Pieces of Pizza
Task
Make 3 pizzas, 1 with 4 slices, 1 with 6 slices, and 1 with 8 slices. If I have 6 friends over, how many slices will each get?
Do you think everyone got a fair share of pizza?
Alternate Versions of Task
| More Accessible Version:
Using a big bowl of pizza dough, I made 1 pizza with 4 slices, and 1 pizza with 6 slices. If 10 of us each get a slice of pizza, will everyone get a fair share?
More Challenging Version:
Using a big bowl of pizza dough, I made a small pizza with 4 slices, a medium pizza with 6 slices and a large pizza with 8 slices. If I have 6 friends over, how many slices will each of my friends get?
Do you think everyone got a fair share of pizza? If not, what would be the fairest way to share the pizza?
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Context
We are investigating fractions and learning how to problem-solve cutting circles into equal parts. This problem allows students to investigate division and fractions. It shows students' understanding of number sense. It introduces an element of ethics if students address how fair shares might be meted out.
What This Task Accomplishes
This task asks students to find a total and divide among a group. It offers a concrete example of addition, division and fractions. They are also asked to think about the issue of fair sharing. What the Student Will Do
Students cut out the three pizzas of different numbers of slices represented by different colored paper. Most students then allocated the pieces by giving each friend one slice at a time. Some students worked in larger units. One tried using a formula. Some students made the connection between different size slices of pizza of different sized children possibly making even division unfair.
Time Required for Task
45 minutes
Interdisciplinary Links
This task can be used during a social studies unit on groups and sharing.
Teaching Tips
Using manipulatives in this problem is very important. It allows students to work on addition and fractions using concrete materials.
Suggested Materials- Paper
- Pencil
- Material to cut and make pieces of pizza with different numbers of slices
Possible Solutions
If the pizza slices are divided evenly, each friend will receive three pieces of pizza. Some students noted that this might not be fair because not all students are the same size. No students thought that the pieces of pizza might be a different size.
| More Accessible Version Solution:
Some students might argue that yes, everyone got a fair share as they each received one piece of pizza. It is possible that each fractional piece is equivalent, if the pizzas as a whole were different sizes. This will not be the case if the pieces themselves are different sizes. The correctness of the student’s solution should be based on how s/he interpreted the task.
More Challenging Version Solution:
Each student will get one piece of the pizza cut into six slices. Four people will each also get one piece of the pizza cut into four pieces. The two people that did not get a piece of the four-piece pizza will each get two pieces of the eight piece pizza. The remaining four slices of the eight-piece pizza would need to be cut again so that each of the six people receives a fair share. Each would get two-thirds of the remaining four slices.
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Task Specific Assessment Notes
Novice:
A Novice would not have a solution. The student might not know how to start the problem or would use a strategy that did not lead to a solution. In this particular case, the student has a solution. Some friends received two pieces and some received four pieces. There is no evidence of the reasoning that led to this solution. These are not fair shares unless the student mentions that the pieces or the friends are of different sizes. The use of mathematical representation is appropriate. Because the student had a strategy, this might be between Novice and Apprentice.
Apprentice:
The student has a partial solution, which is "correct", each friend had three pieces to share. The representation is appropriate and the answer is clear. The answer is incomplete because the student does not answer whether or not fair shares were received by the friends.
Practitioner:
This student's solution shows that s/he understands the problem and uses an appropriate strategy to arrive at a conclusion. The representation and explanation are clear.
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Expert:
This solution shows a deep understanding of the problem, an appropriate strategy and clear explanation. It is an Expert solution because the student identified a useful extension. S/he pointed out that it might not be even because not all pieces were the same size. There were other Experts who said that even though each person received three pieces, the friends were of different sizes and, therefore, these were not fair shares.
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