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HRSB, 2008
Algebra Tiles1 -1
x -x
x2-x2
HRSB, 2008
Algebra TilesAlgebra Tiles
y -y
xy
-y2y2
-xy
HRSB, 2008
Question 1Question 1
)73()423( 22 yxyx
HRSB, 2008
)73()423( 22 yxyx
Display first polynomial
HRSB, 2008
)73()423( 22 yxyx
Display first polynomial
Add to your display the second
polynomial
HRSB, 2008
)73()423( 22 yxyx
Simplify by combining like terms
HRSB, 2008
)73()423( 22 yxyx
Remove “zeros”
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What remains is the answer!
)73()423( 22 yxyx
352 2 yx
HRSB, 2008
Question 2Question 2
)122()534( yxyx
HRSB, 2008
)122()534( yxyx
Display first polynomial expression
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)122()534( yxyx
Remove second polynomial expression
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)122()534( yxyxWhat is left?
42 yx
HRSB, 2008
Question 3Question 3
)33()424( 22 xxxx
HRSB, 2008
)33()424( 22 xxxx
Display first polynomial expression
HRSB, 2008
x
)33()424( 22 xxxx
Can we remove the second?
We cannot remove an if is not in the original display…
x
HRSB, 2008
x
)33()424( 22 xxxxWe have to insert into the display
without changing the value . . .
Add in zero . . . (made of a positive and a negative )
x
x
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)33()424( 22 xxxxNow we can remove the second polynomial
HRSB, 2008
)33()424( 22 xxxx
What remains is the answer!
132 xx
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Question 4Question 4
)3()122( yxyyxy
HRSB, 2008
)3()122( yxyyxy
Display first polynomial
Can you remove the second?
HRSB, 2008
)3()122( yxyyxy
We cannot remove -3
Add in -3 and +3 (they make zero and will not change the value)
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)3()122( yxyyxyNow we can remove all of
the second polynomial
Your answer is what remains
4 yxy
HRSB, 2008
Question 5Question 5
)47()513( yy
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)47()513( yy
Display the first expression
Can you remove the second expression?
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)47()513( yy
Yes!
Go ahead and remove the second expression
The answer is what remains!
16 y
HRSB, 2008
Question 6Question 6
)22()35( 22 yxxx
HRSB, 2008
)22()35( 22 yxxx
Display the first expression
Can we remove the second expression?
Not the way it is!
HRSB, 2008
)22()35( 22 yxxx
We need to add in every term from the second expression.Remember to pair these terms with
their opposite so the value of the
expression does not change.
Double Check that you have not changed the value of the original expression . . .
HRSB, 2008
)22()35( 22 yxxx
Now remove the second expression
Your answer is what remains
526 2 yxx
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Question 7Question 7
)22()33( 2 yxy
HRSB, 2008
)22()33( 2 yxy
Display the first expression
Can we remove the second?
Not the way it is!
HRSB, 2008
)22()33( 2 yxy
Add in the tiles needed.
Make sure the value of the expression has not changed
HRSB, 2008
)22()33( 2 yxy
Remove the second expression.
What remains is the answer.
52 yx
HRSB, 2008
Question 8Question 8
)12()322( yxyyxy
HRSB, 2008
)12()322( yxyyxy
Display the first expression
Add to your display the terms of the
second expression
Combine like terms
HRSB, 2008
)12()322( yxyyxy
Remove “zeros”
What remains is the answer
24 yxy
HRSB, 2008
Question 9Question 9
)32()233( 222 xyxxy
HRSB, 2008
)32()233( 222 xyxxy
Display first expression
Add the second expression to your
display
HRSB, 2008
)32()233( 222 xyxxy
Combine like terms
Remove any zeros
What remains is the answer
xxy 22 35
HRSB, 2008
Question 10Question 10
)32()2( xyxyxyxy
HRSB, 2008
)32()2( xyxyxyxy
Display first expression
See if all of the terms from the second expression can be
removed
Not the way it is!
HRSB, 2008
)32()2( xyxyxyxy
Insert zeros as needed
HRSB, 2008
)32()2( xyxyxyxy Remove second expression
What remains is the answer!
xyxy 23
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How can we simplify How can we simplify the following expression?the following expression?
)2(3 x
2 of sets 3
means expression This
x
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times three2,x
make totiles-alge use
desk,your On
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expression hesimplify t to
termslike combine Now,
simplifiedwhen
63)2(3
thatseecan We
xx
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Can you arrange the tile display to Can you arrange the tile display to create a rectangle?create a rectangle?
What are the dimensions of the rectangle or area model
you created?
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What are the dimensions of the What are the dimensions of the rectangle you created?rectangle you created?
)2(by 3 xThe dimensions are:
3
2x
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Example 2Example 2
4)-2(3x
addition. repeated using
below expression heSimplify t
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Remember repeated addition Remember repeated addition means displaying the polynomial as means displaying the polynomial as
many times as indicated by the many times as indicated by the scalarscalar
times2
)43( show
means
)43(2
x
x
HRSB, 2008
times two4,3x
make totiles-alge use
desk,your On
HRSB, 2008
expression hesimplify t to
termslike combine Now
86)43(2
thatseecan We
xx
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Can you arrange the tile display to Can you arrange the tile display to form a rectangle?form a rectangle?
Notice that the dimensions are the factors
of the original question
)43(by 2 x
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Example 3Example 3
Use repeated addition to simplify Use repeated addition to simplify
the following expressionthe following expression
)12(3 x
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)12(3 x
tiles-algeyour with thisShow
12 of sets 3
means hisRemember t
x
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)12(3 xRearrange to combine like terms
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)12(3 xState your answer
36 x
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Can you rearrange your tile display Can you rearrange your tile display to make a rectangle?to make a rectangle?
12 x
3
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Example 4Example 4
Make an area model Make an area model to answer the next questionto answer the next question
)2(4 x
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Example 4Example 4
Use the two factors to create Use the two factors to create the length and width of a the length and width of a
rectangle.rectangle.)2(4 x
)2( islength theand
4 is width The
x
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4
2 xThen fill it in to make a
complete rectangle
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4
2 xWhat is the area?
84 x
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What do you see?What do you see?
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Number 1Number 1
What are the dimensions of the rectangle?
What is the area?
What can you say about the partial products?
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Number 2
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Number 3Number 3
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Number 4Number 4
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Number 5Number 5
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Number 6Number 6
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