Understanding Multiplication

Multiplication might seem like a brand new math skill, but it is actually a quick and easy way to do something you already know: addition! Specifically, multiplication is a shortcut for adding equal groups of numbers together.

Multiplication as Repeated Addition

When you add the same number over and over, you can use multiplication instead.

For example, if you have $4$ groups of $3$ apples, you could add them like this: $3 + 3 + 3 + 3 = 12$

Writing out all those threes takes time! Instead, we can write a multiplication sentence: $4 \times 3 = 12$

This means "$4$ groups of $3$ equals $12$."

If you see a problem like $5 + 5 + 5 + 5$, you just count how many $5$s there are. There are four $5$s, so as a multiplication sentence, this is written as $4 \times 5 = 20$.

Using Equal Groups

One of the best ways to understand multiplication is to draw equal groups. If you want to solve $3 \times 6$:

1. Draw $3$ big circles (these represent your groups).
2. Put $6$ dots inside each circle.
3. Count all the dots. You will find there are $18$ dots in total.

So, $3 \times 6 = 18$.

Drawing Arrays

An array is a group of objects arranged in neat rows and columns. To draw an array for $3 \times 6$:

• Draw $3$ rows.
• Put $6$ items in each row.

It looks like a neat rectangle. Counting the items by rows ($6 + 6 + 6$) gives you the same answer: $18$!

Jumps on a Number Line

You can also show multiplication on a number line by taking equal-sized jumps forward.

To show $4 \times 3$:

• Start at $0$.
• Take $4$ jumps.
• Make each jump exactly $3$ spaces long.

Your first jump lands on $3$, the second jump lands on $6$, the third on $9$, and the fourth jump lands on $12$. So, $4 \times 3 = 12$.