a graph to display the data.

If there is enough time, you may wish to ask students to conduct more trials to obtain more data. Depending upon their experiences with graphing data, you may wish to ask students to go to the Box Plotter Tool.

Using this tool, students can enter their data and create a box plot of the data collected in this lesson.

### References

• Silverman, Helene. "IDEAS: Games, Measurement, and Statistics." The Arithmetic Teacher. April, 1990, pp. 27 - 32.
• Hindman, Darwin A. Kick the Can and Over 800 Other Active Games and Sports for All Ages. Englewood Cliffs, N.J.: Prentice-Hall, 1956.

Extensions

1. Help the students to order the medians for the group and to determine the median of the medians and the range for the group. Compare individual scores to the group's median and range, emphasizing the amount of variation.
2. Display the pitching cards, the personal data, and the pitching data. Compare these data to the data on the traditional baseball cards.

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### Learning Objectives

Students will:

• Measure distances in centimeters.
• Record data in a table.
• Order data and determine median and range.

### NCTM Standards and Expectations

• Collect data using observations, surveys, and experiments.
• Use measures of center, focusing on the median, and understand what each does and does not indicate about the data set.
• Select and apply appropriate standard units and tools to measure length, area, volume, weight, time,