Use the structure of an expression to identify ways to rewrite it For example: See that is the same as thus recognizing it as a difference of squares that can (x + 3)(x + 3) (x + 3)2 or x4 y4 as (x2)2– (y2)2, – be factored as (x2 y2)(x2 + y2). – HSA.SSE.A.2 3 Limitation: i) Tasks are limited to numerical expressions and polynomial expressions in one variable. ii) Examples: Recognize 532 472 as a difference of squares and see an opportunity to rewrite it in the easier-to-evaluate form – (53 + 47)(53 47). See an opportunity to rewrite a2 +9a + 14 as (a + 7)(a + 2). – Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression* Factor a quadratic expression to reveal the zeros of the function it defines Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines Note: Students should be able to identify and use various forms of a quadratic expression to solve problems. Standard Form: ax2 + bx + c Factored Form: a(x r1)(x r2) – – HSA.SSE.B.3 4 Vertex Form: a(x h)2 + k – Limitation: i) Tasks have a real-world context. As described in the standard, there is an interplay between the mathematical structure of the expression and the structure of the situation such that choosing and producing an equivalent form of the expression reveals something about the situation. ii) Tasks are limited to exponential expressions with integer exponents. Domain: Arithmetic with Polynomials and Rational Expressions Cluster(s): 5. Perform arithmetic operations on polynomials 6. Understand the relationship between zeros and factors of polynomials 7. Use polynomial identities to solve problems 8. Rewrite rational expressions Add, subtract, and multiply polynomials Understand that polynomials, like the integers, are closed under addition, subtraction, and multiplication HSA.APR.A.1 5 Note: If p and q are polynomials p + q, p q, and pq are also polynomials. – HSA.APR.B.3 6 Identify zeros of polynomials (linear, quadratic only) when suitable factorizations are available
HSA.SSE.A.2 3 Use the structure of an expression to identify ways to rewrite it For example: See that (x + 3)(x + 3) is the same as (x + 3)2 or x4 – y4 as (x2)2– (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). Limitation: i) Tasks are limited to numerical expressions and polynomial expressions in one variable. ii) Examples: Recognize 532 – 472 as a difference of squares and see an opportunity to rewrite it in the easier-to-evaluate form (53 + 47)(53 – 47). See an opportunity to rewrite a2 +9a + 14 as (a + 7)(a + 2). HSA.SSE.B.3 4 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression* Factor a quadratic expression to reveal the zeros of the function it defines Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines Note: Students should be able to identify and use various forms of a quadratic expression to solve problems. Standard Form: ax2 + bx + c Factored Form: a(x – r1)(x – r2) Vertex Form: a(x – h)2 + k Limitation: i) Tasks have a real-world context. As described in the standard, there is an interplay between the mathematical structure of the expression and the structure of the situation such that choosing and producing an equivalent form of the expression reveals something about the situation. ii) Tasks are limited to exponential expressions with integer exponents. Domain: Arithmetic with Polynomials and Rational Expressions Cluster(s): 5. Perform arithmetic operations on polynomials 6. Understand the relationship between zeros and factors of polynomials 7. Use polynomial identities to solve problems 8. Rewrite rational expressions HSA.APR.A.1 5 Add, subtract, and multiply polynomials Understand that polynomials, like the integers, are closed under addition, subtraction, and multiplication Note: If p and q are polynomials p + q, p – q, and pq are also polynomials. HSA.APR.B.3 6 Identify zeros of polynomials (linear, quadratic only) when suitable factorizations are available
Algebra_I_2016.docx