Percent of a quantity
Source of all images : Mr Kelsall or Oak National Academy

What is 10% of 300?

What is 30% of 500?

Which is bigger:

There are 1000 athletes.  How many athletes are aged over 31?

Percent of a quantity

﻿Hello everybody, my name is Mr Kelsall. And welcome to today's lesson about finding percentages when we're solving problems. Now before we start, you will need a pen and a piece of paper and somewhere quiet where you're not going to get disturbed. Don't forget to remove any sort of distractions, for example, put your mobile phone on silent or move it away completely. Pause the video and then when you're ready, let's begin. So today's lesson is all about finding a percent of a quantity and specifically looking at problem solving. We're going to start by revising our basic percentage facts. We're going to link all of those facts to percentage, and to fractions. We're then going to create percentage statements. You'll need a pencil and a piece of paper. Our star words are percent and the percentage symbol, %. Per cent that can be broken up into per cent, per 100. We're going to be talking about division and divided. We'll talk about equal parts. We'll link to fractions and decimals, and we'll use the word hundredth and the equivalent. Little bit of revision, cent means 100, percent means per 100. Fractions, we can link percent to fractions, or to decimals. There are a few facts that you need to know, remember, and know how to use these. Your base fact is 50%, and 50% is one half, and you can divide a whole thing by two to get what half. If you know, 50% you can work out 25%, you can half a half, you can divide by two, divide by two, or you can just divide by four. 25% is one quarter. If you know 25%, you can work out 75% because 25% is one quarter, 50% is two quarters, 75% is three quarters. So to find three quarters I'd divide by four, and multiply by three. The next base fact is 10%. If I can find 10%, I can find 20, 30%. To find 10%, I need to find one 10th, I'd divide by 10. To find 20%, I'd divide by 10 and times by two. To find 30% divided by 10 times by three. So 20% is two tenths, 30% is three tenths. Now our new learning in full today. Try to find the percentages of 400 pounds. Can you find 50%, 25%, 75%, 10%, 20%, 30%? Can you find any other percentages? What about 5% or 1%? Pause the video, and when you're ready, press play. I know 50% is 200 pounds, 25% is a hundred pounds, 75% is 300 pounds, 10% I'll divide by 10, it's 40 pounds. 20% is 80 pounds, 30% is 120 pounds. I asked you about other percentages, for example, 5%, 1%. You don't need to know this yet, but I'll just give you the answers. So if I know 10% is 40 pounds to get from 10% to 5%, I can half 10%. So if I half 10% I get 5% , what if I half 40 pounds? I get 20 pounds, so you can find 5%. I can also find 1%. To get from 10% to 1%, I divide by 10. So to get from 40, I divided by 10 to get four pounds. So there are 160 pupils at Wood Lane Primary School. 75% of pupils walk to school. How many ways can you solve this? Pause the video and press play when you're ready. The first way and my standard method is that I prefer to use a bar model. I'm looking at 75%, I know 75% is three quarters. So I'm taking 160, I'm splitting it into four equal parts to get quarters. And I'm interested in three of those parts. 160 divided by four is 40, so each part. Which means that three quarters is three lots of 40. So 40 add 40, add 40 is 120. That's one way of doing it. Another way of doing it, I might have said that, well, I want to find one quarter. I'm going to do 160 and I'll divide it by four to get one quarter. I've managed to find one quarter. I need to times that by three to get three quarters. That's my second way. Another way I might have done it, is I might say, I know that 50% is 80 pupils, half of that, 25%, is 40 pupils. And I can add the two numbers together to get 75%, which is 120 pupils. I might have said, I know 25% is 40, 25% is 40, and 25% is 40. So add them together, it gets me my 75%, which is 120. You might have solved it, differently and that's completely normal. Just want to point out one more method, which many people don't think about. If you start with a hundred percent, which is 160 and you take away 25%, it leaves you 75%. So 160 takeaway at 25%, which is 40 pupils gives me 120. Let's carry on an extend this learning. Use the information below to decide who did better in the penalty shootout. So Mustafa scored four out of 10 shots and Bilal scored six out of 20 shots. Pause the video, have a think, have a go. When you're ready, press play to continue. I know that four out of 10 shots is the same as 40 out of a hundred, which is 40%. So I know that Mustafa's accuracy is 40%. Bilal, however, scored six out of 20. Now I need to convert this to hundredths, to convert it to percent. So 20 times five is a hundred, so six times five is 30. So I know that Bilal's accuracy was less that Mustafa's, the