Find A Pattern Problem Solving

The copyright notice at the bottom of this page must be included in all copies.One important math concept that children begin to learn and apply in elementary school is reading and using a table.

The copyright notice at the bottom of this page must be included in all copies.

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So over here, in this magenta color, I go from 4 to 25 to 46 to 67. 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? And if I were to keep going, if I add 21 I'm going to get to 89. But then I'm not adding 3 anymore to get from 6 to 12, I'm adding 6. I could say, maybe this is times 2, but then to go from 6 to 9, I'm not multiplying by 2. So this one actually does look like I'm just adding 3 every time.

Well there's a couple of ways to think about it. If I were to go from 25 to 46, well I could just add 21 again. If I add 21 to that I'm going to get 110, and I could keep going and going and going. And then to get from 12 to 24, I'm not adding 6 anymore, I added 12. 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. 2 times 12 is 24 and I could keep going 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. 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?

- [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. When I look at it at first, it's tempting to say, 3 plus 3 is 6. Then 6 to 9, I add 3 again, and then 9 to 12, I add 3 again.

If not, however, simply continue with the table until you get to week 8, and then you will have your answer.

I think it is especially important to make it clear to students that it is perfectly acceptable to complete the entire table (or continue a given table) if they don’t see or don’t know how to use the pattern to solve the problem.

A student who is unsure could simply continue filling out their table until they reach the solution they’re looking for.

Helping students learn how to set up a table is also helpful because they can use it to organize information (much like making a list) even if there isn’t a pattern to be found, because it can be done in a systematic way, ensuring that nothing is left out.

When I see 4 and 25, let's see, 25 isn't an obvious multiple of 4. It looks like to go from one number to the next I'm just adding. So I multiply by 2 to go from 3 to 6, and if I multiply by 2 again, I go from 6 to 12. So 3 times 2 is 6, 6 times 2 is 12, 12 times 2 is 24. 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. In this first set of numbers, we just add 21 every time.

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