﻿Hello everyone, it's Mr. Millar here. Welcome to the first lesson on inequalities and in this lesson, we're going to be looking at representing inequalities. So make sure that you've got a pen and paper ready, and let's have a look at this lesson. So, first of all I hope that you're all doing well, and just to introduce myself, in case you haven't seen any of my other lessons on Oak. So my name is Mr. Millar. I'm a maths teacher in a school in Central London, and I'm really excited to be doing this lesson for you because I love teaching maths, and I'd love to spread my enthusiasm for it as well. So anyway, this is the first of eight lessons on inequalities, and I think you should have seen inequalities before in year seven or in primary school, so this will be building on your previous knowledge. And it's a really important topic because when you do maths at GCC, and if you go on to study at A-level and beyond, you'll see inequalities all the time. So without further ado, let's have a look at the try this task. Now in the blue boxes, I've got a number of different statements. Most of them are inequalities. And what I want you to think about is how would you organise these statements into groups. What's the same and what's different about your groups and how would you describe each of those groups? So there's no right or wrong answer here. It's just for you to think about these different statements. So pause the video for a couple of minutes and attempt to group these statements into different groups. Okay. Hopefully you've had a think about this. Let's go through it now. So first of all, let's just make sure that you understand what these inequalities actually mean. So if I look at the first one, this one says A is greater than 5. So any value of A, that is greater than 5 would satisfy this inequality. So for example, if A is 6, if A is 7, A could be a decimal, it could be 7.5, it could be 10. Then those values of A would satisfy that inequality. But values of A that didn't satisfy this equality, well, 3 wouldn't, because 3 is less than 5. So that wouldn't work nor would 4, and nor would 5, that wouldn't work as well, because 5 is the same as 5, it's not greater than 5. If we have a look at the next one, well, this is a little bit different because this says A is less than or equal to 5. That's what this little sign here underneath the less than means, or equal to. So A could be anything, it could be a 3, it could be 4. Those are values less than 5, but A could also be 5 here, that would satisfy that inequality. But anything above 5, so if A was 6 or 7 or 8, that would not satisfy that inequality. So there's a number of ways, as I said, you could've grouped these up. So you could have looked at it in terms of the sign itself. So some are less than, some are greater than, some are less than or equal to, some are greater than or equal to. And there's one, at equal sign as well. The other thing I do want to draw attention to is the fact that there are two pairs of inequalities which are exactly the same. So one pair which is exactly the same is this one. And this one, these two here. So 5 is great than A and A is less than 5. Those two inequalities might look a little bit different, but they're actually the same. Because in both cases, you're looking for a value of A, which is less than 5. Can you see the one other pair of inequalities, which are exactly the same? Well, if you're thinking these two down here are exactly the same, really well done. A is greater than or equal to 5 in both of these cases. Okay. Let's have a look at the next slide. All right, so here are two students who were discussing the numbers -5 and -3. And the first student says that -5 is greater than -3 since 5 is a bigger number, than 3. The other student disagrees, no, -5 is less than -3, because you need to imagine both numbers on a number line. I'll give you a few seconds to have a think about which of these students you would agree with. Okay. So let's, first of all, draw a number line. So if I just do a nice and simple number line like this, and I'll put zero in the middle and then I'll have positive numbers going to the right zero. And then to the left zero, I will have negative numbers. So I'm going to have -1, -2,

3, -4, and -5. And if I think about the relative position of numbers on the number line, well, anything to the right of the number line is going to be greater. Because if I compare, for example, the numbers 3 and 2, well, I know that 3 is greater than 2 and I can see it on the number line as well, because 3 is to the right of two on the number line. What about the numbers -5, and -3? Well, here is -5, and here is -3. So which is bigger?

3 is bigger because it's to the right of -5 on the number line. Therefore, which statement is correct? Well, the second statement is correct.

