A Different Way to Multiply—and Why I Had to Rethink What I Knew

Sometimes helping our children learn means being willing to learn something differently ourselves.

When I first came across front-end multiplication, I had no clue what it was. I just knew it wasn't how I learned.

My memories of multiplication involve timed fact slips, trying to answer quickly, and a lot of pressure around getting the right answer. So when my son's curriculum introduced a strategy that looked different, my first instinct was to go back to what I knew.

I paused the curriculum and taught multiplication the way I had learned it.

Then I realized something important:

My familiarity with a method didn't automatically mean my child understood it better.

So I went back and took a closer look at the strategy his curriculum was teaching.

What I found wasn't a "new math trick."

It was place value, number relationships, and the distributive property working together.

And once I understood that, the strategy made a lot more sense.

What Does It Mean to Break Apart a Multiplication Problem?

Take: 43 × 6

Instead of treating 43 as one solid number, break it apart according to place value:

43 = 40 + 3

Now multiply each part:

40 × 6 = 240

3 × 6 = 18

Then combine the products:

240 + 18 = 258

So: 43 × 6 = 258

Mathematically, this is an example of the distributive property:

(40 + 3) × 6 = (40 × 6) + (3 × 6)

This connection between place-value partitioning and multiplication is important because it helps students see the structure underneath a multiplication algorithm—not simply memorize a sequence of steps.

What Is Your Child Actually Learning? You don't need a complicated lesson to explore multiplication strategies.

The answer is much bigger than 43 × 6 = 258.

1. Place Value

A child who sees 43 as simply a "4 and a 3" is missing important information.

The 4 represents four tens. The 3 represents three ones. So: 43 = 40 + 3

Breaking numbers apart reinforces that digits have value based on their position.

That understanding becomes increasingly important as children work with larger numbers, decimals, and more complex operations.

2. How to Break a Big Problem Into Smaller Parts

A multiplication problem can look intimidating when children see it as one large task.

But: 43 × 6 becomes: 40 × 6 and 3 × 6

Two smaller problems. This teaches a valuable mathematical habit:

When a problem feels big, look for parts you already know how to solve.

That habit extends beyond multiplication. Students use decomposition when adding, subtracting, working with fractions, solving algebraic expressions, and approaching word problems.

3. How to Use What They Already Know

Suppose a child knows: 4 × 6 = 24 They can build from that knowledge: 40 × 6 = 240

The fact didn't disappear because the 4 became 40. The value changed. And the child can reason through why.

This is one way number sense grows: children begin connecting known facts to unfamiliar situations instead of believing every new problem requires a completely new rule.

4. Flexible Strategy Use

There is more than one way to solve many math problems. That's important.

The goal isn't to replace every traditional multiplication method with one alternative strategy. Students still need procedural fluency—the ability to perform procedures accurately, efficiently, and flexibly and to know when and how to use them.

But conceptual strategies give students more tools. If one approach isn't making sense, they have another way to enter the problem.

Instead of: "I don't remember the steps."

We want to move toward: "What do I know about these numbers, and what could I do with that?"

What Outcomes Should We Look For?

When a child practices multiplication by breaking numbers apart, we're not simply looking for faster answers. We're looking for evidence of stronger mathematical thinking.

• Can they identify the value of each digit?

  • Ask: "What does the 4 represent in 43?"

  • We're looking for: 40—not just 4.

• Can they explain why they broke the number apart?

  • Ask: "Why did you turn 43 into 40 + 3?"

  • We're looking for understanding—not just: "Because that's what I'm supposed to do."

• Can they use a known fact to solve a larger problem?

  • For example: "If you know 4 × 6 = 24, what might 40 × 6 be?"

  • This shows whether the child is making connections between facts.

• Can they check whether an answer is reasonable?

  • Before accepting an answer, ask: "Does that make sense?"

For 43 × 6, the answer should be somewhere around 240, because 40 × 6 is already 240.

An answer of 58 should immediately raise a question.

An answer of 2,580 should also raise a question.

This kind of estimation helps children become less dependent on someone else telling them whether they are correct.

• Can they solve a new problem using the same thinking?

  • This is where we start seeing whether learning transfers.

  • If a child understands: 43 × 6 = (40 × 6) + (3 × 6) can they approach: 72 × 4 as:

    (70 × 4) + (2 × 4)? The numbers changed. The underlying idea did not.

Research on multiplication learning emphasizes making the connections among place-value partitioning, multiplication, and the distributive property explicit so students can understand the mathematics underneath procedures and apply their knowledge across contexts.

Try This

You don't need a special program to begin practicing this strategy. Start with a two-digit number.

• Try: 56 × 4

  • Ask your child: "How could we break 56 apart?"

Hopefully: 50 + 6

Then: 50 × 4 = 20, 6 × 4 = 24

Finally: 200 + 24 = 224

Then ask the questions that matter:

• Why did that work?

• What does the 5 represent in 56?

• How did you know 50 × 4 was 200?

• Is 224 a reasonable answer?

• Could you solve this another way?

Evidence-based guidance for elementary mathematics supports systematic instruction, mathematical language, and well-chosen representations to help students develop understanding of mathematical concepts and procedures.

Take Math Off the Page

Once the idea starts making sense, practice doesn't have to stay inside a workbook.

We used whiteboards. We talked problems out loud. And sometimes I would give my son a problem and ask him to teach me.

That last one is worth trying.

When a child teaches a strategy, you get to hear what they actually understand. You may discover that they can perform every step but can't explain why. Or you may discover that their reasoning is stronger than you realized.

Either way, explanation gives you better information than a row of correct answers.

Quick Takeaways

• Breaking numbers apart reinforces place value.

• Partitioning can make larger multiplication problems more manageable.

• Known facts can help children reason through unfamiliar facts.

• Conceptual understanding and procedural fluency should work together.

• Multiple strategies give children more ways to approach a problem.

• Estimation helps students decide whether an answer makes sense.

• The real goal is transfer: can your child use the same thinking when the numbers change?

The Bigger Goal

I don't think the goal of teaching multiplication is simply getting a child to the answer as quickly as possible.

I want to see a child who can look at a problem and recognize its parts.

A child who can use what they already know.

A child who can explain their strategy.

A child who notices when an answer doesn't make sense.

And eventually, a child who doesn't panic when a problem looks unfamiliar.

That's what strong mathematical thinking starts to look like. Not memorizing one path.

Understanding enough to find a path forward.

---