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Georgia - Mathematics: Precalculus
Georgia Math Standards | Adopted: 2021
PC.FGR: : Functional & Graphical Reasoning – Functions and their Characteristics
PC.FGR.2: : Analyze the behaviors of rational and piecewise functions to model contextual mathematical problems.
3.1.1: : Analyze piecewise-defined functions using different representations.
PC.FGR.2.1: : Graph piecewise-defined functions, including step functions and absolute value functions.
Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
Distance-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner complete a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
Distance-Time and Velocity-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner run a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
PC.FGR.2.2: : Describe characteristics by interpreting the algebraic form and graph of a piecewise-defined function.
Absolute Value Equations and Inequalities
Solve an inequality involving absolute values using a graph of the absolute-value function. Vary the terms of the absolute-value function and vary the value that you are comparing it to. Then explore how the graph and solution set change in response. 5 Minute Preview
Absolute Value with Linear Functions
Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview
Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
Distance-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner complete a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview
Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
Distance-Time and Velocity-Time Graphs - Metric
Create a graph of a runner's position versus time and watch the runner run a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview
3.1.2: : Analyze rational functions using different representations.
PC.FGR.2.4: : Divide polynomials using various methods.
Dividing Polynomials Using Synthetic Division
Divide a polynomial by dragging the correct numbers into the correct positions for synthetic division. Compare the interpreted polynomial division to the synthetic division. 5 Minute Preview
PC.FGR.2.5: : Graph rational functions and identify key characteristics.
General Form of a Rational Function
Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview
Rational Functions
Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview
PC.FGR: : Functional & Graphical Reasoning – Trigonometric Relationships and Functions
PC.FGR.3: : Utilize trigonometric expressions to solve problems and model periodic phenomena with trigonometric functions.
4.1.1: : Define and analyze trigonometric relationships.
PC.FGR.3.1: : Use the concept of a radian as the ratio of the arc length to the radius of a circle to establish the existence of 2pi radians in one revolution.
Radians
As factory belt operator, your job is to move boxes just the right distance on the belt, so they can be stamped for delivery. Your only controls are the radius and rotation of the belt’s wheel. How do you set these to get the distance right? See how this relates to arc length, and discover how radians help make this task easier. 5 Minute Preview
PC.FGR.3.2: : Utilize right triangles on the unit circle to determine the values of the six trigonometric ratios for pi/6, pi/4 , and pi/3. Use reflections of the triangles as reference angles to establish known values in all four quadrants of the coordinate plane.
Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
PC.FGR.3.3: : Define the six trigonometric ratios in terms of x, y, and r using the unit circle centered at the origin of the coordinate plane. Interpret radian measures of angles as a rotation both counterclockwise and clockwise around the unit circle.
Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Radians
As factory belt operator, your job is to move boxes just the right distance on the belt, so they can be stamped for delivery. Your only controls are the radius and rotation of the belt’s wheel. How do you set these to get the distance right? See how this relates to arc length, and discover how radians help make this task easier. 5 Minute Preview
Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
PC.FGR.3.4: : Derive the fundamental trigonometric identities.
Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Sum and Difference Identities for Sine and Cosine
Choose the correct steps to evaluate a trigonometric expression using sum and difference identities. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
PC.FGR.3.5: : Determine the value(s) of trigonometric functions for a set of given conditions.
Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
4.1.2: : Analyze trigonometric functions and their inverses.
PC.FGR.3.6: : Graph and write equations of trigonometric functions using period, phase shift, and amplitude in modeling contexts.
Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
Translating and Scaling Sine and Cosine Functions
Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function. 5 Minute Preview
PC.FGR.3.7: : Classify the six trigonometric functions as even or odd and describe the symmetry.
Cosine Function
Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Sine Function
Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview
Tangent Function
Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview
PC.AGR: : Algebraic & Geometric Reasoning – Trigonometric Identities and Equations
PC.AGR.4: : Manipulate, prove, and apply trigonometric identities and equations to solve contextual mathematical problems.
5.1.1: : Verify trigonometric identities and solve trigonometric equations.
PC.AGR.4.1: : Apply the fundamental trigonometric identities to simplify expressions and verify other identities.
Simplifying Trigonometric Expressions
Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
PC.AGR.4.2: : Use sum, difference, double-angle, and half-angle formulas for sine, cosine, and tangent to establish other identities and apply them to solve problems.
Sum and Difference Identities for Sine and Cosine
Choose the correct steps to evaluate a trigonometric expression using sum and difference identities. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
PC.GSR: : Geometric & Spatial Reasoning – Conic Sections and Polar Equations
PC.GSR.5: : Analyze the behaviors of conic sections and polar equations to model contextual mathematical problems.
6.1.1: : Analyze conic sections using different representations.
PC.GSR.5.1: : Identify and graph different conic sections given the equations in standard form.
Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
Ellipses
Compare the equation of an ellipse to its graph. Vary the terms of the equation of the ellipse and examine how the graph changes in response. Drag the vertices and foci, explore their Pythagorean relationship, and discover the string property. 5 Minute Preview
Hyperbolas
Compare the equation of a hyperbola to its graph. Vary the terms of the equation of the hyperbola. Examine how the graph of the hyperbola and its asymptotes changes in response. 5 Minute Preview
Parabolas
Explore parabolas in a conic section context. Find the relationship among the vertex, focus, and directrix of a parabola, and how that relates to its equation. 5 Minute Preview
PC.GSR.5.2: : Identify different conic sections in general form and complete the square to convert the equation of a conic section into standard form.
Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
PC.AGR: : Algebraic & Graphical Reasoning – Vectors and Parametric Equations
PC.AGR.6: : Represent and model vector quantities to solve problems in contextual situations.
7.1.1: : Perform operations with vectors in context.
PC.AGR.6.1: : Represent vector quantities as directed line segments; represent magnitude and direction of vectors in component form using appropriate mathematical notation.
Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
PC.AGR.6.2: : Add and subtract vectors and multiply vectors by a scalar to find the resultant vector.
Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
PC.AGR.6.3: : Add and subtract vectors on a coordinate plane using different methods.
Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
PC.AGR.6.4: : Solve contextual vector problems, such as those involving velocity, force, and other quantities.
2D Collisions
Investigate elastic collisions in two dimensions using two frictionless pucks. The mass, velocity, and initial position of each puck can be modified to create a variety of scenarios. 5 Minute Preview
Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
Golf Range
Try to get a hole in one by adjusting the velocity and launch angle of a golf ball. Explore the physics of projectile motion in a frictional or ideal setting. Horizontal and vertical velocity vectors can be displayed, as well as the path of the ball. The height of the golfer and the force of gravity are also adjustable. 5 Minute Preview
Vectors
Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors. 5 Minute Preview
PC.PAR: : Patterning & Algebraic Reasoning – Sequences and Series
PC.PAR.7: : Demonstrate how sequences and series apply to mathematical models in real-life situations.
8.1.1: : Analyze sequences using multiple representations.
PC.PAR.7.1: : Demonstrate that sequences are functions whose domain is the set of natural numbers.
Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview
Arithmetic and Geometric Sequences
Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview
Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview
PC.PAR.7.2: : Represent sequences graphically, numerically, and symbolically.
Arithmetic Sequences
Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview
Arithmetic and Geometric Sequences
Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview
Geometric Sequences
Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview
Correlation last revised: 5/26/2022
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