Standards Detail
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Subject Area - CC.2:
Mathematics
Mathematics
- Standard Area - CC.2.2: Algebraic Concepts
- Grade Level - CC.2.2.8: GRADE 8
Standard - CC.2.2.8.B.1
Apply concepts of radicals and integer exponents to generate equivalent expressions.
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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).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).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).
Eligible Content - A1.1.1.5.3 Simplify/reduce a rational algebraic expression.
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Assessment Anchor - M08.B-E.1 Demonstrate an understanding of expressions and equations with radicals and integer exponents.
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Anchor Descriptor - M08.B-E.1.1 Represent and use expressions and equations to solve problems involving radicals and integer exponents.
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Eligible Content - M08.B-E.1.1.1 Apply one or more properties of integer exponents to generate equivalent numerical expressions without a calculator (with final answers expressed in exponential form with positive exponents). Properties will be provided. Example: 3^12 x 3^-15 = 3^-3 = 1/(3^3)Eligible Content - M08.B-E.1.1.2 Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of perfect squares (up to and including 12^2) and cube roots of perfect cubes (up to and including 5^3) without a calculator. Example: If x^2 = 25 then x = ±√25.
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Alternate Eligible Content - M08.B-E.1.1.2a Identify the meaning of an exponent (limited to exponents of 2 and 3).
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.
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Eligible Content - M08.B-E.1.1.3 Estimate very large or very small quantities by using numbers expressed in the form of a single digit times an integer power of 10 and express how many times larger or smaller one number is than another. Example: Estimate the population of the United States as 3 × 10^8 and the population of the world as 7 × 10^9 and determine that the world population is more than 20 times larger than the United States’ population.Eligible Content - M08.B-E.1.1.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Express answers in scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology (e.g., interpret 4.7EE9 displayed on a calculator as 4.7 × 10^9).
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