How can you determine the rate of change on a curve? Pupils use the interactive to discover what happens with the average rate of change as the point move closer to the other. Using the definition of the derivative, learners find that it...

Graphically find the derivative of sin(x). Using the interactive, pupils graph the slope of the tangent line to the sine function. Class members use the resulting graph to determine the derivative of the sine function. They verify their...

Optimally, you want the largest box. Given a square piece of box material, pupils determine the size of congruent squares to cut out of the corners to create a box with the greatest volume. Learners determine the equation of the volume...

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.

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...

Use the area of polygons to calculate the area between curves. Pupils calculate areas under income and expense curves by filling the space with squares and right triangles. Using that information, they determine the profit related to the...

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...

Is the inverse of a function also a function? Pupils manipulate the graph of a function to view its inverse to answer this question. Using a horizontal and vertical line, class members determine whether the initial function is...

Find your way around using vectors. Scholars use an interactive to learn about vector addition. They answer a set of questions about modeling a route on a map using vectors.

Two words summarize the interactive: vector projector. An easy-to-use resource lets users investigate vector projections on the coordinate plane. Given the components of two vectors, they determine the projection of one vector onto the...

Hit a home run with a resource that is all fun and games. Learners apply an interactive to determine the horizontal component of the distance a baseball travels. They must consider vector projections for this task.

Help your class develop an understanding of sigma notation. Pupils match the sigma notation with the sums. Using the expanded sums, learners evaluate the summations. The scholars move on to prove a property of sums.

How long does it take to pay off a loan? Pupils use a graph to model the sequence associated with paying off a loan. Using the graph, learners determine the initial value and the common difference of the arithmetic sequence. The learners...

Discover another way to find the volume of a cone. Pupils explore how the area of a cross section changes as it moves through a cone. The interactive uses that knowledge to develop the integral to use to find the volume of the cone....

Finding the volume is an integral characteristic of a vase. Using the idea that summing the areas of cross-sectional disks will calculate the volume of a rotational solid, pupils find the volume of a vase. Scholars determine the interval...

Roll a log into an equivalent expression. Given four expanded logarithmic expressions, pupils write an equivalent condensed expression. They identify which properties allows for the simplification.

Have some fun building squares out of triangles. Pupils investigate the partial sums of odd numbers. Using the sum of the first four odd numbers, learners see that it can be rewritten as a sum containing a triangular number. Simplifying...

Using a slider, scholars build triangular numbers and their associated rectangles and use the geometric display to find the pattern to determine the next triangular number. They then relate that number to the area of the rectangle to...

Investigate ellipses through the lens of medical applications. Pupils use a medical scenario to determine the equation of an ellipse. By using the interactive, learners determine the foci and major and minor axes of the ellipse that...

Envision the function as the point swings. Given a point connected to another point and a line, pupils trace through an invisible graph. Learners identify the name of the given point and the line and determine the type of conic section...

Hyperbolas—practice thinking outside of the box. Pupils alter the end behavior box to create various graphs of hyperbolas. They determine formulas to find the distance from the origin to the foci. Using that information, scholars...

Map this! Help your young mathematicians draw a circular island on a map. Given specifics of the location and size of an island on a map, pupils transform a circle to meet the given requirements. They then determine the location of the...

Fight against the current. Pupils explore the resulting path when they are crossing a river while being pushed downstream by the current. Using vector notation, learners express the speed and direction of a ferry. They finish by...

Investigate the definition of inverse functions graphically. Using the interactive, scholars create a graph of a function and view its resulting inverse. They then determine whether a group of functions have inverses that are also...