Teaching times Ten – Place Holders: Leaves and Rocks

This morning I used the following mental picture to assist students in understanding what happens to numbers when they multiply it by ten. It also allowed for follow up for multiplying by 100.

Example 1

Here’s the set up.

The fan is blowing hard, and pushes all the leaves against the far wall.

The leaf can be moved closer to the fan by multiplying it by 10. Or; when you multiply it by ten, it moves across one column.

Now, the fan is blowing pretty hard, and so that leaf is just going to get blown back against the wall. How can we stop it from being blown back?

That’s right! Put a rock behind it. This rock happens to be of a similar shape to a zero. Coincidence!?

Example 2

Here’s another example with a two digit number. Children often get confused by 58 x 10 becoming 508, rather than 580.

Follow the following images, as with above, to show how the leaves stick together. The five is being blown against the 8, and the 8 is against the wall.


We multiply them by 10, and they both move across, sticking next to each other.


That fan is pretty strong. It’ll blow those leaves right back against the wall if we don’t do something about it…


That’s the trick! Add a rock and it keeps the leaves from blowing away!


Make a link between multiplying by 10 having one rock, and there’s one zero in the number 10.

What do you think will happen when we multiply by 100. How many squares can the leaves move? How many rocks do we need to fill the space? How many zeros in the number 100?


Feel free to use this next time you’re teaching multiplying by ten!