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.
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
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
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.
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.
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]
- 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?