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Methods for subtraction

When subtracting numbers the column method is prevalent, however, this method can lead to confusion if not taught through understanding.
7.8
MICHAEL ANDERSON: So let’s have a closer look at subtraction.
11.5
PAULA KELLY: So if we did a subtraction, let’s start, for example, if we had 237 and we’re going to subtract 61. So again, lots of different methods you could use. Our most common, it’s probably our column. So being really careful to line up our tens, units. If students are more comfortable, you might want to emphasise with them there’s no hundreds that we’re subtracting. Be clear the operation.
39.4
MICHAEL ANDERSON: So taking away here.
41.3
PAULA KELLY: Again, another trap to fall into is starting from this side. We start with my units. So 7 units. Take where 1 unit. We’ve just got 6. This can cause some confusion. We’ve got 3 tens. We can’t subtract 6 tens, so we’re going to borrow some of our hundreds. So it’s important to reinforce with students, if you’re borrowing one of our hundreds, we’ve got one left. The hundreds that we’ve borrowed is effectively 10 tens, Which is why we put a 10 there.
74.4
MICHAEL ANDERSON: So we’ve split that from our 200 into 100, and then we’ve put the other hundred with the 30. So now I suppose we’re doing 130 take away 60.
84.1
PAULA KELLY: Perfect. So we have 130. Take away 60. We know it’s just going to give us 70.
91.3
MICHAEL ANDERSON: And 13 take away 6 gives us 7 in that column.
93.8
PAULA KELLY: Perfect. And then we have 100, no hundreds taken away from it. So we’ve just got one left.
100.6
MICHAEL ANDERSON: So the answer is–
102.1
PAULA KELLY: 176.
103.1
MICHAEL ANDERSON: Brill.
104.8
PAULA KELLY: Another method we could use is like our chunking, but also looking at the difference between these two numbers.
112.5
MICHAEL ANDERSON: So we’re almost starting off at 61, and we’re seeing how far we have to go to get to 237.
118.7
PAULA KELLY: Perfect. So let’s start at 61. So we’ll start at 61. And often, students are quite comfortable with their number bonds. It’s 10, 100. So we want to know, how do we get it down to 100?
134.3
MICHAEL ANDERSON: Well, to add on 39 would work.
137.7
PAULA KELLY: Now, if we keep a tally of what we’re adding on and I be careful as well to line up my tens and units. So we’re at 100. We’re trying to get to 237. Another nice easy jump could be to get down to 200. So we should be happy. We can add on an extra 100. I’ll put the addition there. Our final one, we want to get to 237.
167.6
MICHAEL ANDERSON: Now we’re nearly there.
169
PAULA KELLY: Very nearly there. To get to here, we’re going to add on our 37.
174.5
MICHAEL ANDERSON: So I suppose this method is better for students that maybe don’t like subtraction enough, and they’ve almost formed an addition question. Because to get from 61, we’ve added 39, 100, and 37 together. And that represents the difference between 61 and 237.
192.2
PAULA KELLY: That’s perfect. So let’s put these three things together. We’ve added on three separate numbers to get from 61 to 237. So if we do our units again, we have our 9 units, our 7 units.
206.2
MICHAEL ANDERSON: And 0 from the hundreds.
207.7
PAULA KELLY: And 0 from the hundreds. So we have 6 altogether there. Actually, 16. So we’re going to carry one of our tens.
214.3
MICHAEL ANDERSON: Because 9 to 7, 16. Yep.
216.1
PAULA KELLY: Fantastic. We have our three 10’s, no 10’s, three more 10’s. And an extra 10.
222.9
MICHAEL ANDERSON: From the 16.
224.1
PAULA KELLY: So an extra 7 there. And the hundreds, there’s no hundreds here. Just one here. None here. So 176.
233
MICHAEL ANDERSON: So the difference between 61 and 237, we found another way. It’s 176 again.
238.6
PAULA KELLY: Fantastic. One final method could be to use our number line again. If we start from 237, so we want to get to 237. We’re going to take some jumps backwards. We could use lots of different ways. We could take away 60, take away 1. Think about our number bonds. Some students are more comfortable to get down to even number of 100 or a 10. So if we could just jump backwards 37 paces.
270.9
MICHAEL ANDERSON: So we take off 37 first.
274.5
PAULA KELLY: And we end up at 200.
276.3
MICHAEL ANDERSON: Brill.
279.1
PAULA KELLY: We’ve taken away 37. Really, we want to take away 61.
283.5
MICHAEL ANDERSON: OK. So we need to take off another 24.
286.7
PAULA KELLY: Yeah, that’s perfect. So the difference between 37 and 61 is 24. So we’re going to get another jump. We’re going to go a jump of 24. We could do that in two steps. We could do a 20 and a 4.
301.8
MICHAEL ANDERSON: Oh, so if we take away 20, that would be two 180. And then take off another 4 will be 176 again.
308.3
PAULA KELLY: Yeah. And that bodes well because you’ve got the same answer over here as well.
312.3
MICHAEL ANDERSON: Brill. So lots of different methods. Which one would you recommend?
316.3
PAULA KELLY: Personally, I find this much easier. However, it really depends on the student’s competence. And also, it’s quite good practise to practise a range of different methods so students are clear that they’re doing a subtraction. They’re seeing what the difference between the numbers. And they’re looking at the size of the numbers as well. And they can see them decreasing and in what steps they’re decreasing.
335.8
MICHAEL ANDERSON: I really like these number lines because it’s really clear to see what’s going on here.
339.4
PAULA KELLY: Absolutely.
Similar to our approaches for addition, in this video Paula and Michael demonstrate the following approaches for subtraction:
  • Column method
  • Chunking
  • Number line
When subtracting numbers the column method is prevalent, however, this method can lead to confusion if not taught through understanding. Asking students to explain what they are doing when they ‘borrow’ one can be quite revealing and indicate how little they understand about how the structure of number works. Some students are introduced to the idea of finding the ‘difference between’ numbers rather than taking one number away from the other.

Problem worksheet

Now complete questions seven and eight from this week’s worksheet.

Teaching resources

There are a variety of activities to develop these skills in these collections of SMILE resources on the STEM Learning website:
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Maths Subject Knowledge: Understanding Numbers

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