-Introduce using familiar language

-Review & Reinforce

-Compare & Contrast

-Teach in different context

Increased Student Achievement

LINKING

Use Simple Straight Forward Examples –

Do not get bogged down in arithmetic

I can’t teach ________ , because my students don’t know ________ .

Add / Subtract

Rational Expressions

1

+

3

12

26

36

56

+

1+

312

=56

1+

415

=920

1+

314

=712

1+

315

=815

2+

315

=1315

3+

1023

=2930

3+

415

=

3+

415

=1920

A+

BCD

=AD + BC

BD

A+

BCD

= BD

2+

X3Y

=

XY

2+

X3Y

=2Y + 3X

XY

3+

x-12

x+3=

(x-1)(x+3)

3+

x-12

x+3=

(x-1)(x+3)

3(x+3) + 2(x-1)

Student Assessment

1+

413

=712

5+

247

18=

1824

=34

CD = 72

1824

=34

5=

241572

7=

182872

+

5372

+ Polynomials

6 7 2 = 6(100) + 7(10) + 2(1)

6 10 + 7 10 + 22

6 n + 7 n + 22

6x + 7x + 22

5 3 2 + 3 4 1

8 7 3

Addition - Left

• 412 + 352 + 215 =

• 123 + 502 + 271 =

• 432 + 125 + 301 =

(5x + 3x + 2) + (3x + 4x + 1)2 2

= (8x + 7x + 3)2

Multiplication

3 2 6 7 26 4

3 2 2 1x

3x + 6

x + 2 x + 3

2x + 2x2x + 5x + 6

(x + 3) (x + 2) = x + 5x + 62

(x + 4) (x + 5) = x + 9x + 202

(x + 10) (x + 5) = x + 15x + 502

(2x + 3) (3x + 5)

6x + 8x + 152

10x +15

2x + 3 3x + 5

26x + 9x26x +19x +15

(2x + 3) (3x + 5)

(2x + 3) (3x + 5)

26x + 19x + 15

F O I L

6 2

3 2 2 1x

6 2

3 2 2 1x

7

Relations & Functions

Functions

Special relation in which

no 2 ordered pairs have

the same 1st element.

Menu

Hamburger ……….4

Hotdog ……………3

Sandwich …………5

00

00

00

H, Hd, S,400 300 500

400H, Hd,( ,S)300 500

400(H, ) (Hd, ) (S, )300 500

.501,

2,

3,

100

150

.50(1, )

(2, )

(3, )

(10, ? )

100

150

Cold Drinks

.501,

2,

3,

100

150

.50(1, )

(2, )

(3, )

(10, ? )

100

150

C = n x .50 = .50n or

y = x12

50(1, )

(4, )200

100(2, ) 150(3, )

175(4, )

Slope

50(1, ) 100(2, ) 150(3, )

m =y - y1

x - x1

Equations of Lines

= my - y1

x - x1

y - y1 = m (x - x1)

y - y1 = m (x - x1)

Find the equation of a line passing through the point (2,3), with m = 4

y - 3 = 4 (x - 2)

point - slope

y – 3 = 4x - 8

Solve for y:

y = 4x - 5

y – 3 = 4 (x - 2)

y = mx + b

y = 4x - 5slope - intercept

4x – y = 5

general form

Using linkage, if you know slope, you can reconstruct the other

equations.

-Introduce using familiar language

-Review & Reinforce

-Compare & Contrast

-Teach in different context

Increased Student Achievement

LINKING

Linking

• Fractions

• Decimals

• Percents

Linking

• Pythagorean Theorem

• Distance Formula

• Equation of a Circle

• Trig Identity

Linking

• Special products in algebra

• Special products in arithmetic

Linking

• Quadratic Formula

• Completing the Square

Linking

• Solving Linear Equations

• Order of Operations

Why Linking?

• It’s not a matter of if students are going to forget information, it’s a matter of when. Linking concepts will allow students to reconstruct concepts and skills