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Today we'll be learning to understand what a percentage is and its connection to fractions.

All your need today is a pencil and piece of paper, so go and get your equipment if you haven't done so already.

Here's our agenda for today's learning.

We'll start with a quiz to test your knowledge from our previous lesson, then we'll look at exploring percentages, identifying a percentage of the whole before you do some independent learning.

So we'll go straight into thinking about what percentages are.

I want you to have a look at the hundred square and think about the column that has been covered with the blue strip.

What can you say about the numbers in the covered column? Pause the video now and make some notes.

So here are some things that you may have noticed.

The numbers in the covered column are all multiples of 10.

So we have 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100.

They're all therefore divisible by ten.

And we'll get an answer that's an integer.

The column has 10 numbers in it in total.

And therefore, if the whole is 100, then the column covers 10 out of those 100 squares, and that's 1/10 of the whole.

And then we can convert that using our knowledge of decimals.

We know that 1/10 is equivalent to 0.

1 of the whole being covered.

So now I want you to bear those things in mind and have a look at the statements, thinking about again, the covered column, and then also about the numbers that are uncovered.

Which of the statements are true and which are false? Pause the video now and sort the statements.

So this is how you should have sorted your statements.

So we'll go to the true ones first.

So as we said earlier, that all multiples of ten that are covered.

There's no multiples of 10 that are uncovered.

We know that a multiple of 10 has a zero in its ones column.

We know that 1/10 of the numbers are covered because this is one column out of 10 columns in total.

We know that they're all even numbers because they all have a zero in their ones columns.

So they can be shared equally between two groups.

We know that 10% of the numbers are covered, and that links to this next one, because 10 out of 100 numbers are covered.

And when we're talking about percent, we're talking about out of 100.

So if 10 out of a hundred are covered, then 10% are covered.

And then we can look at the ones that are uncovered.

We've got 90 out a hundred are uncovered.

So we've got 90% that are uncovered.

And that's 9/10 which is not 0.

9.

Then we've got the false statements here, which said one out of a hundred or 1/100 of the numbers are covered.

Well, we know that's not true because actually 10/100 are covered.

99% are not covered, we know that's false because we actually have 90 out of a hundred not covered.

So that's 90%.

And then the final one, which may have tripped you up, it says 10% of the multiples of 10 are covered, but that's wrong.

It's actually a hundred percent of the multiples of 10 are covered, because all of them are covered therefore, a hundred percent are covered.

Now we're going to move on to identify a percentage of the whole.

So if this is the whole, what is the value of the blue part? So we'll do this one together.

I can see that one whole here has been divided into one, two, three, four, five, six, seven, eight, nine, 10 equal parts.

And one of those parts is shaded blue.

Therefore the blue part represents 1/10 of the whole.

One out of 10 has been shaded.

Now to represent this as a percentage, we need the whole to be 100.

So then if we divide this whole into 100 parts, then we can see that 10 out of the hundred are shaded.

So then we can see that that as a fraction is 10/100.

10/100 are shaded.

And we know that percent means per hundred, or out of 100.

Ten out of a hundred are shaded, that's equivalent to 10%.

Now using that train of thought, I would like you to think about now the red part.

So if this is the whole, what is the value of the red part? Pause the video now and write down your statements.

So we can see that the red part, we've got three out of 10 parts shaded, and that is 3/10 of the whole.

Remember when we want to think about this as a percentage, we need the whole to be a hundred.

So if we divided the whole into hundreds, we would have the 30 out of 100 shaded, and that's 30/100.

And then moving that into percentages we know that 30 out of a hundred is the same as 30%.

So now I'd like you to pause the video, and calculate what percentage of the whole is shaded.

Pause it now and make your notes.

So we know that the whole is divided into 10 equal parts, and five of those parts are shaded.

Therefore 5/10 of the whole has been shaded, and that is equivalent to 50%.

And we know that 5/10 is equivalent to 1/2 and 1/2 is the same as 50%, equally 5/10 is equivalent to 50/100, which is equivalent to 50%.

Now let's take it further.

We're going to explore multiples now.

So on my hundred square, I've got multiples of seven shaded in blue.

So you can see these multiples of seven, and you can see a pattern going on in terms of where they appear in the hundred squares.

And then I've shaded multiples of five in purple.

So you can see those.

