Introduction to Multiplication

Equal Groups#

Multiplication starts with the idea of equal groups. When you have several groups with the SAME number of items in each group, you can use multiplication to find the total quickly!

What Are Equal Groups?#

Equal groups means every group has the exact same number of items. If each group has a different number, we cannot use multiplication.

• 3 bags with 4 apples each → equal groups ✓
• 4 plates with 2 cookies each → equal groups ✓
• 2 jars with different numbers of marbles → NOT equal groups ✗

Counting Equal Groups#

Let us say you have 4 plates and each plate has 3 cookies.

You could count one by one: 1, 2, 3... 4, 5, 6... 7, 8, 9... 10, 11, 12. That takes a long time!

Or you could add: 3 + 3 + 3 + 3 = 12.

Or you could multiply: 4 × 3 = 12. Much faster!

Writing About Equal Groups#

When we talk about multiplication, we use the × symbol (called the times sign or multiplication sign).

4 × 3 = 12 means: 4 groups of 3 = 12 in total.

We read this as "four times three equals twelve."

Real-Life Equal Groups#

Equal groups are everywhere in daily life!

• 5 hands × 5 fingers each = 25 fingers
• 3 tricycles × 3 wheels each = 9 wheels
• 6 eggs × 1 dozen carton = (12 eggs per dozen × 1) — wait, let us keep it simple!
• 2 boxes × 6 crayons each = 12 crayons

Setting Up Equal Group Problems#

To write a multiplication expression for equal groups, ask:

1. How many groups? (This is the first number.)
2. How many in each group? (This is the second number.)
3. Write: groups × per group = total

Understanding equal groups is the key to understanding multiplication. Every multiplication fact is just a shortcut for counting equal groups!