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

Video transcript

so what we have in this chart is all the numbers from 1 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 1 to 10 then 11 to 20 then 21 to 30 all the way to undred and we're going to 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 all 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 2 in the ones place or you're going to have a 4 or you're going to have a 6 or you're going to have an 8 or you're going to have a 0 so that one's place digit is always going to be an even number let's do another example here we've highlighted 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 5 5 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 we're gonna have a five in the ones place or they're going to have a zero in the ones place you might have 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 what's a pattern 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 to go from 1 to 10 we add 9 to go from 10 to 19 we add 9 to go from 19 to 28 we added 9 so each number is 9 plus the previous one and if you go all the way to 91 91 plus 9 is of course 100 now it's important to realize these are not multiples of 9 because we started at 1 not at 0 if you started at 0 you go 0 9 18 so forth and so on until you go 9 18 27 36 45 54 63 72 81 those would have been the multiples of 9 but everything got shifted because we started at 1 not at 0 so we go from 1 and then 10 1928 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 9 plus 1 is another way to think about it or this is if we started at 1 and we keep adding nines these are all the numbers that we would highlight but you can see a pattern whenever you add 9 to a number the value of the ones place decreases by 1 you see that here as you go down these diagonals you go from not 9 8 7 6 5 4 3 2 1 and even up here we started at 0 but you don't have a lower digit than 0 so it just goes back to 9 so it goes 0 then goes up to 9 then it keeps going down down down down all the way until it gets to 0 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