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1. Top Ten Common Algebra Mistakes Presentation by: Valerie Beaman-Hackle
Associate Professor of Mathematics
Macon State College
http://facultyweb.maconstate.edu/valerie.beamanhackle/
For the Georgia Tutoring Association (GATA)
10th Annual Conference
Saturday, February 20, 2010
Macon State College
Macon, GA
2. #1 Multiplication before Division? There are only 4 levels in the order of operations agreement!
On the Multiplication and Division level, we must work left to right.
Whats logical and easy to do mentally may not follow the order of operations agreement.
Grits Eaten Daily Makes Students Achieve.
3. #2 Inside vs. Outside There are only 4 levels in the order of operations agreement!
Doing whats inside the parentheses is on the top level, but there is no do whats outside the grouping symbol.
It may be helpful to write in any understood multiplication symbols.
Whats logical and easy to do mentally may not follow the order of operations agreement.
4. #3 Whats negative? There are 3 places a negative can be in an exponential expressionhanging out front, part of the base, or part of the exponent.
If the negative is not in parentheses but instead hanging out front of the base, then just bring it down as part of your final answer and proceed to evaluate the exponential expression.
The base is negative only if the negative is inside the parentheses and the exponent is outside the parentheses.
With a negative exponent, the base is moved to the denominator and the exponent becomes positive.
5. #4 Solving equations vs. simplifying expressions Keep equation balanced!
Order of steps matter
Never combine terms over the equals sign. Think of it like a fence. No jumping over the fence
No sliding =
6. #5 Negative coefficients vs. negative terms -6 + x is different than -6 ? x
Inverse (reverse) of multiplication is division
Inverse (reverse) of subtraction is addition.
May be helpful to show solution to x 6 = 30 along side of solution to -6x = 30 to emphasize the difference in the problems
7. #6 Subtracting Polynomials The first set of parentheses dont require any special consideration, but the second set does
Think of subtraction rule: change subtraction to addition, take opposite of every term in ( )
Or think of distributing a -1 to each term
8. #7 Squaring a binomial Squaring a binomial is different that raising a product to a power.
Rewrite in expanded notation and FOIL.
May want to show an example of raising a product to a power to emphasize difference
9. #8 Simplifying Rational Expressions Differentiate between Factors and Terms
NEVER cancel TERMS.
NEVER cancel parts of terms.
Divide out (cancel) FACTORS!
Only MONOMIALS can be factored using expanded notation
10. #9 Solving Rational Equations Distribute LCD to all terms (even those that arent fractions) before canceling denominators!
Also applies to simplifying complex rational expressions.
11. #10 Solving Radical Equations Order of the step matter!
Isolate radical, THEN square both SIDES (not individual terms)!.
Also remember not to combine terms inside radical with those outside.