Topic A: Multiplication and the meaning of the factors
- [Instructor] What we have here are pictures of running pigs, and we can try to figure out how many running pigs there are by just counting the pigs, but we're gonna start building some new muscles and this muscle's going to involve, hey, if we group the pigs into equal groupings, can that help us figure out how many pigs there are? And you can see that I have groupings of seven. Each of these groups are seven running pigs, so how many total groups do I have? Well, I have one, two, three groups of seven running pigs each. Three equal groups. If I said, what's the total number of running pigs that I'm dealing with? Well, I have three sevens, three groups of seven, and so, that's the same thing as seven plus seven plus seven, and if you wanted to figure out what that is, you could skip count. If we skip count by seven, we go seven then 14 then 21, and so, three sevens, which is seven plus seven plus seven, is 21, so there's 21 pigs here, and you can verify on your own that if you count this, you will indeed see 21 pigs. Let's do another example. Here, I'm looking at a picture of a bunch of blue seals, not something that you are likely to see in the wild. And these blue seals have, once again, been grouped. Let's see how many groups there are. There are one, two, three, four, five, six, seven groups, and how many are in each group? Well, we could see that they're all groups of one, two, three, four, five. They're equal groups. What are dealing with? Well, we're dealing with seven groups of five, so I could write seven groups of five. I could write seven fives. I could write five plus five plus five plus five plus five plus five plus five, so that is seven fives there. And if I wanted to figure out where that is, I could skip count. I could skip count seven fives, so that'd be five, 10, 15, 20, 25, 30, 35. If I were to add all these fives up, five plus five is 10, add another five, you get to 15. Add another five, 20. Add another five, 25. Add another five, 30. Add another five, 35, which is exactly what you see there. We're starting to see that sometimes grouping things can help us appreciate how many things there are there. And I know what some of you all are thinking, well, hey, couldn't I just count things? Well, you could, but what if you had 100 groups of five? Well then, it's gonna take you a little bit more time to count. But the techniques that we're building will help you one day be able to think about those things quite easily.