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Welcome to Math 302B

Welcome to Math 302B. Fall 2009. Agenda. Go over syllabus, class procedures, etc. How to answer a homework problem Begin algebraic thinking Assign homework. A good answer…. Shows how you got the answer (all the work). Explains why you did what you did.

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Welcome to Math 302B

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  1. Welcome to Math 302B Fall 2009

  2. Agenda • Go over syllabus, class procedures, etc. • How to answer a homework problem • Begin algebraic thinking • Assign homework

  3. A good answer… • Shows how you got the answer (all the work). • Explains why you did what you did. • Where appropriate, explains what a child did correctly/incorrectly, and what mathematics the child did/did not understand.

  4. Here’s a problem. • The first five terms of a sequence are 2, 5, 10, 17, 26, … • What is the 10th term? • What is the nth term? • Introduce yourselves at your table. • In your groups, try to figure out the tenth term. Then, write a sentence or two that you think is perfect for a homework answer.

  5. Unacceptable Answers • 10th term is 101 • 2, 5, 10, 17, 26, … 101, … ? • 2, 5, 10, 17, 26, 37, 50, 65, 82, 101, … • This is a trick question. There is no answer.

  6. More unacceptable answers • The 10th term is 101. I did the math in my head. • The 10th term is 101. I did the math on my calculator. • The 10th term is 101. I just did trial and error--lucky me! I got it on the first try.

  7. Acceptable answer • I see the pattern 2, 5, 10, 17, 26, …. So I made a table:Term: 1 2 3 4 5 6 7 8 9 10Pattern: 2 5 10 17 26 37 50 65 82 101 • Then, I saw that 5 - 2 = 3; 10 - 5 = 5; 17 - 10 = 7; 26 - 17 = 9. The differences increase by 2, so to continue, I would add 11, then 13, then 15, and so forth. So the 10th term is 101.

  8. Acceptable answer • I see the pattern 2, 5, 10, 17, 26, …. By itself, there is nothing that leaps out at me. But, if I subtract 1 from each number, I get 1, 4, 9, 16, 25, … which are the perfect squares. So, each number is n2 + 1. So the 10th term is 102 + 1 = 100 + 1 = 101.

  9. Algebraic Reasoning • Organizing data and generalizing data: • Mathematical modeling through graphs • Mathematical modeling through tables. • Generalizing patterns • Relationships involving variables--things that vary. • We use the rules of algebra to express algebraic reasoning.

  10. Does a variable “vary”? • 5x = 60 • y = 3x - 4 • C = π • d • n/n = 1 if n ≠ 0. • y = kx • sin2(x) + cos2(x) = 1

  11. The Equal Sign = • Signifies that the expressions on each side are equivalent. • If 3x + 4 = 12, then 3x + 4 - 4 = 12 - 4. • Look back at the properties: commutative, associative, distributive, identity, inverses • Now look at algebraic “formulas” • (x + 3)(x - 4) = 0 means either x + 3 = 0 or x - 4 = 0. Why?

  12. Function • A special relationship found in algebra is the function. A function is a relation where every value of input has just one value of output. • Your age today: your height today. • Students name: Students ID number • Number of hours worked: Paycheck • Diameter of a circle: area of the circle

  13. These are not functions • Shoe size: number of shoes you own. • Your height: Your age • Date: price of gasoline in the area • Length of a football field: Year of Superbowl • Number of courses you are registered for: number of students in your largest class

  14. In any function • The input is called the independent variable. We usually put this on the x-axis. • The output is called the dependent variable. That is, it depends on the independent variable. We usually put this on the y-axis. • Example: age vs. height; typically, your height depends on your age.

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