Skip to 0 minutes and 7 secondsMICHAEL ANDERSON: In this section, we're going to look at a range of strategies to deal with division.
Skip to 0 minutes and 15 secondsSo let's have a look at, for example, 490 divided by 14. Now, whenever you're doing division calculations, it's often useful to have some times tables, just on the side, for reference. So we're dividing by 14 so we're asking how many 14s go into 490. So it's useful having the 14 times tables as a reference, or at least the start of them. So one 14 is 14. Two 14s, I can add another 14, gives us 28. Three 14s gives us 42. And some students will like to do that all the way till 10. We'll leave that for there. Well, you can actually put 10 in, though, which would be quite useful. So 10 lots of 14 is 140.
Skip to 0 minutes and 59 seconds20 lots of 14 is 280. [INTERPOSING VOICES]
Skip to 1 minute and 3 secondsMICHAEL ANDERSON: Yeah. And 30 lots of 14 is going to be 420. So we'll just keep that as an aside for now. And what we're going to try and do is use these kind of multiplication facts to work up to getting to 490. So by having a look at these times tables, well, the 30 one gets us close, but we're still under. So 30 lots of 14 is 420. So if we're thinking about this as our target number, 490, 420 is only 70 away. And that's 30 lots of 14. So if I take that off, I've got 70 left to play with. Now, I worked out that three lots of 14 was 42.
Skip to 1 minute and 45 secondsSo I could have a look at, say, three lots of 14 giving us our 42. And then take that off. And I'm kind of slowly but surely trying to work this number down towards zero. 42 take away that from 70, well, that's going to give us 28. Oh, and if I look here, two lots of 14 actually gives us 28. So I can take that away to end up with zero. And I've been keeping a track on this left hand side to get from 490 to zero. Well, I had 30 lots of 14, three lots of 14, and 2 lots of 14. So if I add them together, they sum to 35 lots of 14.
Skip to 2 minutes and 26 secondsAnd that will give me my 490. So this multiplication statement means that if I look back at our division, 490 divided by 14, well, it has to be 35.
Skip to 2 minutes and 42 secondsSo when we're thinking about these division questions is to write them out as a fraction instead. So let's have a look at 490 divided by 14 as a fraction. I'm going to write the 490 as the numerator and the 14 as the denominator. And then we can just try to cancel these down so that we have 1 at the bottom. So what numbers go into 490 and into 14?
Skip to 3 minutes and 6 secondsPAULA KELLY: As they're both even, just half them both.
Skip to 3 minutes and 8 secondsMICHAEL ANDERSON: Right. OK. Yeah, I can definitely half 14. That's 7. And half of 490 is 245. And we could carry on cancelling these down, so long as we can see a common multiple. But how many sevens go into 245 is quite tricky. So what we might have to do is just go back to the method that we looked at previously. So we're going to try and chunk our way up to 245. So that's our target number. And quite handily, I've already got these written down here. So the first three multiples of 7, and then I've also got 10, 20, and 30 times 7 as well.
Skip to 3 minutes and 45 secondsAnd if we look at those as our reference, 30 times 7 looks like a pretty good starting point. That gives us 210, which is close to 245, but not quite there. And if I take 210 away from 245, I get 35. And now, we're just trying to find some multiples of 7 that go up to 35. So on our table, we've got three lots of 7 was 21. So I could try that. Three lots of 7 equals 21. And then take that away from 35. 35 subtract 21 gives us 14. And 14 is there as well. It's two lots of 7. So 2 times 7 is 14. Take that away, and end up with 0.
Skip to 4 minutes and 28 secondsAnd to get 245 to 0, I've used 7 times 30, 7 times 3, and 7 times 2. So in total, I've got 30 lots, 3 lots, and 2 lots. That's 35 lots of 7. And that gave me 245. So to go back to our original question, well, 490 divided by 14, that's the same as 245 divided by 7 and 245 divided by 7, has to be 35, just like in our previous method.
Skip to 5 minutes and 8 secondsThe final method we can use to solve these types of division questions is the bus stop method. So we had 490 divided by 14. And I'm going to draw out my bus stop, which looks a little bit like that. We're dividing 490 by 14, so we're going to work our way through from left to see how many 14s we can fit into each of these digits in turn. Now, we can't actually fit 14 into 4, so what I'm going to do is look at 49 instead. So my 14 times table goes 14, 28, 42. And that's three lots of 14.
Skip to 5 minutes and 49 secondsSo I'm going to put 3 here and 42 here and subtract and take that away, just like in my chunking method. Now 49 takeaway 42 gives me 7. I've still got a 0 here, so now, I'm looking at 70. Now, how many 14s go into 70? Well, that's going to be 5, because 5 times 14 gives me 70. So I got to put that there. And we have 70 here. Take that away. And we end up with 0. So the solution to 490 divided by 14 is 35. Now, in the previous step, we thought of this as a fraction, so 490 divided by 14, and that gave us 245 divided by 7.
Skip to 6 minutes and 34 secondsI could do this as a bus stop method as well. And it will give me the exact same answer as 35. So let's just have a quick look at it. So if I draw on my bus stop out again. I've got 7 here and 245 there. 7 and 24, well, three lots of 7 gives me 21. 24 takeaway 21 gives me 3. That 5 is going to come down to make 35. And then 7 into 35, well, 5 lots of 7 is 35. So that's going to give me, again, 35 as the solution.
Dividing whole numbers
As we have seen throughout the course so far, there are many ways to tackle the same problem. Dividing numbers is no different. It is preferable for students to become fluent in a variety of methods. Students can then use the most appropriate method dependent upon the values presented in the question.
An advantage of students being fluent in more than one method is the ability for students to transfer their skills into other areas of mathematics. For example students will be expected to find the gradient of a straight line by expressing the gradient as a fraction and then dividing the numerator by the denominator to express the gradient as a whole number or a decimal.
In this video, Michael and Paula consider different techniques for dividing whole numbers:
- Counting up
- Fraction, simplify and count up
- ‘Bus stop’ method
We will then draw upon these methods and apply them to problems involving fractions, decimals and percentages.
Think about the advantages and disadvantages of each method. Which method do you prefer? How might your preference affect how you teach your students?
In this SMILE teaching resource you will find two packs of games, investigations, worksheets and practical activities supporting the teaching and learning of division, from simple division problems to converting between fractions and decimals.
You may like to complete questions 1 and 2 from this week’s worksheet.
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