 Now that our student knows how to count into the at least all the way from one to one hundred Okay, hopefully into the hundreds thousands hundreds of thousands or millions depending how fast they've progressed But once the student knows how to count from one to one hundred I start introducing them to Edition right and in general We do the single digits, right? So I write down basically two plus three And if the students having a hard time doing this I get them to do it Using their fingers, right? I say, okay, hold up two on this one. Hold up three on this one How many do you have and they go one two three four five, right and I do this a few times if they're in that state, right? Once they're past the finger state, right once they You know, if you're doing four plus three, what is that, right? four plus three Right five seven as long as they can do it all in all the single digits without their fingers We can move on into the double digits, right and the double digits is usually where it's harder to do with the fingers That's why I introduce, you know, I get them to do ticks on paper So once they hit this stage what I give them is eight plus nine Numbers that when added up kick them into the double digits, right? If they can do it with their fingers, right? If I You know tell them, okay use your fingers so they go one two three four five six seven eight, right? Or they start off with eight That's in general what I do But if they're at a state where they're still using their fingers they go eight and they got to add nine they got to go One two, they have to keep in mind. That's ten Three four five six seven eight, so they have a ten plus oh Nine, all right plus nine so that's 17. They keep that in mind Kids usually have a harder time with that or I get them to start off with eight So I say okay, you're at eight already at nine, right? So they go I'm at eight So I go nine ten eleven twelve thirteen fourteen fifteen sixteen seventeen, right? That's their nine being added so that's Two ways you can do it The third way I do it is I get them to do ticks on a piece of paper, right? So if we go seven plus Eight right They can start off at seven and then they go eight nine ten eleven twelve thirteen fourteen fifteen That's eight numbers. Those are the ticks that we talked about in counting that you can get them to group fives, right? So this becomes fifteen or some students that I've seen they do the whole thing, right? They go one two three four five six seven eight nine ten eleven We're one two three four five six seven, right? And then one two three four five six seven eight nine ten eleven twelve thirteen fourteen fifteen, right? And when they do this most of my students don't stick doing this for too long, right? Because they realize that it's too hard visually to see what's happening and really emphasize the visual When you're teaching counting as well to your students right now We got one two three four five six seven eight nine ten eleven twelve thirteen fourteen fifteen, right? If your student does this Show them how it's easier to do if they do One two three four five six seven that's their seven, right? And then one two three four five oops Five six seven eight and then get them to count that way, right? So what you're doing is I should do that more clearly, right? So let's do it more clearly One two three four five six seven eight, right? So we have five and five that's ten two and three that's fifteen so the answer is fifteen, okay It's again very personal very tricky depending on the students I'm even making mistakes using text, right? So your student is going to make mistakes doing using these tick marks. Just Tell them to cross it out do it again if they're having a hard time with it, okay? So when you're teaching adding what Personally when I'm teaching adding and It might work with you as well if you're teaching your student, right? Start off with single digits. Don't get them to go past the single digits yet So you're doing the small single digits when you get into the bigger single digits, right? Get them to use their fingers get them to start off with the first number and add the next number Or get them to use tick marks, okay? Once they're comfortable with this start adding the teens in there, right? Start off with the teen right 13 and then add six in general the easiest way to do this is Is the method where you say okay? You're already at 13 at six, right? So they go okay, it's 13 14 15 16 17 18 19 and they write down 19 It's rare for my students that I've worked with for them to use tick marks when they're doing Double digits starting with double digits and continuing on right in general. That's the way they end up counting Once you have hit this stage Show them two double digits added together 13 plus 17 okay Now make sure you have enough time in your lesson or in your day and your student is Functional enough to be able to do this right because you need time to explain what the process is here Okay, and actually I don't usually do Carry over just yet, right? So I'm doing the low teens first Okay, and I'll explain to you why I don't do that yet, right? So when the student is trying to do this Doing it with the fingers is harder. It takes them a while. They will try They might do it with tick marks, but it's rare, right? Once they struggle with it for a bit and some students will Be able to get the answer quickly some won't if they get the answer quickly Give them harder ones going to the 20s going to the 30s going to the 40s, right? If they're having a hard time with it Basically show them the addition the stacking method, right? So I basically show them, you know I tell them instead of writing it like this Visually it's easier to write them on top of each other. So we basically go 13 Plus 12 a drawn line, right? So that's what I end up showing them and then I tell them all they need to do is add these two guys together Put the number there and add those two guys together put the number there And that's the reason I don't start off with anything That you need to when they're at it they give you a 10 or more Where you have to carry it over, right? So in general when you reach this state They already know how to do these, right? So this becomes easy This becomes five and then one plus one is two, right? And we have videos out. I put some of these videos out For language of mathematics for this on how to add numbers together larger numbers in general I didn't kick it down to this level, right? I usually start off with bigger numbers Okay, but we've got a whole bunch of videos in the language of mathematics showing this or at least one video showing this, right? So once they figure this out, and they should fairly rapidly I give them numbers that You have to carry stuff over, right? 27 plus 34 and in general whenever I'm doing this At the beginning I write them stacked like this for them to practice Later on what I do is I put them in a line like this and get them to stack it because some students need to need Have a hard time Appreciating right off the bat that you're flushing things to the right. Okay Once you get them to do this then 7 plus 4 get them to write the answer, right? So 7 plus 4 is 11 and Students usually in general pause a little bit in this process. They go 11 They really don't know what to do until you show them how to do it Don't let them struggle with it. Show them right off the bat. You go, okay, 7 plus 4 is 11 So you put your 1 here, but you can't put the other one here because that's in the tens So what you do you put it up top, right? 