ALGEBRA TILES Dawne Spangler. Demonstrate Reaffirm Reassure ALGEBRA TILES Using Algebra Tiles makes algebraic logic simpler and easier to comprehend.

ALGEBRA TILESDawne Spangler

Demonstrate Reaffirm Reassure

ALGEBRA TILES

Using Algebra Tiles makes algebraic logic simpler and easier to

comprehend.

Section 1

Use rectangular arrays to model numerical values

Define value in terms of measurement

OBJECTIVES

MODELING A WHOLE NUMBER

The number 9 -

7 8 9 10 11

RECTANGULAR ARRAYS

The area model does not rely upon counting, but it is countable.

THE VALUE OF THE PIECE IS DETERMINED BY ITS AREA.

IF THIS IS “1”UNIT,

THEN THIS IS 11. THE AREA IS 1 SQUARE UNIT, SO THE VALUE OF THE PIECE IS “1”.

1

1

SO, WHAT WOULD TWO LOOK LIKE?

Section 2

Introduce negative models Develop an INATE understanding of the behavior of negative numbers in addition and subtraction problems.

OBJECTIVES

HOW DO WE MODEL A NEGATIVE NUMBER?

WE CAN USE DIFFERENT COLORS…

OR WE CAN MARK PIECES WITH +/-

COMBINE THE TILES

Find the value of-2 + -1

SHOW ME ZERO

-1 +1 = 0

FIND -4 + 2

What happens to the zero pairs?

= -2

MODEL THE FOLLOWING EXPRESSIONS, USING TILES

1 + (-3)

-5 + 2

-3 + (-4)

ADDITION OF INTEGERS

= -2

= -3

= -7

SUBTRACTION OF INTEGERS

3 – 1

-4 – (-2)

= 2

= -2

HOW WOULD YOU MODEL 1 - 3?

METHOD 1 -2

There are not enough positive tiles to take away 3. Add zero.

There are still not enough. Add another .Now it is possible to subtract.

ADDING ZEROS

Determine the value of each set of tiles.

Use the take away model to find 2 – (-3). 2 – (-3) = 5

EXAMPLES

-2-(-3)

3-6

=1

= -3

HOW WOULD YOU MODEL 1 - 3?

METHOD 2, “ADD THE OPPOSITE” 1 +(-3)

-2

Will it always work?

EXAMPLES5 – 2 5 + (-2)

3 3

-4 – (-3)

-1 -1

-4 + (+3)

TRY THESE

3 – (-5)

3 + (+5)

-2 – 4 -2 + (-4)

1 – (4) 1 + (-4)

= 8

= -6

= -3

Section 3

Introduce variables as rectangles Create algebraic expressions Perform addition and subtraction on

algebraic expressions

OBJECTIVES

ALGEBRAIC EXPRESSIONSTHE VALUE OF EACH PIECE IS DETERMINED BY ITS AREA.

A NEW PIECE IS CREATED BY ESTABLISHING A

NEW DIMENSION, “x”.

FOR PRACTICAL REASONS, “x” IS NOT A MULTIPLE OF THE DIMENSION

REPRESENTING ONE.

THE VALUE OF THIS PIECE IS x,

BECAUSE 1 x = x.

1x

Use tiles to express the following:

x + 2

3x

2x -1

EXAMPLES

COMBINING EXPRESSIONS

3x – 2x

x + 4 + x – 3

2x + 3 – x + 1

= x

= 2x + 1

= x + 4

MORE ALGEBRAIC EXPRESSIONS

3(x + 2) - 4

(5x - 6) -(3x - 2)

THE TILES MAKE THE CONCEPTS SIMPLE.

3x + 2

2x - 4

Section 4

Solve one variable equations

OBJECTIVES

SOLVING EQUATIONSMODEL 2x + 1 = 5

TO SOLVE, SUBTRACT 1 TILE FROM EACH SIDE.

NEW EQUATION 2x = 4ISOLATE x BY DIVIDING INTO TWO GROUPS

=

x = 2

2x = 4

x = 2

SOLVING EQUATIONS

2x + 3 = 72x + 3 – 3 = 7 – 3

2x = 4 2 2

Subtract 3 from each side of the equationDivide by 2 on each side of the

equation

The operations and the result are exactly the same.

x = 2

SOLVEx – 4 = 5

x = 9

Solve3x + 2 = 11

3x = 9

x = 3

Solve

2(x - 3) = 10

2x - 6 = 10

2x = 16

x = 8