3 Times Table

What you will learn

• Say and write the answers in the $3$ times table up to $3 \times 12$.
• Use the patterns in the table to check your answers.
• Use the table to solve simple word problems.

Before you start: you should know multiplication as equal groups. See Multiplication: Equal Groups and Arrays.

The idea

The $3$ times table lists $3$ multiplied by $1, 2, 3$ and so on up to $12$. Each answer is the number of objects in that many groups of $3$.

The whole table

Patterns

• Count in threes: $3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36$.
• Double and one more: $3 \times 6$ is $2 \times 6 = 12$ plus $6$, which is $18$.
• Add the digits of any answer: $2 + 1 = 3$ for $21$, $2 + 7 = 9$ for $27$. The total is always $3, 6$ or $9$.
• The answers go odd, even, odd, even: $3, 6, 9, 12, 15, \dots$

Skip counting

Counting in steps of $3$ gives the answers one after another.

An array

An array shows the same facts as rows and columns.

Worked examples

Example 1: Double and one more

What is $3 \times 7$?

1. Double $7$ is $14$.
2. Add one more $7$: $14 + 7 = 21$.

Answer: $21$.

Example 2: Checking with digits

Could $3 \times 8$ be $25$?

1. Add the digits of $25$: $2 + 5 = 7$.
2. That is not $3, 6$ or $9$, so $25$ is not in the table.

Answer: No. $3 \times 8 = 24$.

Example 3: Triangles

How many sides do $9$ triangles have altogether?

1. A triangle has $3$ sides.
2. $9 \times 3 = 27$.

Answer: $27$ sides.

Use the digit-sum trick as a check, not as a way to find the answer. It tells you when an answer is wrong, but a wrong answer can still pass it by luck.

Why it matters

Threes appear in triangles, thirds and in dividing things into three equal shares. The 3 times table also leads to the 6 and 9 times tables, which are doubles and triples of it.