Welcome to math 302b
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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.

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Welcome to Math 302B

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Welcome to math 302b

Welcome to Math 302B

Fall 2009


Agenda

Agenda

  • Go over syllabus, class procedures, etc.

  • How to answer a homework problem

  • Begin algebraic thinking

  • Assign homework


A good answer

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

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

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

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

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 answer1

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

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

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

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

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

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

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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