7. Patterns in algebra

i. Guessing to solve equations (see chapter 8)

ii. Balance pictures (transform operations) to solve equations (see chapter 8)

iii. Solving quadratic equations 10 ways; using iteration, especially (chapter 8 and 8a.).

iv. Binomial expansion (see chapter 9)

v. Iterating functions (chapter 8) and Maura's work .

vi. Abe, a 12 year old, finds a pattern in an infinite sequence. He was iterating -16/x + 8, obtained in the process of solving the equation   x²- 8x+16=0

vii. Mr. Matsumoto's method of using iteration to find square roots .

viii. Maggie builds a box..and does some algebra (the difference of 2 cubes) and the IES Java applet that came from this.

ix. Andy's (a 9th grader) routine to find any polynomial equation given the roots!

x. Exponents (chapter 1)

xi. Sheri's work on the quadratic equation x² - x - 1 = 0  by approximation, leading to the Golden Mean

xii. Sheri uses the quadratic formula to find the base in which Don's age of 114, will give his real age of 71

xiii. Squaring a binomial and completing a square trinomial

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