Curriculum Framework

NQ.1.PC.1: Find the conjugate of a complex number. Use conjugates to find quotients of complex numbers. Use conjugates to find moduli.

Points in the Complex Plane

Roots of a Quadratic

NQ.1.PC.2: Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers). Explain why the rectangular and polar forms of a given complex number represent the same number.

NQ.1.PC.3: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; Use properties of geometrical representation for computation.

NQ.2.PC.1: Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., 𝙫, |𝙫|, ||𝙫||, 𝘷).

NQ.2.PC.2: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

NQ.2.PC.3: Solve problems involving velocity and other quantities that can be represented by vectors.

NQ.2.PC.4: Add and subtract vectors. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. Understand vector subtraction 𝙫 – 𝙬 as 𝙫 + (–𝙬), where –𝙬 is the additive inverse of 𝙬, with the same magnitude as 𝙬 and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order. Perform vector subtraction component-wise.

NQ.2.PC.5: Multiply a vector by a scalar. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; Perform scalar multiplication component-wise, e.g., as 𝘤(𝘷ₓ, 𝘷 subscript 𝘺) = (𝘤𝘷ₓ, 𝘤𝘷 subscript 𝘺). Compute the magnitude of a scalar multiple 𝘤𝙫 using ||𝘤𝙫|| = |𝘤|𝙫. Compute the direction of 𝘤𝙫 knowing that when |𝘤|𝙫 ≠ 0, the direction of 𝘤𝙫 is either along 𝙫 (for 𝘤 > 0) or against 𝙫 (for 𝘤 < 0).

T.3.PC.2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed around the unit circle.

Cosine Function

Sine Function

Tangent Function

T.3.PC.3: Use special right triangles to determine geometrically the exact values of sine, cosine, tangent for π/3, π/4, π/6, and π/2. Use the unit circle to express the values of sine, cosine, and tangent for π–𝑥, π+𝑥, and 2π–𝑥 in terms of their exact values for 𝑥, where 𝑥 is any real number.

Cosine Function

Sine Function

Sum and Difference Identities for Sine and Cosine

Tangent Function

Translating and Scaling Sine and Cosine Functions

T.3.PC.4: Develop the Pythagorean identity, sinĀ²(θ) + cosĀ²(θ) = 1. Given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle, use the Pythagorean identity to find the remaining trigonometric functions.

Simplifying Trigonometric Expressions

Sine, Cosine, and Tangent Ratios

T.3.PC.5: Develop the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

T.4.PC.2: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

CS.5.PC.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem. Complete the square to find the center and radius of a circle given by an equation.

Circles

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

CS.5.PC.2: Derive the equation of a parabola given a focus and directrix.

CS.5.PC.3: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

CS.5.PC.4: Find the equations for the asymptotes of a hyperbola.

CS.5.PC.5: Complete the square in order to generate an equivalent form of an equation for a conic section; use that equivalent form to identify key characteristics of the conic section.

CS.5.PC.6: Identify, graph, write, and analyze equations of each type of conic section, using properties such as symmetry, intercepts, foci, asymptotes, and eccentricity, and using technology when appropriate.

Addition and Subtraction of Functions

Circles

Ellipses

Hyperbolas

Parabolas

Rational Functions

CS.5.PC.7: Solve systems of equations and inequalities involving conics and other types of equations, with and without appropriate technology.

Linear Programming

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Standard Form)

Systems of Linear Inequalities (Slope-intercept form)

F.6.PC.1: Write a function that describes a relationship between two quantities. From a context, determine an explicit expression, a recursive process, or steps for calculation. Combine standard function types using arithmetic operations. (e.g., given that f(x) and g(x) are functions developed from a context, find (f + g)(x), (f – g)(x), (fg)(x), (f/g)(x), and any combination thereof, given 𝑔(𝑥) ≠ 0.) Compose functions.

Addition and Subtraction of Functions

Arithmetic Sequences

Arithmetic and Geometric Sequences

Function Machines 1 (Functions and Tables)

Geometric Sequences

F.6.PC.3: Understand the inverse relationship between exponents and logarithms. Use the inverse relationship between exponents and logarithms to solve problems.

F.7.PC.3: 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.

F.7.PC.4: For a function that models a relationship between two quantities: Interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

Absolute Value with Linear Functions

Exponential Functions

Function Machines 3 (Functions and Problem Solving)

General Form of a Rational Function

Graphs of Polynomial Functions

Logarithmic Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

F.7.PC.5: Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate the rate of change from a graph.

Cat and Mouse (Modeling with Linear Systems)

Slope

F.7.PC.6: Graph functions expressed algebraically and show key features of the graph, with and without technology. Graph linear and quadratic functions and, when applicable, show intercepts, maxima, and minima. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Graph power and polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Graph exponential and logarithmic functions, showing intercepts and end behavior. Graph trigonometric functions, showing period, midline, and amplitude.

Absolute Value with Linear Functions

Cat and Mouse (Modeling with Linear Systems)

Cosine Function

Exponential Functions

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Roots of a Quadratic

Sine Function

Slope-Intercept Form of a Line

Standard Form of a Line

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Zap It! Game

Correlation last revised: 9/15/2020

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