Leap frogs tend toward the center?

Students learn the meanings of the central tendency concepts range, mean, median, and mode. They will make origami frogs, jump them across a track and record the length of their jumps and the total number of jumps across trials.

A lesson plan for grade 6 Mathematics

By Erin Foerster

Learn more

• Shodor Foundation Mean, median, and mode discussion
• Plop It! Activity from Shodor
• Origami Frog lesson plan This lesson plan from the SEQual project contains instructions for crafting an origami frog
• MEASURES tool Another activity from Shodor

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Related topics

• Learn more about arithmetic and mathematics.

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Learning outcomes

Students will:

1. identify that the mean for a set of data will increase if a new piece of data that is larger than the original mean is added. Conversely, they will identify that the mean for a set of data will decrease if a new piece of data, that is lower than the original mean, is added.
2. practice calculating mean, medians, and modes. In doing so, they will see that the mean, median, and mode are not always the same.
3. conduct an experiment, collect data, and calulate the mean, median, and mode for that data.
4. be challenged to make new hypotheses, based on the information they have found while conducting their frog-jumping experiment.
5. cooperate with one another as they work through their activity. They will share jobs and learn from one anothers’ strengths and weaknesses.

Teacher planning

Time required for lesson

4 class periods

Materials/resources

• Origami frog pattern and 3&times5 cards. Refer to this Origami Frogs lesson plan from the SEQual Project and scroll down to the materials section.
• Masking tape. Needed to mark the jumping course on the floor for the frogs.
• Trial Data Recording Chart.
• Final Data Recording Chart .
• Pencils.

Technology resources

• A web browser, such as Firefox, Internet Explorer, etc.
• A computer lab, or at least a one-computer classroom with an LCD projector, in order to project the screen of the one computer onto a screen in the classroom.
• A basic calculator.
• An overhead projector.

Pre-activities

• Review with the students how to record data, specifically, how to measure using their centimeter rulers and how to set up a data chart for recording the data. Each group can have their own data chart. Make sure you circle the room and check their charts before they begin recording.
• Students must be able to add, subtract, multiply, and divide whole numbers, decimals, and fractions.
• Students should be familiar with the basic functions on their calculators (adding, subtracting, multiplying, dividing).

Activities

Steps 1–6 should take the class about two forty-five minute class periods.

1. Begin class by reviewing mean, median, or mode. Refer to the Shodor Foundation Mean, Median, and Mode discussion at the following website: http://www.shodor.org/interactivate/discussions/MeanMedianAndMode/.
2. After a brief discussion, work a simple example by collecting the shoe sizes of all the students in your class. Round shoe sizes to the nearest whole number. For example, 9.5 will become a size 10. Use this data to first calculate the mean. The students should use their calculators. Do not simply give the students the answer, solicit their involvement and interaction.
3. Next find the median and the mode. Discuss the differences and similarities between these three measures of central tendency. Make sure the students are also aware of the range of the data.
4. Now, use an LCD projector to project the Plop It! activity from the Shodor website onto a screen in the classroom. (If you have access to a computer lab, go there and do the same thing and have the students follow along. If not, simply demostrate this to the students.)
5. Explain the general premise of this resource. Enter the shoe sizes into the Plop It! template. This resource will automatically calculate the mean, median, and mode. Once all the data has been entered, ask the students what might happen to the mean, median, and mode if extra data points, both above and below these original measures, are entered. Get their conjectures and then make the changes, using the resource.
6. Call up students and let them try their hand at the resource as well, unless each student already has their own computer.

Steps 7–14 should take the class another two forty-five minute class periods.

7. Before students come into the classroom, divide the class into groups of 3–4 and put their groups on the board. Instruct the students, as they come in, to get into their groups and to go to their designated spot in the classroom.
8. Give each group two pieces of masking tape and a yard stick. They are to place one piece of tape on the floor at one end of the stick, and the other piece of tape at the other end of the stick. They have now marked the course that their frogs will eventually jump.
9. Now give each group one 3×5 card and the instructions on how to make the origami frog. MAKE SURE you go through the instructions with the students, using an overhead projector to help. You can find the pattern for an origami frog at this Origami Frogs lesson plan from the SEQual project. Scroll down to the materials section.
10. Before the student groups begin to jump their frogs, have them WRITE DOWN two hypotheses. The first should be about what they think the average length of a frog jump will be. The second should be about how many jumps, on average, a frog will take to reach the finish line.
11. The students are now ready to begin jumping their frogs. They will do five trials. The students can take turns doing different jobs for each trial:
    • Job 1: Jump the frog.
    • Job 2: Measure the length of the jump.
    • Job 3: Record the length of the jump in centimeters.
    • Job 4: Record the number of jumps the frog takes to get from the starting line to the finish line.

    All of the recorded information should be put into data sheets that are similar to the ones attached at the bottom of this lesson plan.

12. Once they have completed their five trials, they should calculate the average length of each jump across all the trials. Then, they should calculate the average number of jumps the frogs took to get to the finish line.
13. Ask the students if there is a relationship between the average length of frog jumps and the average number of jumps it took the frog to reach the finish line. Have them compare their results with those of other groups.
14. Continue the discussion by asking the students how their results might be different if they had a different-sized frog, or of the course was longer, or of different paper was used. Have the students write down their hypotheses and if there is time, let them test their hypotheses.

Note: To take this activity a little farther, you may also want to enter some of the frog jumping data into the MEASURES tool, which is also found on the Shodor website. Click on the HOW button in order to learn how to effectively use this resource.

Assessment

Student groups will turn in their trial data collection sheets and their final data collection chart.

Check that both of the data collection sheets are filled in accurately and legibly. There should also be evidence of job-sharing (i.e. the handwriting should not all be the same). Use the following rubric to grade these sheets:

4 — sheets are clear and legible, evidence of job-sharing, calculations are correct

3 — sheets are mostly clear and legible, some evidence of job-sharing, most of the calculations are correct

2 — sheets are messy, little job-sharing evidence, few calculations are correct

1 — sheets are mostly blank and unclear, no job-sharing evident, calculations are not correct or missing