POLYGON, POLYHEDRON:

POLYGON, POLYHEDRON:ARE YOU PLANELY OR SOLIDLY SHAPED?

MASTER TEACHER Gladys Tilley

GRADE- K-2

Time Allotment: Four - Five 45 minute class periods with student maturity level and pacing considered.

Overview: This lesson provides students with the opportunity to become familiar with plane and solid shapes in the real world and use terminology identified with each. Through the use of videos and hands on activities, students will achieve lesson objectives.

Subject Matter: Math

Learning Objectives:
Students will be able to:

Ÿ identify plane and solid shapes

Ÿ identify shapes as polygons and polyhedrons

Ÿ describe shapes used in lesson

Ÿ construct plane and solid shapes

Standards:
From the Texas Essential Knowledge and Skills for Mathematics

Chapter A. Elementary

§111.12. Mathematics, Kindergarten

(K.09) Geometry and spatial reasoning. The student uses attributes to determine how objects are alike and different.

The student is expected to:

(A) Describe and identify and compare real-life objects or models of solids;

(B) Recognize shapes in real-life objects or models or models of solids; and

§111.13. Mathematics, Grade 1

(1.6) Geometry and spatial reasoning. The student uses attributes to identify, compare, and contrast shapes and solids. The student is expected to:

(A) Describe and identify objects in order to sort them according to a given attribute using informal language;

(B) Identify circles, triangles, and rectangles, including squares, and describe the shape of balls, boxes, cans, and cones; and

§111.14. Mathematics, Grade 2.

(2.7) Geometry and spatial reasoning. The student uses attributes to identify, compare, and contrast shapes and solids. The student is expected to:

(A) Identify attributes of any shape or solid;

(B) Use attributes to describe how two shapes or two solids are alike or different; and

Media Components:

Videos

Mathica’s Math Shop: The King Comes Calling #102

Mathica’s Math Shop: Help Wanted #101

Mathica’s Math Shop: Food For Thought #103

Eddie Files: Geometry: Invasion of the Polygons #103

Web Sites

PBS TeacherSource Math
www.pbs.org/teachersource/math
This web site has lesson plans, online activities, classroom resources, and professional development projects.

The Math Forum - Teacher’s Place
http://forum.swarthmore.edu/teachers
This web site has math for all levels - Primary, Secondary, College, University, Special Interest, General Interest (Ask Dr. Math, Teacher2Teacher and other topics). The Math Library has extensive geometric topics.

Materials:

For each student:

15 craft picks or tooth picks
1/2 stick of clay
1 die-cut cone, cube and rectangular prism for easy assemblage
Approximately 6-8 cut outs of each plane figure shapes

For teacher:

3-D solid shapes
Various real world items in shapes of solid and plane figures,
examples: rectangular prism (ABC block/ dice), cone (carrot), cube (ABC block), cylinder (food can), sphere (ball), circle (paper plate), paper squares, triangles, rectangles

Prep for Teachers:

Cue videotape to the appropriate starting point. Prepare all hands-on materials and count to make sure there are enough for each student participating.

Introductory Activity: Setting the Stage

The following activities will prepare your students for a lesson on plane and solid shapes and provide them with the ability to recognize, identify by name and describe plane and solid shapes.

Step 1: Establishing recognition, identification and description of plane shapes.

Tell students that you are going to show them several shapes for recognition, identification and to describe their appearance.

Step 2: Show students a paper plate and ask if they recognize the object, to tell what it is and if they know the name of the shape it looks like (paper plate, round, circle). Ask students to tell how may sides and corners they see on the shape (no sides, no corners). Ask students to look around the room and find other circles (door knobs, television and computer buttons, buttons on clothing, wheels, dots, periods, etc.)

Step 3: Next, show students a paper rectangle and ask them to tell if they recognize the shape, to tell what it is and name it if they can (rectangle). Ask them to describe it (four sides and four corners). Again they are asked to look around the room and name any rectangular shapes they see (doors, a sheet of paper, posters, pictures, tables, etc.). Tell them that all rectangles have 4 sides and 4 corners and most have two long sides and two short sides. Depending upon the maturity level of the students, you may wish to introduce angles when talking about corners.

Step 4: Show a paper square. Ask students to tell if they recognize the shape, to name it and describe it (square, 4 corners, 4 sides). Ask them to look around the room and name any square shaped objects they may see (books, cabinet doors, post-it-notes, etc.)

