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CCSS.Math: , , ,

let's think about different ways that we can represent the number 675 675 so the most obvious ways to just look at the different place values so the six is in the hundreds place it literally represents 600 so that's 600 wonder then that red color 600 the 7 is in the tens place it represents seven tens or seventy and then the five is in the ones place it represents five so let me copy and paste this and then think about how we can regroup the value in the different places to represent this in different ways copy and let me paste it and maybe I'll do it three times so let me do it once let me do it one more time so one thing that we could do is we could regroup from one place to the next so for example we could take if we wanted to we could take one from the hundreds place taking one from the hundreds place we'll make this a five that's essentially taking one hundred away so this is really making this a 500 and we could give that hundred to what we could actually give it to either place but let's give it to the tens place so we're going to give we're going to give a hundred we're going to give a hundred to the tens place now if you give a hundred to the tens place and you already had 70 there what's it going to be equal to well it's going to be equal to 170 well how would we represent that is tens 170 is seventeen tens so we could just say that seven becomes a seventeen now we could keep doing that we could regroup some of this value in the tens place to the ones place so for example we could give 10 from the tens place and give it to the ones place let's do that so let's take 10 away from here so that becomes one hundred and sixty this becomes 16 and let's give that ten let's give that 10 to the ones place well what is the ones place now become well 10 plus 5 is 15 so this 5 is now a15 let's do another scenario let's take let's do something let's do something nutty let's take 200 from the hundreds place let's give take 200 from the hundreds place so this is going to be now 4 and this is going to become 400 that's what this for now represents and let's give 100 let's give 100 to the tens place and let's give another hundred to the ones place so notice I'm just regrouping that 200s those 200s I've taken from the hundreds place I'm going to give it to these other places so now the tens place is going to be a hundred seventy we're going to we're going to have a hundred seventy here which is 1710 so you could say the tens place is now 17 and now the ones place well I had five I'm going to add a hundred to it so it's going to be a hundred and five it's going to be 105 and 105 ones is literally 105 and notice this is four hundred plus seventeen tens which is 170 plus 105 you add these together you're still going to get 675 let's do that again so let's take I don't know let's take let's take all of the hundreds away let's take all of the hundreds away so that goes zero that goes zero and let's give four hundred to the tens place so let's give four hundred to the tens place well that'll make that four hundred and seventy let me do that in that green color that'll make that four hundred and seventy which is the same thing as forty seven forty seven tens and then I still have two hundred to give to the ones place let me do that so I still have two hundred to give to the ones place and so that's going to go from five to two hundred and five five to two hundred five once again all I've done is I've regrouped the value in the number 675 any of these still represent 675 you can add these numbers on the right they all add up to 675