Gizmos for California - Mathematics: High School: Algebra (Common Core State Standards adopted 2014)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

A-SSE: : Seeing Structure in Expressions

1.1: : Interpret the structure of expressions

A-SSE.1: : Interpret expressions that represent a quantity in terms of its context.

A-SSE.1.a: : Interpret parts of an expression, such as terms, factors, and coefficients.

A-SSE.1.b: : Interpret complicated expressions by viewing one or more of their parts as a single entity.

A-SSE.2: : Use the structure of an expression to identify ways to rewrite it.

1.2: : Write expressions in equivalent forms to solve problems

A-SSE.3: : Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A-SSE.3.a: : Factor a quadratic expression to reveal the zeros of the function it defines.

A-SSE.3.b: : Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

A-APR: : Arithmetic with Polynomials and Rational Expressions

2.1: : Perform arithmetic operations on polynomials

A-APR.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.

2.2: : Understand the relationship between zeros and factors of polynomials

A-APR.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.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.

2.3: : Use polynomial identities to solve problems

A-APR.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.

A-CED: : Creating Equations

3.1: : Create equations that describe numbers or relationships

A-CED.1: : Create equations and inequalities in one variable including ones with absolute value and use them to solve problems.

A-CED.2: : Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A-CED.3: : Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

A-CED.4: : Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

A-REI: : Reasoning with Equations and Inequalities

4.1: : Understand solving equations as a process of reasoning and explain the reasoning

A-REI.1: : Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

4.2: : Solve equations and inequalities in one variable

A-REI.3: : Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

A-REI.3.1: : Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context.

A-REI.4: : Solve quadratic equations in one variable.

A-REI.4.a: : Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form.

A-REI.4.b: : Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

4.3: : Solve systems of equations

A-REI.5: : Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

A-REI.6: : Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

A-REI.8: : Represent a system of linear equations as a single matrix equation in a vector variable.

A-REI.9: : Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

4.4: : Represent and solve equations and inequalities graphically

A-REI.10: : Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

A-REI.11: : Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

A-REI.12: : Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Correlation last revised: 12/27/2023

California - Mathematics: High School: Algebra

Common Core State Standards | Adopted: 2014

A-SSE: : Seeing Structure in Expressions

A-APR: : Arithmetic with Polynomials and Rational Expressions

A-CED: : Creating Equations

A-REI: : Reasoning with Equations and Inequalities