Interactive
CK-12 Foundation

Area Sums: Estimation with Rectangles

For Students 11th - Higher Ed
The more rectangles, the better the estimate. Using the interactive, pupils explore estimating the area under a curve using left-hand sums. Learners respond to challenge questions on how to get better estimates using the same technique.
Interactive
CK-12 Foundation

Square Roots and Irrational Numbers: Estimating Radicals

For Students 8th - 10th
Try out a resource using triangles to estimate radicals. An interactive app allows learners to approximate some irrational numbers involving square roots. They find the two consecutive numbers that an irrational number lies between...
Interactive
CK-12 Foundation

Distance Between Two Points: Biking the Blocks

For Students 9th - 12th Standards
Distance estimates would be easy if the world were a grid. Scholars work to determine the distance between two structures using a coordinate plane. As an introduction, the lesson focuses on vertical and horizontal distances.
Interactive
CK-12 Foundation

Sampling Distribution of a Sample Mean: The Mean of the Average Ages

For Students 9th - 12th
What does it mean to take the mean of the mean? An easy-to-use interactive has users adjust the mean ages of different samples. Finding the average of these sample means gives an estimate of the population mean.
Interactive
CK-12 Foundation

Tangent Line Approximation: Estimating Square Roots

For Students 11th - Higher Ed
Estimating a square root is as easy as evaluating a linear equation. Using the derivative of the square root function, pupils calculate an estimation of square roots. Class members determine the equation of the tangent line at the value...
Interactive
CK-12 Foundation

Trapezoidal and Midpoint Approximations: Area of a Skirt

For Students 11th - Higher Ed
When are trapezoids better than rectangles? Using trapezoids pupils approximate the area of fabric defined by a function. Just like with rectangles, learners realize the more trapezoids the more accurate the approximation. Scholars use...
Interactive
CK-12 Foundation

Length of a Plane Curve

For Students 11th - Higher Ed
Challenge your class to use straight lines when estimating the length of a curve. An engaging interactive allows individuals to place line segments one after another along the arc. Learners determine that the more lines used, the better...
Interactive
CK-12 Foundation

Multiplication and Division of Radicals: Totally Radical Dude's Height

For Students 8th - 10th
Watch as your learners reach even loftier heights of understanding. Individuals use a slider to estimate the height of a person whose height is given in radical form. Rationalizing the denominator comes in handy here.
Interactive
CK-12 Foundation

Finding Exact Trigonometric Values Using Double Angle Identities: Trig Values Using Double and Half Angle Formulas

For Students 10th - 12th
The more you know, the more you can learn. Scholars apply the double angle and half angle formulas to determine trig values based on known values. They use an interactive that provides sine and cosine values to aid calculations.

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