Multiplication by Ten

In base-10, multiplication by ten (or any other power of ten) is a very special operation. When you multiply a number by ten, you can think of it as shifting the digits to the left, or as writing a zero at the end. If you think about the number with blocks, then you are exchanging each block that you have with the next size bigger block, or you are magnifying each block. Using the blocks, students can discover the power of multiplying by ten on their own.

Start by asking the students to multiply a number by ten. Let’s do 12 * 10. The students can solve the problem by building 10 groups of 12 blocks.

Then they must pack as much as possible to find the answer.

The goal is for the students to notice that the answer, 120, looks just like one of the original piles of 12, only bigger.

Is this a coincidence? Will this happen again if we choose a different number to multiply by 10? Why does this happen?

Through a group discussion, students will come up with explanations for why multiplying by ten has this special property.