If you’re like me, one of your most dreaded tasks is arranging and re-arranging student desks. Consider asking students to design the room. Not only does it give students ownership of their space, the design process poses a mathematical challenge.

Day 1: Inquiry

• What kind of room formation would you like to see?
• What do you need to know?

As I watched the fifth graders work on these questions, I noted the following conversations:

“The width of the room is 6 and a half.”
“Six and a half what?”
Silence.
“Six and a half what?”
“These sticks.”
“Are they meter sticks or yard sticks?”

Another student said, “Are you measuring in inches or centimeters?”
“Inches.”
Wide, frightened eyes. “Noooooooooooooooo,” they pleaded.
“Okay. I’ll measure in centimeters.”

“How big are our desks?”
“Mine is 61 by 49.”
“Mine is 55 by 46.”
“Mine is 60 by 50.”
“But all our desks are the same size!”

“We need to measure the round table. Mrs. A, do you have any string?”
I watched the students wrap string around the circumference and report the measure.
I said, “I notice you are measuring the circumference of the table. Can you tell me why you chose to do that?”
“To know how big it is,” they replied.

I made the decision to not correct them (yet). They would be playing with the room arrangement as homework and I wanted them to struggle with how circumference might or might not help them.

In the end, students had to consider the following:

• Agreed-upon units of measure
• Accuracy of measurements
• Furniture that can be moved and furniture that cannot be moved
• Usefulness of circumference and area when placing a round table in the room.
• The need for all students to see the front boards
• Walkway spaces

Students were asked to work on the assignment for 20 minutes at home.

Day 2: Looking at initial work

Sure enough, a few students came entered the classroom the next morning and asked if they could take a few more measurements. I overheard them say to one another, “I think we need to measure the distance across the table.”

I watched a few more students work together to figure out optimal spaces between desks so that chairs could scoot back a comfortable distance.

Later in the day, as I checked students’ initial work, I noticed the following:

Some students spent the whole work time doing calculations. They wanted to divide the total number of centimeters into numbers of desks. Implications for instruction:

1. These students know calculations procedures, but may not be sure what their answers mean. Spend some time discussing/drawing what they figured out when they divided.
2. These students did not consider estimation. They divided 781 centimeters (the full length of the room) by desks that were 61 cm in length and 49 cm wide. 
   

Some students drew pictures with no mathematical explanation. Implications for instruction:

1. These students may or may not understand how to apply measurement in real-life situations.
2. Conversations with individuals are necessary to determine whether they rushed through the assignment, whether they did not include their calculations, or whether they sincerely didn’t know how to apply measurement to real-life situations.

Some students made a basic legend and gave a proportion to each grid square. Below are some of the room designs:

Did I miss any implications for instruction (if so, please share!)? What would be your expectations for final products at your grade level?

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