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Marshmallow Peeps All In a Row

Marshmallow Peeps come 10 in a package.
Each peep is 5.2 centimeters long.
How long will 1 package of peeps be if each peep is lined up in a row with 1.6 centimeters between them?
How long would 2 packages of peeps be if each peep is lined up in a row with 1.6 centimeters between them?
How long would 3 packages of peeps be if each peep is lined up in a row with 1.6 centimeters between them?
How long will 75 peeps be if they are lined up in a row with 1.6 centimeters between them?
Can you write a rule to determine how long any number of peeps would be lined up in a row with 1.6 centimeters between them?
Show all your work. Make a math representation and use as much math language as you can.

Context

This task was originally written for students in grades K-2 as seen below. I was curious to see how sixth graders would handle a similar problem.

Marshmallow Peeps come 10 in a package.
Each peep is 2 inches long.
How long will 1 package of peeps be if they are lined up in a row with 1/2 inch between them?

What this task accomplishes

This task allows the teacher to assess the degree to which students can manipulate decimals, as well as use pattern and function concepts to achieve a general rule for solving for any number of peeps. The task can be solved concretely as well as abstractly, making it easily accessible to all students.

Time required for task

One 45 minute class period.

Interdisciplinary links

This task could link to other Easter activities you have going on in your classroom, or the items in the task could be adapted to fit another theme you are studying. For instance, if you were studying trees, you could write a similar task substituting maple leaves for peeps.

Teaching Tips

This task can be made less complicated by using the 3-5 version stated above. Students with algebra experience can apply their skills to create a formula for solving the task. My students were told that when they handed the task in, they could have a marshmallow peep which motivated them all to turn the task in on time!

Suggested Materials

Manipulatives that can serve as peeps, rulers, calculators and peeps to eat!

Possible Solutions

1 PACKAGE
10 peeps x 5.2 cm = 52 centimeters.
Spaces in between 9 spaces x 1.6 centimeters = 14.4 centimeters

Total = 66.4 centimeters

2 PACKAGES
20 peeps x 5.2 cm = 104 centimeters.
Spaces in between 19 spaces x 1.6 centimeters = 30.4 centimeters

Total = 134.4 centimeters

3 PACKAGES
30 peeps x 5.2 cm = 156 centimeters.
Spaces in between 19 spaces x 1.6 centimeters = 46.4 centimeters

Total = 202.4 centimeters

75 PEEPS
75 peeps x 5.2 = 390 centimeters
74 spaces x 1.6 centimeters = 118.4 centimeters

Total = 508.4 centimeters or 50.84 meters

ANY NUMBER OF PEEPS
N = Number of Peeps
5.2N + [(N-1)(1.6)

Task Specific Rubric/Benchmark Descriptors Click on a level for student example.
Novice	The novice will show little or no understanding of the problem. Work will be unclear. The student may confuse metric and standard units of measure. The novice will use little or no math language, and the solution will lack correct reasoning.
Apprentice	The apprentice will attempt to deal with both parts of the problem, the length of the peeps and the length of the spaces between them. However, the apprentice will fail to arrive at a correct answer for a variety of reasons: Some might incorrectly assume that there will be 10 spaces if there are 10 peeps. Some who use a meter stick may also arrived at an incorrect solution, as the method may not be precise enough. Those who attempt to create a scale drawing may get bogged down by constraints of the paper length. Others miscalculate because they use an incorrect strategy for finding for multiple boxes of peeps.
Practitioner	The practitioner will understand that the lengths of the peeps and distances between them need to be added. They will correctly calculate the solution by doing this and using their drawings of the problem. The practitioner will use math language, but it may lack sophistication. The drawings will be labeled, and the reader will be able to follow the student's correct reasoning. The practitioner will be able to write the steps used as a "rule" for solving the task.
Expert	The expert will fully understand the problem by representing the problem visually and by clearly calculating the solution efficiently. The approach and reasoning will be presented clearly, and the student will be able to write a rule for solving the task. The expert will explain the reasoning behind the rule.

Author

Carol McNair teaches 6th grade at the Camels Hump Middle School in Richmond, Vermont. She has a master's degree in curriculum and instruction from the University of Vermont. She has worked as a mathematics consultant to the Vermont Department of Education, and is an editor for Exemplars.