# Visualizing Math Concepts with Sketchpad

Simply click on the titles below to access the content.

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.

Act 17 Exponent
• ACT 17 Exponent link
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.
Area
• Area link
Construct the dynamic area function using rectangles.
Then use animation to explore how they area function is related to the original function.
Area Limits
• Area Limits link
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.
Average Rate
• Average Rate link
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)
Build Area
• Build Area link
Explore different types of rectangles and how they estimate area under curves. Then use the sketch to build your own.
Build Area2
• Build Area 2 link
Explore how the Accumulating Area under the curve is related to the function and its antiderivative.
Continuity
• Continuity link
Explore whether a function is continuous or not by dragging and tracing points. Find the left-hand and right hand limits to verify this.
Definite Integral
Domain Range
• Domain Range link
Drag the pentagon on each dynagraph to explore the domain and range of different functions.
Exponential Functions
• DomainRange link
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.
Functional Geometry
• Functional Geometry link
Use geometric figures to explore the relationships between various aspects of that figure. Which relationships are functions and which are not?
Instantaneous Rate
• Instantaneous Rate link
Using this sketch, explore a function that models opening a door and how that function's rate changes as the door opens and closes.
Limits Epsilon Delta
MaxMin2
• MaxMin2 link
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.
Plot Derivative
• Plot Derivative link
Use sketchpad to construct the derivative of a function graphically. Then use your sketch to find patterns between a function and its derivative.
SecondDerivative
• SecondDerivative link
Use sketchpad to construct the second derivative of a function graphically. Then use your sketch to find patterns between a function and its first and second derivatives.
SwansGiraffes
• SwansGiraffes link
Use this sketch to experiment with Linear Programming. Then find out why the maximum or minimum is always at one of the vertices of the polygon created by a problems constraints.
Tangents
• Tangents link
Use this sketch to explore the relationship between a curve and its tangent line. Learn how to find a derivative graphically.
Transformations
• Transformations link
Drag the slider on each of the pages in this sketch to explore what transformation occurs to a basic graph.
Trapezoidal Accumulation