College Readiness Standards

References to ‘Middle School’ convey that select Washington State College Readiness Mathematics Standards (CRS) are more aligned with Washington State Middle School-level (MS) standards (especially those in the geometry and probability sections). There are also some CRS that exceed the knowledge and skill expectations of the high school standards and fit in the realm of pre-calculus as noted as well. Some of these standards match the blue, italicized extra expectations found in the CRS.

The student accurately describes and applies concepts and procedures from algebra.

Component 7.1Recognize and use appropriate concepts, procedures, definitions, and properties to simplify expressions and solve equations.

Evidence of Learning

College Readiness Standards	Wash. State K–12 Math Standards
Footer information goes here Alignment Code Legend: 0 = No match for CRS item 1 = Approximate match; wording or grain size differences 2 = Clear match
7.1a Explain the distinction between factor and term.	Notes We think these are middle school concepts.
7.1b Explain the distinction between expression and equation.	Notes We think these are middle school concepts.
7.1c Explain the distinction between simplify and solve.	Notes We think these are middle school concepts.
7.1d Know what it means to have a solution to an equation.	1 A1.2B Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables. 1 A1.2D Determine whether approximations or exact values of real numbers are appropriate, depending on the context, and justify the selection. 1 A1.8C Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution in the context of the original problem.
7.1e Use properties of equality to solve an equation through a series of equivalent equations.	Notes We think these are middle school concepts. This is used whenever equations are solved, e.g. 1.5,2.2,2.3,2.4.
7.1f Use appropriate properties to simplify an expression, resulting in an equivalent expression.	1 A1.2C Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions. 1 A1.2.E Use algebraic properties to factor and combine like terms in polynomials.
7.1g Recognize the equivalence between expressions with rational exponents and radicals.	1 A1.2C Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions. 1 A2.2B Use the laws of exponents to simplify and evaluate numeric and algebraic expressions that contain rational exponents. 1(2 based on examples but examples don’t match the wording.)

Component 7.2Combine and simplify algebraic expressions that contain polynomials, rational expressions, radicals, or rational exponents.

Evidence of Learning

College Readiness Standards	Wash. State K–12 Math Standards
Footer information goes here Alignment Code Legend: 0 = No match for CRS item 1 = Approximate match; wording or grain size differences 2 = Clear match
7.2a Find the sum, difference, or product of two polynomials, then simplify the result.	2 A1.2.F Add, subtract, multiply, and divide polynomials.
7.2b Factor out the greatest common factor from polynomials of any degree and from expressions involving rational exponents.	2 A1.2.E Use algebraic properties to factor and combine like terms in polynomials.
7.2c Factor quadratic polynomials with integer coefficients into a product of linear terms.	2 A1.2.E Use algebraic properties to factor and combine like terms in polynomials.
7.2d Simplify quotients of polynomials given in factored form, or in a form which can be factored or determine if irreducible over the real numbers.	1 A1.2.F Add, subtract, multiply, and divide polynomials.
7.2e Add, subtract, multiply, and divide two rational expressions of the form a/(bx+c), where a, b, and c are real numbers such that bx+c ≠0 and of the form p(x)/q(x), where p(x) and q(x) are polynomials.	2 A2.2C Add, subtract, multiply, divide and simplify rational and more general algebraic expressions.
7.2f Simplify products and quotients of single-term expressions with rational exponents (rationalizing denominators not necessary).	2 A1.2C Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions. 1 A1.2.F Add, subtract, multiply, and divide polynomials. 1 A2.2C Add, subtract, multiply, divide and simplify rational and more general algebraic expressions. 1 A2.4A Know and use basic properties of exponential and logarithmic functions and the inverse relationship between them.
7.2g Simplify products and quotients of expressions with rational exponents and rationalize denominator when necessary.	Precalculus
7.2h Simplify rational expressions that involve complex fractions.	1 A2.2C Add, subtract, multiply, divide and simplify rational and more general algebraic expressions. 1 (depends on what they mean by complex fractions) Precalculus
7.2i Simplify logarithmic expressions.	2 A2.4A Know and use basic properties of exponential and logarithmic functions and the inverse relationship between them. Precalculus
7.2j Factor polynomials over the complex numbers, if possible, and relate to the Fundamental Theorem of Algebra.

Component 7.3Solve various types of equations and inequalities numerically, graphically, and algebraically;
interpret solutions algebraically and in the context of the problem; distinguish between exact and approximate answers.

