Marshmallow Peeps 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 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. Marshmallow Peeps - Page 1- Vol. 8 Winter MATH 2001
Grade Level 3 5 Note: This task was originally written for grades K 2 and published in the Volume 4, April issue of Exemplars. This task was expanded for grades 6 8 and published in our Volume 7, Spring issue. Consider using this task with its variations as a school wide assessment. Marshmallow Peeps 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 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 the pattern and write a rule to go with it. What This Task Accomplishes 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. - Page 3- Vol. 8 Winter MATH 2001
Time Required for Task 1 2 hours depending on whether students attempt the challenge. Many students think they re finished in 15 20 minutes. Interdisciplinary Links 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 and yard sticks 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 2 Packages = 49 1/2 inches 24 1/2 inches x 2 = 49 inches + 1/2 inch of space between packages - Page 4- Vol. 8 Winter MATH 2001
75 Peeps = 187 inches 75 peeps = 150 inches 74 spaces = 37 inches ANY NUMBER OF PEEPS N = Number of Peeps 2N + [(N-1)(.5)] Benchmark Rubric Novice The novice shows little or no understanding of the problem. Work is unclear. The novice uses little or no math language, and the solution lacks 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. The apprentice fails 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 measuring stick may also arrive 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 solving for multiple boxes of peeps. Practitioner The practitioner understands that the lengths of the peeps and the spaces need to be added. The solution contains some math language, although some may not be correct. The task is correctly solved, although the student does not correctly address the challenge. Work is clear, labeled, and the reader is able to understand the reasoning used. Expert The expert clearly presents his/her approach and reasoning. The expert solves the challenge and explains reasoning behind the rule. The expert student solves the problem efficiently using algebraic language and notation. - Page 5- Vol. 8 Winter MATH 2001
Author This task was originally written for grades K 2 by Meg Atkins. The 3 5 version of this task was piloted by Amy Caffry. She teaches a multi age 3 4 at the Warren Elementary School in Warren, Vermont. Amy has a Master's degree in curriculum and instruction from the University of Vermont. - Page 6- Vol. 8 Winter MATH 2001
Novice - Page 7- Vol. 8 Winter MATH 2001
Novice (cont.) Some math reasoning is incorrect. It is unclear what strategy/reasoning the student used. The solution shows inappropriate concepts and procedures used. - Page 8- Vol. 8 Winter MATH 2001
Apprentice Some parts are correct. - Page 9- Vol. 8 Winter MATH 2001
Apprentice (cont.) - Page 10- Vol. 8 Winter MATH 2001
Apprentice (cont.) - Page 11- Vol. 8 Winter MATH 2001
Apprentice (cont.) This strategy is useful, but the student does not follow through long enough to come to a full solution. There is some use of math terminology and notation. - Page 12- Vol. 8 Winter MATH 2001
Practitioner Work is labeled and easy to follow. The student addresses all parts of the assigned task. - Page 13- Vol. 8 Winter MATH 2001
Practitioner (cont.) Appropriate and accurate math representations are used. Effective math reasoning and procedures are used. - Page 14- Vol. 8 Winter MATH 2001
Practitioner (cont.) The student attempts the challenge but is unable to reach a conclusion. - Page 15- Vol. 8 Winter MATH 2001
Expert - Page 16- Vol. 8 Winter MATH 2001
Expert (cont.) The student uses an efficient strategy to lead directly to a solution. - Page 17- Vol. 8 Winter MATH 2001
Expert (cont.) - Page 18- Vol. 8 Winter MATH 2001
Expert (cont.) - Page 19- Vol. 8 Winter MATH 2001
Expert (cont.) The student makes relevant observations. The student finds and explains a rule. Explanation of the solution is clear and effective. - Page 20- Vol. 8 Winter MATH 2001
Expert (cont.) - Page 21- Vol. 8 Winter MATH 2001
Expert (cont.) - Page 22- Vol. 8 Winter MATH 2001
Expert (cont.) Accurate math representations are used. - Page 23- Vol. 8 Winter MATH 2001