MATERIALS:
Per Group (of 4 students):
• A set of three-dimensional wooden or plastic shapes. Set should include one each of the following: a cube, a square pyramid, a cylinder, a cone, and a sphere and a variety of prisms such as a rectangular prism, a triangular prism, a pentagonal prism, a hexagonal prism, or an octagonal prism.
• Tape
• One set of building materials. (Provide each student group with one set of materials. Choose from the items listed below.)

• Recording Sheet: Constructions
• One cardboard box that has been taken apart (the net of the box) NOTE: Select a variety of boxes to represent various sizes and shapes. Examples include boxes from food packages such as cereal, cookies, breakfast bars, gelatin, hot chocolate mix, etc. Try finding boxes with irregular shapes such as a cylindrical (hat box), hexagonal, or octagonal box.

Per Student:
• One copy of the 2-D to 3-D Student Activity Sheets
• One pair of scissors
• Tape or glue

Per Teacher:
• A set of three-dimensional wooden or plastic shapes. Set should include one each of the following: a cube, a square pyramid, a cylinder, a cone, and a sphere and a variety of prisms such as a rectangular prism, a triangular prism, a pentagonal prism, a hexagonal prism, or an octagonal prism.

Per General:
• Computer with Internet access or computer with PC/TV adapter or projector.
• VCR Tape of CYBERCHASE, Episode: Eureeka
• Television with VCR
• Chart Paper
• Pencils
• Paper

PREP FOR TEACHERS:
Prior to teaching this lesson:
1. Bookmark the web site: http://pbskids.org/cyberchase/games/23dgeometry/index.html.
NOTE: The teacher should try the activities on each Web site and print copies of the items featured on the web pages to use when instructing students.
2. View the tape: Eureeka
3. Students should also have prior experience with two-dimensional figures before this lesson.

Preparation for the hands-on component of the lesson:
1. Make copies of the student-recording sheet: Constructions.
2. Prepare chart paper for the class discussions.
3. Students should also have prior experience with two-dimensional figures before this lesson.
4. Important Geometric Terms: cube, pyramid, prism, cylinder, sphere, cone.
• Polygon: A closed two-dimensional figure that is made up of line segments that intersect only at their end points.
• Faces: Polygonal regions that make up the surface of a solid.
• Edges: The line segments created by the intersection of two faces of a solid.
• Vertices (singular, vertex): The points of intersection of two or more edges.
• Net: A two-dimensional representation used to create a three-dimensional shape.

When using media, provide students with a FOCUS FOR MEDIA INTERACTION, a specific task to complete and/or information to identify during or after viewing of video segments, Web sites, or other multimedia elements.

INTRODUCTORY ACTIVITY:
Step 1. Introduce lesson topic to students by telling students, “Two-dimensional shapes lie flat and are sometimes called flat or plane shapes. We can draw these shapes on paper and they are often represented in books. Today we will enter the world of three-dimensional shapes. Three-dimensional figures can stand up – they have height.” Show students a cutout of a two-dimensional shape such as a square and show students one of the three-dimensional shapes such as the cube.

Step 2. Allow students to brainstorm a list of two-dimensional shapes. (The list may include: circles, triangles, squares, rectangles, circles, pentagons, hexagons, etc.) Show students the three-dimensional figures. Choose one solid and ask students to describe the solid. Ask questions such as: “How is the solid like the flat (2-D) shapes: How is it different? Can you make this solid using some of the two-dimensional shapes?” As a class, list the similarities and differences between two-dimensional and three-dimensional shapes. Discuss the class findings.

LEARNING ACTIVITY:
1. Show students a cube. Ask students “Is it possible to use two-dimensional (flat) shapes to construct a cube?” Ask students, “What shapes are used to make the cube?” Students should note that the cube is made up of squares. Provide your students with a FOCUS FOR MEDIA INTERACTION. Tell students that today’s episode is about Professor Archimedes who disguises himself as a two-dimensional object to hide from Hacker. Tell students to watch the video segment to see how Archimedes looks before and after he changes shape. Insert the video, CYBERCHASE episode – Eureeka into your VCR. START the tape at the beginning and allow students to watch the tape until Professor Archimedes goes flat to hide from Hacker. PAUSE the tape after Archimedes becomes a flat shape. Check for comprehension. (Students should note that Archimedes was a three-dimensional figure at the beginning of the tape and that he became a two-dimensional figure to disguise himself from Hacker. Students should describe the shapes they observed.)

2. Ask students if they have ever built or constructed a three-dimensional object. Allow time for a brief discussion from students. Provide your students with a FOCUS FOR MEDIA INTERACTION. Tell students that sometimes we can use two-dimensional figures to construct three-dimensional objects. Instruct the students to watch the next video segment to find out what materials Jackie, Inez, and Matt will use to try to rebuild Archimedes’ terminal. FAST FORWARD the tape to the segment that shows the kids and Archimedes’ assistants standing at the building site with the rods. PLAY the video until they make their first attempt at rebuilding the terminal (the students try to make a square). STOP the tape. Check for comprehension. Students should note that the outline on the ground shows a bunch of squares and a pile of rods. Distribute a set of building materials (toothpicks and marshmallows) to each small group of students. Tell students to use the toothpicks and marshmallows to construct a square.

