comparing and ordering numbers

all right so in today's lesson we are going to be looking at comparing and ordering numbers we're going to start off at with comparing numbers and basically what we're going to be doing is we're going to be looking at two numbers and determining which number is bigger and which number is smaller and we use the symbols over here that you see this symbol here which means less than and it's important to know we every we read this from left to right so we look at where this little arrow is pointing the tip of this arrow is pointing to it's pointing to the left so that symbol represents that it means less than that means the number on the left is less than the number on the right and another way to look at this is the opening of this Arrow which is on the right side over here it's like mouth and it wants to eat the bigger number if you look way over here with this symbol this is the greater than symbol which means the number the bigger number is on the left and it's the same thing you that opening of this symbol is facing is going to face the bigger number and the point will face the smaller number and this will make more sense when show you this next example and of course this middle symbol that just means equal to that means the numbers are equal to and we can also use these symbols when comparing different equations where you might have something like 3 + 3 is equal to greater than less than you know 3 + 2 or whatever and and we'll we'll get into that later on in the year but just take look down here at these different numbers and and how we use these symbols to compare numbers this first example have 56 on the left and then have the number 72 and in the middle is this circle and that's where we insert our symbol it's like blank that we need to insert our symbol and so we need to determine is 56 less than or greater than or equal to 72 and we know that by using place value we look at the and it's five so that represents 50 on this left number and on the right number over here it's 70 and 70 is greater than 50 it's bigger than so this would actually read 56 is less than 72 so we want to use the less than symbol remember that arrow is going to point to the smaller number and the opening or the mouth it reminds me sort of like of an alligator it's going to be facing the bigger number because it wants to eat the bigger meal so again we read this left to right 56 is less than 72 okay now let's take look at this next example we have 432 blank 289 is it less than greater than or equal to 289 now in this case it's actually greater than so we want to make sure we use the proper symbol the greater than symbol okay because this number on the left remember we read everything just like like when we're reading story or book we read everything left to right so just like that the number on the left going to the right is greater than the number on the right so the mouth of the aligator is going to be facing the bigger number and that's the greater than symbol so we read it left to right 432 is greater than 289 okay now there's two things when when you're comparing numbers to remember the first is you want to use the proper symbol you have you can't get those two symbols confuse the less than and the greater symbol confuse the opening is always going to eat the bigger number and the the point of the arrow is always going to point to the smaller number so if the smaller number is on the left like in the first example down here then we're going to use the less than symbol if the bigger number is on the left then we're going to use the greater than symbol okay and the other really important thing to remember when comparing numbers is to always remember to look at the place value of the numbers this last example down here we have two numbers and some people they just want to look right away at the first digit in each number like this one's three and then over here it's nine and say well 9 is greater than three so this must read that the it must read this way that the number on the left is less than the number on the right because know that three is smaller than nine however if you look at the place value it's much different value for each number for instance this number on the right the nine is in the hundreds place while the number on the left the three is in the thousand's place and while the digit nine is bigger than the three because the three is in the thousand's place value the three is actually bigger number because it represents 3,000 the nine only represents 900 and remember thousands are much bigger than hundreds so in fact this would actually read the opposite that 3,00 475 is greater than 987 so make sure you're really paying ATT attention to the the numbers and the digits and what place value they have when comparing numbers now let's take look at ordering numbers and ordering numbers really is comparing numbers but it's it's comparing more than two numbers it's it's three or more and and when you're ordering them you're putting them in order and you can put them in order in couple different ways you can put them in order from the least to the greatest which means you're putting them in order from the smallest to the biggest okay so from least to greatest or you may be even putting them in order from greatest to least or from the biggest number to the smallest number and that's really important to pay attention when you're reading word problems or when you're reading some questions that you pay attention to what order they're looking for you to put them in you don't want to be told to put something in order from greatest to least and then order them least to Grace because you'll get it wrong right so this is really important you really want to focus on what is being asked is this being asked or or is this going to be or is this going to be asked here okay and let me give you let me show you an example down here let's take these four numbers for instance if told you hey look at these four numbers and put them in order from least to greatest you want to make sure you're doing it from the smallest to the biggest and not the opposite away okay so start with the smallest which happens to be 45 and drag it over then slide these out way then the next smallest is going to be 65 then 67 and then finally the biggest number out of all those numbers is 92 that's going from smallest to biggest from least to greatest if went from greatest to least really it's just the opposite I'm just going to really flip flopping these numbers around would start with 92 and would work my way up to or work my way down rather to the smallest number okay that's going from greatest to least it's really really important when comparing numbers to pay attention what is being asked are you being asked to go from the biggest to the smallest or from the smallest to the biggest okay sh that and then another important thing to remind you about too is just like comparing numbers you want to make sure that you're really paying attention to the place values and not just going by the first digit in the number because just like when you comparing the numbers they could look lot different for instance if you look at these numbers if just go by the first digit in every number okay then might have something that look like this yeah let's move these out of the way if was telling you to order these numbers from smallest from yeah from smallest to biggest or from least to greatest okay and just looked at the first digits of every number then might have something that looked like this would start with 2,444 then go to 3563 3 then 3,653 and then finally the 987 but again remember that this would be incorrect because my my place values are determining really what numbers are bigger this nine is not bigger because it's in the hundreds these are all in the thousands which means they are actually bigger so this number would actually be the smallest and would need to be put in front so it's very important to pay ATT attention to these place values take look at the practice lessons and give it try for yourself