### Visualizing Math Concepts with Sketchpad

Using Dynamic Geometry Software

Dynamic geometry software (DGS) is a powerful tool for improving student learning. Incorporating an engaging visual component, it allows learners to explore, test conjectures, discover patterns, and think creatively.

The Geometer’s Sketchpad® is the world’s leading software for teaching mathematics. Sketchpad® gives students at all levels—from third grade through college—a tangible, visual way to learn mathematics that increases their engagement, understanding, and achievement. Make math more meaningful and memorable using Sketchpad.

Use sketchpad to construct the derivative of an exponential function graphically. Then use your sketch to discover the relationship between the function and its derivative and then write a formula for the derivative.

Construct the dynamic area function using rectangles.
Then use animation to explore how they area function is related to the original function.

On each page, drag the slider for n to change the number of rectangles used to estimate the area. You can double-click the function on each page to explore different function area.

Explore the relationship between average rates and slopes on various functions. To use the tools, Average Rate, Slope, or Plot Slope tools, just click on either the given two points or make your own points.
(Note: on page 1, when you change the function, you will need to remerge points A and B)

Explore different types of rectangles and how they estimate area under curves. Then use the sketch to build your own.

Explore how the Accumulating Area under the curve is related to the function and its antiderivative.

Explore whether a function is continuous or not by dragging and tracing points. Find the left-hand and right hand limits to verify this.

Use this sketch to examine how an integral is related to the area under a curve.

Drag the pentagon on each dynagraph to explore the domain and range of different functions.

Use this sketch to construct and exponential function and explore it’s properties.
First create two parameters, a and b.
The graph a*b^x.
Experiment with changing a and b to explore the shape and properties of an exponential function.

Use geometric figures to explore the relationships between various aspects of that figure. Which relationships are functions and which are not?

Using this sketch, explore a function that models opening a door and how that function's rate changes as the door opens and closes.

Explore the definition of a limit by manipulation sliders for epsilon and delta.

Explore Optimization by dragging dynamic points and seeing the sketch objects change in size. For each page, find the point where the object is optimized.

Use sketchpad to construct the derivative of a function graphically. Then use your sketch to find patterns between a function and its derivative.