Transcript

INSTRUCTOR:

How many buses do I need to carry 1,960 passengers if each bus carries 43? First, I will begin by using an intuitive method whereby I will add up multiples of 43 until I can carry all 1,960 people.

So I'm going to start by working out how many 10 buses would carry. 10 times 43 is 430. I obviously need a lot more than 10 buses. I will try 4 lots of 10 buses, which is 40 buses. That will be 4 times 430-- I could double and double again, that will give me 1,720 passengers. This is closer to 1,960, but adding another 10 buses will take me well over the 1,960, so I'm now going to add smaller numbers of buses.

I could add 5 buses. That'll be half of 430. So 5 times 43 will be 215. I'm going to add those together, just the last two lines, to give me 45 lots of 43. So that will be 1,935. So that's not quite enough passengers yet can be taken, so I need to add another bus. Let's try 46 buses by adding 43 onto my last figure. So that will give me 1,978. So I can definitely carry all 1,960 people, and they will also be 18 spaces left. So I need 46 buses.

The traditional way to work out how many buses are needed is to do a division. So I'm doing 1,960 divided by 43. I'm going to use a short division method even though I have a two-figure number as a divisor. Years of teaching experience shows me that learners struggle with the long division method with its complicated procedure.

So 43 into 1,960, I'm going to have to work out how many 43's are in 196. So I'm going to write the 43 times table down the side. So two of them will be 86, three will be 129, four will be 172. So that's below 196, but another 43 would take it over. So 43 is into 196. It must be 4, then of course, it's actually 443-- this is 172, so there's a remainder of 24, which I put next to the 0, and read it as 240.

So 43 is into 240, I just need to go a bit further with my 43 times table, add another one of those on. So that's 215. That's just less than 240. Another 43 would take it over, so 43 is into 240, go 5. And of course, five 43's a 215. So there's a remainder of 25.

So we've got an answer-- 45 remainder 25. What does remainder 25 mean? Do 25 people have to walk? We can't have that, so I will order them another bus. So altogether, I will need 46 buses.