Do Your Students Know How to Multiply by 10 — or Just Remember the Rule?

The rule looks obvious — until it isn’t!

“Adding a zero makes a number ten times bigger.”

Does it?

I find myself restating this rule to students, yet students look blankly at me. They solve the next example, but forget as soon as they are presented with a multi-part problem.

Or perhaps the worded question throws them?

They say things like:

“What do I do again?”

“How do I do that with this problem?”

And the all encompassing:

“I got that wrong because you didn’t teach me how to do that with this sort of problem!”

Who’s with me?

Teachers that have taught their students well – explicitly, progressively and thoroughly – can still find that, when students are asked to apply their learning in a new context, they are totally bamboozled!

Applying learning to different contexts and generalising mathematical ideas is truly tricky.

I find that giving the students time to investigate the mathematics can actually save me time later.

Why?

Students may confidently know the classroom rule, but are sketchy on their conceptual understanding.

Consider the familiar rule:

“When you multiply by 10, add a zero.”

It works as a shortcut when multiplying whole numbers by 10, but the zero isn’t actually what makes the number ten times as large.

The mathematics lies in our base-ten place-value system. When a whole number is multiplied by 10, each digit moves one place to the left, changing its value by a factor of 10.

That’s a much more powerful idea for students to understand than simply remembering to add a zero.

When students have lesson time to investigate when the rule works, why it works, and what happens when we change the numbers, they begin to build the conceptual understanding needed to use the procedure flexibly.

Students can then begin to notice patterns, make generalisations and apply their understanding across contexts.

So how do we get our kids to test the rule?

Rather than beginning with a rule and having students practise adding zeros, I recommend giving students opportunities to explore representations and quantities first.

Let them notice what happens when a quantity is multiplied by ten.

Let them look for patterns.

Let them test their ideas, and make mistakes.

Let them explain why the pattern works.

And, importantly, let them encounter examples that challenge them to think beyond a memorised procedure, because knowing the rule isn’t necessarily the same as understanding the mathematics.

Ten Times Ten | Investigating the Rules does this beautifully.

The bounded investigation provides an accessible entry point while allowing students to progress towards deeper mathematical thinking.

And rather than simply asking students to remember a rule, the task helps reveal what they understand about the mathematics behind it.

Here is the Ten Times 10 Multiplying by Ten Bounded Investigation, ready for you to download and teach tomorrow.