accuracy was 30%. There're different ways that I can use to solve this, for example, solving using equivalent fractions, I can say six out of 20 is the same as three out of 10 and four out of 10 is better than three out of 10. Now let's give you some more information. They each took five more shots, who did better? Now, Mustafa scored two more goals, Bilal scored four more goals. To start with, Mustafa scored four out of 10, he then scored two more goals, which took into six, but it's not one out of 10, he took five more shots. So it's now out of 15. So Mustafa scores six out of 15. Bilal started with six out of 20. He then scored four more goals to take him to 10 out of 25. So which is better? Six out of 15 or 10 out of 25? Have a think, pause the video and press play when you're ready. If we use my equivalent fractions again, I know six and 15 are both in my three times table. So if I divide this by three, I know that six fifteenths is the same as two fifths. And I'd like to get the 10-25ths into fifths as well. I know 10 and 25 are in my five times tables. So if I divide by five, I get two fifths also. Now actually they are equal. So I know that after the second round, we've got two people who have got the same accuracy. However, this lesson is still about percentages in our problem solving. So what are these percentages? What these fractions as percentages? Well, two fifths, I know is the same as four tenths. I know four tenths is the same as 40 hundredths. And therefore I know it's 40%. So I can still use my percentage to help solve these problems. And that brings us to our develop learning section of today. Have a look at the question on the screen. Pause the video, have a think through it. And when you're ready, perhaps press play to continue. We are told that Olivia and Marta are playing basketball, Olivia scores, 18 out of 24, and Marta scores, 18 out of 30, are the equal? Who has a better percent? And what are these as fractions? They scored the same amount, however, Marta had taken more shots. So they're not equal. That means that Olivia has scored more from less shots. Olivia had scored 18 from less shots and Marta scored 18 from more shots. So actually Olivia is going to have a better percentage. Let's start having a look at these as percentages and fractions. 18 out of 24, I recognise they're both in my three times tables, 18 divided by three is six, 24 divided by three is eight. I also recognise I can convert that a little further. Six eighths is three quarters. So I know that Olivia scored three quarters. I know three quarters is 75%. So Olivia's accuracy is 75%. Marta scored 18 out of 30, and I know the 18 and 30 are my three times tables, but I've just spotted there also in my six times tables. So I'm going to divide by six, 18 divided by six is three, 30 divided by six is five. Now three fifths. If I go back to my learning, right at the beginning of the lesson, I know that three-fifths is 60%. And if you can remember that great, if you can't remember it, you can convert to equivalent fractions. So I know that's six tenths and I know six tenths is 60 hundredths and I know 60 hundredths is 60%. So I know Olivia, her accuracy is 75%. However, Marta's accuracy is only 60%. Now it's time for your independent task. Have a read of these questions and decide if these are true or false. Pause the video, when you're ready press play to continue. I know that half of 120 is 60. So that time it's true. 50 hundredths of 120, I know 50 hundredths is the same as one half. And I know that one half of 120 is 60. So this statement is true. 50% of 120, 50% is a half, half of 120 is 60. A half times 120 is 60, that is true. 50 over 100 times 120, I know 50 over a hundred is half and a half times 120 is 60, so this is true. And 50% of times 120 is also true. Congratulations on completing your task. If you'd like to, please ask your parent or carer to share you work on Twitter, tagging @OakNational and also hashtag learn with Oak. Before we go, please complete the quiz. That brings us to the end of today's lesson on finding percentages and solving problems. A really big well done for all the fantastic learning that you've achieved. Now, before you finish, perhaps quickly review your notes and try to identify the most important parts of your learning from today. All that's left for me to say is thank you, take care and enjoy the rest of your learning today.

Finding percent of a quantity - problem solving
Source of all images : Mr Kelsall or Oak National Academy

What is 50% of 300?

There are 160 pupils at school. 20% of pupils walk to school.  how many walk to school?

Which is smallest?

There are 500 athletes.  How many athletes are aged between 21 and 30?

Finding percent of a quantity - problem solving

In this lesson, we will learn how to find percent of a quantity and solve problems.

Lesson overview:Finding percent of a quantity: Problem solving

Fractions, decimals and percentages: