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Subject Area - CC.2:
Mathematics
Mathematics
- Standard Area - CC.2.2: Algebraic Concepts
- Grade Level - CC.2.2.HS: GRADE High School
Standard - CC.2.2.HS.D.9
Use reasoning to solve equations and justify the solution method.
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Assessment Anchor - A1.1.1
Operations with Real Numbers and Expressions
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Anchor Descriptor - A1.1.1.1 Represent and/or use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, square roots, and exponents).
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Eligible Content - A1.1.1.1.1 Compare and/or order any real numbers (rational and irrational may be mixed).
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Eligible Content - A1.1.1.1.2
Simplify square roots (e.g., √24 = 2√6).
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Anchor Descriptor - A1.1.1.2 Apply number theory concepts to show relationships between real numbers in problem solving settings.
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Eligible Content - A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials.
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Anchor Descriptor - A1.1.1.3 Use exponents, roots and/or absolute value to solve problems.
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Eligible Content - A1.1.1.3.1 Simplify/evaluate expressions involving properties/laws of exponents, roots and/or absolute value to solve problems (exponents should be integers from -10 to 10).
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Anchor Descriptor - A1.1.1.4 Use estimation strategies in problem-solving situations.
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Eligible Content - A1.1.1.4.1 Use estimation to solve problems.
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Anchor Descriptor - A1.1.1.5 Simplify expressions involving polynomials.
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Eligible Content - A1.1.1.5.1 Add, subtract and/or multiply polynomial expressions (express answers in simplest form – nothing larger than a binomial multiplied by a trinomial).
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Eligible Content - A1.1.1.5.2
Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax2+bx+c where a is equal to 1 after factoring out all monomial factors).
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Eligible Content - A1.1.1.5.3 Simplify/reduce a rational algebraic expression.
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Assessment Anchor - A1.1.2
Linear Equations
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Anchor Descriptor - A1.1.2.1 Write, solve and/or graph linear equations and inequalities using various methods.
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Eligible Content - A1.1.2.1.1 Write, solve and/or apply a linear equation (including problem situations).
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Eligible Content - A1.1.2.1.2 Use and/or identify an algebraic property to justify any step in an equation solving process (linear equations only).
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Eligible Content - A1.1.2.1.3 Interpret solutions to problems in the context of the problem situation (linear equations only).
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Anchor Descriptor - A1.1.2.2 Write, solve and/or graph systems of linear equations using various methods.
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Eligible Content - A1.1.2.2.1 Write and/or solve a system of linear equations (including problem situations) using graphing, substitution and/or elimination (limit systems to 2 linear equations).
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Eligible Content - A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear equations only).
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Assessment Anchor - A1.1.3
Linear Inequalities
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Anchor Descriptor - A1.1.3.1 Write, solve and/or graph linear inequalities using various methods.
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Eligible Content - A1.1.3.1.1 Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities).
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Eligible Content - A1.1.3.1.2 Identify or graph the solution set to a linear inequality on a number line.
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Eligible Content - A1.1.3.1.3 Interpret solutions to problems in the context of the problem situation (limit to linear inequalities).
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Anchor Descriptor - A1.1.3.2 Write, solve and/or graph systems of linear inequalities using various methods.
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Eligible Content - A1.1.3.2.1 Write and/or solve a system of linear inequalities using graphing (limit systems to 2 linear inequalities).
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Eligible Content - A1.1.3.2.2 Interpret solutions to problems in the context of the problem situation (systems of 2 linear inequalities only).
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Assessment Anchor - A2.1.3
Non-Linear Equations
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Anchor Descriptor - A2.1.3.1 Write and/or solve non-linear equations using various methods.
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Eligible Content - A2.1.3.1.1 Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).
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Eligible Content - A2.1.3.1.2
Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x – 2) = 1 or √( x2 + 21x) = 14).
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Eligible Content - A2.1.3.1.3 Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).
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Eligible Content - A2.1.3.1.4 Write, solve and/or apply linear or exponential growth or decay (including problem situations).
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Anchor Descriptor - A2.1.3.2 Describe and/or determine change.
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Eligible Content - A2.1.3.2.1 Determine how a change in one variable relates to a change in a second variable (e.g., y=4/x, if x doubles, what happens to y?).
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Eligible Content - A2.1.3.2.2 Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r).
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Alternate Eligible Content - CC.2.2.HS.D.9.a Order a given sequence of steps to solve an equation.
Alternate Eligible Content is designed for students assessed using the PA Alternate System of Assessment (PASA). Essentialized Example resources assist teachers in designing instruction that reduces content complexity while maintaining alignment to academic standards.
