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Math
Virginia Math
Algebra 1: Expressions and Operations
Translate between verbal quantitative situations and algebraic expressions, including contextual situations.
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Evaluate algebraic expressions which include absolute value, square roots, and cube roots for given replacement values to include rational numbers, without rationalizing the denominator.
Determine sums and differences of polynomial expressions in one variable, using a variety of strategies, including concrete objects and their related pictorial and symbolic models.
Determine the product of polynomial expressions in one variable, using a variety of strategies, including concrete objects and their related pictorial and symbolic models, the application of the distributive property, and the use of area models. The factors should be limited to five or fewer terms (e.g., (4𝑥 + 2)(3𝑥 + 5) represents four terms and (𝑥 + 1)(2𝑥² + 𝑥 + 3) represents five terms).
- Binomial special products review
- Multiply binomials
- Multiply binomials by polynomials
- Multiply binomials by polynomials: area model
- Multiply binomials intro
- Multiply binomials: area model
- Multiply monomials by polynomials
- Multiply monomials by polynomials (basic): area model
- Multiply monomials by polynomials: area model
- Multiply perfect squares of binomials
- Multiplying binomials
- Multiplying binomials by polynomials
- Multiplying binomials by polynomials review
- Multiplying binomials by polynomials: area model
- Multiplying binomials intro
- Multiplying binomials: area model
- Multiplying monomials by polynomials
- Multiplying monomials by polynomials review
- Multiplying monomials by polynomials: area model
- Special products of binomials intro
- Special products of the form (ax+b)(ax-b)
- Special products of the form (x+a)(x-a)
- Squaring binomials of the form (ax+b)²
- Squaring binomials of the form (x+a)²
- Warmup: Multiplying binomials
Factor completely first- and second-degree polynomials in one variable with integral coefficients. After factoring out the greatest common factor (GCF), leading coefficients should have no more than four factors.
- Difference of squares
- Difference of squares intro
- Difference of squares intro
- Factor quadratics by grouping
- Factoring by grouping
- Factoring difference of squares: analyzing factorization
- Factoring difference of squares: leading coefficient ≠ 1
- Factoring difference of squares: shared factors
- Factoring perfect squares
- Factoring perfect squares: 4th degree polynomial
- Factoring perfect squares: missing values
- Factoring perfect squares: negative common factor
- Factoring perfect squares: shared factors
- Factoring quadratics as (x+a)(x+b)
- Factoring quadratics as (x+a)(x+b) (example 2)
- Factoring quadratics by grouping
- Factoring quadratics in any form
- Factoring quadratics intro
- Factoring quadratics with a common factor
- Factoring quadratics: common factor + grouping
- Factoring quadratics: Difference of squares
- Factoring quadratics: leading coefficient = 1
- Factoring quadratics: leading coefficient ≠ 1
- Factoring quadratics: negative common factor + grouping
- Factoring quadratics: Perfect squares
- Factoring simple quadratics review
- Factoring using the difference of squares pattern
- GCF factoring introduction
- Identifying perfect square form
- Intro to grouping
- More examples of factoring quadratics as (x+a)(x+b)
- Perfect square factorization intro
- Perfect squares
- Perfect squares intro
- Quadratics by factoring
- Quadratics by factoring (intro)
- Solving quadratics by factoring
- Solving quadratics by factoring
- Solving quadratics by factoring review
- Solving quadratics by factoring: leading coefficient ≠ 1
- Strategy in factoring quadratics (part 1 of 2)
- Strategy in factoring quadratics (part 2 of 2)
Determine the quotient of polynomials, using a monomial or binomial divisor, or a completely factored divisor.
- Divide polynomials by linear expressions
- Divide polynomials by x (no remainders)
- Divide polynomials by x (with remainders)
- Divide polynomials by x (with remainders)
- Divide quadratics by linear expressions (with remainders)
- Dividing polynomials by linear expressions
- Dividing polynomials by linear expressions: missing term
- Dividing polynomials by x (no remainders)
- Intro to factors & divisibility
- Intro to factors & divisibility
- Intro to long division of polynomials
- Polynomial division introduction
Represent and demonstrate equality of quadratic expressions in different forms (e.g., concrete, verbal, symbolic, and graphical).
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Derive the laws of exponents through explorations of patterns, to include products, quotients, and powers of bases.
Simplify multivariable expressions and ratios of monomial expressions in which the exponents are integers, using the laws of exponents.
Simplify and determine equivalent radical expressions involving the square root of a whole number in simplest form.
Simplify and determine equivalent radical expressions involving the cube root of an integer.
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Add, subtract, and multiply radicals, limited to numeric square and cube root expressions.
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Generate equivalent numerical expressions and justify their equivalency for radicals using rational exponents, limited to rational exponents of 1/2 and 1/3 (e.g., √5 = 5 1/2; ³√8 = 8 1/3 = (2³) 1/3 = 2).