A Fair Snack?
A lesson by Deb Armitage
This math lesson uses the following benchmarks: Novice, Apprentice, Practitioner, and Expert (see below). The Student Samples are examples of work that falls into each category, with annotations explaining why.
Grade Level: 35
Task
I brought a large jar of animal crackers to school. Travis and Margaret asked me what they were for. I told them that each student would be allowed to take one handful of animal crackers for snack time. Travis thought this was a great idea but Margaret thought it was unfair because her hand was a lot smaller than most of the other students' hands. Travis and I then had to agree with Margaret. Conduct an investigation to determine the typical serving of animal crackers the students should have at snack time so that everyone will get their fair share.
Context
This class of fourth grade students had been working on the statistical concepts of range, mean, median, and mode.
What This Task Accomplishes
This task allows students the opportunity to apply a variety of math skills to a problemsolving situation. Not only do statistical concepts come into play, but some students may also focus on measurement concepts when deciding what is fair.
Time Required For Task
One hour
Interdisciplinary Links
This task could link to studies of consumerism. How do companies who are packaging products ensure that each product is equal to another? How can packaging mislead consumers? Is it cheaper to buy a large jar of animal crackers, or would individual boxes be less expensive? What is the typical serving in a box of animal crackers? How does it compare
to the definition of "typical" that the class came up with?
Technology Link: Spreadsheets are a great way for students to record and manipulate data as well as display their conclusions in charts and graphs.
Teaching Tips
I brought the "bear jug" of animal crackers from Costco. It's cute, and hands fit into it. Each student was given a plastic glove for sanitary purposes.
When giving the task to your students, you will want to personalize the names to students in your class. A student who had severe special needs added up 214 crackers from a list the class compiled on the board of their data. He then counted out 214 crackers, and proceeded to put them into groups for the thirteen students in the class.
Suggested Materials
animal crackers, scales, rulers, objects that could represent crackers
Possible Solutions
Solutions will vary depending on the data collected and how it is analyzed. Look for accurate and complete documentation of data, correctness of the mathematics used, and reasonable application of concepts of central tendency.
Benchmark Descriptors
Novice
The novice will demonstrate little or no math reasoning. No language will be used but a representation may be attempted.
Apprentice
The apprentice will show some work but may never state a conclusion. Computation or other math errors may be present that lead to an incorrect answer. Math language and representations may be attempted.
Practitioner
The practitioner will show all work that supports a mathematically based conclusion. Math language and representations will be used and accurate.
Expert
The expert will show a command of statistical concepts and will apply them to find a correct solution. Work will be labeled and math language will be used throughout. Data collected will be shown and organized into a mathematical representation.
Author
This task was written by Deb Armitage, K8 Mathematics Assessment Consultant at the Vermont Department of Education, and piloted by her in collaboration with teachers in Vermont.
Student Samples 
1 
2 
3 
4


