Iowa Core K-12 Mathematics (PDF) - Green Hills AEA

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Algebra Overview Seeing Structure in Expressions • Interpret the structure of expressions • Write expressions in equivalent forms to solve problems Arithmetic with Polynomials and Rational Expressions • Perform arithmetic operations on polynomials • Understand the relationship between zeros and factors of polynomials • Use polynomial identities to solve problems • Rewrite rational expressions Creating Equations • Create equations that describe numbers or relationships Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Reasoning with Equations and Inequalities • Understand solving equations as a process of reasoning and explain the reasoning • Solve equations and inequalities in one variable • Solve systems of equations • Represent and solve equations and inequalities graphically Disclaimer: This document is up-to-date as of 11/17/2010. The language provided may not be Page 64 of 98 modified in any way. The most current Iowa Core can be found at http://iowacore.educateiowa.gov.
Seeing Structure in Expressions A-SSE Interpret the structure of expressions 1. Interpret expressions that represent a quantity in terms of its context. ★ a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r) n as the product of P and a factor not depending on P. (A-SSE.1.) 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.2.) Write expressions in equivalent forms to solve problems 3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. ★ a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15 t can be rewritten as (1.15 1/12 ) 12t ≈ 1.012 12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. (A-SSE.3.) 4. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. ★ (A-SSE.4.) Arithmetic with Polynomials and Rational Expressions A-APR Perform arithmetic operations on polynomials 1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. (A-APR.1.) Understand the relationship between zeros and factors of polynomials 2. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). (A-APR.2.) 3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. (A-APR.3.) Use polynomial identities to solve problems 4. 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. (A-APR.4.) 5. (+) Know and apply the Binomial Theorem for the expansion of (x + y) n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. 1 (A-APR.5.) 1 The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument. Disclaimer: This document is up-to-date as of 11/17/2010. The language provided may not be Page 65 of 98 modified in any way. The most current Iowa Core can be found at http://iowacore.educateiowa.gov.
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Mathematics November 17, 2010
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Introduction Iowa Core Mathematics
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These Standards endeavor to follow
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How to read the grade level standar
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4. Model with mathematics. Mathemat
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Mathematics | Kindergarten In Kinde
Page 13 and 14: Counting and Cardinality K.CC Know
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Page 45 and 46: Expressions and Equations 6.EE Appl
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Page 51 and 52: Geometry 7.G Draw, construct, and d
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Page 61 and 62: The Real Number System N-RN Extend
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Page 69 and 70: Functions Overview Interpreting Fun
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Page 77 and 78: Geometry Overview Congruence • Ex
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Page 83 and 84: Statistics and Probability Overview
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Page 97 and 98: Schmidt, W., Houang, R., and Cogan,
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Iowa Core K-12 Mathematics (PDF) - Green Hills AEA

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