If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:4:20

Video transcript

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 see if 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 2 plus 2 plus 2 plus 2 and this of course is going to be 2 plus 2 is 4 4 plus 2 is 6 6 plus 2 is 8 we see that over here we could even skip count 2 4 6 8 4 times 2 is equal to 8 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 can imagine 4 times 2 being all right so this is 1 times 2 2 times 2 3 times 2 and 4 times 2 so we started at 0 and we took 4 hops of 2 along the number line to end up at 8 we went from 0 to 2 4 6 8 we just kept counted our way to 8 so if I were to ask a similar question actually let me draw a little a series of hops and I want you to think about it the other way what 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 that I'm gonna go there then I'm gonna go there and then I'm going to go over there so what would that represent if we use the same type of ideas that we just thought about well I went from 0 to 4 8 12 16 20 I'm skip counting by 4 so you can imagine this is probably something times 4 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 twenty 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 we got and you could also you to skip counting we went from 0 to 3 6 9 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 all right over there we 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