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### Course: 3rd grade > Unit 1

Lesson 2: Multiplication on the number line# Multiplication on the number line

Sal uses a number line to represent and solve simple multiplication expressions.

## Want to join the conversation?

- why is the answer the same if you do it both ways

7x3=21 and 3x7=21(19 votes)- This is an important property of multiplication called the commutative property. We can multiply numbers in any order and get the same answer.

Think of 3x7 as the number of (smallest) squares in a grid with 3 rows and 7 columns.

Think of 7x3 as the number of (smallest) squares in a grid with 7 rows and 3 columns.

Turning either one of these two grids 90 degrees gives the other grid. Turning a grid does not change the number of (smallest) squares.

So it makes sense that 3x7 is the same as 7x3.

Have a blessed, wonderful day!(35 votes)

- How do you use multiplication on a number line?(5 votes)
- First, you break the multiplication down, for example: 4*4 is the same as 4+4+4+4. So on a number line, you would start at 0, and "jump" 4 places 4 times. and since there were 4 "jumps" of 4 places, the expression would be 4*4.(29 votes)

- how do i multiply on a numberline to 100(7 votes)
- by drawing out the numberline from 0 to 100

As you would notice though it would end up too long. There's techniques used to deal with big multiplication like 100 by using patterns found in multiplying by 10s and 1s

For example, if you draw a number line of any number and skip count to 10 you'll notice they'll all end up with an extra 0

Say like 2

10 + 10 = 20

lets try 5

10 + 10 + 10 + 10 + 10 = 50

See the trend of how anything multiple by 10 is just the number with a zero?

Now what would happen if I added an extra zero(100)?

And that's how you would address your number line issue.. by not using a number line(2 votes)

- At about3:14minutes into the video Sal says; 'seven equal hops'. What does he mean by this?

Why did he mention the word 'equal'?

They've got to be equal hops / groups right?(3 votes)- "7 equal hops" means that he is moving forward 7 times, each time moving the same amount on the number line.(6 votes)

- I don't get it(2 votes)
- Why do we skip count(2 votes)
- could you times inf(2 votes)
- yes you can but you will get the same number(1 vote)

- because it is a flip flop(2 votes)
- why do you allways use 4(1 vote)
- The commutative property of multiplication states that the order of numbers in a multiplication problem doesn't change the result. So, 7 x 3 = 3 x 7. This property is beneficial when solving problems because it allows us to rearrange numbers to make calculations easier

Think of it like this: Imagine you have 7 baskets with 3 eggs in each basket. That would be 7x3 because you have 7 baskets (groups) with 3 eggs in each one.

Now imagine you have 3 baskets that have 7 eggs in each basket. That would be 3x7 because you have 3 baskets (groups) with 7 eggs in each one.

Hope this helped and if you are still confused I can clarify further!(1 vote)

## Video transcript

- [Instructor] What we're
going to do in this video is think about different ways
to represent multiplication. And especially connect it to the notions of skip counting and the number line. So if we were to think about
what four times two means, we've already seen in other videos, you could view this as four groups of two. So we could have four groups, so one group, two groups, three groups, and four groups, and each of them have two of something. I'll just put two little circles here. So you have two there, you have two there, you have two there, and you have two there, and you could also view that as four twos, or four twos added together. So we could view it as two plus two plus two plus two. And this, of course, is going
to be two plus two is four, four plus two is six,
six plus two is eight. We see that over here, we could even skip count. Two, four, six, eight. Four times two is equal to eight. We can also think about
that on a number line. So I'm gonna make a little
bit of a number line here. And so we could imagine four
times two being, all right. So this is one times two, two times two, three times two, and four times two. So we started at zero, and we took four hops of
two along the number line to end up at eight. We went from zero to
two, four, six, eight. We just skip counted our way to eight. So if I were to ask a
similar question, actually, let me draw a little series of hops, and I want you to think
about it the other way. What multiplication does that represent? So let's say I start here and then I'm going to hop like this. So I'm gonna go there and then I'm gonna go there. I'm taking equal jumps every time. Then I'm gonna go there. Then I'm gonna go there. Then I'm going to go over there. So what would that represent, if we used the same type of ideas that we just thought about? Well I went from zero to
four, eight, 12, 16, 20. I'm skip counting by four. So you could imagine this is
probably something times four. Now how many hops did I take? I took one, two, three,
four, five hops of four. So this is five times four. And we can see that we ended up at 20. We could also view this
as being the same thing as five fours or four plus four plus four plus four plus four, and
you see that over here. You have, we're starting
at zero, we're adding four, then another four, then another four, then another four, and another four. We have five fours here. Let's do one more. So I'm gonna have a number line here and think about what it would mean to say, do something like
seven times three, times three. Well, we could view that
as seven hops of three starting at zero, seven equal hops. So one, two, three, four, five, six, and seven. We end up at 21, so this is equal to 21. You could also view this
as we took seven threes and added them together. And you could also view
it as skip counting. You went from zero to
three, six, nine, 12, 15, 18, and 21. Now just out of interest, what if we went the other way around? What if we were to take
three hops of seven? What would that be? Well, we would start here and so we would take our first hop of seven right over there. Get to seven, then if we
take another hop of seven, we get to 14, and then if we take another hop of seven, we get to 21, interesting. At least for this situation, whether we took seven hops of three or three hops of seven, we
got to the exact same value. I encourage you to think about
whether that's always going to be the case. I'll see you in a future video.