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BBC - KS2 Bitesize Maths - Addition and subtraction : Read

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A key stage 2 revision and recap resource for Maths - Additions and subtractions.

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Push yourself with your challenge level

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Dartboard Centre Total - 6-11 year olds - Topmarks

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Using the image of a dartboard this site is a great teaching tool for teaching and learning number bonds to 100 and 1000 and also multiples of 5 and 10. It also includes decimal number bonds. Good on IWB.

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This website is designed to help you with subtraction by the decomposition method. It expands the numbers to help you to understand. Different levels of difficulty including decimals. Good as a teaching tool on an interactive whiteboard.

Have you tried...

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This website is designed to help you with subtraction by the decomposition method. It expands the numbers to help you to understand. Different levels of difficulty including decimals. Good as a teaching tool on an interactive whiteboard.

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Improve your subtraction skills against the clock. Suitable for 6 to 11 year olds. Different levels of difficulty. Find either one or two numbers in the number grid to equal the answer. Great for improving mental maths skills.

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Choose your challenge level!

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A clever interactive whiteboard resource which is great for demonstrating inverse operations. Click on the words to see the sums. Useful for mental maths starters or plenaries.

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Work with your partner to work out the answers (the answers are not given! So you must agree!)

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Horizontal Addition Using Place Value Cards - 6-11 year olds - Topmarks

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See how TU and HTU mental addition can be made easier through the use of place value cards. Good on an interactive whiteboard.

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Breaking apart 3-digit addition problems

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Sal shows ways to break up addition problems using place value.

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We've got 6,798 minus 3,359. So let's see how far we can get with the subtraction. So immediately, when we go into the ones place, we're going to try to subtract a 9 from an 8. So we immediately reach a little bit of a stumbling block. And to see what our options are here in terms of regrouping, I'm going to rewrite both of these numbers. So I'm going to rewrite 6,798 literally. So this is equal to 6,000. That's this right over here. That's 6,000, plus 700, plus 90, plus 8. Minus all of this. So I could subtract each of the places. So I could say this is going to be minus 3,000 minus 300 minus 50-- a 5 in a tens place is just 50-- minus 9. So here, we're just explicitly showing what those place values represent. A 6 in the thousands place is 6,000. A 3 in the hundreds place is 300. Let's go back to our problem. We wanted to subtract a 9 from an 8. Well, that's a little bit of a stumbling block. But what if we could take some of the value from some of these and give it to the 8? In particular, we could go one place value up to the 90. And what if we were to take 10 from the 90? So let's do that. If we were to take 10 from the 90, then 90 becomes 80. But we don't want to change the value of the entire number. So we're going to give that 10 to this 8. We're essentially regrouping right over here. And then that 8 can become an 18. Notice, I did not change the value of the number. I just essentially changed how I represented it. Instead of saying it's 6,000 plus 700 plus 90 plus 8, I'm just saying that it's 6,000 plus 700 plus 80 plus 18. Those are both going to give you 6,798. But now it becomes a little bit easier for us to actually subtract. Now, if we subtract, I have 18 minus 9, which is 9. I have 80-- not 90, now. I have 80 minus 50, which is 30. And these are all positive, so this is plus 9. This is a positive 30. 80 minus 50 is 30. I have 700 minus 300, which is 400. And I have 6,000 minus 3,000, which is 3,000. So this is literally going to be 3,000 plus 400 plus 30 plus 9, or 3,439. Now, how would you do it if you didn't want to write it out like this? And this is where you'll see a kind of shorthand notation. This is often called borrowing. So you say, look, I've got an 8 in the ones place. I want to take a 10 from this 90. So it's going to become an 80. But we'll just write it as an 8 because it's in the tens place. This 8 represents the 80. And I'm going to give that 10 to the ones place. So 10 plus 8 is 18. And now you can subtract. 18 minus 9 is 9. 8 minus 5 is 3. 7 minus 3 is 4. 6 minus 3 is 3-- 3,439.

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Multi-digit subtraction with regrouping: 6798-3359 (video) | Khan Academy

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We've got 6,798 minus 3,359. So let's see how far we can get with the subtraction. So immediately, when we go into the ones place, we're going to try to subtract a 9 from an 8. So we immediately reach a little bit of a stumbling block.

