1. Teaching note Supply tiles for students

2. 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

3. 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 ).

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.

5. 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

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

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

9. 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 2 + 2 x + 1

10. 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 …

11. (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

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