# Building Blocks

• ### Estimation of Pi

This applet is designed to approximate the value of Pi. It accomplishes this purpose by firing random data points at a circle inscribed within a square. The probability of a data point landing within the circle is a ratio of the circle's area to the area of the square.
• ### Least Squares & Data Fitting

Allows the user to select points on a grid, select the degree of the polynomial, and provides the resulting regression equation.
• ### Least Squares & Data Fitting (DUPLICATE)

Allows the user to select points on a grid, select the degree of the polynomial, and provides the resulting regression equation.
• ### Monty's Dilemma

Explains Monty's Dilemma and allows the user the run an applet to simulate it with up to 1000 doors. To run the source code, change the extension to .java.
• ### Shodor

Currently requires user to log in to the site and register. I am waiting to see if there is an easier way, and if not, can I give out the username and password. Update 5/10/05: They said they would not feel comfortable giving this out.
• ### SnagIT

Whatever you can see on your screen, SnagIt will easily capture for your immediate use. Once you've taken your capture, SnagIt lets you edit, enhance, save, and use the capture for numerous tasks.
• ### Star Library: Breaking the Code -- A Graphical Exploration Using Bar Charts

The Caesar Shift is a translation of the alphabet; for example, a five-letter shift would code the letter a as f, b as g, ... z as e. We describe a five-step process for decoding an encrypted message. First, groups of size 4 construct a frequency table of the letters in two lines of a coded message. Second, students construct a bar chart for a reference message of the frequency of letters in the English language. Third, students create a bar chart of the coded message. Fourth, students visually compare the bar chart of the reference message (step 2) to the bar chart of the coded message (step 3). Based on this comparison, students hypothesize a shift. Fifth, students apply the shift to the coded message. After decoding the message, students are asked a series of questions that assess their ability to see patterns. The questions are geared for higher levels of cognitive reasoning. Key words: bar charts, Caesar Shift, encryption, testing hypotheses
• ### Star Library: Regression on the Rebound

This activity is an advanced version of the "Keep your eyes on the ball" activity by Bereska, et al. (1999). Students should gain experience with differentiating between independent and dependent variables, using linear regression to describe the relationship between these variables, and drawing inference about the parameters of the population regression line. Each group of students collects data on the rebound heights of a ball dropped multiple times from each of several different heights. By plotting the data, students quickly recognize the linear relationship. After obtaining the least squares estimate of the population regression line, students can set confidence intervals or test hypotheses on the parameters. Predictions of rebound length can be made for new values of the drop height as well. Data from different groups can be used to test for equality of the intercepts and slopes. By focusing on a particular drop height and multiple types of balls, one can also introduce the concept of analysis of variance. Key words: Linear regression, independent variable, dependent variables, analysis of variance
• ### Virtual TI

A TI graphing calculator emulator. Emulates the TI-82, TI-83, TI-83 Plus, TI-85, TI-86, TI-89, TI-92, TI-92 II, and TI-92 Plus. Features a graphical debugger, grayscale, send/receive, black-link, parallel link and more. User must transfer calculator's ROM to the computer through TI-Graph Link.
• ### Star Library: Simulating Size and Power Using a 10-Sided Die

This group activity illustrates the concepts of size and power of a test through simulation. Students simulate binomial data by repeatedly rolling a ten-sided die, and they use their simulated data to estimate the size of a binomial test. They carry out further simulations to estimate the power of the test. After pooling their data with that of other groups, they construct a power curve. A theoretical power curve is also constructed, and the students discuss why there are differences between the expected and estimated curves. Key words: Power, size, hypothesis testing, binomial distribution