We've got the column with five in the ones, and the column with zero in the ones multiples of five.

Then you'll notice for example, for 35 and 70, they are shaded both blue and purple, meaning that they are both multiples of seven, and multiples of five.

So I'd like you to think now about what can you say about the percentage of numbers within a hundred that are multiple of seven or multiples of five? So you can pause the video now, and do some thinking.

If you're not feeling fully confident yet, then just keep the video rolling, and I'll take you through the solutions.

So now let's look at the hundred square in more detail.

My multiples of seven are coloured in blue, and my multiples of five are coloured in purple.

So I can see that 12 out of these 100 numbers are only multiples of seven.

So I'm going to just check that.

One, two, three, four, five, six, seven, eight, nine, 10, 11, 12.

I didn't count the 35 because that is not only a multiple of seven, it's also a multiple of five.

So if 12 out of a hundred are only multiples of seven, that's 12% of the numbers are multiples of seven.

Then I can see that two out of 100 numbers are multiples of both five and seven.

That's 35 and 70.

They are both multiples of five and seven.

Two out of a hundred is equivalent to 2%.

And then I can also see that 18 out of 100 numbers are only multiples of five.

So that's counting down these two columns of 10, and taking out the 70 and the 35.

So only multiples of five, 18 out of a hundred, 18%.

So therefore the conclusion I can draw is that 32 out of 100 numbers are multiples of five or seven.

So that's 32%, and that's all of these percentages added together.

And also that's the number of squares that are coloured in.

And then therefore the rest of them are not multiples of five or seven, and that is 68%.

So 68% are not shaded at all.

And I can also see that if I add 68% and 32%, that equals to 100%.

So I'm looking at all of the numbers together, and then I split it into multiples of five or seven, and then not multiples of five or seven.

It's time for you to complete some independent learning.

So pause the video and complete your task, and then click restart once you're finished, and we'll go through the answers together.

For question one, you were asked, what percentage of numbers within a hundred are multiples of four? So I have highlighted all of the multiples of four on my grid, and I can see that that is 25%, because 25 out of 100 numbers are shaded, and that is equivalent to 1/4.

Then looking at multiples of six.

So again, I've highlighted them on my grid, and I counted the numbers out of a hundred, and converted it to a percentage, and that is 16%.

16 out of 100 numbers within a hundred are multiples of six.

Then multiples of eight.

So we're getting less and less each time.

I can see that 12 out of a hundred are shaded, that's 12%.

And the final one, which was a tricky one, prime numbers.

So numbers that can only be divided by one and themselves.

There's a lot more prime numbers here, that's 25%.

So 25 out of a hundred numbers within a hundred, sorry, are prime numbers.

In question two your hundred square had been made smaller containing only the numbers one to 50.

So how many squares would be covered if 50% of the squares were covered? So here, the whole is 50.

I know that 50% is equivalent to 1/2, and half of 50 is 25.

So 25 squares need to be covered.

For part B, we're looking at how many squares will be covered if 10% of the squares were covered.

Well, I know that the whole is 50.

I know 10% is equivalent to 1/10, and 1/10 of 50 is 50 divided by 10, which is equal to five.

So five squares would be covered if we were to cover 10% of that grid.

Onto question three, you were asked to use the hundred square first of all, to find what percentage of the numbers up to 100 are square numbers, and the square numbers were coloured in green.

We can see that 1/10 of the hundred squares are square numbers because 10 out of a hundred are square numbers.

Therefore, 10% of the numbers within a hundred are square numbers.

The next one you were asked, what percentage of numbers up to 100 are multiples of three? And you could see these coloured in blue, but you could also see that some of our square numbers are all so multiples of three.

So, nine, 36, 81, also multiples of three.

So if we counted all of those up, we had 33 out of a hundred are multiples of three.

So that's 33%.

Then we're looking at what percentage of numbers are both square and multiples of three.

And I drew your attention to those before that was nine, 36 and 81.

So that's three out of a hundred, which is 3%.

And then your final question, what percentage of numbers up to 100 are neither a square number or a multiple of three? And that is 60%.

60% of the squares are uncovered.

Now it's time for your final quiz, so pause the video and complete the quiz, and then click restart once you're finished.

Well done for your hard work today year six.

In our next lesson, we'll be learning to recall and use equivalences between fractions, decimals, and percentages.

I'll see you then.