1 plus 2 is 3 plus 3 is 6 Okay So the answer is 61 Student will appreciate this give them a whole bunch of practice work with them showing more examples, right? 56 plus 79 Okay Once you show a few different Example for them to do and you get them to do it make sure you stay below 100 And then you could click it up to numbers that add up to be above 100 and again This process here. I'm going through it fairly rapidly, right? This process here might take a day might take a week might take a couple of weeks Okay, depending on how fast the student Is absorbing the information and how many lessons you've had and how many practice problems they've done, okay? But once they're comfortable Sticking within the two-digit range being able to kick the numbers up Then you can kick them into numbers that add up to more than 100, right? 9 plus 6 is 15 And you bring the 1 up right 5 plus 1 or 1 plus 5 is 6 6 plus 7 is 13 and you can put 13 down here from here What I end up doing is giving them gigantic numbers, okay? I don't go up Slow from here, right? So from here Let's take this down. Let's do some numbers And I'm going to give you some of the patterns that I show you how to do, right? And one of the things before we move on one of the things I also do when we're doing this Your student has to read every number that you're adding and the result, right? So get them to say 13 plus 12 is equal to 25 56 plus 79 is equal to 135 That Helps them Not forget how to count numbers not forget how to read numbers, right? And gets it into their muscle memory mental memory Okay Now once my students in general learn how to add two two digit numbers together I start giving them Numbers in the hundreds and then right away kick Kick them into numbers that are into the tens of tens of thousands or hundreds of thousands, right? As long as they know how to count to those numbers, right? So for example, I would give them something like this And what I end up doing is when we reach this state, I don't stack it for them I get them to restack this put it in the proper position so they can add it, right? So they take this and they go oh Two five seven plus six seven four right And the process again, it's quite easy seven plus four is 11. You put the one in the bottom and the one up top five plus One is six plus seven is 13. You put the three here. You put the one up top One plus two is three plus six is nine, right? and The student has to read this number as well And then I give them numbers that don't have the same number of digits in them, right? Seven four seven five plus six four Let's go five okay now One thing I've noticed when students are learning how to add, okay When you need to stack these things They end up stacking them here. They go they write it like this. I'm going to write it incorrectly first, right? They go seven four seven five Six four five, right? Sometimes they do it that way Sometimes They're all over the place in general. They're all over a place. They would go something like this seven four seven five and then six four five right So visually it's hard for them to line things up, right? It is extremely important to correct them When they're doing this make sure they're flushing everything to the right side, right? So six four five The whole purpose here for us is to Take stress away from the student learning this and doing this because this can be a little bit repetitive for the student right because You have to get them to do a few of these before They're very comfortable with it, right? So really important to Help them in that process by getting them to line things up properly, right? And in general when they're Initially they write both numbers But students usually catch on pretty fast that all they have to do is just take that number Put it below this guy if they haven't saved them time Tell them that hey, you could take this number and put it here, right? And put the addition here. You don't have to rewrite it, right? And then you add this five plus five is 10 you put the zero you put the one eight 12 one 10 11 one And you get an eight Right and get them to read this number if they're in a hard time reading it Tell them to put the comma in there, right? Once you give them a few of these things where they're adding Double digit numbers three digit numbers two three digit numbers two four digit numbers A four digit number and a three digit number Give them numbers that are larger And vary in the number of digits that they have, right? For example seven five six four three two plus five six four three plus Five zero zero one Right get them to do numbers like this Get them to read it Right when you write it down Before they begin you say okay read this number In general they need to put a comma 756,432 Get them to move their fingers across if they need to Put your comma 75,643 And five thousand and one in general students don't have a hard time with four digits Okay Get them to add these by stacking them Usually my students Write this number here because they're not comfortable at the beginning to realize that this is five digits So they can just go to the five digits here and stack them, right? So this is usually what they end up doing three four six comma five seven okay, and one zero zero five Two plus three is five plus one is six Three plus four is seven plus zero is seven and a lot of students actually say that, right? Seven Let them say it Okay Six plus four plus six is ten You put the zero you put the one up top Get them to say it put the one up top put the two up top if there's a two, right? Three five six whatever it is one plus six is seven Five plus five is ten so that's 17 once you start doing this The students will do this One plus six is seven seven plus five is 12 12 plus five is 15 That's what they'll do they'll go in order. Let them do that Slowly Teach them The grouping right that they can go five plus five is 10 Six plus what one plus six is seven ten plus seven is 17, right? Move the one up One plus five is six six plus seven is 13 Put the one up One plus seven is eight Get them to read this number If they need to And the odds are they will They need to put the comma in eight hundred thirty seven thousand and seventy six Okay Now once you Reach the state Where you're giving them random numbers and it doesn't have to be just two numbers or three numbers given four or five numbers to stack, right? They don't necessarily need to be this big but give it to them anyway, right because that way When they do one problem you've tested them the equivalent of Five of the smaller problems, right? So they're getting a lot more practice in without even in general realizing it. Okay, so give them like Two or three large numbers Three numbers four numbers or five numbers get them to line it up properly Get them to read every single number and the result and put the commas in the appropriate places Once they're able to do that Give them numbers that force them To quickly distinguish between one number and the other number and we showed this This set of three numbers In the counting section, right where we went get them to add 720 plus What was it 702 plus 712? Right Get them to add those numbers Once you reach this level and they're reading it properly They're adding it properly and they're reading the result properly put in the commas in the right places We're going into multiplication Okay Once you reach this level We can start teaching them planting seeds for them to learn multiplication. So let me show you how that works