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3.13

## National STEM Learning Centre

Skip to 0 minutes and 7 seconds MICHAEL ANDERSON: So let’s have a look at another strategy for finding a percentage of an amount.

Skip to 0 minutes and 12 seconds PAULA KELLY: OK. If we started off with 100%, and we’re going to say that’s going to be worth 40. Could be any number. For now we’ll use 40. So we’re going to find a number of different percentages of 40. We could start off, if we find 50%. So we’ve halved a 100%. So we divide that by 2. We do the same to our starting amount. So I know 50% of 40 is 20. And then this leads us onto some other percentages. We can find 25%.

Skip to 0 minutes and 56 seconds So again, we’re just halving. We’re halving our amount here to give us 10.

Skip to 1 minute and 6 seconds Also, so this could lead us onto– if we multiply it by 3 to give us 75%. And we do the same to our number here to get 50.

Skip to 1 minute and 20 seconds MICHAEL ANDERSON: So I suppose, to find 75%, well we could have done as well is looked at what we’ve already worked out, so that 50% and that 25%, and added them together. So 20 plus 10 would give us 30 as well.

Skip to 1 minute and 33 seconds MICHAEL ANDERSON: So if I was to start a different branch, say over here, I could work out maybe 10%. And because to get from 100 to 10, I have to divide by 10, I’m going to take my 40, and divide by 10 as well. So from the original statement, I can now also say that 10% is equal to 4.

Skip to 1 minute and 55 seconds MICHAEL ANDERSON: OK. I could carry on dividing by 10, I suppose. So if I go up here maybe, divide by 10 again, that’s going to give me 1%. And that’s going to be 0.4.

Skip to 2 minutes and 12 seconds MICHAEL ANDERSON: So where next?

Skip to 2 minutes and 13 seconds PAULA KELLY: Well, this is really useful. If you have 1%, we can find any percent. Similar to how we used them, dividing by 2, we could divide this by 2. So we can have another chain, and have a 5%. So again, we’re divided by 2. We’ll divide this by 2, which also gives us 2.

Skip to 2 minutes and 39 seconds We could go further still, and divide this by 2 again, which will give us 2.5%.

Skip to 2 minutes and 47 seconds MICHAEL ANDERSON: So half of 5 is 2.5. And then half of 2, so 2.5% is going to be equal to 1.

Skip to 2 minutes and 53 seconds PAULA KELLY: Just 1. Perfect. Lovely.

Skip to 2 minutes and 58 seconds MICHAEL ANDERSON: I suppose I could go back to this 1%, and I could double that. So I could work out that 2% is equal to 0.8, just by taking that 1% statement and times them both by 2. And I could also, I suppose, times by 3 if I wanted to get 3%. And that’s going to be equal to 1.2 by multiplying both by 3.

Skip to 3 minutes and 21 seconds PAULA KELLY: Absolutely. So why we would use this method, and why is it so useful? We can use some of these values to find lots of different percentages. So say, for example, if we were to find 99%.

Skip to 3 minutes and 35 seconds MICHAEL ANDERSON: OK. So that’s quite a tricky percentage to work out just straight away.

Skip to 3 minutes and 39 seconds PAULA KELLY: Does seem tricky. But if we consider we know 100% is 40. We take off 1%, 0.4.

Skip to 3 minutes and 48 seconds MICHAEL ANDERSON: Add 100, take away 1, that will give us that 99.

Skip to 3 minutes and 51 seconds PAULA KELLY: Fantastic. So if we do our 40, subtract 0.4, we could have 39.6.

Skip to 3 minutes and 58 seconds MICHAEL ANDERSON: So could you make, for example, 45%?

Skip to 4 minutes and 1 second PAULA KELLY: OK. Let’s try 45. So how would you put together some of these values to help you?

Skip to 4 minutes and 7 seconds MICHAEL ANDERSON: Well, I could look at this 10. 10% is 4. So I could maybe try and make 40%. So multiply everything by 4. 4 multiplied by 4 is 16. So that could help. I’ve got 40% is 16. And I think somewhere, up there, we had 5%. So I could add 5 and 40 together to get 45, 2, add 16, would be 18.

Skip to 4 minutes and 35 seconds PAULA KELLY: Fantastic. Again, with math, lots of ways to do the same thing.

Skip to 4 minutes and 40 seconds PAULA KELLY: So we could even use our 50%, which is 20. Then if we subtracted our 5%–

Skip to 4 minutes and 46 seconds MICHAEL ANDERSON: I see. Yeah.

Skip to 4 minutes and 48 seconds PAULA KELLY: –that still comes out to 18.

Skip to 4 minutes and 49 seconds MICHAEL ANDERSON: Nice. So let’s think of a more challenging one. Maybe 37%. What would that be equal to?

Skip to 4 minutes and 56 seconds PAULA KELLY: 37%. Again, lots of ways of working this out. So which of these percentages would you put together?

Skip to 5 minutes and 3 seconds MICHAEL ANDERSON: Well, we’ve got 10%. So I could try three lots of those. Then plus a 5, plus a 2. So that might be one way. Is there an easier way that you’ve spotted?

Skip to 5 minutes and 17 seconds PAULA KELLY: I think we could definitely do it your way. We’d get the same answer. A bit more efficiently, if we did 40%, and we know 3%.

Skip to 5 minutes and 27 seconds MICHAEL ANDERSON: We can take away.

Skip to 5 minutes and 28 seconds PAULA KELLY: Yeah. So if we did 40%, subtract 3%.

Skip to 5 minutes and 31 seconds MICHAEL ANDERSON: So 16, take away 1.2, that’s going to give us 14.8.

Skip to 5 minutes and 37 seconds PAULA KELLY: Absolutely. So lots of different percentages, one really easy method.

# Finding a percentage of an amount: the cloud method

In this step we look at an excellent ‘goal free’ teaching activity.

Students are asked to find as many percentage value as they can if they know that 100% = 40.

The ‘goal free’ aspect of this challenge is that students are not asked to find a specific value, say 37% of 40, but rather be creative and find as many percentages as you can. The second stage of the activity could be, rather than find the value of 37% of 40, pose the question: how many different ways can you show that 37% of 40 has a value of 14.8?

To extend this activity, give students a starting value of something other than 100%. For example pose the problem: if we know that 30% of a value is 42 what else can you tell me?

## Problem worksheet

Complete questions 7 and 8 from this week’s worksheet. As a reminder, the worksheet can be found in the first step of this week.