Skip to 0 minutes and 7 secondsMICHAEL ANDERSON: So our base-10 place value number system allows us to do some relatively complicated calculations quite easily. Let's see how this works with addition.

Skip to 0 minutes and 16 secondsPAULA KELLY: OK. So there's a number of methods we can use, depending what students feel more comfortable with.

Skip to 0 minutes and 21 secondsMICHAEL ANDERSON: OK.

Skip to 0 minutes and 21 secondsPAULA KELLY: So, say, for example, we'll do 128.

Skip to 0 minutes and 24 secondsMICHAEL ANDERSON: Mm-hmm.

Skip to 0 minutes and 28 secondsPAULA KELLY: And we'll add 35.

Skip to 0 minutes and 29 secondsMICHAEL ANDERSON: OK.

Skip to 0 minutes and 30 secondsPAULA KELLY: OK. So the most common method that lots of students see at primary, we line up our 100s, 10s, units. So we have 128.

Skip to 0 minutes and 39 secondsMICHAEL ANDERSON1: OK.

Skip to 0 minutes and 41 secondsPAULA KELLY: Key thing here is to line up our 10s and units.

Skip to 0 minutes and 44 secondsMICHAEL ANDERSON: OK. Yeah.

Skip to 0 minutes and 45 secondsPAULA KELLY: Yeah. Add on our 35. OK. And be clear what we're doing-- operation.

Skip to 0 minutes and 50 secondsMICHAEL ANDERSON: Mm-hmm.

Skip to 0 minutes and 51 secondsPAULA KELLY: So with this said, we've got our-- where do we start from? This side. Start with our units. So 8 add 5 we know is 13.

Skip to 0 minutes and 59 secondsMICHAEL ANDERSON: Yeah.

Skip to 1 minute and 0 secondsPAULA KELLY: Just to be really clear, though, that's going to give us 3 units.

Skip to 1 minute and 3 secondsMICHAEL ANDERSON: So 13 has, yeah, 3 units.

Skip to 1 minute and 5 secondsPAULA KELLY: But also an extra 10.

Skip to 1 minute and 7 secondsMICHAEL ANDERSON: Mm-hmm.

Skip to 1 minute and 7 secondsPAULA KELLY: So I'll pop that just there.

Skip to 1 minute and 8 secondsMICHAEL ANDERSON: OK.

Skip to 1 minute and 9 secondsPAULA KELLY: OK. So again, across-- add our 10s. So 2 add 3 give me 5. Our extra 1 here gets 6.

Skip to 1 minute and 17 secondsMICHAEL ANDERSON: OK. Because that's the 20 from the 128 plus the 30 from the 35. So 20 plus 30 plus that extra 10 from the 13 gives us 6 lots of 10. So 60?

Skip to 1 minute and 27 secondsPAULA KELLY: Yeah. So though we're writing a 6, it's in our 10s column-- is indeed 60.

Skip to 1 minute and 31 secondsMICHAEL ANDERSON: Brilliant.

Skip to 1 minute and 32 secondsPAULA KELLY: OK. So no other extras to carry over. If students are more comfortable, they could always put a 0 in there as a placeholder.

Skip to 1 minute and 40 secondsMICHAEL ANDERSON: Because 35 has 0 hundreds.

Skip to 1 minute and 42 secondsPAULA KELLY: Fantastic. Just 1 hundreds, so just 1 there.

Skip to 1 minute and 46 secondsMICHAEL ANDERSON: OK. So--

Skip to 1 minute and 47 secondsPAULA KELLY: So our final answer is 163.

Skip to 1 minute and 50 secondsMICHAEL ANDERSON: Brill.

Skip to 1 minute and 51 secondsPAULA KELLY: OK. Another method that some students might want to use as well is to see how this number increases using our number line.

Skip to 1 minute and 57 secondsMICHAEL ANDERSON: OK.

Skip to 1 minute and 58 secondsPAULA KELLY: OK. So if we start [INAUDIBLE] here. Our number line could start at 128.

Skip to 2 minutes and 3 secondsMICHAEL ANDERSON: OK.

