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What Is Multiplication?
Understanding it through groups

Early elementary · About 3 min read

"3 × 4 = 12" actually starts as a very simple picture: "3 groups of 4." Before playing with the multiplication table, let's see what multiplication really means.

🎮 Try the Multiplication Arrays activity 📚 See other topics
🧑‍🤝‍🧑 Read this together with a grown-up. Some words may still be tricky to read alone. Reading it out loud together makes it easier to understand.

1Multiplication is "adding the same number over and over"

Imagine a bag has 4 candies in it. If there are 3 of these bags, how many candies are there in all? You add 4, then 4, then 4: 4 + 4 + 4 = 12.

Multiplication is simply a short way of writing "adding the same number over and over."

4 + 4 + 4 = 12  →  3 × 4 = 12

Adding 4 three times gives the same answer as 3 × 4.

2Group pictures make it easier

On the Multiplication Arrays activity, we use circles instead of candy bags. If there are 3 groups, with 4 circles in each group, you don't have to count every circle — you can just calculate 3 × 4. Move the sliders to change the number of groups and the number in each group, and watch the circles grow or shrink right before your eyes.

12
3 groups of 4 — you don't even need to count, it's 3 × 4 = 12
Number of groups × items in each group = total count
Remember just this one sentence, and you can draw a picture for any multiplication problem.

3The order doesn't change the answer

3 groups of 4 looks different from 4 groups of 3, but the total is the same either way: 12. That's why 3 × 4 = 4 × 3.

This is called the commutative property, but you don't need to know the fancy name. Just remember: "swapping the order gives the same answer." Try pressing the "swap groups and items" button on the activity to see it for yourself.

4The multiplication table is a map of multiplication

In a multiplication table, the box where a row and column meet holds the answer to multiplying those two numbers. For example, where row 3 meets row 4, you'll find 12. The more you look at the table, the more familiar you become with roughly where each answer lives, even before you calculate it.

5Try playing like this

Move the sliders to any two numbers, then ask yourself: "how many groups, and how many in each group?" Try answering first, then count the circles to check. You can also use the preset buttons (2×3, 5×5, 7×8, 9×9) to quickly explore different combinations.