The problem states:

*In preparation for back to school, the school administration has planned to replace the tile in the cafeteria. They would like to have a checkerboard pattern of tiles two rows wide as a surround for the tables and serving carts.*

*I wonder ... when a contractor gets a tiling job, does he use math to determine the number of tiles needed? What planning does he do before laying out a pattern?*

I would give students just the context in italics above ... with some thinking time ... and then proceed:

1. What questions come to mind?

2. In teams, go to our 9th grade cafeteria and collect information that will be helpful to you.

3. In teams, use the graph paper and colored pencils provided to create a diagram that fits the problem description.

4. Determine how many colored tiles will be needed to create the pattern your team drew.

5. Suppose the school administration changes its mind and now wants to tile the cafeteria in the 1100 building instead of the 9th grade cafeteria. Create a generalization or rule that will work on any size cafeteria. Does it matter if the cafeteria floor is square or rectangular? Explain your thinking.

6. The cafeteria manager looks at your diagram and comments that his serving equipment will need more than 2 rows of checkerboard pattern. He requests 4 rows. How does that change the rule you created for the contractor?

7. Create a mini poster with your floor design, calculations, and generalizations.

I made two changes. First, I asked students what they need to know from the problem situation to encourage their own thinking, curiosity, and problem solving ideas. Second, I took away the square diagram, choosing instead to use real data.

*How would you modify the problem?*

I agree that the context of the cafeteria is not going to light the fire of any of my high schoolers. And changing the location of the checkerboard pattern isn’t going to help.

ReplyDeleteI included the trip to our school’s cafeteria not so much as a motivating factor, but because in our curriculum we have standards that require gathering and recording data.

• Algebra 1: Gather and record data and use data sets to determine functional relationship between quantities

• Algebra 2: Collect and organize data, make and interpret scatterplots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments.

In each of our units of study we spend one class period collecting/organizing/interpreting data … shooting rubber band cannons, measuring the wing span of our classmates, determining the height of a dropped bouncy ball, measuring Barbie’s descent, etc. Collecting data does take time – and there were times last year when I thought how much easier it would be if I gave students nice, neat, clean data to use.

In my proposed change I sent teams to the cafeteria to collect information that would be helpful to them. I intentionally left this open ended. Would they simply measure the perimeter? Would their team form a human square and create a table of values (walking outward from one square in the center or starting from a larger square walking inward). While in the cafeteria, I might direct students to look for a pattern in successive squares to push them in the right direction. And then, since I’m fairly certain our cafeteria is not square, how might they use that information in their patterning?

I agree with Dan that we are going to lose class time by going to the cafeteria. So if this isn’t one of our purposeful data collection activities, then it would be better to work in the classroom with graph paper.

As I ponder this problem today, I wonder about using it as a first day activity since no specific high school mathematics is needed to solve it. Watching how teams might work through this problem would be insightful and helpful to me – especially if I had a strong observational tool for noticing leaders, problem solvers, those who are persistent in the work, those who assist even if they appear somewhat lost, and those that simply hang back.

This discussion around revising textbook problems is intriguing. I almost want to lurk instead of participate. I am very curious about how others view the chosen problem. I look forward to the next challenge!