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Skip to 0 minutes and 8 seconds MICHAEL ANDERSON: So let’s have a closer look at subtraction.

Skip to 0 minutes and 12 seconds 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.

Skip to 0 minutes and 39 seconds MICHAEL ANDERSON: So taking away here.

Skip to 0 minutes and 41 seconds 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.

Skip to 1 minute and 14 seconds 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.

Skip to 1 minute and 24 seconds PAULA KELLY: Perfect. So we have 130. Take away 60. We know it’s just going to give us 70.

Skip to 1 minute and 31 seconds MICHAEL ANDERSON: And 13 take away 6 gives us 7 in that column.

Skip to 1 minute and 34 seconds PAULA KELLY: Perfect. And then we have 100, no hundreds taken away from it. So we’ve just got one left.

Skip to 1 minute and 41 seconds MICHAEL ANDERSON: So the answer is–

Skip to 1 minute and 42 seconds PAULA KELLY: 176.

Skip to 1 minute and 43 seconds MICHAEL ANDERSON: Brill.

Skip to 1 minute and 45 seconds PAULA KELLY: Another method we could use is like our chunking, but also looking at the difference between these two numbers.

Skip to 1 minute and 53 seconds MICHAEL ANDERSON: So we’re almost starting off at 61, and we’re seeing how far we have to go to get to 237.

Skip to 1 minute and 59 seconds 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?

Skip to 2 minutes and 14 seconds MICHAEL ANDERSON: Well, to add on 39 would work.

Skip to 2 minutes and 18 seconds 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.

Skip to 2 minutes and 48 seconds MICHAEL ANDERSON: Now we’re nearly there.

Skip to 2 minutes and 49 seconds PAULA KELLY: Very nearly there. To get to here, we’re going to add on our 37.

Skip to 2 minutes and 55 seconds 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.

Skip to 3 minutes and 12 seconds 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.

Skip to 3 minutes and 26 seconds MICHAEL ANDERSON: And 0 from the hundreds.

Skip to 3 minutes and 28 seconds 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.

Skip to 3 minutes and 34 seconds MICHAEL ANDERSON: Because 9 to 7, 16. Yep.

Skip to 3 minutes and 36 seconds PAULA KELLY: Fantastic. We have our three 10’s, no 10’s, three more 10’s. And an extra 10.

Skip to 3 minutes and 43 seconds MICHAEL ANDERSON: From the 16.

Skip to 3 minutes and 44 seconds PAULA KELLY: So an extra 7 there. And the hundreds, there’s no hundreds here. Just one here. None here. So 176.

Skip to 3 minutes and 53 seconds MICHAEL ANDERSON: So the difference between 61 and 237, we found another way. It’s 176 again.

Skip to 3 minutes and 59 seconds 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.

Skip to 4 minutes and 31 seconds MICHAEL ANDERSON: So we take off 37 first.

Skip to 4 minutes and 35 seconds PAULA KELLY: And we end up at 200.

Skip to 4 minutes and 36 seconds MICHAEL ANDERSON: Brill.

Skip to 4 minutes and 39 seconds PAULA KELLY: We’ve taken away 37. Really, we want to take away 61.

Skip to 4 minutes and 44 seconds MICHAEL ANDERSON: OK. So we need to take off another 24.

Skip to 4 minutes and 47 seconds 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.

Skip to 5 minutes and 2 seconds MICHAEL ANDERSON: Oh, so if we take away 20, that would be two 180. And then take off another 4 will be 176 again.

Skip to 5 minutes and 8 seconds PAULA KELLY: Yeah. And that bodes well because you’ve got the same answer over here as well.

Skip to 5 minutes and 12 seconds MICHAEL ANDERSON: Brill. So lots of different methods. Which one would you recommend?

Skip to 5 minutes and 16 seconds 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.

Skip to 5 minutes and 36 seconds MICHAEL ANDERSON: I really like these number lines because it’s really clear to see what’s going on here.

Skip to 5 minutes and 39 seconds PAULA KELLY: Absolutely.

Methods for subtraction

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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This video is from the free online course:

Maths Subject Knowledge: Understanding Numbers

National STEM Learning Centre