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!