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ALGEBRA TILES. Variables such as ‘x’ and ‘y’ are used to represent an unknown number Algebra tiles are the generally accepted manipulative to help students understand the concepts of variables and “POLYNOMIALS” POLYNOMIALS: a series of terms with a number of different variables in it.

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Algebra tiles l.jpg

ALGEBRA TILES

Variables such as ‘x’ and ‘y’ are used to represent an unknown number

Algebra tiles are the generally accepted manipulative to help students understand the concepts of variables and “POLYNOMIALS”

POLYNOMIALS: a series of terms with a number of different variables in it.

i.e., x2 + 2x + 3 or 3x – 2xy + 4y


Algebra tiles2 l.jpg
ALGEBRA TILES

Let the blue square represent X2

x

y

x and the yellow square = y2y

Therefore,

y

X2

y2

X

xy

y2


Using overhead set of tiles l.jpg
Using overhead set of tiles

What are the polynomials?

Copy and solve….


2x 2 3xy y 2 l.jpg
2x2 + 3xy + y2


2x 2 3xy y 25 l.jpg
2x2 + 3xy + y2

X2

X2

xy

xy

xy

y2


The additive inverses negative l.jpg
The Additive Inverses (negative)

These are the negatives of the terms. i.e.,

-xy

- x2

-xy

-xy

-y2

-y2


2x 2 x 2 xy 2xy l.jpg
-2x2 + x2 + xy -2xy

- x2

- x2

X2

-xy

xy

-xy


2x 2 x 2 xy 2xy8 l.jpg
-2x2 + x2 + xy -2xy

- x2

- x2

X2

-xy

xy

-xy


1x 2 1xy or x 2 xy l.jpg
-1x2 -1xy (or -x2 –xy)

- x2

-xy


Change of representation l.jpg
Change of representation

X2

x2 + x + 1

x

1


Slide11 l.jpg

2x2 - 2x + 3

X2

X2

1

1

1

x

x


Slide12 l.jpg

2x2 + 2x + 3

  • (x2 + x + 2)

X2

X2

1

1

1

x

x


Slide13 l.jpg

2x2 + 2x + 3

  • (x2 + x + 2)

X2

X2

1

1

1

x

x



X 1 x 215 l.jpg
(x + 1) (x + 2)

X 1

X

2

X2

x

x

1

x

1


Slide16 l.jpg
Try

  • (x – 3) (x + 1)


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