South Carolina ETV

South Carolina ETV
1101 George Rogers Boulevard
Columbia, SC 29201-4761
Phone: 803-737-3545

Living in a Geometrical World (Grade 4)

Master Teacher

Gina Stevenson

Time Allotment

Two class periods (1 hour each)

Overview

Students will participate in a series of hands-on, online, and multimedia activities to examine the concepts of 2-dimensional and 3-dimensional shapes. After reviewing six geometric solids, students will use the information from the discussion to work together to create their own rectangular prisms from straws and pipe cleaners. They will view clips from the Cyberchase episode “Eureeka” to see how the Cyberchase team overcomes problems in trying to link 2-dimensional rods together to create a 3-dimensional shape. After the video, students will go on the Internet and explore interactive Web sites where students will revisit the idea of 3-dimensional shapes.

Subject Matter

Mathematics

Learning Objectives

Students will be able to:

Describe common geometric solids, including prisms, pyramids, cylinders, cones, and spheres, and investigate their properties.
Construct rectangular prisms using straws and ribbon, and construct a cube from a paper net.
Write and solve “What Am I?” riddles about geometric solids.

South Carolina Standards

(These Standards for grades 3-5 are available online at http://www.myscschools.com.)

4th grade Geometry

I.A.1. Choose appropriate models of two- and three-dimensional shapes from descriptions of attributes.

I.C.1. Subdivide two-dimensional shapes to form new shapes and draw conclusions about area and fractional relationships.

I.E.1. Using models and mathematical vocabulary, make and test conjectures about geometric properties and relationships and explain the conclusions.

IV.B.1. Write a description of a given three-dimensional object.

IV.C.1. Identify and build a rectangular prism from a given two-dimensional representation.

Media Components

Video

Cyberchase , episode 1 13: “Eureeka!” Pursued by Hacker, Digit and the Cyberchase kids land on cybersite Eureeka where their mission is to find Professor Archimedes. But Archimedes is nowhere to be found . . . only a pile of 2-dimensional rods where Archimedes’ factory used to be . The kids discover by linking the 2-dimensional rods together into certain geometrical patterns they can create a surprising 3-dimensional shape that leads to unraveling the mystery of Archimedes’ strange disappearance.

Web Sites

3D Solids
http://www.interactivestuff.org/match/maker.phtml?featured=1&id=15
This site is a “Concentration” type game where students match the correct 3-dimensional shape with its definition.

Shape and Space in Geometry
http://www.learner.org/teacherslab/math/geometry/space
Probe your spatial visualization skills and get practice with the three interactive activities on this Web site. They include “I Took a Trip on a Train,” where you get a map and some snapshots that you have to put in the correct order; “Plot Plans and Silhouettes,” which asks you to design a structure that would have the given silhouettes as seen from the front and side; and “Shadows,” which gives you a 3-dimensional figure and a shape of a shadow, and asks whether the figure could cast the shadow given.

Materials

Models of Geometric Solids (pyramid, cone, cube, rectangular prism, sphere, and a triangular prism)
Straws and pipe cleaners
Scissors
Geometric Solid Scavenger Hunt (Activity Sheet 1)
Paper Net of a Cube (Activity Sheet 2)
Chart paper
2 triangle pattern blocks per student

Equipment

Television and VCR
Computer with Internet access
LCD projector

Prep for Teachers

Bookmark all Web sites used in this lesson and CUE the videotape to the appropriate starting point, which is when you see the Cyberchase kids in the middle of the pattern of a cube (net).
Construct a cube with 12 straws, all the same length. You will need 16 pipe cleaners, 2 for each vertex. Use this cube to demonstrate how to construct geometric solids.
Place pipe cleaners and equal numbers of full size, ½ size, and ¾ size straws in four separate boxes. Each pair of students will need 16 pipe cleaners and 8 straws of each length.
Makes copies of the Geometric Solid Scavenger Hunt (Activity Sheet 1) and Paper Net of a Cube (Activity Sheet 2) for each student.
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: Distribute the Geometric Solid Scavenger Hunt handout.

