Times Tables

A times table is an organized list of the products you get when you multiply one number by 1, 2, 3, and so on, usually up to 10 or 12. For example, the "3 times table" lists \(3 \times 1 = 3\), \(3 \times 2 = 6\), \(3 \times 3 = 9\), and continues in the same pattern. Once these facts are memorized, multiplication problems can be answered instantly instead of being solved from scratch every time.

Times tables grow naturally out of ideas students already know, especially repeated addition as multiplication and counting equal groups. Multiplying \(4 \times 5\) is the same as adding 4 groups of 5, or 5 groups of 4: \(5 + 5 + 5 + 5 = 20\).

A multiplication chart, sometimes called a times table chart, arranges every product in a grid. To find a fact, look down the column for one factor and across the row for the other factor; the number where they meet is the product. The chart below shows facts up to \(6 \times 6\), with the cell for \(4 \times 5\) highlighted.

Every times table follows a steady skip-counting pattern. The 3 times table, for instance, goes up by 3 each time: 3, 6, 9, 12, and so on. This pattern can be seen as points that all sit on the same straight line, since each product is simply 3 times the factor.

Noticing patterns like this makes the whole chart easier to learn. A few well-known shortcuts include:

• Multiples of 2 are always even.
• Multiples of 5 always end in 0 or 5.
• Multiples of 10 always end in 0, since multiplying by 10 just adds a zero.
• For the 9s, the digits of the product always add up to 9 (for example, \(9 \times 4 = 36\), and \(3 + 6 = 9\)).

These strategies connect closely with multiplying using mental strategies, which build on the same number relationships to speed up recall.

One reason a times table is only "half full" of new information is the commutative property: \(a \times b = b \times a\). This means \(6 \times 7\) and \(7 \times 6\) both equal 42, so once one fact is learned, its reverse is automatically known too. This also connects to using models to multiply, where arrays visually show why swapping the factors does not change the total.

Example 1: Use the times tables to find \(8 \times 7\). Recall that \(8 \times 7 = 56\), the same fact as \(7 \times 8\).

Example 2: Find the missing factor in \(6 \times n = 42\). Since the 6 times table gives \(6 \times 7 = 42\), the missing factor is \(n = 7\).

Example 3: Use skip counting to check \(4 \times 5\). Counting by 4s five times gives \(4, 8, 12, 16, 20\), so \(4 \times 5 = 20\), matching the highlighted cell in the chart above.

Practicing a little every day works better than trying to memorize the whole chart at once. Start with the easier facts (the 1s, 2s, 5s, and 10s times tables), then move on to trickier ones like the 6s, 7s, and 8s. Reviewing a multiplication chart regularly, saying facts out loud, and timing quick quizzes are all effective ways to build speed and confidence with every times table from 1 to 12.

Related lessons

• Math 3