## The Celebrated Jumping Frog

• Lesson
• 1
• 2
6-8
1

Using the story "The Celebrated Jumping Frog of Calveras County" by Mark Twain, students simulate a jumping-frog contest and determine the distances "jumped." The students record the distance of individual jumps in centimeters and determine the total distance jumped (the sum of the three separate jumps) and the official distance (the straight-line distance from the starting line to the end of the frog's third jump). The students compare the range and median of the total distances with those of the official distances of the group.

Read The Celebrated Jumping Frog to the students.

Distribute a cotton ball to each student. This cotton ball will be each student's "frog." Distribute the The Celebrated Jumping Frog Activity Sheet to each student.

Demonstrate how to place the frog on a large paper clip that has been slightly spread apart, and make it "jump." By placing the frog on the smaller end and pushing down on the elevated large end, the player can usually make the frog hop over her or his finger. Also demonstrate how to record the distances in centimeters on the activity sheet.

Allow the students to practice jumping their frog a few times. Then, divide the students into small groups and show them how to set up a track with a starting line and a course for the official distance.

Guide the students as they work in small groups to simulate the frog jump and record the data on their chart. The "Total Distance" is the sum of the three jumps, but the "Official Distance" is the straight-line distance from the starting line to the position of the last jump.

Discuss the variations from the median of the group for each player and compare the medians and ranges for the total distance with those for the official distance.

### References

• Silverman, Helene. "IDEAS: Games, Measurement, and Statistics." The Arithmetic Teacher. April, 1990, pp. 27 - 32.
• Twain, Mark. "The Celebrated Jumping Frog of Calaveras County." The Celebrated Jumping Frog of Calaveras County and Other Sketches. New York: C.H. Webb, 1987.

Extensions

1. Collect the data for each group. Determine a class median and range for both the total distances and the official distances. Guide the students as they compare the data for their group with the data for the class.
2. Help the students to set up contests and simulations of their own.
3. Move on to the next lesson, Spinning Tops.

Questions for Students

Could the Total Distance ever equal the Official Distance?

[Yes, it's possible, but unlikely. To be equal, the three jumps would have to occur in a straight line.]

### Spinning Tops

6-8
Students measure distances using standard and nonstandard units and record their measurement in various tables. Then they are asked to use descriptive statistics to report the results. During a top-spinning contest, students measure the distance along a curve using indirect measurement. They record the data for their group in a chart, and compute their individual median and the group median.

### Learning Objectives

Students will be able to:

• Measure distances jumped in a simulated jumping-frog contest.
• Record data.
• Determine median and range of the obtained data.

### NCTM Standards and Expectations

• Use common benchmarks to select appropriate methods for estimating measurements.
• Find, use, and interpret measures of center and spread, including mean and interquartile range.

### Common Core State Standards – Mathematics

Grade 6, Stats & Probability

• CCSS.Math.Content.6.SP.A.3
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.