By Phil Nast, retired middle school teacher and freelance writer

National Library of Virtual Manipulatives houses concept activities for numbers & operations, algebra, geometry, measurement, and data analysis & probability leveled grades PreK-12.

For example, data analysis and probability activities are provided for all grades.

• Spinners, lets students in grades Prek-2 determine the number of spins (1-999) on a color wheel and record the results in a bar chart.
• Histogram lets students in grades 3-5 summarize data using a histogram graph. The Java applet provides three examples of histograms with data analysis and permits adjustment of cell width and entry of original data.
• Hamlet Happens lets students in grades 6-8 discover that rare events happen. Type a word up to five letters in length chosen from the box “TO BE OR NOT TO BE” and letters are randomly selected. A test run using the word “TENOR” had drawn more than 18,000 letters without success before being abandoned, which should give some idea of how long it would take a troop of monkeys to type Shakespeare’s plays.
• Whammy Awards reveals to students in grades 9-12 how five different voting schemes can produce contradictory outcomes. One example is provided and then students can enter their own data (preference ranking) and set number of voters.

A menu at the top of the page provides related activities, parent/teacher information, and instructions. NCTM members can find education standards.

Teachers can register to use eNLVM . Registration allows you to organize online materials for your class and track your students’ work. For a brief introduction to eNLVM and steps to register, download the Quick Start Guide ( PDF, 465 KB, 14 pgs.).