Teaching note

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Teaching note

• Supply tiles for students

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A-APR.4 Objective
Adding Subtracting Polynomials

• Prove polynomial identities and use them to
  describe numerical relationships. For example,
  the polynomial identity (x2 y2)2 (x2 y2)2
  (2xy)2 can be used to generate Pythagorean
  triples.

3
A-SSE.2

• Use the structure of an expression to identify
  ways to rewrite it. For example, see x4 y4 as
  (x2)2 (y2)2, thus recognizing it as a
  difference of squares that can be factored as (x2
  y2)(x2 y2).

4
A-SSE.3

• Choose and produce an equivalent form of an
  expression to reveal and explain properties of
  the quantity represented by the expression.

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Algebra tiles can be used to model polynomials.
These 1-by-1 square tiles have an area of 1
square unit.
These 1-by-x rectangular tiles have an area of x
square units.
These x-by-x rectangular tiles have an area of x
2 square units.
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You can use algebra tiles to add the polynomials
x 2 4x 2 and 2 x 2 3x 1.
Form the polynomials x 2 4x 2 and 2 x 2 3x
1 with algebra tiles.
x 2 4x 2







2 x 2 3x 1






7
You can use algebra tiles to add the polynomials
x 2 4x 2 and 2 x 2 3x 1.
To add the polynomials, combine like terms. Group
the x 2-tiles, the x-tiles, and the 1-tiles.
2x 2 3x 1
x 2 4x 2














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You can use algebra tiles to add the polynomials
x 2 4x 2 and 2 x 2 3x 1.
To add the polynomials, combine like terms. Group
the x 2-tiles, the x-tiles, and the 1-tiles.
2x 2 3x 1
x 2 4x 2
Find and remove the zero pairs.
The sum is 3x 2 x 1.














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Find the sum. Write the answer in standard format.
(2 x 2 x 5) (x x 2 6)
SOLUTION
Horizontal format Add like terms.
(2 x 2 x 5) (x x 2 6)
(2 x 2 x 2) (x x) (5 6)

3x 2 2 x 1
10
You are enlarging a 5-inch by 7-inch photo by a
scale factor of x and mounting it on a mat. You
want the mat to be twice as wide as the enlarged
photo and 2 inches less than twice as high as the
enlarged photo.
Write a model for the area of the mat around the
photograph as a function of the scale factor.
Use a verbal model.
SOLUTION
Area of photo
Verbal Model
Area of mat
Total Area
7x
14x 2
Area of mat A
(square inches)
Labels
5x
Total Area
(10x)(14x 2)
(square inches)
10x
Area of photo
(5x)(7x)
(square inches)

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You are enlarging a 5-inch by 7-inch photo by a
scale factor of x and mounting it on a mat. You
want the mat to be twice as wide as the enlarged
photo and 2 inches less than twice as high as the
enlarged photo.
Write a model for the area of the mat around the
photograph as a function of the scale factor.
SOLUTION

7x
(10x)(14x 2) (5x)(7x)
A
14x 2
Algebraic Model
140x 2  20x 35x 2
5x
105x 2  20x
10x
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Application

• Enrichment Test worksheet
• Non-Enrichment algebra Tiles worksheet
• Due next class