Multiplication facts

What is this skill?

Multiplication facts are the products of two one-digit numbers, such as 6 × 7 = 42 or 4 × 9 = 36, often called the times tables. In third grade, children are expected to understand what multiplication means and, by the end of the year, to know the facts within 100 well enough to recall them quickly. Some programs also include the 11s and 12s.

Multiplication starts as equal groups. 6 × 7 means 6 groups of 7, which can be shown as an array of 6 rows with 7 in each row. Children first find products by skip counting or repeated addition, then move to strategies that use facts they already know: doubling (4 × 7 is double 2 × 7), adding one more group (6 × 7 is 5 × 7 plus 7), and the turnaround rule (7 × 6 is the same as 6 × 7).

Why it matters

Multiplication facts are used in almost every part of math that comes after third grade: division, fractions, area, multi-digit multiplication, long division, ratios and algebra. When a child has to stop and count up to find 7 × 8 in the middle of a long division problem, the bigger idea gets lost. Quick recall frees their attention for the new learning.

How the facts are learned matters as well as whether they are known. Children who understand the strategies can rebuild a fact they forget, and they see the connections between facts, such as the 9s being one group less than the 10s. That kind of understanding is more durable than memorizing a chart.

Common mistakes

• Mixing up multiplication with addition, so 6 × 3 becomes 9. Drawing 6 groups of 3 dots shows the difference straight away.
• Mixing up neighboring facts, like 7 × 8 and 6 × 8. Linking a hard fact to an anchor helps: 7 × 8 is 7 × 7 plus one more 7, or 56.
• Forgetting that zero times any number is zero, and saying 5 × 0 = 5. Ask "What is 5 groups of nothing?"
• Counting on fingers for every fact, even easy ones. That is fine at first, but if it continues, focus on one small family of facts at a time, such as the 2s, 5s and 10s, before moving on.

How to help at home

• Practice a few facts often rather than many facts at once. Five minutes a day with one family, like the 4s, is more effective than a long session.
• Look for equal groups everywhere: wheels on cars, legs on chairs, eggs in a carton, socks in pairs. Ask "How many in all?" and "What multiplication fact is that?"
• Play a simple card game: each player flips two cards and the first to say the product wins them. Use only the facts your child is working on.
• Teach the strategies, not just answers. "You know 5 × 8 is 40. How could that help you with 6 × 8?"

Worked examples

These are real questions from the Tutorsaurus multiplication facts practice, with the answers worked out.

1. Example 1

   1 × 4 = ?

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   Answer: 4. 1 × 4 = 4. That is 1 group of 4: 4.

2. Example 2

   2 × 9 = ?

   Answer: 18. 2 × 9 = 18. That is 2 groups of 9: 9 + 9.

3. Example 3

   9 × 3 = ?

   Answer: 27. 9 × 3 = 27. That is 9 groups of 3.