How Do We Draw a Rectangular Prism?
Name: Laura Voegeli
Date of Lesson: 9-19-2002
Subject Area/Topic: Mathematics/Geometry
Grade Level: 3rd Grade

Standards: Geometry Standard: Use visualization, spatial reasoning, and geometric modeling to solve problems. Connections Standard: Recognize and apply mathematics in contexts outside of mathematics. Communications

Standard: Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

Outcomes/Objectives: The learner will be able to identify the terms rectangular prism, vanishing point, and perspective. The learner will be able to draw three rectangular prisms on a two-dimensional surface. The learner will be able to identify the various ways in which a rectangular prism can be seen by working together in groups using the (attached) worksheet. The learner will gain respect for others opinions and ideas as the class makes suggestions and works together to solve the mathematical problem. The learner will realize that rectangular prisms are a part of the world around us.

Materials: markers, rulers, white drawing paper (one for each student), scrap paper (one for each student), pencils, worksheets (two for each table), and plastic rectangular prisms.

Engage: Ask students about the differences between seeing objects up close or far away. How do they look different? Ask students if they think there are any differences in the way an object is viewed and drawn depending on the location of the person viewing it (if they are to the right or left, above or below). (Communication).
Explore: Hand out a set of the plastic rectangular prisms to each table. Distribute to each student the attached worksheet. Have students work with a partner at their table to manipulate the rectangular prisms to look like the pictures on the worksheet. Model this to the students with the first picture on the page. Once they have demonstrated all the pictures on the worksheet, ask the students to come up with two more ways to look at the prism, but tell them NOT to draw them. -Concrete.
Formative assessment: Walk around to observe how students are manipulating the prisms to come up with the various points of view.

Explain: Ask students if the drawing of a rectangle would look the same as the drawing of a box. What makes them different? Is it important to be able to show the difference between them? How might you show this on paper? Any ideas? (Communication). Would someone like to come to the board and show us a possible way? If a student volunteers and does it properly then have them point out what they did in order to draw it in such a fashion. If no student volunteers or it is not done properly, tell the students that you will demonstrate how it can be done. Draw on the board a picture of a rectangle and add a vanishing point. Describe what vanishing point and perspective are. Ask students why it might be called a vanishing point and why we might want to show a perspective in our drawings. (Communication). Demonstrate to the students how you connect the corners of the drawn rectangle to the vanishing point using a ruler. Next, use the ruler to measure any given distance such as 1" from the sides of the rectangle to create the sides ofthe prism. Erase the vanishing point and the lines left over that are connected to the vanishing point. Demonstrate the same only on the opposite side of the vanishing point. -Pictorial.

Expand: Have the students get out their pencils and hand out to each of them a piece of scrap paper. Instruct the students to try to draw some of their own rectangular prisms. Have them use a vanishing point in their drawings. Students sitting at the same table may help each other if need be. Suggest that students try drawing at least three rectangular prisms, labeling their vanishing point. -Pictorial.

Formative assessment: Observe students as they draw their objects to make sure they have an understanding of how to draw rectangular prisms using a vanishing point. After about 15 minutes, ask students where they have seen objects such as those they just created. Have students discuss at their table the various objects that they see in everyday life that are rectangular prisms. After about 5-7 minutes have each group take a turn to report three different objects that are rectangular prisms. Ask students what makes these rectangular prisms. Are there variations among rectangular prisms? What are they? (Communication).

Evaluate: Students will now be introduced to the art project they are going to create. Hold up a self-completed art project showing a room of your own design that contains three rectangular prisms of varying sizes. Point out where your vanishing point was located. Pass out a sheet of drawing paper to each student. Instruct the students that they are to design the room of their choice containing three rectangular prisms of various sizes. They can use the markers at their table to decorate and color it once they are done drawing and erasing. -Abstract.

Summative Assessment: Look at the completed artwork of the students to see if they understand how to draw a three-dimensional rectangular prism on a two-dimensional surface using perspective and a vanishing point.

Expand: Students will be creating odd shaped prisms for another art project, making sure that the objects are made by only using straight lines. One possibility is creating their name in block letters and then showing them in perspective using a vanishing point.

References: Principles and Standards for School Mathematics (2000). Reston, VA: The National Council of Teachers of Mathematics, Inc.

Reflection: I feel that this is a good lesson because it incorporates artistic, linguistic, and mathematic skills. It requires students to be creative and draw from their preferences and feelings. Students are also allowed to realize that mathematical concepts, such as rectangular prisms,are a part of the world around them. This makes the learning concept much more meaningful, thusly helping the students to learn more effectively. The only problem that I could see with this lesson is students creating their art projects how they normally would without using any three-dimensional concepts. I do, however, feel that if the first part of the lesson is done properly, then this will not be the case. Time might also cause a problem, especially if the teacher prefers to have the work completed in class.

Ideas for Integration: Students could connect this to science by writing science terms in perspective on the front of small pieces of poster board and then writing the terms’ definitions on the back in regular writing. They can use these as flash cards.