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Interactive
CK-12 Foundation

Reciprocal Identities

For Students 10th - 12th Standards
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...
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Interactive
CK-12 Foundation

Domain, Range, and Signs of Trigonometric Functions: Sine and Cosine

For Students 10th - 12th Standards
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...
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Interactive
CK-12 Foundation

Conversion between Degrees and Radians: Clock Angles and Measures

For Students 10th - 12th Standards
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.
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Interactive
CK-12 Foundation

Six Trigonometric Functions and Radians: Degrees to Radians and Back Again!

For Students 10th - 12th Standards
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...
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Interactive
CK-12 Foundation

Conversion between Degrees and Radians: Arc and Radians Relationship

For Students 10th - 12th Standards
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...
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Interactive
CK-12 Foundation

Horizontal Translations or Phase Shifts: Horizontal Translations

For Students 10th - 12th Standards
Find out what causes a function to slide. Pupils move a function along the x-axis and see the resulting change in its equation. Scholars determine the effects that the translation has on the intercepts, domain, and range of the function.
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Interactive
CK-12 Foundation

Horizontal Translations or Phase Shifts: Cosine

For Students 10th - 12th Standards
If cosine is shifted, how is its equation affected? Learners manipulate the graph of cosine by moving the y-intercept to different locations on the coordinate plane. Pupils determine the new equation that models the shifts.
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Interactive
CK-12 Foundation

Changes in Period and Amplitude of the Sine Function

For Students 10th - 12th Standards
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...
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Interactive
CK-12 Foundation

Fraction and Mixed Number Comparison: Pumpkin Pie

For Students 6th
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...
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Interactive
CK-12 Foundation

Whole Number Addition: Let's Go Fishing!

For Students 6th
Practice adding whole numbers by combining the amount of fish Alice and Bob catch. As young mathematicians work through each problem, they are asked to find one more plus the amount of fish already caught. They can manipulate the...
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Interactive
CK-12 Foundation

Improper Fractions as Mixed Numbers: Sharing Scratch-n-Sniff Stickers

For Students 6th Standards
No, you can't actually smell these 13 scratch-n-sniff stickers. But you can group them into equal groups of four, with one sticker remaining. Using that information, learners create a mixed number based on the improper fraction, 13/4.
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Interactive
CK-12 Foundation

Mixed Numbers as Improper Fractions: Pineapple Slices

For Students 6th Standards
Practice adding and subtracting improper fractions with pineapple slices. Young mathematicians move whole pineapple slices to visualize the addition of the 2/5s that is on Sally's plate. Pupils also use a combination of mixed numbers and...
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Interactive
CK-12 Foundation

Rotations in Radians: Clock Conundrum

For Students 10th - 12th Standards
Pupils use an interactive clock to set specific times. They apply math to an everyday task as they determine the measure of the angle formed by the hands in degrees and in radians. 
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Interactive
CK-12 Foundation

Length of a Chord: Distance Across a Ferris Wheel

For Students 9th - 12th Standards
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.
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Interactive
CK-12 Foundation

Angular Velocity: 200 Meter Dash

For Students 10th - 12th
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 or the...
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Interactive
CK-12 Foundation

Vertical Translations: Translating a Square Root Function

For Students 10th - 12th Standards
How does the equation of a function reflect translations? Scholars manipulate the starting point of the parent square root function before determining the new equations that result from the translations. Class members also determine the...
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Interactive
CK-12 Foundation

Horizontal Translations or Phase Shifts: Horizontal and Vertical Translations

For Students 10th - 12th Standards
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 to...
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Interactive
CK-12 Foundation

Horizontal Translations or Phase Shifts: Tangent

For Students 10th - 12th Standards
Patterns can be shifty! Find the pattern when shifting the graph of tangent. Pupils move the graph of tangent to different locations on the coordinate plane. They observe what happens to the function and its vertical asymptotes before...
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Interactive
CK-12 Foundation

Horizontal Translations or Phase Shifts: Sine

For Students 10th - 12th Standards
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...
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Interactive
CK-12 Foundation

Radical Equations: Geometric Visual of a Square Root

For Students 8th - 11th Standards
How can you draw a number? A set of questions takes learners through the reasoning for why a geometric construction can be drawn to represent the square root of a number. An interactive helps visualize the construction.
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Interactive
CK-12 Foundation

Distance Formula: Right Triangles

For Students 8th - 10th Standards
Go the distance with a far out resource. Individuals use an interactive to create right triangles on a coordinate plane to help find distance between two points. Challenge questions aid them in developing the distance formula.
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Interactive
CK-12 Foundation

Midpoint Formula

For Students 8th - 10th
By selecting the resource, you're already halfway to understanding midpoints. Pupils use a slider to locate midpoints on the coordinate plane. They connect this conceptual understanding to the formula for the midpoint of a line segment.
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Interactive
CK-12 Foundation

Evaluation of Perfect Square Roots: Neighborhood Park

For Students 7th - 9th Standards
Walking in the park can be good for the body and for mathematics skills. Young scholars use an interactive app to investigate the relationship between squares and square roots using a square with adjustable length. The program also takes...
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Interactive
CK-12 Foundation

Joint and Combined Variation: Variable Sliders

For Students 8th - 10th
Learners use a pair of sliders to investigate how changes in a variable affects other variables in joint variation. A set of five challenge questions tests understanding.

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