Main content

### Course: 3rd grade > Unit 8

Lesson 4: Patterns in arithmetic- Finding patterns in numbers
- Recognizing number patterns
- Math patterns
- Intro to even and odd numbers
- Patterns with multiplying even and odd numbers
- Patterns with even and odd
- Patterns in hundreds chart
- Patterns in hundreds chart
- Patterns in multiplication tables
- Patterns in multiplication tables
- Arithmetic patterns and problem solving: FAQ

© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Finding patterns in numbers

This video discusses how to identify patterns in number sequences. By analyzing three different sequences, the speaker demonstrates that patterns can involve adding a certain amount to each number, or multiplying each number by a certain amount. It's important to ensure the pattern remains consistent throughout the sequence.

## Want to join the conversation?

- In the 1st pattern isn't 67 + 21= 88 ?

Why is the next number 89 in the pattern?(30 votes)- There was something on the side that said the "Sal meant to say 88 but accidently said 89."(5 votes)

- Can a pattern alternate? ie. Add three, then subtract five, then add three again, then subtract five, etc.(15 votes)
- Yes

for example -

1,2,5,6,9 (+1+3+1+3)(6 votes)

- Is 91 an odd number?(0 votes)
- 91 is not divisible by 2 so it's not even. It's odd.(4 votes)

- what if I have the numbers, 2,5,11,23,47,___, whats the next number in the pattern?(1 vote)
- Note that each number is a little more than double the number before it. Looking more closely, we see that each number is 1 more than double the number before it:

2 * 2 + 1 = 5.

2 * 5 + 1 = 11.

2 * 11 + 1 = 23.

2 * 23 + 1 = 47.

If this pattern continues, the next number would be 2 * 47 + 1 = 95.

Have a blessed, wonderful day!(0 votes)

- Can we not divide in a pattern?(0 votes)
- Dividing in a pattern is basically negative exponents. While 2^2 is 2*2. 2^-2 is (1)/(2^2). If you have any more questions about this, feel free to ask. :)(1 vote)

- at2:30,sal said 3,6,12,24's pattern is*2,but itcould be+3,+6,+9,+12...(0 votes)
- The pattern you speak of is one that always changes, in this way, you are changing the pattern by having it have it's own pattern, which is a rate of change to the pattern by 3.

However, the "+3, +6, +9, +12.." pattern will not work for if you apply it to the sequence of numbers:

3, 6, 12, 21, 33...(1 vote)

- Sal, in your first example you made 2 mistakes: 1.) 67+21= 88 not 89, therefore 88+21=109 not 110.(0 votes)
- What is the difference between an arithmetic and geometric pattern?(0 votes)
- Arithmetic is a pattern that changes by addition or subtraction, and geometric is a pattern that changes by multiplication or division.

To the first and third patterns in the video are arithmetic patterns and the second one is a geometric pattern.

Hope that helps.(0 votes)

## Video transcript

- [Voiceover] What I want to in this video is get some practice figuring
out patterns and numbers. In particular, patterns that take us from one number to a next number in a sequence. So over here, in this magenta color, I go from 4 to 25 to 46 to 67. So what's the pattern here? How did I get from 4 to 25 and can I get the same way from 25 to 46 and 46 to 67, and I could just
keep going on and on and on? Well there's a couple of
ways to think about it. When I see 4 and 25, let's see, 25 isn't an obvious multiple of 4. Another way to go from
4 to 25, I could add 21. Let's see, if I add 21, 4 plus 21 is 25. If I were to go from 25 to 46, well I could just add 21 again. It looks like to go from
one number to the next I'm just adding. I wrote 12 by accident, 21. I'm just adding 21 over and over again. That's going to be 46 plus 21 is 67. And if I were to keep going, if I add 21 I'm going to get to 89. If I add 21 to that I'm going to get 110, and I could keep going
and going and going. I could just keep adding
21 over and over again. The pattern here is I'm adding 21. Now what about over here, in green? When I look at it at first,
it's tempting to say, 3 plus 3 is 6. But then I'm not adding 3 anymore to get from 6 to 12, I'm adding 6. And then to get from 12 to 24, I'm not adding 6 anymore, I added 12. So every time I'm adding twice as much. But maybe an easier pattern might be, another way to go from 3 to 6, isn't to add 3, but to multiply it by 2. So I multiply by 2 to go from 3 to 6, and if I multiply by 2
again, I go from 6 to 12. 6 times 2 is 12. If I multiply by 2 again, I'll go to 24. 2 times 12 is 24 and I could
keep going on and on and on. 2 times 24 is 48, 96, I
could go on and on and on. The pattern here, it's
not adding a fixed amount, it's multiplying each
number by a certain amount, by 2 in this case, to get the next number. So 3 times 2 is 6, 6 times
2 is 12, 12 times 2 is 24. Alright, now let's look at this last one. The first two terms here
are the same, 3 and 6. The first two numbers here. I could say, maybe this is times 2, but then to go from 6 to 9,
I'm not multiplying by 2. But maybe I am just adding 3 here. So 3 to 6, I just added 3. Then 6 to 9, I add 3 again, and then 9 to 12, I add 3 again. So this one actually does look like I'm just adding 3 every time. The whole point here is to see,
is there something I can do, can I do the same something
over and over again to get from one number to the next number in a sequence like this? What you want to make sure
is even if you think you know how to go from the first
number to the second number, you've got to make sure
that that same way works to go from the second
number to the third number, and the third number to the fourth number. But here we figured it out. In this first set of numbers,
we just add 21 every time. This one we multiply by 2 every time. This one we add 3 every time.