The Sampling Distribution

This GeoGebra Worksheet enables the student or instructor to create multiple examples of sampling distributions of different sizes.  Students can instantly compare the shape of the sampling distribution with that of the population.  Also, for a given sample size, multiple 100-sample collections are available, so that students can compare their standard deviations with that which would be predicted by the formula.

Poisson Probability Simulation

Inspired by the article "What does randomness look like?" by Empirical Zeal, I designed
this GeoGebra worksheet to generate random distributions similar to the Poisson probability distribution.  Select the size of the grid and the number of dots to be selected at random on the grid, and the spreadsheet counts the number of squares which receive 0 dots, 1 dots, 2 dots, etc.  Compare the results with what would have been predicted by the Poisson distribution.  Then try it again with a different sized grid or a different number of dots.  Careful!  Large grids with a lot of dots may take a long time to process.

The Domain of a Logarithmic Function

This GeoGebra worksheet illustrates the connection between the argument of a logarithmic function, its domain, and its vertical asymptote.  Move the sliders to change the base, the argument, and the constant outside the argument.  Watch the changes that take place in the domain and the vertical asymptote.

Calculating and Visualizing Binomial Distributions

Students and teachers alike can use this GeoGebra worksheet to compare binomial distributions by instantly changing the value of n or p.  Then specific calculations can be made using particular values of x.

A Manual Approach to Finding the Line of Best Fit

When trying to find the equation of the straight line which best "fits" a set of points in the plane, one approach is to find the line which minimizes the sum of the squares of the vertical distances between the y-coordinates of the data points and the y-coordinates of the corresponding points on the line.  This so-called "least squares" approach produces the "linear regression equation" whose graph is called the "line of best fit."  Precise formulas exist for computing the slope and y-intercept of this line, and graphing calculators can handle it in a snap.  But for students being presented with the concept for the very first time who may be having a hard time seeing exactly what is going on, this GeoGebra worksheet is a manual, yet very visual approach.  As they move sliders or input specific guesses as to what they think the slope and y-intercept of the linear regression equation might be, the graph of the line they produce gives them instant feedback.  When they get close enough to the actual line, a congratulatory message appears with the correct answer.  If  they need a hint, either the slope or the y-intercept can be displayed, greatly simplifying the task.

The Archer and the Discriminant

This GeoGebra worksheet demonstrates a visual application of the discriminant.  When friction is neglected, the path of an arrow can be modeled using a quadratic function.  GeoGebra randomly generates an initial velocity (the vertical component), an initial height, and a target height.  Then it calculates the discriminant of the resulting quadratic equation and asks whether or not the arrow will reach the desired height.  The arrow is then fired so that we can see if our prediction is correct.

A Classic Mixture Problem

Today's GeoGebra Worksheet can be used to generate numerous different versions of a classic mixture problem.  The unit prices of two different blends of coffee, the total weight of the mixture, and the unit price of the mixture can all be adjusted with sliders.  GeoGebra then calculates the amount of each blend which should be used to obtain the correct amount of revenue.  An interesting connection can be made between the ratio of the blends in the final answer and the position of the unit price of the mixture relative to the unit prices of each of the blends.