Evidence of Learning

College Readiness Standards	Wash. State K–12 Math Standards
Footer information goes here Alignment Code Legend: 0 = No match for CRS item 1 = Approximate match; wording or grain size differences 2 = Clear match
7.3a Solve linear equations in one variable.	2 A1.4.A Write and solve linear equations and inequalities in one variable. 2 A1.1.B Solve problems that can be represented by linear functions, equations, and inequalities.
7.3b Solve linear inequalities in one variable, including those involving “and” and “or.”	2 A1.4.A Write and solve linear equations and inequalities in one variable. 2 A1.1.B Solve problems that can be represented by linear functions, equations, and inequalities.
7.3c Solve systems of linear and nonlinear quations in two variables.	2 A1.4.D Write and solve systems of two linear equations and inequalities in two variables. 2 A1.1.C Solve problems that can be represented by a system of two linear equations or inequalities. 2 A2.1B Solve problems that can be represented by systems of equations and inequalities.
7.3d Solve linear inequalities in two variables (graphically only) and nonlinear inequalities—numerically, graphically and algebraically.	2 A1.4.D Write and solve systems of two linear equations and inequalities in two variables. 2 G.4.D Determine the equation of a circle that is described geometrically in the coordinate plane and, given equations for a circle and a line, determine the coordinates of their intersection(s). 2 A1.1.C Solve problems that can be represented by a system of two linear equations or inequalities. 2 A2.1B Solve problems that can be represented by systems of equations and inequalities. 1 A2.3C Solve quadratic equations and inequalities, including equations with complex roots. 1 extra
7.3e Solve absolute value equations of the form \|ax + b\| = c.
7.3f Use a variety of strategies to solve quadratic equations including those with irrational solutions and recognize when solutions are non-real. Simplify complex solutions and check algebraically. Solve quadratic equations by completing the square and by taking roots.	2 A1.1D Solve problems that can be represented by quadratic functions and equations. 2 A2.1C Solve problems that can be represented by quadratic functions, equations, and inequalities. 1 A1.5.C Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers. 1 A1.5.D Solve quadratic equations that have real roots by completing the square and by using the quadratic formula. 1 A2.2A Explain how whole, integer, rational, real, and complex numbers are related, and identify the number system(s) within which a given algebraic equation can be solved. 1 A2.3.B Determine the number and nature of the roots of a quadratic function. 1 A2.3 C Solve quadratic equations and inequalities, including equations with complex roots.
7.3g Solve equations in one variable containing a single radical or two radicals.	A2.3.C Solve quadratic equations and inequalities, including equations with complex roots. A1.5.D Solve quadratic equations that have real roots by completing the square and by using the quadratic formula.
7.3h Solve exponential equations in one variable (numerically, graphically and algebraically).	2 A1.1E Solve problems that can be represented by exponential functions and equations. 2 A2.1D Solve problems that can be represented by exponential and logarithmic functions and equations. 2 (including extra) 2 A2.4 C Solve exponential and logarithmic equations. 2 including extra 1 A1.7.B Find and approximate solutions to exponential equations.
7.3i Solve rational equations in one variable that can be transformed into an equivalent linear or quadratic equation (limited to monomial or binomial denominators).	2 A2.1.E Solve problems that can be represented by inverse variations of the forms f(x)= + b, f(x)= + b, and f(x)= …They build on what they learned in Algebra I about linear and quadratic functions and are able to solve more complex problems. Additionally, students learn to solve problems modeled by exponential and logarithmic functions, systems of equations and inequalities, inverse variations, and combinations and permutations. Turning word problems into equations that can be solved is a skill students hone throughout Algebra II and subsequent mathematics courses.
7.3j Solve literal equations (formulas) for a particular variable.	2 A1.7.D Solve an equation involving several variables by expressing one variable in terms of the others.
7.3k Solve logarithmic equations.	2 A2.1D Solve problems that can be represented by exponential and logarithmic functions and equations. 2 A2.4 C Solve exponential and logarithmic equations.
7.3l Solve rational equations and inequalities with polynomial denominators.
7.3m Solve absolute value and polynomial inequalities and justify solution.	1 A2.3 C Solve quadratic equations and inequalities, including equations with complex roots 1 only quadratic inequalities

Component 7.4 (Extra Expectations)Demonstrate an understanding of matrices and their applications.

Evidence of Learning

College Readiness Standards	Wash. State K–12 Math Standards
Footer information goes here Alignment Code Legend: 0 = No match for CRS item 1 = Approximate match; wording or grain size differences 2 = Clear match
7.4a Add, subtract and multiply 2x2 matrices.
7.4b Find the inverse of a 2x2 matrix.
7.4c Evaluate the determinant of 2x2 and 3x3 matrices.
7.4d Solve 2x2 and 3x3 systems of linear equations using matrices or the determinant.	1 A2.7A Solve systems of three equations with three variables.

Component 7.5 (Extra Expectations)Demonstrate an understanding of sequences and series.

Evidence of Learning

College Readiness Standards	Wash. State K–12 Math Standards
Footer information goes here Alignment Code Legend: 0 = No match for CRS item 1 = Approximate match; wording or grain size differences 2 = Clear match
7.5a Identify a sequence as arithmetic or eometric, write an expression for the general term, and evaluate the sum of a series based upon the sequence.	2 A1.7.C Express arithmetic and geometric sequences in both explicit and recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific terms in the sequence.
7.5b Construct terms of a series from the general formula and use summation notation.	2 A2.7B Find the terms and partial sums of arithmetic and geometric series and the infinite sum for geometric series.
7.5c Use induction to prove theorems about sums of series.