Alge-Tiles an Overview. x x2x2 y y2y2 xy 1 Set 1 Set 2.

Alge-Tilesan Overview

x

x2

y

y2xy

1

Set 1

Set 2

x

x2

y

y2xy

1– x

– x2

– y

–y2 – xy

–1

+ = 0

Adding Integers

(+ 5) + (+ 7)

= 12

+

Adding Integers

(– 5) + (– 7)

= – 12

+

Adding Integers

8 + (– 5)

= + 3

(– 2) – (– 4)

Subtracting Integers

+

= 2

–

(– 4) – (+ 6)

Subtracting Integers

= – 10

–

+

Multiplying Integers

(2)(3) 6

(2)(–3) –6

(–2)(–3) 6

x2 + 2x + 4

Algebraic Expressions

x2 – 3x – 2

2x2 – x + 2

(4x + 5) + (2x – 3)

Adding Polynomials

= 6x + 2

+

(5x + 2) – (3x – 4)

Subtracting Polynomials

= 2x + 6

–

+

3(x + 2)

Multiplying Polynomials

x + 2

3

Guiding tiles

3(x + 2)


3x + 6

x(x – 3)


x – 3

x

Guiding tiles

x(x – 3)


x2 – 3x

(x + 2)(x + 3)

Multiplying Polynomialsx

+ 2

x + 3Guiding tiles

(x + 2)(x + 3)


x2 + 5x + 6

(x – 2)(x + 2)


x – 2

x +

2

(x – 2)(x + 2)


(x – 2)(x + 2)


x2 – 4

x2 + 6x + 8

Factoring Polynomials

x + 4

x +

2

x2 + 6x + 8 = (x + 2)(x + 4)

Form a rectangle

Solving Equations: solve for x

x + 3 = 8x + 3 – 3 = 8 – 3


x + 3 = 8x + 3 – 3 = 8 – 3

x = 5


2x – 1 = 52x – 1 + 1 = 5 + 1


2x – 1 = 52x – 1 + 1 = 5 + 1

x = 3


3x – 1 = x – 5


3x – 1 = x – 5

x = –2

Check3x – 1 = x – 5

x = –2

Both sides have seven white tiles.

Substitutefor

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