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Video transcript

we've got 9601 - 8023 and immediately when we try to start subtracting in our ones place we have a problem this three is larger than this one and we also have that problem in the tens place this two is larger than this zero so we're going to have to do some type of borrowing or regrouping and so the way I like to think about it I like to go to the first place value that has something to give obviously the tens the tens place is in no position to give anything to the ones place it needs things itself and so we're gonna go to the hundreds place and the hundreds place has an abundance of a value that it can regroup into the tens and ones place this six right over here represents 600 so why don't we take 100 from that 600 so then this will become 500 and then give that hundred over to the tens place now if we give a hundred to the tens place well how would I represent that in the tens place well I have zero tens and now I'm going to give a hundred 100 is the same thing as ten tens so I'm not going to have it's going to be zero plus a hundred a hundred in the tens place is just ten so let me write it this way so this right over here is now going to be rewritten as ten now you might be saying wait wait wait wait what's going on here Sal you took a hundred from the hundreds place that's why it became five hundred now why did this become ten and not a hundred now remember this is ten tens so this is still representing a hundred you have not changed the value of this top number before the value was nine thousand plus six hundred plus one now it's nine thousand plus 500 plus 110 tens is one hundred plus one I have not changed the value here now we're still not done yet we don't want to just subtract because we still have the problem with the ones place the ones placed is still not hat still doesn't have enough a value now the good thing is we've given some value to the tens place so why don't we take 10 from the tens place so if you have ten tens and you take 110 away you're going to be left with nine tens or ninety then we can take that 10 and give it to the ones place so let's do that you take that 10 we just took from there you give it to the ones place you now have 11 here and now we are ready to subtract 11 minus 3 is 8 9 minus 2 and this is really 90 minus 20 is 70 but in the tens place we represent that as a seven five hundred minus zero hundred is five hundred represented as a five in the hundreds place nine thousand minus eight thousand is one thousand and we're done and just to make things really clear I'm going to redo this problem now but with things expand it out so this first number is nine thousand nine thousand plus 600 plus 600 plus zero tens plus zero tens plus one plus one and this number right here we're subtracting eight thousand we're subtracting zero hundreds we're subtracting two tens which is 20 subtracting 20 and subtracting three ones so I've just rewritten this exact same statement but it's the the regrouping and the borrowing is going to be a little bit clearer now so the same exact thing we said hey we can't subtract the 3 from the 1 or the 20 from the zero we have a lot of value right over here in the 600 so why don't we take a hundred from that so this becomes 500 and we give we give that hundred to the tens place so this this becomes this becomes one hundred notice this the value has not changed this is nine thousand plus 500 plus 100 plus one that's the same thing as nine thousand plus 600 plus one we've just put the value in different places and here we've explicitly written 100 but when we represented it in the tens place ten tens is the same thing as 100 now we aren't done regrouping just yet we want to give some value to the ones place so we can take 10 from the tens place and this becomes a 90 and give that 10 to the ones place 10 plus 1 is 11 so notice I did the exact bar throwing the exact regrouping that I did here I just represented it a little bit different this 500 was represented by a five in the hundreds place this 90 was represented by nine in the tens place but either way we're ready to subtract now 11 minus 3 is 8 90 minus 20 is 70 is 70 all right a plus there 500 minus zero is 500 and then nine thousand minus 8,000 is 1,000 and we got the same result because 1,000 plus 500 plus seventy plus eight is 1578

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Multi-digit subtraction with regrouping twice (video) | Khan Academy

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Sal shows the relationship between 2+3=5, 5-2=3, and 5-3=2.