3. Show students the cube. Ask students if they can think of a way to use their building materials to construct the cube. Allow students to share their ideas. Instruct students to use the toothpicks and marshmallows to construct a cube. Allow time for students to build their cubes. Show students the cube and remind them of the earlier discussion where they pointed out that a cube is made up of squares. At this time introduce the terminology faces, vertices, and edges. Use the cube as an example and show students the faces, vertices, and edges. Record this information on the class chart. See example:

4. Ask each group to select one three-dimensional figure from the set of solids. Instruct students to work cooperatively to construct one of the faces on their solid. Discuss the characteristics of the plane (flat) shape they created. “How many vertices (corners) does the shape have? How many edges (sides)? Were you able to create non-square rectangles? If yes, how? Can you make triangles that aren’t equilateral?” NOTE: Students will have to use their problem solving skills to discover that the toothpicks can be cut to varying lengths to create non-square rectangles and triangles with sides of varying lengths. Students can also mix coffee stirrers with toothpicks to create these shapes. Allow students to complete their construction by making the remaining faces of the three-dimensional object. Students should record information about their three-dimensional object on the group chart. Questions to ask students: “How many toothpicks are stuck in each gumdrop (marshmallow, etc.)? Is the number the same for every vertex? How can you “see” the faces of the solid? How is your model like an x-ray?”
NOTE: If time permits, provide time for students to construct as many three-dimensional objects as they can.

5. Allow students to display their constructions placing the constructions next to the appropriate three-dimensional object. Provide your students with a FOCUS FOR MEDIA INTERACTION. Tell students that they have just used building materials similar to the rods in the video to make two-dimensional figures and they used the two-dimensional figures to make three-dimensional objects. Tell students to watch the video segment to see how the kids use problem-solving skills to rebuild the terminal. Ask students to make note of any similarities to their construction activities. FAST FORWARD the video to the segment that shows Dr. Marbles contacting Digit. PLAY the video until the terminal is rebuilt. STOP the video. Check for comprehension. Students should note that the rods are similar to the toothpicks. Students should also note that the students built two-dimensional figures (triangles) first and then connected the two-dimensional figures to make the three-dimensional terminal. This process is similar to the method the students used to construct their figures.

CULMINATING ACTIVITY:
1. Tell students that similar to the CYBERCHASE kids, they used two-dimensional figures to make three-dimensional objects. Show students a box that has been taken apart. Allow students to identify the two-dimensional figures used to make the box.

2. Distribute an unfolded box to each small group of students. Allow students to identify the two-dimensional shapes used to make the box. Provide each group with tape and allow students to reconstruct the boxes. Introduce the vocabulary word, net to students at this time.
NOTE: You may want to demonstrate the concept to students by tracing the outline of an unfolded box onto a piece of chart paper, cut out the net (the traced outline) of the box, reconstruct the box, and use the net to cover the box.

3. Distribute the Student Activity Sheets from the 2-D to 3-D activity on the CYBERCHASE Web site. Download the activity sheets from http://pbskids.org/cyberchase/games/23dgeometry/index.html. Provide students with scissors and tape or glue to make the three-dimensional objects that feature the CYBERCHASE kids.

4. Assessment Procedures
• Teacher Observation
• Class Participation
• Student performance on the class activities.
• Student work will be evaluated based on the successful completion of all assigned tasks and the completed recording sheets for all activities.

CROSS-CURRICULAR EXTENSIONS:
ART:
• Allow students to view the CYBERCHASE for Real segment where Howie must make a dollhouse from flat folded boxes. Howie demonstrates the process by making a paper airplane. Allow students to make simple origami shapes. Students will see how they can use paper-folding techniques to make a three-dimensional object. Allow students to make the paper box using origami.
LANGUAGE ARTS:
• Read the book, The Greedy Triangle. Allow students to name the shapes used in the book and point out shapes in everyday life that resemble the shapes in the story. Instruct students to write their own version of the story, using three-dimensional objects.
MATHEMATICS:
• Try this extension activity to reinforce lesson concepts. Take apart several boxes and trace the outline of the unfolded boxes. This will leave you with a copy of the net of the box. Divide students into groups of four. Provide each group of students with an outline of a box and allow students to match the net of the box to the appropriate box.

COMMUNITY CONNECTIONS:
• Visit a local business or production facility that uses boxes to package their goods. Students should observe that the boxes are flat before the contents are placed in the boxes. Encourage questions such as “Why are the boxes flat or two-dimensional for storage purposes? Students should observe that it is more practical to store and deliver boxes in a two-dimensional format.

STUDENT MATERIALS:
See attached. Student Materials include:
• Constructions Recording Sheet (  PDF )