Given a strip of paper, how might you divide it into fourths without using a ruler?  Undoubtedly, you’d fold the strip in half and then in half again to locate the quarter marks. Now suppose that your goal is to divide a strip into sixths. You might start by folding the strip into thirds and then folding each third in half. Or perhaps you’d first fold the strip in half and then fold the two halves into thirds.

These activities depend on your being able to divide the paper strip into equal parts. Halves and thirds are not so terrible, but the folding gets harder as you add more creases to the strip or if you must divide the strip into, say, sevenths.

The Web Sketchpad model below (and here) makes it a snap to create even divisions. The model comes with a set of tools that allow students to divide intervals into even parts ranging from halves to eighths. (Watch the short movie at the end of this post to learn how the tools work.)

If you challenge students to divide an interval into 24ths, some might use the Thirds and Eighths tool while others might use the Fourths and Sixths tool. Students can explore more than one method on the same page and then drag the divided segments onto or near each other to see if their methods produce the same result.

Below (and here) is a variation of the fraction model that grew out of my discussions with Toni Cameron of Reimagined. Unlike the first model where the right endpoint is always 1, here you can change the right endpoint to any value you like. With the value set at 24, students can use the various tools to find and label the locations of the factors of 24. They can also label the fraction associated with  each factor to create a double-number line.

An annotated list of all our elementary-themed blog posts is here.