Ask students to tell what they know about rectangles (4 sides, 4 corners). Ask them to describe the square (4 sides, 4 corners). Ask them to tell if a square has 2 long sides and 2 short sides (no). Remind them that all rectangles have 4 sides and 4 corners. Ask students if having 4 sides and 4 corners will make the square a rectangle also (answers may range from yes, no, maybe to I don’t know). Tell students that a square is a very special rectangle with four sides that are the same length and that it is the only special rectangle that can be described that way.

Step 5: Show an equilateral paper triangle. Have students observe, name and describe (triangle, 3 sides and 3 corners). Tell students that the triangle shown has 3 sides that are all the same length but that not all triangles do. Show differently shaped triangles and establish that they all have 3 sides and 3 corners. Depending upon the maturity level of the students you may wish to name the triangles -isosceles, equilateral, scalene, acute, obtuse, right. Also depending upon the maturity level, students my be told that the isosceles, equilateral and scalene triangles are named according to the length of their sides and acute, obtuse, and right triangles are named according to their angle sizes. Accelerated first graders and second graders may better understand these terms and descriptions.

Learning Activities:

Provide students with a Focus For Media Interaction by asking them watch the video -Mathica‘s Math Shop‘s- The King Comes Calling and ask how many shapes they can find in the video and how they are used.

Lesson 1

Begin video where Mathica says, “What can I do to please him?” and snaps her fingers. Pause video when Mathica hangs the King’s picture on the wall and says, “If this doesn’t please him, nothing will.”

After students have viewed the video segment, ask them a) What shapes did you see in the video segment? b) How were the shapes used? (rectangles - folders, king’s pictures, king’s eyeglasses.

Tell students to watch again to see what other shapes are seen and how they are used. Fast Forward video to where the King sits and says, “Here’s my problem.” Pause video after Mathica counts the coins. Ask students to tell what shape was seen in this segment and how it was used (circle, coins).

Again Fast Forward video to where Mathica hangs up the telephone and says, “Gotcha! I’ll get on it right away.” Ask students to tell what shapes were on the chart and how they were used (square, triangle used as tables for seating guests). End video when Mathica says, “If you want to have some fun, try sorting the guests as I sorted the kings”.

At the end of this first part of the lesson, you may wish to review all information learned. Advanced/accelerated students may be ready to learn that the shapes discussed in the lesson are all flat and therefore called plane shapes. Another name for them is polygon because they are flat. You may wish to give students paper shapes and have them create different objects with them as a culminating activity for this part of the lesson.

Lesson 2: Establishing recognition, identification and description of solid shapes.

Using paper shapes, review the plane shapes used in lesson 1. Tell students you will show them four shapes for recognition, identification and describing.

Show a grapefruit (ball, orange, etc.) for student identification. Ask them to tell

what plane shape it most resembles (circle). Ask them to tell if there are sides and corners (no). Pass the ‘grapefruit’ and a circle around for examination.

If the class is large, you may need more than 1 ‘grapefruit’ and paper circle.

When all have had a chance to examine both, ask students to tell the difference between the ‘grapefruit’ and the circle (the ‘grapefruit’ is round and heavier; the circle is light and flat). Tell students that the ‘grapefruit’ is indeed heavier because it has space and the space is filled. The ’grapefruit’ shape is called a sphere and it is a solid. Show the geometric wood sphere shape for comparison. Establish that the ‘grapefruit’ can roll but not be stacked and will not slide.

Next, show a jar (a can, paper towel tube, etc.) and ask what this might be called. Establish that this is a cylinder because it is round on both ends and curved on the sides. It can stack, slide and roll. Ask students to tell if the cylinder is a solid or plane figure and why (a solid because it occupies space). Pass the jar and the geometric solid cylinder around for comparison.

The shape to show next is a soapbox (cereal box, book, etc.) for identification.

Ask students to tell what it is and if they know the name for it. Have students describe it (four sides, four corners, looks like a rectangle). Ask students to tell if it is a solid or plane shape and why (solid because it has space). Tell students that this is a rectangular prism. It may be stacked and will slide but will not roll. Pass it around along with the wooden rectangular prism for comparison.

The final shape shown for this lesson is an ABC block (certain boxes, dice, etc.).

Ask students to tell what they see about the shape and size of the block (6 sides, each side looks like a square). Tell learners they are correct. Establish that the shape they are about to examine is a cube. Ask if the shape is plane or solid figure and tell why (solid because it has space). Pass the block and wooden cube solid for comparison. Tell students that the cube will stack and slide, but not roll.

When all shapes have been returned, ask students if they remember what the plane figures were called and why (polygons, they were flat). Again, depending upon the maturity level of your students the term polyhedron may be introduced. Tell students that polyhedron shapes occupy space. Therefore, the solid shapes are polyhedrons.

