“Visualizing Geometry”



“Visualizing Geometry”

7th Grade Math

Objectives Targeted (from Common Core Standards Initiative):



Draw construct, and describe geometrical figures and describe the relationships between them.

o 7.G.3. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

o 7.G.6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Analyze proportional relationships and use them to solve real-world and mathematical problems.

o 7.RP.2. Recognize and represent proportional relationships between quantities.

Lesson Objective:

Students will be able to:

• Set up and solve proportions for similar figures, including shapes that have been rotated and/or flipped.

• Build, describe, and draw representations of 3-dimensional figures from the front, top, and side perspectives.

• Visualize, describe, and analyze cross-sectional views (slicing) of 3-dimensional figures.

Materials

1. Tracing paper or Patty paper

2. Centimeter cubes (or other cube blocks)

3. Playdough or clay

4. Student Handouts

5. SmartBoard (can be used, if desired)

6. Classroom Response System Remotes (can be used for multiple choice questions, if desired)

Lesson Description

Part One: Similar Figures

1. Students begin setting up proportions for similar figures, using the tracing paper to help aid in lining up corresponding sides. A student may use the flip and rotating features on the SmartBoard to also model what is being done with the tracing paper. Have students put the smaller figure into the larger figure.

2. Students may also want to color-code corresponding sides on both paper and on the classroom board being used.

Part Two: 3-dimensional Views

3. Distribute centimeter blocks (or other cube blocks). Each student will need about 20 blocks. Have students build the figures shown on the handouts and draw the 2-dimensional views.

4. Have students use a different color to mark each of the different views seen (i.e. green for top view blocks, red for front view blocks, blue for side view blocks).

5. The slide showing the 2-dimensional views (Slide 8) asks students to build the 3-d representation of that figure. You may want to have a student build the figure for the class once you have given everyone sufficient time. (The document camera works great!)

Part Three: Cross-sectional Views

6. Using Playdough or clay, build a representation of a cylinder. Cut the cylinder two ways: parallel to the base to reveal circles and perpendicular to the base to reveal rectangles. Show the students what it looks like when opened, and have them make predictions for other 3-d shapes.

7. Have students answer the multiple choice questions provided using a CPS system, or simply use dry-erase boards to make all students’ answers valuable. (Answer key for all problems is provided below.)

Answer Key:

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Slide 9 (Cone): Answer A

Slide 10 (Cylinder): Answer B

Slide 11 (Square Pyramid): Answer B

Slide 12 (Square Pyramid): Answer A

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