Constructing a Three-Dimensional Model

3-5
3

In this lesson, students build a three‑dimensional model from their two‑dimensional blueprint. In addition, they solve problems related to constructing and decorating their clubhouse.

In this lesson, students will create a model of the clubhouse that they designed. Note that students with visual‑perception problems may have difficulty with this part of the unit, and you may want to offer alternative activities for them. In addition, depending on how you chose to handle the previous lesson, Creating a Two-Dimensional Blueprint, you may either allow students to work individually or in pairs on this lesson. Note that communication may be enhanced if students work in pairs.

Present a shoebox, cereal box, or some other container, and ask the students to identify the total number of faces the container has. Ask for a volunteer to draw the container as a flat two‑dimensional figure, as if it had been cut along several sides and unfolded. Repeat the same task with other shapes and other students. Allowing students to attempt this on their own can lead to a worthwhile mathematical discussion.

In addition, you may want to have several nets for various geometric figures available. Allow students to fold the nets into the solids they represent, so that students fully understand the concept. Examples of nets for cubes can be found in many real-world situations, so this is a good opportunity to share the nets for octahedrons and other, more complicated shapes.

Explain that a geometric net is a two‑dimensional figure that can be folded or made into a three‑dimensional model. In the figure below, the nets of a rectangular prism, a square pyramid, and a triangular prism are shown. (In addition, several other three‑dimensional figures are shown, and you might want to ask students what the nets of those objects would look like.) You can copy and display this image on an overhead projector using the Nets and Solids Overhead Sheet.

Then, ask students to discuss the following:

1. How are geometric nets like architectural drawings of buildings?
2. What would a net of your classroom look like? …your school?
3. How many faces would the net of a tetrahedron have? …an octahedron?

Serving as the "building inspector," inspect the two‑dimensional designs of the student clubhouses. Base your inspection on the architectural criterion that has been used throughout the project. Some of the items on the checklist for inspection are:

• blueprints with straight lines;
• 90° angles on all doors and windows; and,
• proper spacing of windows.

After the design is approved, students receive poster board to begin construction. Students measure the walls using the calculations and drawings on their blueprints, and then cut out the walls with windows and doors. Four rectangular walls are cut from the cardboard pieces, and two rectangles and two triangles are cut for the roof (see the image below). These pieces are taped together and the calculations and measurements begin. Students should use protractors to make sure that the doors and windows are perpendicular to the floor, and they should use their scale drawings to help with the placement of the doors and windows.

This task of transferring measurements from the blueprint to construction paper and building the model can be very challenging for the junior architects. Students need practice using the ruler to measure in inches and in fractions of an inch. One advantage of the project is that students learn how to use a ruler properly in a meaningful context, rather than as an isolated skill measuring segments or static pictures. Students engaged in this project will measure using tools, revise their drawings, and design with a purpose in mind.

Unlike textbook problems, this project allows for many explorations with student‑generated problems. Students will ask questions such as, "How can I fit a door and three windows in the front of my house? What should the dimensions be? How many feet should be between the windows and doors?" These types of questions will allow you to take advantage of teachable moments whenever they present themselves.

After students finish with the clubhouse, distribute the Junior Architects Problem-Solving Packet, which contains several open‑ended tasks involving area, perimeter, and money concepts for students to make decisions about decorating their own clubhouse. In one of the tasks, students compare prices from three different paint stores and determine which store gives them the best bargain on paint. In other tasks, students determine the perimeter of the doors and windows of their clubhouse.

The amount of information contained in the Problem Solving Packet is substantial, and it may require another day of class time to get through all of it. In addition, depending on the time of year that this unit is used and what skills have been mastered by students, you may want to omit some pages of the packet before distributing it to students. Without question, you should work through the problems in the packet before handing them out, to ensure that all problems are appropriate for your students.

References

• Cook, Shirley. Math in the Real World of Architecture. Nashville, TN: Incentive Publications. 1996.
• Suh, Juennifer, Patricia S. Moyer, and Donna Sterling. "Junior Architects: Designing Your Dream Clubhouse Using Measurement and Geometry." Teaching Children Mathematics, November 2003, Volume 10, Issue 3, p. 170.

Assessment Options

The teacher’s focus during the evaluation phase should be as much on the learning process as on the final clubhouse products. During the project, you should use non‑traditional assessment methods such as anecdotal notes, records from group discussions, and students’ written responses in their architect design logs. Students have opportunities to discuss individual and group solutions for each problem. Articulation in class discussions and reflection on their thinking processes reflect students’ understanding of many complex ideas. You may use the rubric below to assess various aspects of the design of the clubhouse project. The assessment involves students' mastery with accuracy of measurement, construction of a three‑dimensional model, solving problems, and writing in their design logs. The criteria for judging the clubhouses helps students assess their own progress throughout the project.

 Performance Tasks Points per Category Calculations on Budgeting Worksheet Accuracy of Measurements on Blueprint Three-Dimensional Model Problem-Solving Tasks Design Log Total Points

Within each category, award up to 4 points, as follows: 4 = Superior; 3 = Good; 2 = Satisfactory; and, 1 = Needs Revision. Use the following scale to judge the overall quality of a student's project: 18‑20 = Superior; 14‑17 = Good; 9‑13 = Satisfactory; and, 5‑8 = Needs Revision. If a 1 is scored in any category, require the students to revise their work and re‑submit the project.

Extensions

1. While others finish the construction of their model clubhouse, those who have finished can decorate theirs. The budget is set at \$10 for buying items to decorate the clubhouses. The teacher can bring in items such as buttons, straws, cellophane paper, wallpaper samples, toothpicks, fabric swatches, and aluminum foil for students to purchase. Students may use bright buttons for doorknobs and decorations, the cellophane paper to create stained glass windows, the fabric swatches to make curtains for the windows, and the aluminum foil to make solar panels (which makes the clubhouse more gas efficient) and satellite devices (to pick up sports channels).

2. Allow students to explore geometric solids using the Geometric Solids Interactive.
Geometric Solids

Questions for Students

1. How are geometric nets like architectural drawings of buildings? How would an architect or construction worker use nets?
2. How did you determine the sizes of the doors and windows for your clubhouse?
3. How is "real-world" mathematics involved in this lesson?

Teacher Reflection

• What real‑life mathematics emerged from this project?
• How could the integration of technology make some aspects of this project less cumbersome so that students can focus on the mathematics?
• How did the students perform in relation to the stated behavioral objectives?
• What advantages are there in presenting mathematical ideas in a project‑based scenario?
• What were some of the ways your students illustrated that they were actively engaged in the learning process?

Junior Architects

3-5

Learn the major concepts such as using basic linear measurement, understanding and creating scale representations, and exploring perimeter and area measurement.

Getting to Know the Shapes

3-5
In this lesson, students discover the uses of geometry and measurement in the world of architecture as they are introduced to the clubhouse project.

Finding Perimeter and Area

3-5
In this lesson, students develop strategies for finding the perimeter and area for rectangles and triangles using geoboards and graph paper. Students learn to appreciate how measurement is a critical component to planning their clubhouse design.

Creating a Two-Dimensional Blueprint

3-5
In this lesson, students draw a two-dimensional blueprint of their clubhouse using graph paper.

Learning Objectives

Students will:

• Transform a two‑dimensional plan into a three‑dimensional figure.
• Apply problem‑solving strategies.

NCTM Standards and Expectations

• Identify and build a three-dimensional object from two-dimensional representations of that object.
• Use geometric models to solve problems in other areas of mathematics, such as number and measurement.