A Study in Geometry

1. A Study in Geometry Based on Chapter 7 in Teaching Student-Centered MATHEMATICS: Grades 5-8 By John A. Van de Walle and LouAnn H. Lovin

2. Big Idea 1 • “What makes shapes alike and different can be determined by an array of geometric properties. For example, shapes have sides that are parallel, perpendicular, or neither; they have line symmetry, rotational symmetry, or neither; they are similar, congruent, or neither.” pp. 179

3. Big Idea 2 • “Shapes can moved in a plane or space. These changes can be described in terms of translations (slides), reflections (flips), and rotations (turns).” pp. 179

4. Big Idea 3 • “Shapes can be described in terms of their location in a plane or in a space. Coordinate systems can be used to describe these locations precisely. In turn, the coordinate view of shape offers another way to understand certain properties of shapes, change in position (transformation), and how they appear or change size (visualization).” pp. 179 [Ah, this is where “dilation” fits in … the visualization piece. Plus, “similar” is an attribute for conversation about dilation.]

5. Big Idea 4 • “Shapes can be seen from different perspectives. The ability to perceive shapes from different viewpoints helps us understand relationships between two- and three- dimensional figures and mentally change the position and size of shapes.” pp. 179 • http://learnzillion.com/lessons/1134-describe-2dimensional-cross-sections-of-right-rectangular-prisms

6. Activity Page • 7.1 Shape Sort • “Have students work in groups of four with a set of 2-D Shapes. [Do the guided activities in order].” • pp. 188 guiding questions • BLM 12-18 www.ablongman.com/vandewalleseries • Colored shape sorts already made. 

8. 7.2 “What’s My Shape?” • pp. 188-189 • Using another set of the shapes, the teacher creates small secret shape folders from construction paper using about 1/3 of the shapes. • Student leader gets to choose the secret shape folder. His/her team can play Twenty Questions to try and guess the shape in the folder.

9. “What’s My Shape?” 3-D Style • Students will gather 3-dimensional shapes. The class will assemble a set of these shapes that have volume. • The teacher will make secret shape folders from this set. • Students will repeat the steps for “What’s My Shape?”.

10. Assessment Moment • Level 0: classify into a group • Advancing levels: will create categories based on properties and can classify other shapes (shapes that are not given as examples) into the groups formed

11. “Constructing and Dissecting Shapes” • What shapes can you make using these tools? • Pattern blocks • Tangrams • Mosaic puzzle • Begins on pp. 189 • BLM 19 • www.ablongman.com/vandewalleseries

12. “Constructing and Dissecting Shapes” • Assignment: Try cutting up squares and rectangles to make other 2-D shapes. Be ready to report on your findings. • http://www.geogebratube.org/student/m7053 • Project Assignment: You have a twelve inch by twelve inch quilt block. Using polygon shapes, create your own design. Your quilt block should be unique and unlike anyone else’s. You must use least eight shapes, with some of the shapes not having parallel sides, and the maximum number of sides is twenty.

13. Newspaper Bridges • Roll up three full sheets of newspaper on the diagonal tightly. • Experiment with which shapes would make the best bridge trusses. • Overlap rods of newspaper 6 inches at the joints.

14. Newspaper Bridges • Where are our local bridges? • Build the longest bridge that will not sag or break. • Rules: You choose the shapes for your design. • Overlap rods of newspaper 6 inches at the joints. • Your design should have an obvious repeating feature. • Your rods may be one rod length, ½ rod length, or 1/3 rod length. • Your bridge should have a base and sides like a real bridge.

15. Did anyone come up with these bridge designs? • What shape makes the best bridge truss?

16. Can You Build a Bridge Out of Cards? • Using just a deck of cards, build a bridge.

17. Another Bridge