Introduction 

What is Algebra?

• Algebra is a problem-solving technique. 
• It is abstract in that you can discuss relationships without knowing all of the the "numbers" involved.    

Why learn algebra?

• It helps us make decisions in business, science, and life. 
• It is a foundation skill for higher-levels of mathematics
• It helps build areas of the brain that solve problems (see quote below). 

"Learning algebra isn't about acquiring a specific tool; it's about building up a mental muscle that will

come in handy elsewhere.  You don't go to the gym because you're interested in learning how to

operate a StairMaster; you go to the gym because operating a StairMaster does something laudable

to your body, the benefits of which you enjoy during the many hours of the week when you're not on a StairMaster."

-- Steven Johnson, "Everything Bad Is Good For You"

Algebra is like English

• Writing English sentences requires you to know the rules of grammar and punctuation.
• Solving algebraic problems requires you to know the rules of arithmetic, exponents, and order of operations.
• Remember the example below from class.  You understood the sentence becuase you knew  English rules.
• You will learn many rules to make algebra easy!

then he if should Bill hard “A” receive works an

 

Patterns

Algebra should be fun becuase it involves puzzles.  Much of algebra is recognizing patterns and simplifying problems using a set of rules.

Recall the examples from class:

 

Also, recall that adding up large lists of numbers is easier if you reorganize the numbers into easier patterns (or groups)

1 + 2 + 3 + 4 + ... + 97 + 98 + 99   -->    (1 + 99) + (2 + 98) + (3 + 97) + (4 + 96) with one 50 unpaired