Step 2: Display models of the six geometric solids shown on the Geometric Solid Scavenger Hunt handout (cube, rectangular prism, pyramid, cone, cylinder, sphere, and triangular prism). Begin with the rectangular prism. Hold it up and ask students to find examples of rectangular prisms in the classroom. (Some examples may include a box of tissue, the television, a stapler, an eraser, etc.) Students should find examples and write them on their Geometric Solid Scavenger Hunt handout. You may wish to keep a list on the chart paper for future reference. Continue this procedure for the remaining solids. Students may wish to walk around the room quietly while they complete the remainder of their scavenger hunt. Another possibility that will be up to your discretion is to allow students to explore the school for more examples to add to their lists.

Step 3: Once students have completed the scavenger hunt, begin a discussion by asking the following questions:

Which solids were easiest to find? (Students will probably say the rectangular prisms, cylinder, and sphere; although answers may vary.)
Which were hard to find? (Probably the pyramid, triangular prism, and cone)
Why do you think some solids are more common than others? (Students may answer that they are easier to make or are more useful for storing things.)

Step 4: Now that students have familiarized themselves with common geometric solids, refer back to the model solids you used in Step 2 . Use the display models to review vocabulary associated with geometric solids. Pose questions like the following:

Which of these geometric solids has 6 faces? (Rectangular prism)
What is a face? (A flat surface on the solid)
Which solids have a curved surface? (Sphere, cone, and cylinder)
Which has the most edges? (Rectangular prism) How many? (12)
How do you know where the edge is located on a solid? (The edges of a solid are the line segments or curves where surfaces meet.)
Which solid has two faces and one curved surface? (Cylinder)

Step 5: Show the class the cube you constructed out of the straws. (See Prep for Teachers. ) Point out that it shows only the edges of the faces. It is a “frame” for the geometric solid; the flat surfaces of the cube must be imagined. Ask students what geometric solid this construction represents. (Cube) Demonstrate how the vertices are put together. Distribute straws and pipe cleaners. Have partners work together to make a rectangular prism. One way is to start with a rectangle and build up. Have the straw cube available for inspection. Circulate as students work and assist as necessary.

Step 6: Once students have completed their rectangular prisms, asks students to identify the number of square faces in the rectangular prisms they made. (Depending upon thestraw sizes they used, the prisms will either have 0 or 2 square faces.) Students will not be able to construct cubes because they only have 8 straws of equal length. Pose the following questions:

How many faces does your rectangular prism have? (6) Show them to me.
How many edges does your rectangular prism have? (12) Show them to me.
How many vertices does your rectangular prism have? (8) Show them to me.
Does your rectangular prism have any curved surfaces? (no) How do you know? (It does not roll and is not curved.)
Are all of the faces polygons? (yes)

Learning Activities

Step 1: Tell students that they will now view a few video clips from the Cyberchase episode “Eureeka.” Set up the clips with an overview of the episode to familiarize the students with what has occurred thus far. Pursued by Hacker, Digit lands on cybersite Eureeka, where his mission is to find Professor Archimedes, the maker of the encryptor chip, a unique computer chip that can fix Motherboard. But once Digit arrives, Professor Archimedes is nowhere to be found. All that is left is a pile of 2-dimensional rods where his chip factory used to be. The kids arrive to help and must deal with a number of situations that call for applying what they know about 2-dimensional and 3-dimensional shapes.

Step 2: CUEthe tape to where you see the Cyberchase kids standing on the middle of a pattern of a flat cube (net). Provide your students with a Focus for MediaInteraction by asking students to think about ways the Cyberchase kids could possibly use the pile of rods to make a square. PLAYthe tape. STOPwhen you hear Jackie say, “I thought this was going to be easy.” Check for predictions. There are no right or wrong answers, and answers will vary. This focus question is just to have students begin to think logically about what they would do if faced with a similar situation. Accept all predictions and then tell students to continue to watch to see if any of their predictions come true.

Step 3: FAST FORWARDto the scene where you once again see Matt. He says, “Houston we have a problem.” PAUSE. Provide students with a Focus for Media Interaction by asking students to see how the Cyberchase kids solve their problem. How do they use the rods to make a square? PLAY the tape and PAUSEafter Inez says, “It’s just not possible to make a square out of two triangles.”

Step 4: Distribute pattern blocks and then begin a discussion by asking students to explain how the Cyberchase kids used rods to make a square. (Since the rods are not long enough to make a square, they decide to make two triangles instead. They will arrange the triangles to form a square.) If anyone had a prediction that matched this scenario make sure to point that out and validate. Inez thinks it is impossible to make a square out of two triangles. Do you agree or disagree? (Answers will vary.) Say to students: “By using the pattern blocks at your desk, arrange two triangles to show me if it is possible to make a square.” (Students should arrange the pattern blocks to prove that it is possible to create a square by using two triangles.)

