# Spatial Visualization and Perspectives

**Subject**

Math

**Author**

Lisa Castaneda, Math Teacher

**School / Organization, City and State / Province**

Shoreline, WA

**rade Level**

6 or 7

**Common Core Standards Met**

- Solve real-world and mathematical problems involving area, surface area, and volume
- 6.G.4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems
- Solve real-life and mathematical problems involving angle measure, area, surface area, and volume
- 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

**Time Needed**

2 class periods.

**Objectives**

- What do we see when we view objects from different perspectives?
- Students will be able to identify from which perspective they are looking at an object
- Students will be able to articulate how a view from a particular perspective will change when the object’s shape is modified
- Explore how these changes affect the surface area of the room

**Summary**

Building on the ideas of nets from the previous lesson (or not), students will begin by exploring the ideas of perspective when rotating the main room in the Puzzle Maker. Surface area will be introduced and students will explore the concept of surface area by modifying the Puzzle Maker room. They will also experience getting “inside” their figure when they build the game. Finally, Wheatley will give the students directions for constructing rooms with particular surface areas and students will explore the idea that there are a variety of configurations that still result in the same surface area

**Vocabulary**

- Area – the number of square units enclosed in a figure
- Surface Area – the sum of the areas of all of the exposed sides of a figure; the sum of the area of the bases and lateral faces of a space figure
- Net – a 2-D figure that can be folded along its segments to form a 3-D figure

**Teacher Materials Needed**

- If possible, a computer that will allow you to project the Puzzle Maker for class discussion purposes
- An example of a net/object (perhaps a cube or rectangular prism shape for simplicity)

**Student Materials Needed**

- The Puzzle Maker
- Rulers
- Graph paper
- Copy of the “Wheatley Room Design Sheet”

**Lesson Plan**

Download Spatial Visualization and Perspectives