Web 画板 Mathematics

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

的 Geometer’s 画板® is the world’s leading software for teaching mathematics. 画板® 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 画板.

• ACT 17 Exponent link
  Use sketchpad to construct the derivative of an exponential 函数 graphically. 然后用你的 sketch to discover the relationship between the 函数 and its derivative and then write a formula for the derivative.
  
  
• 区域链接
  Construct the dynamic area 函数 using rectangles.
  然后使用 animation to explore how they area 函数 is related to the original 函数.
  
  
• Area Limits link
  On each page, drag the slider for n to change the number of rectangles used to estimate 该地区. You can double-click the 函数 on each page to explore different 函数 area.
  
  
• Average Rate link
  Explore the relationship between average rates and slopes on various 函数s. 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 函数, you will need to remerge points A and B)
  
  
• Builld 区域链接
  Explore different types of rectangles and how they estimate area under curves. 然后 use the sketch to build your own.
  
  
• Build Area 2 link
  Explore how the Accumulating Area under the curve is related to the 函数 and its 不定积分.
  
  
• 连续性的链接
  Explore whether a 函数 is continuous or not by dragging and tracing points. 找到 the left-hand and right hand limits to verify this.
  
  
• DefiniteIntegral link
  Use this sketch to examine how an integral is related to 该地区 under a curve.
  
  
• Domain Range link
  Drag the pentagon on each dynagraph to explore the domain and range of different 函数s.
  
  
• Exponential Functions link
  Use this sketch to construct and exponential 函数 and explore it’s properties.
  First create two parameters, a and b.
  图像a*b^x.
  Experiment with changing a and b to explore the shape and properties of an exponential 函数.
  
  
• Functional Geometry link
  Use geometric figures to explore the relationships between various aspects of that figure. Which relationships are 函数s and which are not?
  
  
• Instantaneous Rate link
  Using this sketch, explore a 函数 that models opening a door and how that 函数's rate changes as the door opens and closes.
  
  
• Limits Epsilon Delta link
  Explore the definition of a limit by manipulation sliders for epsilon and delta.
  
  
• MaxMin2链接
  Explore Optimization by dragging dynamic points and seeing the sketch objects change 的大小. For each page, find the point where the object is optimized.
  
  
• Plot Derivative link
  Use sketchpad to construct the derivative of a 函数 graphically. 然后用你的 sketch to find patterns between a 函数 and its derivative.
  
  
• SecondDerivative link
  Use sketchpad to construct the second derivative of a 函数 graphically. 然后使用 your sketch to find patterns between a 函数 and its first and second derivatives.
  
  
• SwansGiraffes link
  Use this sketch to experiment with Linear Programming. 然后 find out why the maximum or minimum is always at one of the vertices of the polygon created by a problems constraints.
  
  
• 切线的链接
  Use this sketch to explore the relationship between a curve and its tangent line. Learn how to find a derivative graphically.
  
  
• Transformations link
  Drag the slider on each of the pages in this sketch to explore what transformation occurs to a basic graph.
  
  
• Trapezoidal Accumulation link
  Use trapezoids and rectangles to approximate 该地区 under the curve.