This week, I’m going to describe one of my favorite activities for introducing young learners to multiplication and factors. It comes from Nathalie Sinclair, a professor of mathematics education at Simon Fraser University.

In the interactive Web Sketchpad model below, press *Jump Along* to watch the bunny take 2 jumps of 4 along the number line. The bunny leaves behind a trail of its path, providing a visual representation of 2 x 4 = 8.

With the bunny back at 0, it’s time to find other ways to reach 8. Enter new values for “Number of Jumps” and “Jump By.” Before pressing *Jump Along*, however, drag the red point that sits on the multi-colored segment. The color of this point controls the color of the bunny’s jumps. By making each set of jumps a different color, it’s easier to distinguish one from another, and the resulting rainbow-like pattern is an attractive artifact of students’ work.

Below are all four ways to reach 8. While students often meet the equivalence of *a* x *b* and *b* x *a* with a shrug, here we have a nice visual representation that distinguishes 2 x 4 and 1 x 8 from 4 x 2 and 8 x 1. We can also see the factors of 8 by noting where each of the four paths first lands on the number line (The red path, for example, lands first at 4, indicating that 4 is a factor of 8.)

Students can now explore other destinations on the number line. To jump to numbers larger than 12, just drag the point at 1 closer to 0 to rescale the number line.

As students explore factor rainbows, they can explore questions like: Do certain numbers create prettier factor rainbows than others? For larger target destinations, are there more ways to reach the target? Which factor rainbows have only 2 paths? Do all factor rainbows contain an even number of paths?

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