Skip to 0 minutes and 7 secondsPAULA KELLY: So let's have a look now at what we could do to find a percentage of an amount but without a calculator.

Skip to 0 minutes and 14 secondsMICHAEL ANDERSON: So let's have a look at 60% of 30. Now, with these types of questions, we can think of it as a proportion question, so we can use a little bit of proportional reasoning. So our original amount was 30, and that's going to represent 100% of the value. What we're trying to find is 60% of 30, so we're looking for 60%. Now, it's quite tricky to find a number that we're going to multiply 100 by to get 60, so we're going to do it in two steps. And we're going to, first of all, divide 100% by 10, and that's going to give us 10%.

Skip to 0 minutes and 54 secondsNow, whatever I do to this box, I'm going to do the same to the side, so 30 divided by 10 is going to give us a value of 3.

Skip to 1 minute and 3 secondsPAULA KELLY: So I can see you've divided by 10 to get 10%. Now it's easier to see that 10% into 60% goes six times.

Skip to 1 minute and 13 secondsMICHAEL ANDERSON: Yep, so our second step is going to be to multiply by 6.

Skip to 1 minute and 17 secondsPAULA KELLY: The same again, this into both sides-- we times this by 6. So we've got 10% multiplied by 6 to get 60%, 3 multiplied by 6 to get 18.

Skip to 1 minute and 29 secondsMICHAEL ANDERSON: Now, that example worked really well because 60 has a factor of 10, and 10 is also a factor of 100. But let's look at a slightly different method because we could be asked more difficult percentage questions, like 57% of 30 or 29% of 30. So we're going to look at a different method called the unitary method. So again, we start off with 100%, and that equals 30. We're going to instead divide this time by 100. So when we divide by 100, that's going to give us the value of 1%. I'm going to divide 30 by 100, and that's going to give me 0.3. And now, I've got 1%. I can then multiply up.

Skip to 2 minutes and 13 secondsPAULA KELLY: So it's really useful to have the 1%. If we're aiming for 60%, I can see that we're going to have to multiply this by 60, OK. And then, to keep it the same size, we'll do the same to this, and multiply this by 60. So if we're doing 3, or 0.3, lots of 60, I could times that by 10 and then by 6. If I times this by 10, I get 3. If I times that by 6, I get 18, which, thankfully, is the same as this.

Skip to 2 minutes and 45 secondsMICHAEL ANDERSON: Yep, and the nice thing with the unitary method is, once we get to this stage with 1%, we can multiply by any value to get whatever percentage we've been asked to work out.

Skip to 2 minutes and 54 secondsPAULA KELLY: Great.

Finding a percentage of an amount: proportional reasoning

Providing students with the opportunity to develop a variety of methods with which to find a percentage of an amount enables students to make connections between different areas of the mathematics curriculum.

In this video, Paula and Michael explain that finding a percentage of an amount uses the same basic skills which are used when performing proportional reasoning problems.

This means that the methods we used in the proportional reasoning course can also be applied to this problem: scaling and the unitary method. For example scaling directly from say 20 up to 100 where the scaling is easy and obvious, or the unitary method where we calculate the value of 1% before scaling up to 100%.

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This video is from the free online course:

Maths Subject Knowledge: Fractions, Decimals, and Percentages

National STEM Learning Centre