## Jumping Jack Math

• Lesson
3-5
2

In this lesson, students prepare jumping jack data to send to officials on the planet Jumpalot. Students record how many jumping jacks they can do in ten seconds and use their knowledge of time conversions to figure out how many jumping jacks they could complete in a minute all the way to a year if they never tired. Students then organize class data and explore mean, median, and mode and the effects extreme values have on these measures. Students then brainstorm the advantages and disadvantages each measure offers.

Pass out the Jumping Jack Math and Jumpalot Data activity sheets. Read the introductory paragraph to students and explain that students will be developing a jumping jack data set which they will use to discuss mean, median, and mode. Students should be familiar with or have at least been introduced to mean, median, and mode before beginning this activity to get the most out of this lesson.

 Jumping Jack Math Activity Sheet Jumpalot Data Activity Sheet

Read the introduction of the Jumping Jack Math activity sheet and have students complete the time conversion chart in Question 1. Next, students should complete Question 2. Explain that students need to count how many jumping jacks they can complete in 10 seconds, and then write that number in the first row of their chart. An easy way to organize this is to have every other student stand up in the room and spread out. If your room is particularly small you could have every third or fourth student stand up at a time. Have the students sitting help count for the students jumping so everyone is engaged. Tell students that you will be the official timer, and then using a timer or a clock with a second hand, tell students, "Go!" and then "Stop!" when the time is up. Continue until all students have collected their data.

Next, have students pair up; you may want to encourage students with similar numbers to work together Students who have completed the same number of jumping jacks will have identical charts for Question 2. Have students complete Question 2 together. You may either allow students to use calculators the entire time, or have students complete the chart using paper and pencil and then allow them to check their answers with a calculator. The chart goes up to one year is to give students experience with very large numbers and to help develop number sense.

During this time, circulate and have students explain the math behind the time conversions when you come to them. Some students may want to multiply by ten to get from ten seconds to a minute, instead of multiplying by six, which would make the rest of their data chart incorrect.

Groups who finish Question 2 should move on to Questions 3 and 4 after checking with the teacher. Encourage students who find they have a vastly different number from the other students at the hour mark to go back and check their work. Many students will correct themselves when they are collecting data in Question 3 from classmates, but you may have to point it out for some students.

After students have completed Questions 3 and 4, bring the group together and have students share their answers to Question 4. Ask students:

Why do you all seem to have different values for the mean, median, and mode?

[Because everyone used data sets with information from ten different people, rather than the whole class]

Next, explain Questions 5–8 and have students go back to their partner or group to work on completing Questions 5 through 8.

After students have completed Questions 7 and 8 bring the students together to discuss their answers. Students should say that Jumpalot School District should admit Speedy because his jumping jack value increases the value of the mean which would mean more energy production for the school. For Question 8, students should find that the extreme values affect the mean with an extremely low value making the mean lower and an extremely high value making the mean higher, but have little effect on the median or mode.

Summary Activity

Have students brainstorm the best times to use mean, median, or mode. To complete this, you have a few options:

• Students can complete it with the partner or group they are working with then you can have a class discussion
• You could break the class into groups and give each group a different measure to focus on. Then you could have each group write their results on a poster to share with the class. You could have a class discussion about them in which you wrote student responses on the board, interactive whiteboard, or overhead.

Assessments

1. Have students develop their own survey question that has a numerical response. For example, "How many minutes of homework do you do a night?" or "How many minutes does it take you to get to school in the morning?" Have students go around the room and collect data from at least eight students. Have students organize the data from least to greatest, and then find the mean, median, and mode. Have students create a small poster that contains their question, their organized data and their calculations for mean, median, and mode. Have students present their findings to the class.
2. Have students time another activity, such as Every Beat of Your Heart or Every Breath You Take, to use for data for a comparison of mean, median, and mode.
3. Give students a set of data and have them calculate the mean, median, and mode. Allow students to check their answers for mean and median using the Mean and Median tool. To use this tool numbers must be between 0 and 100.
4.  To Mean and Median Tool

Extensions

1. Have students complete the To Jumpalot and Beyond activity sheet. Students predict results and develop a plan to test out other activities that officials in Jumpalot could use to gain power.
2.  To Jumpalot and Beyond Activity Sheet
3. Have students research how mean, median, and mode are used in the real world.

Questions for Students

1. Why would it be useful to know both the median and the mean for a set of data?

[It gives you more information about the data set and helps you know if there are any extreme values in the data set.]

2. Why is it useful to know the mode of a set of data?

[To see which number is most popular or most frequent; to see what the majority of responses are]

Teacher Reflection

• Were the concepts of central tendency presented too abstractly? How could you change them?
• Did you find it necessary to make adjustments while teaching the lesson? If so, what adjustments and were they effective?
• Was your lesson developmentally appropriate? If so, how could you tell? If not, what was inappropriate? What would you do to change it?

### Learning Objectives

Students will:

• Use student-created data to calculate mean, median, and mode
• Practice time conversion (seconds, minutes, hours, days, weeks, year)
• Develop number sense
• Discover the effects of extreme values on the mean
• Analyze the advantages and disadvantages of using mean, median, and mode

### Common Core State Standards – Practice

• CCSS.Math.Practice.MP1
Make sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP4
Model with mathematics.
• CCSS.Math.Practice.MP5
Use appropriate tools strategically.
• CCSS.Math.Practice.MP7
Look for and make use of structure.