In my very first Sine of the Times blog post from January 2012, I wrote about the paucity of fractions that young learners typically encounter in their math classes. While they might construct visual representations of 1/2, 2/3, and 8/12, it’s unlikely they’ll create models of 7/31, 36/19, or 5/101. That’s a shame because without the ability to build and explore out of the ordinary fractions such as these, students’ understanding of fractions is grounded in a very limited set of examples.
When my original blog post appeared in 2012, I provided a downloadable Sketchpad file of fraction tools that allowed students to easily and accurately construct any fraction whatsoever. Now, thanks to Web Sketchpad, there is no need to download anything. You can play with our fraction tools directly in your web browser using the Web Sketchpad model below.
The video at the end of this post gives a short overview to get you and your students started with fraction investigations. Your students can use the tools to construct any fraction they like, whether it be 1/2, 13/100, or 29/17. They can represent fractions as either parts of a circle or parts of a rectangle. They can build more than one fraction and compare them by dragging one onto the other. They can also create a memorable experiment to explore whether a fraction grows larger as its denominator increases. By using the Animate tool, students start with a fraction like 1/2 and watch what happens to its area representation as the denominator grows by 1s from 2 to 3 to 4 to 5 and upward, as high as they’d like it to go. Rest assured that if you stop the animation when the fraction reaches 1/20, students will demand that you resume the animation until the denominator climbs to at least 100!
In upcoming posts, I’ll provide interactive number line models of fractions to complement the area representation.