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## Patterns in arithmetic

Current time:0:00Total duration:4:04

# Patterns in hundreds chart

CCSS.Math:

## Video transcript

- [Instructor] So what
we have in this chart is all the numbers from
one to 100 organized in a fairly neat way. It's a somewhat intuitive
way to organize it where each row you have
10, so you go from one to 10, then 11 to 20, then
21 to 30, all the way to 100. And what we're gonna
look at is interesting patterns that might emerge from this. So if you look at what's highlighted here in this purplish color, what
numbers are highlighted there? Pause this video and think about it. Well, what's highlighted
are all of the even numbers. And you can see the even
numbers form these nice, neat pillars or columns on this chart. And we can look at that
and immediately start to see some patterns. For example, what numbers are always going to be in the ones place for an even number looking at this chart? Well, you can see in the
ones place you're either always going to have a
two in the ones place or you're going to have
a four or you're going to have a six or you're
going to have an eight or you're going to have a zero. So that ones place digit is always going to be an even number. Let's do another example. Here we've highlighted different numbers. So pause this video and
think about what's true about all of the numbers
that we've highlighted? Well, you might notice that
these are all multiples of five. Five, 10, 15, 20, 25, 30,
35, 40, so on and so forth. And so these form these
two columns on this chart. And here we can see very
clearly that multiples of five are either going to have a five in the ones place like
we have right over here. So they're either gonna have a five in the ones place or
they're gonna have a zero in the ones place. You might've realized
that before but you see it very clearly in these
two, you see it very clearly in these two columns. Let's do one other example. This one is really
interesting because it's not just one of those clean
column-type patterns. It looks like we started
one, and then we have this diagonal, then we go to 100. What's a pattern that
could describe how we go from one number to the
next, or another way of saying it, what's a rule for why we highlighted these numbers in purple? Pause the video and think about that. All right, well, one thing is if we go from one number to the next, you go from one to 10, we add nine. To go from 10 to 19, we add nine. To go from 19 to 28, we added nine. So each number is nine
plus the previous one. And if you go all the
way to 91, 91 plus nine is of course 100. Now, it's important to
realize these are not multiples of nine because we
started at one, not at zero. If you started at zero,
you go zero, nine, 18, so forth and so on until
you go nine, 18, 27, 36, 45, 54, 63, 72, 81. Those would've been the multiples of nine. But everything got
shifted because we started at one, not at zero. So we go from one and then 10, 19, 28, all the way down this diagonal
and then we go back to 100. And so this is a really interesting
thing to think about it. These are all the
multiples of nine plus one is another way to think about it or this is if we started
at one and we keep adding nines, these are all the numbers that we would highlight. But you can see a pattern. Whenever you add nine
to a number, the value of the ones place decreases by one. You see that here as you
go down these diagonals. You go from nine, eight,
seven, six, five, four, three, two, one. And even up here, we started at zero but you don't have a lower digit than zero so it just goes back to nine. So it goes zero, then goes up to nine, then it keeps going
down, down, down, down, all the way until it gets to zero again and then it starts going
down from there again. So once again, interesting
patterns to look at. I encourage you to look
at a chart like this and think about what
patterns can you find?