Teaching note Supply tiles for students

A-APR.4 Objective: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x 2 + y 2 ) 2 = (x 2 – y 2 ) 2 + (2xy) 2 can be used to generate Pythagorean triples. Adding & Subtracting Polynomials

A-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x 4 – y 4 as (x 2 ) 2 – (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 – y 2 )(x 2 + y 2 ).

A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

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. +– +–+– 1–1x–xx 2x 2 –x 2 MODELING ADDITION OF POLYNOMIALS

You can use algebra tiles to add the polynomials x 2 + 4x + 2 and 2 x 2 – 3x – – – MODELING ADDITION OF POLYNOMIALS –– 1Form the polynomials x 2 + 4x + 2 and 2 x 2 – 3x – 1 with algebra tiles. x 2 + 4x x 2 – 3x – 1

MODELING ADDITION OF POLYNOMIALS You can use algebra tiles to add the polynomials x 2 + 4x + 2 and 2 x 2 – 3x – – –++–– x 2 + 4x + 2 2x 2 – 3x – 1 2To add the polynomials, combine like terms. Group the x 2 -tiles, the x -tiles, and the 1 -tiles ––– + +– =

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

Find the sum. Write the answer in standard format. (2 x 2 + x – 5) + (x + x 2 + 6) Adding Polynomials 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 x + 1

Total Area = (10x)(14x – 2) (square inches) Area of photo = 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. Using Polynomials in Real Life Write a model for the area of the mat around the photograph as a function of the scale factor. Verbal Model Labels Area of mat = Area of photo Area of mat = A (5x)(7x) (square inches) Total Area – Use a verbal model. 5x5x 7x7x 14x – 2 10x SOLUTION …

(10x)(14x – 2) – (5x)(7x) 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. Using Polynomials in Real Life Write a model for the area of the mat around the photograph as a function of the scale factor. A = = 140x 2 – 20x – 35x 2 SOLUTION = 105x 2 – 20x A model for the area of the mat around the photograph as a function of the scale factor x is A = 105x 2 – 20x. Algebraic Model … 5x5x 7x7x 14x – 2 10x

*******Application *****Enrichment: “Test” worksheet ****Non-Enrichment: algebra Tiles worksheet Due next class