# A Math lesson introducing Plane Geometry

Subject:

Math

4, 5

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

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.

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