CK-12 Foundation
Reciprocal Identities
Get a better understanding of the trigonometric functions by taking a look at the flip side. Pupils create angles within a unit circle and compare the values of the standard trigonometric functions to their reciprocal functions. The...
CK-12 Foundation
Domain, Range, and Signs of Trigonometric Functions: Sine and Cosine
Is there a relationship between the sign of sine and cosine and the angle on the unit circle? Scholars use an interactive to see the value of sine and cosine within different quadrants. they then use the information to determine the...
CK-12 Foundation
Conversion between Degrees and Radians: Clock Angles and Measures
It's 3:30, what radian is it? Pupils create clock angles on a clock and determine the radian measure to the minute hand. They then use a conversion factor to convert from one measurement to another.
CK-12 Foundation
Six Trigonometric Functions and Radians: Degrees to Radians and Back Again!
How do degrees relate to radians? The interactive allows pupils to manipulate the size of an angle in a unit circle to help see that relationship. Users determine the radian measure for given degree measures of angles, realizing the...
CK-12 Foundation
Conversion between Degrees and Radians: Arc and Radians Relationship
How are arc lengths and radians related? An interactive resource demonstrates the relationship as pupils create arc lengths in a unit circle and compare them to the angle measurements. Questions ask individuals to build upon this...
CK-12 Foundation
Changes in Period and Amplitude of the Sine Function
How does a change in amplitude or period affect the equation of a sine function? Scholars move sliders to change the frequency and period of the sine function. The interactive displays the resulting equation, and pupils determine the...
CK-12 Foundation
Fraction and Mixed Number Comparison: Pumpkin Pie
Compare fraction models to fractions on a number line in an interactive that uses pumpkin pies as the model. Pupils look at pumpkin pie models to determine their improper fraction value. They use their knowledge to answer five questions...
CK-12 Foundation
Length of a Chord: Distance Across a Ferris Wheel
An interactive presents two friends on a ferris wheel with the task of finding the distance between the them. Pupils create the chord between the two friends and calculate its lengths using trigonometric ratios.
CK-12 Foundation
Angular Velocity: 200 Meter Dash
Do curves slow runners down or help their speed? Pupils simulate a 200-meter dash to calculate the angular and linear velocity of a runner. They then determine whether the runner is faster around the curved section of the track...
CK-12 Foundation
Horizontal Translations or Phase Shifts: Horizontal and Vertical Translations
It is all about the shift. Pupils translate the graph of a cubic function to different marked locations on the plane and determine the new equation that represents the shifts. The activity is designed to encourage individuals begin...
CK-12 Foundation
Horizontal Translations or Phase Shifts: Sine
Shift a trigonometric function and find its new equation. Pupils translate a sine function on a graph. The scholars determine the equation of the function that represents the translated graph and observe the connection between a...
CK-12 Foundation
Vertical Translations
Change the y-intercept by adding a constant to the function. Individuals move three functions vertically along the y-axis. As they observe how the equation of the functions change with the vertical movement, learners determine how...
CK-12 Foundation
Factorization of Quadratic Expressions: Algebra Tiles
What does it mean to factor the difference of two squares? The interactive presents an area model of the difference of two squares. Pupils rearrange the model to create a rectangular area. The learners determine the length and width...
CK-12 Foundation
Monomial Factors of Polynomials: Mystery Boxes
Shortcut the work in finding total volumes. Pupils determine a polynomial expression that would represent the combined volume of three boxes. Each box has the same height, and the scholars rewrite the expression by factoring out the...
CK-12 Foundation
Polynomials in Standard Form
Set the standard for working with polynomials. Pupils arrange two polynomial expressions in standard form. The scholars respond to questions about the terms, coefficients, and degrees of the polynomials. They then discuss how they...
CK-12 Foundation
Addition and Subtraction of Polynomials: Adding Polynomials
Stack the like terms to add vertically. The resource contains a visual aid to help with the addition of polynomials using the vertical method. Pupils use the aid to calculate the sum of two polynomials.