Observing Student Connections
 Introduction | Cutting Squares | Problem Reflection #1 | Designing a Paper Quilt | Problem Reflection #2 | Classroom Practice | Observe a Classroom | Reflection Questions | Your Journal

Reflect on the following questions about the problem you just observed. Select "Show Answer" to see our comments, or if you need help thinking about the questions.

 Question: What connections are woven into this activity? Show Answer
 Sample Answer: A variety of connections are integral parts of this activity, for example, (1) geometry: identifying shapes and congruence (when one piece fits on top of the other, they are the same size and shape); (2) measurement: cutting the square in half and area; (3) the idea that when you cut a square in half horizontally, the pieces are the same as when you cut the square vertically; and (4) the concept of half a square being both a rectangle and a triangle.
 Question: How does the classroom conversation reinforce students' thinking about these ideas? Show Answer
 Sample Answer: Students are working together to test their ideas. Peter suggests that Maria can show that her pieces are the same by placing one piece on top of another. When Igor suggests that Maria's pieces are smaller than Roy's, the students work together to show that they are the same. The discussion about Robbie's triangular pieces stretches students to think about halves of a square in a new and different way.
 Question: What are some of the students' misconceptions, and how does the discussion help address them? Show Answer
 Sample Answer: Igor doesn't think that Maria's pieces are the same as Roy's, even though they are halves of the square, because they "look different." Students determine a way to see if they are the same. Also, when Robbie explains that the triangles are halves, students think that this is not possible because they are not rectangles, and so the students must come up with a way to prove or disprove Robbie's conjecture.

 Teaching Math Home | Grades K-2 | Connections | Site Map | © |