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# A Math lesson introducing Plane Geometry

Subject:

Math

Grades:

5, 4

T267

Elementary Mathematics

Subject: Lesson Plan

Michael D. Brewer

15 April 1997

1. Topic: Introduction to Plane Geometry

2. Grade Level: 4 – 5

3. Overview: A Tangram is a Chinese puzzle made up

of 5 triangles, 1 square, and 1 parallelogram. The 7 pieces of

a Tangram can be arranged to form different shapes. Often when

students are introduced to Tangrams, they are asked to put the

pieces together to form a square. This is often a difficult and

frustrating task

because they have no background as to

how the pieces fit together. It is suggested that you have students

begin with smaller shapes requiring them to use 2, 3, 4, or 5

pieces before asking them to make a square using all 7 pieces.

4. Purpose: To provide students with some insight

as to how the Tang ram pieces fit together, and to stimulate their

interest in forming shapes and exploring patterns using the Tangram

pieces.

5. Objectives: Students will:

pieces.

A. Construct the Tangram pieces from a square paper

by following directions to fold and cut.

B. Make observations on the pieces formed and compare

how they are related to each other.

C. Explore patterns and shapes with Tangram

6. Resources/Materials:

A square sheet of paper (8.5" x 8.5") for

each student. Plastic sets of Tangram pieces. Overhead Projector

and Tangram set for demonstration.

7. Lesson Procedures: This is the introductory lesson

for a new unit in Plane Geometry. Take time to explain to your

students that understanding the characteristics of basic geometric

shapes will be helpful in later study of Pologons, perimeter and

area. Point out to students that many, many man – made and

natural objects have geometric shapes.

a. Have students seated in small groups so they can

discuss and record observations after each step.

b. Students should fold their square paper in half

along the diagonal. Unfold and cut along the crease. "What

observations can you make about the two pieces you have?"

"How can you prove your observations are correct?"

c. Take one of the halves and fold it in half and

cut along the crease. Have students make more observations and

be able to support their statements.

d. Take the other remaining half of paper and lightly

crease to find the midpoint of the longest side. Fold so that

the vertex (the vertex is the point where two sides meet to form

an angle) of the right angle (90 degree angle) touches that midpoint

and cut along the crease. Continue with observations. Congruent

and similar triangles may be discussed, as well as trapezoid.

e. Take the trapezoid (a quadrilateral with just

two parallel sides), fold it in half and cut. "What shapes

are formed?" Students may not realize that these pieces are

trapezoids as well. "What relationships do the pieces cut

have?" "Can you determine the measure of any of the

angles?"

f. Fold the acute base angle (angle less than 90

degrees) of one of the trapezoids to the adjacent right base angle

and cut on the crease. "What shapes are formed?" "How

are the pieces related to the other pieces?"

g. Fold the right base angle of the other trapezoid

to the opposite obtuse angle (angle larger than 90 degrees). Cut

on the crease. You now should have the seven Tangram pieces. "Are

there any more observations you can make?"

8. Activities/Practice: Have the students mix up

their 7 pieces and try to put them together to make the following:

Or you can have them use the plastic Tangram pieces.

a. Have the students order the pieces from smallest

to largest and explain what criteria they used for their arrangement.

b. Use 2 pieces to form a square.

c. Make a square using 3 pieces.

d. Can you make a square using more than 3 pieces?

e. Form a triangle using 2 pieces.

f. Make a triangle using 3 pieces.

g. Can you make a triangle using 5 pieces?

h. Make a parallelogram with 2 pieces?

i. Make a parallelogram with 3 pieces?

j. Make a parallelogram with 4 pieces?

k. Can you form a parallelogram with 5 pieces?

l. Can you make a square using all 7 pieces?

9. TYING IT ALL TOGETHER:

1. Have students focus on the arrangement of pieces

based on area. Use the small triangle as the basic unit of area.

What are the areas of each of the other 6 pieces?

2. Have students form squares with 3 pieces, 4 pieces,

5 pieces, 6 pieces, and all 7 pieces. "What is the area of

each square?" "Are there multiple solutions? "Are

there no solutions for any?" "Do you notice any patterns?"

3. Have students turn in a list of their observations

from Tangram folding. If the length of a side of the original

square is 2, what are the lengths of the sides of each of the

Tangram pieces?

4. Have the students make conjectures based on their

findings from the making squares activity. Students may observe

that the areas of the squares appear to be powers of 2 and that

they are unable to make a 6 piece square. When all combinations

of 6 pieces are considered, the possible areas are not powers

of

2.

Bibliography:

Zenigami, Fay,

TANGRAMS.

Leeward District

Office. Waipahu, HI.

Connections.

__ __

1996. Grade

Level 5.

D.C. Heath and Company, USA. ISBN: 0 – 669

401 21 – 8. Chapter 5, Lesson 5.6

Navarro, C.F. 1990.

Early Geometry

.

Alexandria, VA. The Start Smart Books.

ISBN 1 – 878396 – 04 – 8