Numerical patterns with a constant value: Explanation

6, 9, 12, 15. These numbers are all connected somehow. How, exactly? Let’s see. How do we get from 6 to 9?

Well, let’s count up from 6. 7, 8, 9. We add three. How do we get from 9 to 12? Let’s count up again.

10, 11, 12. We add three again! How do we get from 12 to 15? 13, 14, 15. We add three!

We can say that these numbers form a pattern, and the pattern’s rule is going up by threes. Let’s look at another pattern. 10, 8, 6, 4. There’s something different about this one. How do we get from 10 to 8?

We can’t count up. We have to count down, instead. Let’s count down from 10. 9, 8. We take away 2!

How do we get from 8 to 6? Let’s count down again. 7, 6. We take away 2 again! This pattern’s rule is going down by twos.

Take a look at the next pattern and see if you can find the rule. This pattern is going up by fours. Now we know the pattern’s rule, let’s see if we can carry it on. What comes after 15? Let’s add 4.

16, 17, 18, 19. The next number is 19! And after that… 19 add 4… 23! We’ve used the pattern’s rule to help us carry on the pattern. Look at the next pattern.

See if you can find the rule, then carry it on. This pattern is going down by fives and the next number in the pattern is five. Knowing a pattern’s rule can help us with something else, too. Look at this pattern. It’s missing a number.

6, 12, 18, something, 30. First, let’s find the rule. To get from 6 to 12 we… add 6. To get from 12 to 18 we… add 6. This pattern is going up by sixes.

Now we know this, we can look at the number before the missing number, and add 6. 18 add 6 is… 24. Let’s check our answer. What’s 24 add 6? 30!

We got the missing number right. Now we’ve learned to find the rule for patterns that go up or down. And we know that, once we’ve found a pattern’s rule, we can carry on the pattern or find a missing number. Take a look at this last pattern. See if you can find the pattern’s rule, find the missing number, and carry it on.

You’ve got this! This pattern is going down byin threes, and the missing numbers are nine and three.