Superlesson
Algebra
Chapter 6
Systems of Equations and Inequalities
Shadowgraphs and Shadowplay are artistic modes found throughout history. Another form of play dating back to the 19th century is tangrams.
Part A, Graphing Linear Inequalities
1. Browse through the site titled Tangram. Open the site New Tangram Puzzles and examine the puzzles. Refer to the Rectangle Tangram Puzzle and focus on the square tangram piece of this puzzle. Print a copy of the New Tangram Puzzles. Place the origin of a coordinate axes at the bottom right corner of the square piece of the Rectangle Tangram Puzzle.
a. Let the units along each axis be equal in length to the length of the sides of the square. What region is bounded by the inequality y < 1?
b. Refer to the square piece of the Rectangle Tangram Puzzle and use the same origin and the same coordinate axes as in b. What region is bounded by the inequality x > 0?
Part B, Graphing a System of Linear Inequalities
2. Refer to the square piece of the Rectangle Tangram Puzzle from 1. Again, place the origin of a coordinate axes at the bottom right corner of the square piece. Let one unit along each axis be equal in length to the length of the sides of the square.
a. What region is bounded by the axes and the inequalities y < 1 and x > -1?
b. What region is bounded by the axes and the inequalities y < 1 and x - y < 0?
c. What inequalities describe the parallelogram tangram piece of the puzzle ?
Part C, Making Connections
3. Working with a partner and using the New Tangram Puzzles, choose a point for the origin and draw a coordinate axes on a piece of graph paper.
a. Mark a convenient scale on each axis.
b. Write a system of inequalities to describe each of the seven pieces of the Rectangle Tangram Puzzle.