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🔢 Using Patterns to Find New Facts

You don't have to memorize every fact — you can grow new ones from patterns you already know. Spot the rules hiding in the times tables and use one fact to unlock the next.

lessons

~15 min

to learn

🔢 Math

subject

Ages 6–12

level

Start the course →

What you’ll learn

Patterns in the Times TablesRecognize the counting patterns in the 5- and 10-times tables and use them to check facts.Times tables are full of patterns. Counting by 5s (5, 10, 15, 20) always ends in a 5 or 0, and multiplying by 10 simply adds a zero to the end. Spotting these rules means you can figure facts out instead of only memorizing them.
Use a Fact You KnowDerive unknown multiplication facts by adding a group to, or doubling, a known fact.A fact you already know is a stepping stone. Since 5 × 7 is one more group of 5 than 5 × 6, you can do 30 + 5 = 35. And the 6-times facts are exactly double the 3-times facts, so 3 × 8 = 24 gives 6 × 8 = 48. Arrays make these moves easy to picture.
Grow the PatternExtend a skip-counting sequence to discover new facts and choose the best pattern strategy.Patterns keep going by the same rule. The sequence 3, 6, 9, 12 adds 3 each time, and the 7th hop lands on 21 — which is 3 × 7. With three tools in hand (add a group, double a fact, or extend a skip-count) you can reach any fact by reasoning, not guessing.

Questions this course answers

Every answer in the 5-times table ends in which digits?

Counting by 5s gives 5, 10, 15, 20 — each ends in 5 or 0.

Using the ×10 pattern, what is 8 × 10?

Multiplying by 10 puts a zero on the end: 8 becomes 80.

You know 5 × 6 = 30. What is 5 × 7?

5 × 7 is one more group of 5 than 5 × 6, so 30 + 5 = 35.

You know 3 × 8 = 24. Using doubling, what is 6 × 8?

The 6-times facts are double the 3-times facts: 24 × 2 = 48.

The pattern 3, 6, 9, 12, 15... adds 3 each time. What is the 7th number?

Keep adding 3: 3, 6, 9, 12, 15, 18, 21 — the 7th number is 21, which is 3 × 7.

To find 6 × 7 quickly, which pattern is smartest?

The 6s are double the 3s, so 6 × 7 = 2 × 21 = 42.

Grounded in trusted sources

Khan Academy
NRICH — University of Cambridge
NCTM — teaching standards
Britannica Kids

Every Wunder lesson is built from real, reputable sources — never invented.

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