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## PowerPoint Slideshow about ' Welcome to Math 302B' - britanni-howell

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### 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.
- Where appropriate, explains what a child did correctly/incorrectly, and what mathematics the child did/did not understand.

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.

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.

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.

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.

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.

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.

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

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?

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

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

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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