Session 10, Part C:
Activities That Illustrate Geometric Reasoning (55 minutes)

In This Part: Cutting Corners Activity | Shape-Sorting Activities

In this part, you'll look at some activities designed for students in grades K-2. As you read each activity, answer these questions:

 a. What is the geometry content in this activity? b. What skills do students need to work through this activity? What skills will this activity help them develop for later work? c. What level of geometric thinking is expected of students in the activity? Does it ask students to bridge levels? d. What other questions might extend students' thinking about the activity? e. Describe a lesson that you could develop based on the content of this activity.

Note 6

Activity Summary
Students explore ways to cut rectangles to make other shapes, including smaller rectangles, triangles, and shapes of the same size.

Materials Needed:

 • one pair of scissors for each student • six sheets of 8 1/2" x 11" paper • paste • six sheets of 12" x 15" colored construction paper for each student • a straightedge for each group of students • a pencil for each student

Begin Activity
Hold up a rectangular piece of paper and ask students to identify the shape. Also ask questions such as, "How many sides does a rectangle have? How many vertices does a rectangle have? What is special about the angles of a rectangle?" As students answer, point out the sides and vertices to reinforce the vocabulary and review right angles.

Ask, "How can I cut this rectangle to get two smaller rectangles whose shape and size are the same?" Take several suggestions from different students and follow their methods to cut several sheets of paper. Have the class verify that the resulting pieces are rectangles, and have them compare the rectangles' sizes and shapes. You can introduce the word "congruent" to describe two figures that fit perfectly on top of each other.

Using a new sheet of paper, call on students to tell where the paper should be cut to make two triangles. Have students compare a couple of different methods, as well as the sizes and shapes of the triangles they create. Also ask students to identify sides and vertices of the triangles to reinforce the vocabulary.

Main Activity
Hold up a fresh sheet of paper and say: "I will make one straight cut. I will start here (point to one side) and stop here (point to an adjacent side). Tell me about the shapes you think I will get." After the students describe the shapes, cut off a corner of the rectangular piece of paper, leaving a small triangle and a large pentagon. Have the students identify the number of sides and vertices of each shape, and repeat the word "pentagon" with students as that shape is discussed.

Review the names, numbers of sides, and number of vertices for several figures, including circle, triangle, square, rectangle, trapezoid, and pentagon. Give students scissors, paste, sheets of paper, and large construction paper. Tell them that their task is to create shapes by drawing a line from one side or vertex of the white paper to another side or vertex with a straightedge and then cut along the line. The students can then paste the resulting two pieces on the construction paper and record the names of the shapes. Have them repeat the activity six times, each time trying to create two new shapes.

Extension
Begin with an equilateral triangle or a trapezoid instead of a rectangle. Have the students follow the same procedure. (1) Identify the shapes that can be made with one straight cut from one side or vertex of the original shape to another side or vertex; and (2) compare the sizes and shapes of the cut figures to identify those that are congruent.

Problem C1