Lesson video

Hello everyone, it's Mr. Millar here.

Welcome to the first lesson on percentages.

In this lesson, we're going to look at percentages on a number line.

Okay, so, percentages are a really important topic.

You've probably already seen them before, but in this unit we're going to go a little bit further.

And we use percentages all the time in maths, particularly when you get to A level, but we also use percentages a lot of the time in real world.

So later on in your life, you'll be using percentages a lot.

So, without further ado, let's have look at the try this task.

So for each of these number lines, I want you to work out the marked value, the one with the red circle, and you must make sure that between each of the lines, the bars, you have the same amount.

So, for example, the first one, you could try going up in one.

So zero, one, two, three, four, five, six, seven, eight, nine, but that wouldn't work because the next one on from nine is 10, but it's 20, so we're going to have to figure out another way of doing this.

So, see if you can have a go at these three examples.

It shouldn't take you any more than four or five minutes.

So pause the video now and have a go at these examples.

Okay, fantastic.

So hope that you managed to get these, and the first one at the top, you should have seen that they actually go up in twos.

So you have zero, two, four, six, eight, I won't fill out the rest but it goes up in twos, so the mark value is six , For the next one, you should have worked out that they go up in sixes.

So you have zero, six, 12, 18, and then 24 30, 36, 42, 48, 54, and finally 60.

And the final one, we're actually going to have to look into decimals here or fractions, because they go up in a 0.

1 or a 10th.

So 0.

1 to start off with 0.

2, 0.

3, 0.

4, and then it goes up, keeps on going, 0.

5, 0.

6.

0.

7, 0.

8 0.

9 and one.

So there we have it, those are the answers.

For the final one, as I said, you could have gone up in tenths.

So the first one being one tenth, two tenths, et cetera.

So you would have got four tenths, which is equal to two fifths if you cancel it down, and then nine tenths for the second circled value.

Okay, let's have look at the connect slide now.

Okay, so here's the connect slide, and on this one, we have another number line, but this time we've got percentages on it.

So starting off at 50% and ending up on a hundred percent, and I want you to give your answers as percentages and fractions.

Now, just to start you off here, you should know that what a percentage is, it is an amount out of a hundred.

So 50% as a fraction would be 50 over a hundred, which you could actually cancel down if you wanted to, to one half.

So whenever you have a percentage, put it over a hundred and then cancel down if you can.

So here's the three things that you need to find, three values that you need to find.

So pause the video now and see if you can work out these three values here.

Okay, great.

So first of all, you should have worked out that we go up in 5% here, so we've got 55% first of all, and then 60% is our first value.

And just as we did with 50%, we can say that 60% as a fraction is 60 over 100, and we can cancel that down.

You could notice that we can cancel a zero from the top and the bottom, so dividing by 10, and then you could divide both sides, both top and bottom, by two here to give you three fifths.

We're going to keep on going up, so we have 65%, 70% and 75% here.

And 75% is 75 over a hundred, which is equal to three quarters.

Keep on going up, so 80%, 85%, 90%, and then 95%.

And the final one, C, well that is between 90% and 95%, so roughly what do you think it is? Well, I think to me, it looks about a little bit like maybe 94%, and how to make this one a fraction, again, you're just going to say it's 94 over a hundred, and you should notice that you can divide top and bottom by two, and that will give you 47 over 50.

Now another interesting thing to point out here is that it's very easy to convert from a percentage to a decimal because if you've got, for example, 50 over a hundred, you should know that decimal is 0.

5, and then 60 over a hundred would be 0.

6.

When we get to 75 over a hundred, we're going to have 0.

75.

And then what do you think 94 over a hundred would be? If you're thinking 0.

94, then really well done.

So very easy to go from a percentage to a fraction, and also from a percentage to a decimal, And we're going to be looking at that a little bit later on in the unit, in more detail as well.

Okay, now it's time for the independent task, so let's have a look.

Okay, so first question, we've got a number line from zero to one, and we've got some decimals and percentages and some fractions to put on that number line.

Second question, we're just going from a percentage to a fraction and then the final one, we are going from a fraction or decimal to a percentage.

So see how much you can do here, and pause the video now to have a go at these questions.

Okay, great, and on the next slide, we will see the answers.

Okay, great, so here are the answers.

First one should be quite straightforward.

And in the second one, well, 50%, we saw that one before, we start off with 50 over a hundred, which we cancelled down to a half.

23%, we actually cannot cancel the fraction so it's just 23 over a hundred.

And the final one, 142%.

That's going to be 142 over a hundred.

And if we divide both numerator and denominator by two, that's going to give me 71 over 50.

And in the final question, well nine over a hundred is just a 9%.

One fifth, well we can say that that is equal to 20 over a hundred, which is 20%.

And 0.

4 is going to be 40%.

Okay, let's have a look at the final slide, the explore task.

Okay, so here's the explore task, and it's quite nice and straightforward.

It's asking you, do you agree with these students? So the first one says every point on a number line between zero and one represents a percentage and the second one says, every percentage can be represented on a number line between zero and one.

So I will let you have a think about this for a few seconds and then we will go through it.

Okay, great.

So the first student, if you're thinking that he is correct, then I would agree with you.

And the reason why is that if we have a number line between zero and one, every single point between those two will be a percentage.

So zero will just be 0%, one will be 100%, and any point on that number line can be a percentage, even if it's a decimal.

So we could have something like at 0.

214, and that would be 21.

4%.

We'll have a look at how we do that in the next lesson.

And we could have something like two thirds.

So we could have a fraction, which, as we know with two thirds, is 0.

66666, it goes on forever.

but that can also be turned into a percentage as well.

That would just be at 66.

6 recurring percentage.

So we can always represent any point on the number line as a percentage.

But the second one, every percentage can be represented on a number line between zero and one.

Well, that's actually not true.

And because I can find an example of a percentage, which is outside zero and one on the number line.

And we actually saw one in the independent task.

If we have something like 142%, that is bigger than one, so it's not going to be on that number line.

So yeah, anyway, that is the end of the lesson.

And next time we're going to be having a look in more detail about the conversion between percentages and decimals.

So look forward to seeing you in the next lesson.

Thanks very much.

Have a nice day and take care.

Bye bye.