Welcome to Math 302B

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Welcome to Math 302B - PowerPoint PPT Presentation

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

Fall 2009

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

• 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.