Multiplication is a shortcut for repeated addition of equal groups. Instead of writing 5 + 5 + 5 + 5 = 20, we can write 4 × 5 = 20, read as '4 groups of 5.' The multiplication symbol (×) connects the number of groups to the size of each group. Second graders are introduced to this relationship conceptually; formal multiplication fluency is developed in third grade.
Present equal-groups and array situations and write both the repeated addition equation and the corresponding multiplication equation. Let students use whichever is more comfortable — the goal is connecting them. Skip-counting fluency (by 2s, 5s, 10s) accelerates this work.
You already know that addition joins equal groups together. When you have 3 bags with 5 apples each, you can add: 5 + 5 + 5 = 15. Multiplication is just a shortcut for writing this. Instead of listing all those fives, you write 3 × 5 = 15, which means "3 groups of 5." The × symbol is shorthand for "groups of."
The two numbers in a multiplication expression have roles: the first is the number of groups, and the second is the size of each group. So 4 × 7 means "4 groups of 7." You can always check a multiplication by writing out the repeated addition: 4 × 7 = 7 + 7 + 7 + 7 = 28.
One of the most useful discoveries in multiplication is that the order does not matter: 3 × 5 gives the same answer as 5 × 3. You can see this with an array — a rectangle of dots. A 3-row by 5-column array has 15 dots. If you rotate it 90°, it becomes a 5-row by 3-column array — still 15 dots. This is called the commutative property, and it means you only need to memorize half as many multiplication facts.
A common trap: multiplication does not always make things bigger. 5 × 1 = 5 (unchanged) and 5 × 0 = 0 (smaller). For now, most of your practice will involve whole numbers greater than 1, where products do get bigger — but keep this in mind for later when you multiply fractions.