Get the class to take an extreme look at functions. The interactive presents a function on a closed interval with a movable tangent line. Using the given function, pupils determine the extrema, critical points, and points of...

Does the accuracy of the first guess make a difference down the line? Learners investigate the effects of the iterative process of finding roots, using Newton's Method. By moving the initial guess of a root on a graph, pupils observe the...

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...

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...

Use an iterative process to find an approximation of a square root. Pupils use the interactive to find an approximation to find the positive root of a quadratic function with Newton's method. With the graphs, learners position the...

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...

Approximate the volume of a solid of revolution. Using a method similar to approximating the area under a curve, pupils investigate the volume of a solid of revolution. The learners use a given definite integral to find the volume of...

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...

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...

Topple misunderstandings of geometric sequences. Using a context of creating ever-increasing sizes of dominoes, pupils develop a geometric sequence. The scenario provides the size of the first domino and the common ratio between...

Show budding mathematicians how to model a diminishing bacteria colony two ways—graphically and algebraically. Using the coordinate axis, pupils create a graph to represent the decay of a bacteria colony. They determine the number of...

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...

Work through a sequence in discovering number patterns. Using the interactive, pupils explore arithmetic and geometric sequences by setting the initial value and the common difference or ratio. Learners distinguish between the two types...

Learners explore ellipses by changing the lengths and orientation of the major and minor axis. Using the interactive, they determine the equation of the ellipse and its eccentricity. Given an equation the scholars identify the center,...

Perform a switch to find the inverse of a parametric equation. Pupils match four parametric functions with the graph of the their inverses. Using the graphs, learners determine whether particular points are on the original parametric...

Using the answers to the challenge questions, class members work through simplifying a complex logarithmic expression that requires changing bases. Pupils drag values to fill in the steps to arrive at a numerical equivalent expression.

Take a look at another alternating sequence. The resource provides a graphical display of a sequence that alternates between two values. Pupils use the display to determine whether the sequence has a limit. Given a theory of limit,...

Calculate galactic orbits in a far-out resource. Pupils drag a point on a circle to graph the orbit of a fictional planet. Using the equation, they find points through which the orbit passes. To finish the simulation, users determine the...

How many bones can a dog on a leash reach? Class members move a dog on the end of its leash and determine whether it can reach bones located at specific points. The learners see whether the bone lies on the circle or outside of the...

Where does a circular table fit best? Individuals move a circle representing a table into different quadrants of a room. Pupils determine which equation of the circle will place the table in the appropriate quadrant. A discussion...

Six questions make up an interactive designed to boost scholars' knowledge of integers. Mathematicians move symbols over a horizontal number line to aid in findings answers between 10 and negative 10. Question types include...