Skip to 2 minutes and 5 secondsPAULA KELLY: Then we're going to continue this along. Because we're adding, we know it's going to increase.

Skip to 2 minutes and 10 secondsMICHAEL ANDERSON: Yeah.

Skip to 2 minutes and 10 secondsPAULA KELLY: We're going to find out where we end up.

Skip to 2 minutes and 12 secondsMICHAEL ANDERSON: OK.

Skip to 2 minutes and 12 secondsPAULA KELLY: OK. So what students may like to try and do is add on their 10s and their units.

Skip to 2 minutes and 18 secondsMICHAEL ANDERSON: OK. So we'll add, like, the 30 first, and then the 5?

Skip to 2 minutes and 21 secondsPAULA KELLY: Lovely. So for 128, if we add on just our 10s-- so we'll add on our 30, and be really clear here what we're actually doing. So we add on our 30 to 128. We're going be at 158.

Skip to 2 minutes and 37 secondsMICHAEL ANDERSON: OK.

Skip to 2 minutes and 38 secondsPAULA KELLY: And then finally, we add our units. So an extra 5.

Skip to 2 minutes and 45 secondsSo 158, add on our 5. We're going to end up with 163.

Skip to 2 minutes and 50 secondsMICHAEL ANDERSON: And I suppose some students could just count that up. So 158, 159, 60, 161, 162, 163.

Skip to 2 minutes and 59 secondsPAULA KELLY: Exactly. And the same with their 10s. We could start with 128, 138, 148, 158.

Skip to 3 minutes and 7 secondsMICHAEL ANDERSON: OK. Is there any way of using our kind of number bonds as another method?

Skip to 3 minutes and 12 secondsPAULA KELLY: Yes. And lots of students might feel more comfortable if we can make this to have a multiple of 10.

Skip to 3 minutes and 18 secondsMICHAEL ANDERSON: OK. Yeah.

Skip to 3 minutes and 19 secondsPAULA KELLY: So if we start off with 128-- if we had 128, if we added on just 2 to make our whole number bond to a multiple of 10, this would give us 130.

Skip to 3 minutes and 35 secondsMICHAEL ANDERSON: OK.

Skip to 3 minutes and 36 secondsPAULA KELLY: But we know we're not just adding 2. We've still got some more to add on.

Skip to 3 minutes and 40 secondsMICHAEL ANDERSON: OK.

Skip to 3 minutes and 41 secondsPAULA KELLY: So at 35-- subtract our 2, we've done already, is 33.

Skip to 3 minutes and 46 secondsMICHAEL ANDERSON: OK.

Skip to 3 minutes and 46 secondsPAULA KELLY: So what we need to do now is 130, then we add on our remaining 33.

Skip to 3 minutes and 53 secondsMICHAEL ANDERSON: OK.

Skip to 3 minutes and 55 secondsPAULA KELLY: Then, like we did before with our column addition, we'll start with our units. There's 0 units, 3 units. We've just got 3. Our 3 10s, 3 more 10s. Our 100s-- we could put a placeholder if we wish. So we've still got 163.

Skip to 4 minutes and 16 secondsMICHAEL ANDERSON: So by breaking it up, students might find it a little bit more easy to calculate than the original, first method that we had.

Skip to 4 minutes and 22 secondsPAULA KELLY: Yeah. And we can see, no matter what method they use, all three give us the same answer. It's all about what students are more comfortable with and what they feel is most efficient.

Skip to 4 minutes and 32 secondsMICHAEL ANDERSON: Brill.

Methods for addition

Many people automatically use a method called column addition when required to add numbers together without the aid of a calculator.

The method is efficient and simple to understand. Primary school students may be introduced to a variety of methods such as addition with the use of a number line or a number grid. These methods can be useful to develop mental methods of adding numbers without the use of a pencil and paper.

For example, when adding 18 to a number, some students will automatically add on 20 then subtract 2. It is important that students are fluent in a range of methods and develop the skill to use each method appropriately.

In this video, Paula and Michael discuss a variety of different methods for addition.

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This video is from the free online course:

Maths Subject Knowledge: Understanding Numbers

National STEM Learning Centre