Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

 Observing Student Reasoning and Proof
 Introduction | Problem: Building Rafts with Rods | Solution: Building Rafts with Rods | Student Work #1 | Questions and Answers #1 | Student Work Reflection #1 | Student Work #2 | Questions and Answers #2 | Student Work Reflection #2 | Observe Classroom | Classroom Practice | Your Journal

Following are some examples of questions you might ask Sara. For each question, think about an answer that Sara might provide. Then, select "Show Answer" to see one possible answer. Keep in mind that this exchange is just one approach; middle school students will come up with a variety of ways to tackle this problem.

 Teacher: You have seen a pattern as you work down the surface area column in the chart. Using your pattern, what would be the surface area for five, six, and seven rods? Show Answer
 Student: The pattern is to add 6 for each rod, so for five rods it would be 34 square centimeters, for six rods it would be 40 square centimeters, and for seven rods it would be 46 square centimeters.
 Teacher: What if there were 100 rods? Show Answer
 Student: It would take a lot of time to extend the table to 100!
 Teacher: Do you think you could use the pattern you found to come up with a general rule that will work for any number of rods, without having to extend the table all the way to that number? Let's start small, with just one rod. How would you find its surface area? Show Answer
 Student: To find the surface area, I would do 4 • 2 for the long sides and then add 2 for the ends.
 Teacher: Look at how the two-rod raft is put together. You said that the surface area for two rods was 6 more than the surface area for one rod. Think about how you are finding the surface area. Can you see where the extra 6 comes from? Show Answer
 Student: Part of the extra 6 –– 2 –– comes from two more ends. The other 4 must be from another top side and another bottom side.
 Teacher: Look at the raft from different views. What do you notice? Show Answer
 Student: The top and bottom are the same. The front and back are the same. The sides are the same.