Now tell students they are going to watch a video to see how well they have learned to recognize solid shapes. Tell them that they are going to watch Mathica again as she sees some solid shapes. You will ask them the names of the shapes and how Mathica presented them.

Begin video when Mathica takes her mesh bag and says, “I’ll make you another deal.” End video after the Math Magician gives Mathica some riddles to solve. Ask students to name the solid shapes Mathica presented and to describe each. Ask which will a) stack, b) slide, c) roll?

Holding the sphere, ask: “How many sides and corners does a sphere have? (none)

Holding the rectangular prism, ask: “How many sides and corners does a rectangular prism have?” (4 sides, 4 corners)

Holding the cube, ask: “How many sides and corners does a cube have?” (6 sides, 8 corners - these may have to be counted for students to actually know).

Holding the cylinder, ask: “How many sides and corners does the cylinder have?” (no sides, no corners)

Tell students that the rectangular prism, cube and cylinder have some flat surfaces and these flat surfaces are called faces. Therefore, a cylinder has 3 faces, two on which it can stack and slide, the rectangular prism has 6 faces on which it can stack and slide and the cube has 6 square faces on which it can stack and slide. The sphere has none. It can only roll.

Students may wish to experiment with the shapes to see if they actually slide, stack and roll at the end of today’s lesson.

Lesson 3: Establishing recognition, identification and description of solid shapes.

Review shapes lesson identified and described in lessons 1 and 2. Tell students that today, they will be introduced to a new solid (polyhedron). Show students a carrot. Ask them to tell what it is and what solid shape they think it resembles. If no one guesses, tell them it resembles a cone. The carrot is pointed on one end, basically flat on the other end and is rounded from top to bottom. It will roll. Ask students to tell another object that is in the shape of a cone (ice cream cone, witch’s hat). Tell students they are going to watch Mathica’s Math

Shop’s Help Wanted to see if they can find the new solid and other solid shapes studied in the lessons.

Begin video when Mathica enters 1 Wonder Way and says, “Whew! Some set up.” Pause video when the Math Magician says, “Estimate!”

Ask students a) what solid shapes did Mathica find at 1 Wonder Way? (cube, cylinder); b) what was found on each shape? (its name); c) what is the shape of the jar that held Jack’s beans? (cylinder)

Fast Forward video to where the Wicked Witch comes in. Pause video when the Wicked Witch says, “I make problems.”

Ask students to tell the shape of the witch’s hat. (cone) Hold up a cube solid and ask students to describe it. (6 sides, flat on all sides, sides look like squares, 8 corners) Show cone solid and have it described. (pointed at one end, one end is flat, rolls in a circle)

Fast Forward to where the magician says, “Guess the riddles and find the shapes. Whoever does best shall make this her home.” Pause video after each riddle to give students a chance to interact with video. Stop and Rewind video when Mathica says, “It’s the same shape as this cone. So we’ll just put it down next to it.”

NOTE: Asking students to name and draw some polygons. Naming and drawing some polyhedrons may serve as the lesson assessment if teacher chooses. Students may also be asked to describe orally some polygons and polyhedrons as part of the assessment.

End of third lesson.

Culminating Activities:

1. Show the Eddie Files video on Geometry with the sound off. Have students identify as many shapes as possible as the video plays.

The following activities may be done as a group or divided into smaller groups.

2. Give each student at least 15 craft picks and clay. Tell them to construct at least one polygon and one polyhedron.

3. Give students 1 die-cut of each solid (cone, rectangular prism, cube) for construction.

Cross-Curricular Activities:

VISUAL ART/ LANGUAGE ARTS CONNECTION
Provide students with drawing paper, pencils, and crayons. Have them draw and color polygons and polyhedrons. Label the shapes drawn.

VISUAL ART
Have students use polygons and polyhedrons to construct other objects.

Community Connections:

Ÿ Contact a local architect and ask him/her to visit the class and show how shapes are used in his/her profession.

Ÿ Contact a local builder and ask him/her to visit the class and discuss how shapes are used in his/her profession.

Ÿ Contact the local school district’s carpentry department to visit the class and show some of the tool shapes used in carpentry and discuss the shapes the tools can construct.

Ÿ A local school district geometry teacher may be contacted to visit the class in an off period to show how geometry classes use shapes.

· A local interior designer may be contacted to visit the class and describe how shapes are used in his/her profession.

· Take a field trip to a local grocery store to identify different shapes.

Updated: April 01, 2008