Standards-based assessment and Instruction

## Marshmallow Peeps All In a Row

Marshmallow Peeps come 10 in a package. Each Peep is 2 inches long.

How long will one package of Peeps be if each Peep is lined up in a row with 1/2 inch between them? How long would 2 packages of peeps be if each Peep is lined up in a row with 1/2 inch between them? How long will 75 individual Peeps be if they are lined up in a row with 1/2 inch between them?

Challenge (optional) - Can you write a rule to determine how long any number of Peeps would be lined up in a row with 1/2 inch between them?

Remember to show all your work, use math representation and as much math language as you can.

### Context

Throughout our school all children use the Everyday Mathematics program. Much of the ongoing work in this series focuses on patterns and developing rules. I was interested to see how well my students could detect a pattern and write a rule to go with it.

This task allows the teacher to see how well students can extend patterns, discover and express general rules, and add basic fractions. This task can be solved concretely, pictorially and abstractly - making it easily accessible to all students.

1-2 hours depending on whether students attempt the challenge. Many students think they're finished in 15-20 minutes.

This task, with slight adaptations is easily linked to other curriculum areas. Although I did this task when it was close to Easter, we do not specifically teach about Easter. For my students, food, especially special treats, has always been a great motivator. If you want to stick with the food theme, anything is possible. Otherwise it could be linked to science or social studies by changing the peeps to trees, plants, canoes, trains, cars...anything!

### Teaching Tips

As I said above, food is a great motivator - if you use food in your task, have some available for the students!

To make the task even more accessible to students, I would recommend adding in a few more numbers between zero and two boxes of Peeps; many of my students just figured out the answer for one box of peeps and then doubled it from there. This strategy doesn't work due to the space needed after peep number 10.

### Suggested Materials

Peep and space manipulatives (such as beans, tiles, etc.) graph paper, rulers, yard sticks and calculators.

### Possible Solutions

1 PACKAGE = 24 1/2 inches
10 peeps x 2 inches = 20 inches
9 spaces x 1/2 inch = 4 1/2 inches

Total = 66.4 centimeters

2 PACKAGES = 49 1/2 inches
24 1/2 inches x 2 = 49 inches + 1/2 inch of space between packages

75 PEEPS = 187 inches
75 peeps = 150 inches
74 spaces = 37 inches

ANY NUMBER OF PEEPS
N = Number of Peeps
2N + [(N-1)(.5)]

Click on a level for student example.
Novice The Novice will show little or no understanding of the problem. Work will be unclear and the student may confuse metric and standard units of measure. Little or no math language will be used and the solution will lack correct reasoning.
Apprentice The Apprentice will attempt both parts of the problem, the length of the peeps and the length of the spaces between them. However, a correct answer will not be found for a variety of reasons, such as:
• Some students might incorrectly assume that there will be 10 spaces if there are 10 peeps.
• Some students who use a meter stick may also arrive at an incorrect solution, as the method may not be precise enough.
Individuals that attempt to create a scale drawing may get bogged down by constraints of the paper length. Others may 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. The primary task will be solved correctly and appropriate math language will be used. Work will be clear and labeled. The reader will be able to understand the reasoning used.
Expert The Expert clearly presents his/her approach and reasoning. The main task and the 'Challenge' will be correctly solved, and the reasoning behind the rule will be explained. The Expert will solve the problem efficiently using algebraic language and notation.

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