Scope and sequence

Combine matching variable terms into one equivalent expression.

Use multiplication across grouped terms to write an equivalent expression.

Substitute a known value for a variable and evaluate.

Use given values in a formula to find a result.

Undo addition to solve an equation.

Undo multiplication to solve an equation.

Undo addition or subtraction, then multiplication or division.

Substitute a possible solution to verify an equation.

Find the amount for one unit in a proportional relationship.

Identify the constant k in y = kx.

Recognize a table with a constant ratio.

Use a percent as a rate out of 100.

Slope tells how much y changes when x increases by 1.

The y-intercept is the value when x is 0.

Match a graph, table, and equation that describe the same line.

Find the constant change in y for each increase in x.

Translate a situation into an equation with a variable.

Explain what a coefficient means in context.

Interpret the solution to an equation in the original situation.

Find when two linear situations have the same value.

Classify polynomial terms, coefficients, degree, and standard form.

Combine like terms when adding or subtracting polynomial expressions.

Use distribution to multiply binomials and collect like terms.

Solve linear equations by simplifying, then using inverse operations.

Collect variable terms on one side before solving.

Rearrange formulas to solve for a specified variable.

Solve inequalities and represent solution sets on a number line.

Solve and graph intersections or unions of inequality statements.

Interpret absolute value inequalities as distance from a center.

Identify input and output sets for functions from tables, graphs, and contexts.

Evaluate and interpret functions written with notation such as f(x).

Represent arithmetic sequences with explicit and recursive rules.

Write and interpret linear equations in y = mx + b form.

Use a point and slope to write a linear equation.

Compare slopes to identify parallel and perpendicular lines.

Solve a system by finding the point where two lines intersect.

Substitute one expression into another equation to solve a system.

Add or subtract equations to eliminate a variable in a system.

Model repeated percent increase with exponential functions.

Model repeated percent decrease with exponential functions.

Connect recursive exponential rules to explicit formulas.

Interpret coefficients and values of quadratic functions in standard form.

Factor quadratic expressions to reveal zeros.

Use vertex and intercepts to describe key features of a quadratic graph.

Interpret vertex form to identify the vertex and transformations of a parabola.

Rewrite a quadratic by completing the square to reveal vertex form.

Use the quadratic formula to solve quadratic equations that do not factor easily.

Recognize when a quadratic has non-real solutions and express them with i.

Use degree and leading coefficient to predict how polynomial graphs behave at both ends.

Factor higher-degree polynomials by grouping and known patterns.

Use polynomial division or synthetic division to divide by a linear factor.

Connect repeated factors to graph behavior at polynomial zeros.

Simplify rational expressions while tracking excluded values.

Clear denominators to solve rational equations and check for extraneous values.

Solve radical equations by isolating the radical and checking the solution.

Model inverse variation where the product xy stays constant.

Interpret growth and decay factors in exponential models.

Use logarithm properties to rewrite and evaluate logarithmic expressions.

Solve exponential equations by rewriting with common bases or logarithms.

Use natural logarithms to interpret continuous growth models.

Evaluate and interpret composed functions such as f(g(x)).

Find and evaluate inverse functions by reversing operations.

Describe shifts, reflections, and stretches from transformed function rules.

Evaluate piecewise functions by choosing the rule for the input domain.

Distinguish arithmetic differences from geometric ratios.

Evaluate finite arithmetic series written with sigma notation.

Solve systems involving a line and a quadratic by substitution.

Solve nonlinear systems by substitution and checking ordered pairs.

Use the Pythagorean theorem to connect right-triangle side lengths.

Use complementary acute angles to connect sine and cosine.

Recognize that similar right triangles preserve trig ratios.

Define sine, cosine, and tangent from right-triangle side ratios.

Use trig ratios to solve for unknown right-triangle side lengths.

Use inverse trig reasoning to find an unknown acute angle.

Connect secant, cosecant, and cotangent to reciprocal trig ratios.

Find the acute reference angle associated with a non-acute angle.

Convert between degrees and radians using a full circle.

Use memorized unit-circle coordinates for 30, 45, and 60 degree angles.

Evaluate trig functions at axes on the unit circle.

Use symmetry to evaluate trig functions for negative and related angles.

Recognize the parent sine and cosine graphs by key features.

Read amplitude and period from transformed sine and cosine equations.

Describe horizontal shifts in trigonometric graphs.

Identify tangent graph intercepts, period, and vertical asymptotes.

Use sin^2(x) + cos^2(x) = 1 to verify trig values.

Apply angle-sum identities to evaluate trig expressions.

Use double-angle identities to rewrite trig values.

Simplify trig expressions by substituting equivalent identities.

Model height and distance using angle of elevation.

Use sinusoidal functions to model repeating real-world behavior.

Interpret amplitude and midline in simple harmonic motion models.

Resolve navigation bearings into perpendicular components.