A Typical Algebra Exercise
For a = 3, b = 5, c = -4,evaluate ab + c2
You Never See This
• For a = 3.1, b = , c = ,• evaluate• • ab + c2
Important Ideas
• Substitution• Order of Operations
Another way to use Substitution
• Is x = -2 a solution of the equation•
What does = mean?
• True or False [try x = -2, 0, 1, 3] ?• • • •
Do Useful Formulas
• For a = 3, b = 5, c = -4,• evaluate• 2 4b ac
2 4b ac
Practice and Test
• For a = 3, b = 5, c = -4,• evaluate
2
2
4
2
4
2
b b ac
a
b b ac
a
Late October, after a test:
• Noel: This must be really important.
A voice cries out
• It’s the Quadratic Formula
Student Discoveries Matter
• It’s in chapter 7• I can solve any quadratic equation
V.I.E. [Very Important Example]
• For a = 4 and b = 6, evaluate
22 2
2 22
a b
a b
a ab b
Another way to put it
• True or False?
2 2 2
2 2 2
(1)
(2) 2
a b a b
a b a ab b
Distributivity????
• No such thing as THE Distributive Property• There is a Distributive Property of
Multiplication over Addition• There Is NOT a Distributive Property of
Exponentiation over Addition• There IS a Distributive Property of
Exponentiation over Multiplication
General Idea of “Distributivity”
• Distributive Property of * over
• a * (b c) = (a * b) (a * c)
An Identity Crisis in Trig
Let and so 2 =
• Evaluate• sin() = sin(2) =• 2sin() = 2sin()cos() =
6
A Student’s Conclusion
• With regard to sin(2x) = 2 sin(x)• “It doesn’t work for radians, but it must be
true for degrees.”
Some Reasons for Using PREVIEW
• Head off mistakes• Point out typical misconceptions• Get students used to new ideas• Teaching Difficult Topics
Other areas for preview
• Logarithms• Mathematical Induction• Properties of Quadrilaterals• Slope/Graphing• and Lots More
A motto
• LOOK BOTH WAYS BEFORE TEACHING
Title: Meta-preview
• It’s a preview of PREVIEW
Time’s Up!