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Let's do a bunch more of these addition problems. So let's say I have 9,367 plus 2,459. So we can do this the exact same way we've done in the last few videos. We start in the 1's place or you can even think of it as the 1's column. So you're going to add the seven 1's plus the 9 1's. So you're going to have 7 plus 9, which we hopefully know by now is 16. So what we do is we write the 6 in the 1's place and we carry the 1. Let me switch-- if this 1 is going to be the same thing as that 1 right there. And this might look like a little bit of a mystery or magic, and the whole reason we did that is that this is the 10's place. And when you write 16 you have six 1's and one 10. If you view this as money, what's the best way to get $16 in a world where there weren't $5 bills? Where you only had $1 bills, $10 bills, $10 bills, and so on. Only multiples of 10. And we don't have any $5 bills. In that world you would represent 16 as one $10 bill just like that. And then six $1 bills. So that's two $1 bills. That's two more $1 bills. And then that's two more $1 bills. The whole reason why I'm drawing it this way or I'm even using this analogy or drawing the dollar bills is to show you what these places mean. When I say that this right here is the 10's place, I'm essentially telling you how many $10 bills do I have? If I've $16 and I'm doing it as efficiently as I can in a world without $5 bills. I only have $1's, $10's, and $100's and $1,000 bills and so forth. And this is the 1's. So when I write it this way I'm literally telling you, I have one $10 bill and I have six $1 bills. That's what $16 is. And so when I have 7 plus 9 is equal to 16 I say that I have six $1 bills and I have one $10 bill. And I add that one $10 bill to everything else in the ten space. And the tens place is essentially telling you how many-- that's the tens. I could write it like that or I could write the 10's place. When I have 67-- 67 means I have six $10 bills plus another seven $1's. So that's six 10's, five 10's. So I add up everything in the tens place. So 1 plus 6 plus 5. Let me do that in a new color. 1 plus 6 plus 5 is equal to-- 1 plus 6 is 7. 7 plus 5 is 12. So I write the 2 in the 10's place because remember, this is twelve $10 bills because we're in the 10's place. So I have two in the 10's place and I put the 1-- I carried this 1 right here into the 100's place. Because if I have twelve $10 bills, I have $120. I have one $100 bill. And I have two $10 bills. I'll stop going to the dollar bill analogy just so we can make sure we understand the process. But I think you see how it works. You start at the right, you add the two numbers up. If it's a two-digit answer you carry the left most digit up to the next column. And you just keep doing that. So let's do this one right here. 1 plus 3 is 4. Let me write this down in another color. 1 plus 3 plus 4. 1 plus 3 is 4. Plus 4 is 8. So 1 plus 3 plus 4 is 8. Nothing to carry. It was a one-digit number. And then finally, I have 9 plus 2. That's equal to 11, so I write the 1 down there. I write this 1 and then if there was anything left here I would carry the 10's or the other 1-- the 1 in the 10's place in 11-- I would carry it. But there's no where to carry it to, so I write it down just like that. So 9.367 plus 2,459 is 11,826. And I just put that comma there because it's easier for me to read. Let me do a bunch more of these. Let's do a really, really daunting problem. Let's do something in the millions. Just to show you that you can do any problem. So let's say we have 2,349,015. Let's throw a 0 in there. We have nothing in the hundreds place there. And I want to add that to-- let me switch colors just for fun. I want to add that to 7,-- let's put a 0 there-- 15,999. Let's add these two numbers. It seems like a hard problem, but if we just focus on each of the places I think you'll find that it's not too bad. So we start off with 5 plus 9. That's equal to 14. Write the 4 down here, carry the 1. Then you go into the 10's place. 1 plus 1 is 2. 2 plus 9-- let me switch colors. 1 plus 1 is 2. 2 plus 9 is 11. Carry the 1. Now we're in the 100's place. 1 plus 0 is 1. Plus 9 is 10. So we write the 0 from the 10, carry the 1. Let me switch colors again. 1 plus 9 is 10. 10 plus 5 is 15. Now we're in the 10,000's place. 1 plus 4 is 5. And 5 plus 1 is 6. And there's nothing to carry. Now we're in the 100,000's place. 3-- we have nothing to carry, so we just have the three 100,000's plus zero 100,000's. Well, that's just three 300,000. And then finally, we're in the millions place. 2,000,000 plus 7,000,000 is 9,000,000. Just like that. So this was a super crazy number. 2,349,015 plus 7,015,999. Just by keeping track of our places and carrying the two-digit numbers or the second digit in the two-digit numbers as necessary, we were able to figure out that the answer is 9,365,014. So hopefully this gives you a pretty good sense. And let me just do one more, just to really make sure that we really understand how all of this carrying business works. So let's do 15,999,001 plus 6,888,999. Let's just see how this one's going to turn out. This seems like a like a difficult problem. But once again, if we just focus and don't get lost, we're going to get the right answer hopefully. So 1 plus 9 is 10. Write the 0, carry the 1. 1 plus 0 plus 9 is 10. Write the 0, carry the 1. 1 plus 0 plus 9. That's 10 again. Write the 0, carry the 1. Now 1 plus 9 is 10, plus 8. 10 plus 8 is 18. Write the 8, carry the 1. 1 plus 9 is 10. Plus eight is 18. Write the 8, carry the 1. 1 plus 9 is 10. Plus 8 is 18. Write the 8, carry the 1. Now we're in the 1,000,000's place. 1,000,000 plus 5,000,000 is 6,000,000. Plus 6,000,000 is 12,000,000. Write the 200,000,000 and then carry the 1 because 12,000,000 is 2,000,000 plus 10,000,000. 10,000,000 plus 10,000,000. This is one 10,000,000 plus another one 10,000,000. That's 1 plus 1 is 2. And then we are done. 15,999,001 plus 6,888,999 is 22,888,000. So you just saw, we're just doing 7 and 8 digit number additions, but you could apply this-- if I had a number with 100 digits in it, you could do the exact same thing. You just have to start at the right, go each column by each column, and then if you end up with a two-digit answer when you add the two one-digit numbers, you just carry the 10's place. You just doing that and work your way left. And if you make no errors, you'll get the right answer.

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Multi-digit addition with regrouping (video) | Khan Academy

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