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.
1. Understands concepts of area.
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.
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).
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.
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).
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).
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