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ConnectionsSession 06 OverviewTab atab btab ctab dtab eReference
Part A

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


These first-grade students have been studying shapes. They first heard the story The Quiltmaker's Gift by Jeff Brumbeau. Students were then given square pieces of construction paper and were told to begin by cutting each square in half. We join them as they are sharing the results of their work with the rest of the class.

Cutting Squares

Roy's results

Teacher: How many pieces did you get when you cut the square in half?
Roy: Two.

Teacher: (to the class) What do you notice about Roy's pieces?
Rita: They are long and skinny.
Marco: There are two pieces.

Teacher: Does anyone remember what these pieces are called?
Terry: Rectangles.

Teacher: That's right. There are two rectangles. What do you notice about the rectangles?
Roy: They have four sides and four corners.

Maria's results

Teacher: How many pieces did you get when you cut the square in half?
Maria: Two.

Teacher:What do you notice about your pieces?
Maria:They're the same.

Teacher:How are they the same?
Maria:They are the same shape and the same color.

Teacher: Are they the same in any other way?
Maria: I think they are the same size.

Teacher: How can Maria check to see if they are the same size?
Peter: She could put one piece on top of the other, and they would be the same.

Teacher: What else do you notice about Maria's pieces?
Igor: They are smaller than Roy's.

Teacher: Why do you think they are smaller?
Igor: Because they are not as long.
Roy: No, I think they are the same as mine -- see, if you turn mine on its side and put it on top, it's the same.

Teacher: And so, Maria, can you tell me the name of your pieces?
Maria: I think they are rectangles.

Robbie's results

Teacher: Robbie, your halves look different. What do you notice about your pieces?
Robbie: They are triangles.

Teacher: What do you think of Robbie's pieces?
George: I don't think they are halves -- they don't look the same as the others.

Teacher: What do you think about that? Does Robbie have two halves?
Patty: I think so, because there are two and they are the same.

Teacher: How are they the same?
Patty: They both have three sides.
Jose: They are the same shape.

Teacher: How can we tell if they are halves of the square?
Robbie: They are both the same size. See, if I put one on top of the other, they are the same.
Alex: I don't know how Robbie got those.

Robbie moves the pieces around to make the square and demonstrates how he made his cut.

Next  Reflect on the Cutting Squares problem

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