Aim:

1. To explore fractional relationships among shapes.

2. To connect fractional relationships among shapes to the concept of area.

3. To develop understand of the concept of area.

4. To apply the concept of area to real life situations.

Standards:

1. Understands concepts of area.
2. Understands how changes in dimension affect the area of a polygon. Understands that measurement is approximate.
3. Understands that precision is related to the unit of measurement used and the calibration of the measurement tool.
4. Understands that the precision and accuracy of measurement is affected by the measurement tools.

5. Uses models to reason about the relationship between area and the measurement of the sides of a polygon in simple situations.

Materials: tangram pieces, graph paper, pencil, drawing application such as AppleWorks.

Vocabulary:

 area square units measure dimensions width length fractional part by

Motivation:

1. Developing the concept of area:

Students count the total number of floor tiles on the classroom floor. If each square is one unit, what is the area of the classroom floor? If each square equaled 2 units, what would the area of the room be? In which situations would you need to know the are of a polygon? (covering a table with a tablecloth, carpeting a floor, tiling a wall).

Development:

1. Log onto http://mathforum.org/trscavo/tangrams/area.html.This is A Math Forum Web Unit: Areas of Tangram Pieces by Tom Scavo. Students follow the warm up activities as described on the web site.
2. Using tangram pieces, and establishing the small square to equal one square unit, answer these questions.

• Which of the tangrams pieces have an area of 1 square unit?
• Which of the tangram pieces have an area of 1/2 square unit?
• Which tangram pieces have an area of 2 square units?
• Describe in words various ways in which you can create a figure that has the area of 1 square unit, 2 square units, 3 square units? 4 square units. Fill in the chart below:
 Number of Square Units Draw the Figures 1 2 3 4 5 6 7 8 9 10

Summary:

Find the area of each tangram character created in Grandfather Tang's Story. (Establish the small square as having the area of one square unit). Use your tangram pieces to model each character. (characters include: Grandfather, Little Soo, cat, rabbit, dog, squirrel, hawk, turtle, crocodile, goldfish, goose, and lion).

Evaluation:

Use tangram pieces to find the area of three of the characters in your original tangram story. Complete the chart. (assume the small square is one square unit).

 Tangram Character Picture of the character Area

Explain in words how you calculated the area of each character.

The concept of perimeter may be developed next. Since some of the tangram pieces are not equilateral figures, the concept of Pythagorean theory might also need to be developed or students may use a ruler to measure each side of each tangram piece when calculating perimeter.

Related Web Sites:

1. This site provides a lesson in which students develop a basic understanding of area without formulas, a familiarity with the names of certain polygons, and the meaning of the term congruent. http://mathforum.org/trscavo/tangrams/area.html

2. This site provides different floor tile plans that may be used in making up problems to be solved as a way to reinforce the concept area. http://bedrosians.com/flrpatt1.htm