Main content

## Patterns in arithmetic

Current time:0:00Total duration:5:16

# Patterns in multiplication tables

CCSS Math: 3.OA.D.9

## Video transcript

- [Voiceover] We are asked,
"What numbers should replace "the A and B in the multiplication table?" So let's just make sure we can read this multiplication table. The way you think about it is,
if you wanted to figure out-- It goes up to six. So if you want to figure
out what any number up to six times another
number up to six is, this table will tell you. So for example, if you
wanted to figure out what three times two is, you say, "Ok, three. Let me take the
row that has this three in it. "And then the column for the two. "So three times two." So if you're in this row, the three row, and you're in the two column, three times two is going to be six here. Or you could go the other way around. This 12, this means that 3 times 4 is 12. Or right over here, this 25. Notice, this is the same row as this five and the same column as that 5. So it's saying that five times five is 25. And so you notice that
if you go in any row, you're counting by that number
and if you go in column, you're also counting by that number. So for example, in this
two's column right over here you're counting by twos. Two, four, six, eight. In this five column,
you're counting by fives. Five, 10, 15, 20. And that makes sense because
five times one is five. Five times two is 10.
Five times three is 15. Five times four is 20. And the same thing is
happening as you go up a row. Two, four, six, eight. Because two times one is
two. Two times four is four. On and on and on, you're counting by twos. Here you're counting by sixes. Six times one is six. Six times two is 12. Six times three is 18.
Six times four is 24. So hopefully now we understand
the multiplication table. And it is actually pretty cool
to just keep looking at it and thinking about how it works. But let's answer their
question, what would A and B be? Well we have this A right over here. So one way to think about it, it needs to be whatever
four times four is. And you might know that
four times four is 16. Four times four is 16. Or another way is, you could just go down this column and count by fours. Four, eight, 12 and
then you add four again. 12 plus four is 16. Now let's figure out what B is. And actually, let's do it that way. B is in this column so
we can count by threes. Three, six, nine. Add three
to that and you get to 12. So b could be 12. Or you could go from the row. You could go four, eight, add
four to that and you get 12. And that makes sense
because this, where B is, that should be whatever
four times three is. Cause four times three is 12. Then they say, "Complete the inequalities "with the greater-than,
less-than or equal symbol." So A is greater than B. Greater than. And I always remember
the greater than symbol because it is opened
to the number on left. The number on the left is greater than, it's opened to larger number. A is greater than B
because four times four is going to be greater
than four times three. Is greater than four times three. All right, four times four is
greater than four times three. It makes sense. If four times four is four fours and if four times three is three fours, you have more fours here. So hopefully that makes sense. Let's do a couple more of these. So now what number should replace A and B in the multiplication table? So same idea. So A should be whatever
four times five is. So it should be 20. Or you could look at whatever
row or column it's in. If you look at its
column, five, 10, 15, 20. Now let's do the same thing for B. B should be whatever five times four is. Well that's going to be 20 as well. That's going to be 20. And you could say, "Well
look, A is gonna be "four times five which is 20. "And B is gonna be five
times four which is 20." So either way you look
at it, they are the same. So, complete the inequalities? Well, A is equal to B
because four times five is the same thing as five times four. It doesn't matter what
order you multiply them in. Let's do one more of these. I think you're getting the sense of it. So what is A? So we see where it's located, it's in this row for this two
and the column for the six. So it needs to be
whatever two times six is. Which is 12. And you could count by sixes. Six, 12. Or you could count by twos. Two, four, six, eight, 10, 12 to get to A. Now B, this is going to be
whatever six times 2 is. Well, that's gonna be 12 again. And so it's just like the last one we saw. A is gonna be equal to B because two times six is
equal to six times two. Let's do one more, this
is actually a lot of fun. All right, so A is
whatever four times one is which we know is gonna be four. B is gonna be whatever one times four is which is also gonna be four. And I think you see a pattern here. A equals B because four times one is the same thing as one times four.