Step 5: Provide a Focus for Media Interaction by asking students to see if the Cyberchase kids arrange their triangles the same way they did. PLAYthe video. PAUSEthe video after Inez says, “How do we use what we have to make a big square?” Students will see that the Cyberchase kids validated their answers and that it is possible to make a square from two triangles. Ask students to think about Inez’s question right before you paused the video. Ask for ways that they can now use the little square that they made out of two triangles to now make the bigger square? (Answers may vary but most students will say that they will need to form 4 little squares to make the big square. This will require 8 triangles).

Step 6: FAST FORWARDthe video until you see Digit once again. He says, “We gotta come up with something quick.” PAUSE. Provide a Focus for Media Interaction by asking students to see if their predictions were correct. How do they use the little square to make the big square? PLAY the video and PAUSEafter Inez says, “The walls of the terminal will be done.” Students will see from this clip that the Cyberchasekids build four more little squares to make the large square and that it takes a total of 8 triangles to do this. Continue the discussion by asking students to determine how many little squares it will take to make the entire pattern? (24 little squares) How many triangles will it take to make the entire pattern? (48 triangles)

Step 7: Now say: “Let’s see what happens after they build all of the squares.” Provide students with a Focus for Media Interaction by asking students to look for the 3-dimensional shape that is built once the Cyberchase kids construct all of the squares. PLAY the video. STOP the video when all of the kids say, “Archimedes’ Terminal!” Ask students to tell you about the 3-dimensional shape that was built. (A cube) Based on what they learned in the Introductory Activity, ask students to tell you the properties of a cube. (It has 6 square faces. It has 12 edges and 12 vertices.) From what 2-dimensional shapes can a cube be made? (squares) Once the discussion is completed, give each student a paper copy of the cube net (Activity Sheet 2) and have them cut it out and assemble it to make a 3-dimensional cube.

Step 8: Be sure to end this portion of the lesson with a reference back to the main idea of the Cyberchase video—when you follow simple rules to make 2-dimensional shapes, and join them together, you can discover new shapes that, instead of staying flat, rise up to make 3-D objects.

Culminating Activity

Step 1: Tell your students that they will now have the opportunity to visit a variety of Web sites where they will be further exploring 3-dimensional shapes. Have your students log onto to the 3-D Solids Web site at http://www.interactivestuff.org/match/maker.phtml?featured=1&id=15.

Provide students with a Focus for Media Interaction, by asking your students to practice matching the 3-D shapes with their definitions in the style of the game Concentration. After completing the problems, discuss what difficulties (if any) the students had with correctly matching the shapes with their definitions.

Step 2: Have students log onto the next Web site which is Shape and Space in Geometry at http://www.learner.org/teacherslab/math/geometry/space and click Activities. Provide your students with a Focusfor Media Interaction by asking them to do the three interactive activities. They are “I Took a Trip on a Train,” where you get a map and some snapshots that you have to put in the correct order; “Plot Plans and Silhouettes,” which asks you to design a structure that would have the given silhouettes as seen from the front and side; and “Shadows,” which gives you a 3-dimensional figure and a shape of a shadow, and asks whether the figure could cast the shadow given. Discuss answers with students after each activity.

Cross-Curricular Extensions

English/Language Arts: Have students solve the following riddle: “I have the same number of faces as vertices.” What am I? (Rectangular prism)

On the board, write additional riddles for students to solve. You may choose from some of the sample riddles below. You may need to uncover one clue at a time and have students guess each time. When all clues have been given, have students name the solid and explain how he or she knew it was that particular solid. Once students have had enough practice, allow them to create their own riddles individually or with a partner.

Riddles
I am a geometric solid. I have six faces. All of my faces are square. What am I? (Cube)

I am a geometric solid. I have 2 surfaces. My base is formed by a circle. I come to a point at the top. What am I? (Cone)

I am a geometric solid. I have only one surface. My one surface is round. I have no base. What am I? (Sphere)

Community Connections

Take a field trip to the local grocery store. Take a copy of the Geometrical Solids Scavenger Hunt handout to look for more examples of geometry in everyday life.

Student Materials

Geometric Solid Scavenger Hunt (Activity Sheet 1)
Paper Net of a Cube (Activity Sheet 2)