Multiplication guide: how it works and how to teach it

What is multiplication?

Multiplication is repeated addition of equal groups. "4 × 3" means 4 groups with 3 in each group, which is the same as 3 + 3 + 3 + 3. The × sign says "groups of".

Once your child understands what multiplication means, the times tables become shortcuts instead of magic. Multiplication appears everywhere: price tags, cooking recipes, area, and arrays in real life.

How multiplication works

• Equal groups: 3 × 4 is 3 baskets with 4 apples each — 12 apples in total.
• Arrays: 3 rows of 4 dots make a rectangle. Arrays make the answer visual and also preview area.
• Skip counting: 2, 4, 6, 8, 10 … counts by 2s; 5, 10, 15, 20 … counts by 5s. Multiplication facts are just skip counting.
• Switching: 4 × 3 and 3 × 4 give the same answer. This is called the commutative property, and it halves the number of facts to memorize.

Worked examples

1. 3 × 4 = ?

   1. Think: 3 groups of 4.
   2. Add them: 4 + 4 + 4 = 12.
   3. 3 × 4 = 12.

2. 2 × 6 = ?

   1. Skip count by 2 six times: 2, 4, 6, 8, 10, 12.
   2. We counted 6 numbers and landed on 12.
   3. 2 × 6 = 12.

3. 7 × 8 = ?

   1. Break it into easy pieces: 7 × 4 = 28.
   2. Double it: 28 + 28 = 56.
   3. 7 × 8 = 56.

4. 12 × 4 = ?

   1. Split 12 into 10 + 2.
   2. 10 × 4 = 40 and 2 × 4 = 8.
   3. Add them: 40 + 8 = 48, so 12 × 4 = 48.

Tips for parents and teachers

• Teach meaning first, memorization second. A child who can draw 4 × 3 will learn the fact far faster than one who is just drilled.
• Learn tables in a sensible order: 0s, 1s, 2s, 5s, 10s first, then 3s, 4s, and finally the harder ones like 7s and 8s.
• Use skip counting songs and patterns. Rhythm helps facts stick.
• Point out multiplication in daily life: "We need 4 packets for 4 people at 3 each — that is 4 × 3."

Frequently asked questions