Last week I brought the stamps my class made down to the post office to hang up. Karen, the postmaster, said she had other things to display and wanted to know how much space was needed to hang up all the stamps. If the stamps are 8 1/2" x 11" and there are 17 of them, what would you tell her? How did you come to this solution?
The school I work in is in a rural area. The post office is very small and simple. The postmaster asked me if I would have my kids participate in a stamp contest and allow her to hang the stamps they made in the post office for people to see. The children created stamps on 8 1/2" x 11" paper. This task was a much bigger problem for the children than I expected it to be. They had a tough time with scaling down the size of the stamps, with the concept of giving dimensions, and with the reality that when you hang things up you want them to look nice and usually have spaces between them. The fact that there were fractions involved as well as an odd number of stamps also added difficulty to the task. Although the children knew there were many ways to solve this, most only solved it one way because of the time factor. The task allows the children to become engaged in solving a real-life problem that involves many different math concepts such as measurement, fractions, geometry and more. A surprising number of students actually put 17, 8 1/2" x 11" pieces of paper down on the floor and measured, (or attempted to measure), them. I had thought more children would have drawn a diagram using some introductory concepts about scale. In my class, this was not the case. About half of my third and fourth graders arranged the papers in a way they thought would look good and the other half of the students did it the simplest way they could think of ... 17 pieces of paper in one row.
4 - 5 hours A problem of this type could easily fit into many units or activities. A practical application for it would be for hanging student work in the classroom. It could also fit into units on map skills, measurement, building or art. As I stated earlier, I expected this to be a straightforward task. It was not. I would suggest a couple of things to be aware of depending on what your objectives are. Depending on the skill level of your students you may want to use "friendlier" numbers such as 18 pieces of paper that are 8" x 11". The odd number of papers and the fractions caused problems for some kids. You should make sure your students have a concept of scale before doing this task or simplify the task and use it as an instructional piece to teach about the importance of scale. Children also need to know measurement skills including how to measure things that are larger than their measuring tool.
- Graph paper of various sizes
- Construction paper
- Scissors
- Rulers
- Yard/meter sticks
- Markers
- Calculators (optional)
Solutions will vary depending on how the student sets up the stamps. Things to keep in mind:
- Did the student give dimensions for the space needed or just the perimeter or area?
- Did the student include spaces between the stamps? Is this important to you?
- Is the student aware that there is more than one solution?
- Did the student measure, add and/or multiply correctly?
It is unclear what this student has done. There is no explanation, no solution and no evidence of a strategy.
This student uses a strategy that is partially useful, which is marking off on graph paper where the stamps are. S/he then has a problem finding the dimensions for a six-sided figure. The student also seems to understand that the sides of the stamps need to be added together, but uses the dimensions of 8" x 11" instead of 8 1/2" x 11". There is some evidence of reasoning and an attempt at using math language and representation.
This student shows a broad understanding of the problem and the major concepts needed to solve it. S/he uses effective reasoning by giving the dimensions for a rectangle with extra spaces in it. There is a clear explanation and mathematical procedures are used appropriately.
This student shows a good understanding of the task and verifies his/her solution. S/he acknowledges the fact that there is more than one solution to this task. This fourth grader gives a clear explanation of how the problem was solved and applies mathematical procedures correctly.
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