Math Applets

Illuminations Applet: Equivalent Fractions
http://illuminations.nctm.org/ActivityDetail.aspx?ID=80
Grade Level: 3-5
Purpose: Students divide and shade virtual square and circle manipulatives to promote conceptual understanding of fractions and equivalent fractions.

How it works: Students begin by choosing whether to work with a circle or square. The applet then generates a square/circle that has been subdivided into equal sections, a certain number of which are shaded. The fraction represented by shaded portion is plotted on a number line below. The student must then create, through as series of clicks and drags, two more subdivided and shaded squares (or circles) that represent the equivalent fraction. As the students work, the application plots their creations on a number line, allowing students to visualize where any given fraction exists in relation to 0 and 1.  After they've created their two shapes, they click on a blue check mark to have their work evaluated.

Advantages:  Students can either create fraction equivalents of applet-generated fractions, or design their own challenge, making it accessible to users of all abilities. All applet functions require simple mouse/track pad clicks and drags. The applet also resets easily with a single click.

Disadvantages: When a student makes an error, the software offers virtually no guidance as to how to proceed. The most it will suggest is that the student attempt a different denominator, and then only if they've duplicated a denominator. In addition, there is no means by which to adjust the level of difficulty of the applet-generated fractions. Finally, there is no built-in mechanism to record students' work.

Recommendations: This applet is ideally suited to the student who has basic understanding of fractions but would benefit from visual confirmation that two fractions are, indeed, equivalent. I would suggest having the students build at least a few fractions based on the teacher's recommendations before creating their own. This way the learner can be assured that they are using the application properly before entering uncharted territory.

Shodor Interactivate Applet: Adjustable Spinner
http://www.shodor.org/interactivate/activities/AdjustableSpinner/
Grade Level: 6-8
Purpose: The purpose of this applet is to allow students to explore the difference between actual and theoretical probability using an adjustable spinner game.

How it works: Students can choose the number of regions on their spinner and the relative area of each. As they do, they can observe two things: (1) as the number of equally sized regions increases, the theoretical probability of the spinner stopping on any one region decreases; and (2) as the size of a given increases, so does the theoretical probability that the spinner will stop there. Students can then spin the spinner up to 10,000 times and the applet records the experimental probability.

Click on image to enlarge.

Advantages: A clear advantage of this applet is how quickly students can see the results of a large number of trials that would be impractical to perform with a hands-on manipulative.

Click on image to enlarge.

Disadvantages: It is far too easy to determine the theoretical probability for any given spinner arrangement. It also does not lead into any further challenges. For instance, imagine a game where a player receives twice as many points for the spinner stopping on a color with relatively lower theoretical probability. Would the additional points make up for the probability gap?

Recommendations: This applet has limited, yet useful, application potential. I can see students losing interest rather quickly without some guiding questions.