5 is less than -3, because if we think about the numbers on a number line,

3 is to the right of -5 on that number line. So this is a common misconception with negative numbers here, make sure that you really understand this before we move on. Okay. So here is the independent task, so make sure that you are writing these out on your piece of paper. So for the first eight statements, you need to decide whether each statement is true or false. So for example, if you're doing the first one, 2 plus 20, well that's equal to 22, and 3 plus 20 is equal to 23. So that statement says 22 is less than 23. And that of course is true. So you would just write a T for true. And on the right-hand side, you have got four different statements and I want you to place a less than, greater than, or equal sign in the middle to make each statement correct. For example, the first one, 2 plus 40 is 42, and 3 plus 20 is 23, so what sign would go there? Well, if you're thinking a greater than sign would go there, really well done. Okay, pause the video to have a go at these remaining questions. Shouldn't take you any more than five or six minutes. Okay. And make sure you've had a good go at this. And on the next slide, I'm going to show you the answers. Great. So here are the answers to these questions. So just to make sure that you have got these right. There's just one I want to go through, which is the last one in the first set of questions. 2 divided by 10, comparing that to 3 divided by 10. So I can write these as a decimal. So 2 divided by 10 is going to be 0.2 because I just move a decimal place, one back, and 3 divided by 10 is, 0.3. But I could also think about these in terms of a fraction. So 2 divided by 10 is 2/10, and 3 divided by 10 is 3/10. So therefore this statement is true because the numbers on the left-hand side are smaller than the numbers on the right side. Okay. When you're ready to move on, let's have a look at the final slide of today. Okay. So here's the explore task. Let's have a read through to see what's going on here. So there are some red, green and blue counters in a bag. There are more red counters than blue counters, and there are more green counters than red and blue combined. So first of all, how can you express this information using inequalities? Well, I'll do the first one for you. There are more red counters than blue counters. I can use letters, R, B, and G to represent the number of counters of each colour there are. So if there are more red counters than blue counters, I can write, R is greater than B. What do you think the second one would be? Well, there are more green counters than red and blue combined, so green is going to be greater than red and blue combined. What's that going to be? If you're thinking, R plus B, super job, well done. Okay. Now let's have a look at the next part. How many red, blue and green counters could there be, if there were 10 counters in total? And you must make sure that, these counters meet the conditions attached, so there must be more red than blue, and there must be more green than red and blue combined. See if you can have a think about a combination of counters that meet all of these conditions. Well, there are actually two different possibilities for the first one here. If I have a think about the number of blue, red, and green counters, one way I could do this is 1, 2, and 7. And that meets all of these conditions because there are 10 in total, 1 plus, 2 plus 7 equals 10, and there are more red than blue counters 'cause there's 2 red, and 1 blue. And there are more green counters, 7, than red and blue combined, only 3. Can you think of the other possibility here? Well, if you were thinking 1, 3, and 6, then, well done, you got it. Okay. Finally, what if there are 11 counters? There's actually four different possibilities here. So pause the video, and see if you can get all four possibilities. Well, here they are. 1, 2, and 8, 1, 3, and 7, 1, 4, and 6, the final one, 2, 3, and 6. Those are all the possibilities here. Okay. That is it for today. I hope you've enjoyed this video, and we're going to be looking at more inequalities in the next video. Have a great day and see you next time. Thanks very much. Bye.

Which of the following statements is TRUE? Select one.

Which inequality fits in the gap? 5 + 8 ____  7 + 8?

Which value of x does NOT satisfy the inequality x ≤ 6 (where x is a number)?

Representing Inequalities

In this lesson, we will discuss what different inequalities mean, and we will see an example of where we might see inequalities used in context.

Maths

Y8 Maths

Key Stage 3

Year 8

Representing inequalities

Forming and solving inequalities

Algebra

THEME

UNIT

Inequalities and substitution (Part 1)

Inequalities and substitution (Part 2)

Solving inequalities

Forming and solving inequalities (Part 1)

Forming and solving inequalities (Part 2)

Manipulating inequalities

Manipulating equations and inequalities

Given that x = 6 and y = -5, which of the following statements is false? It may help to sketch a number line.

Look at the diagram. Which of these statements is true according to the diagram?

Which of the following values of x satisfy the inequality x + 2 < 11 ? Select ONE

Which of the following inequalities is satisfied if x = 3 and y = 4?

What is the solution to the following inequality: 3x + 4 > 10

I'm thinking of a number (call it x). If I multiply it by 3 then add 4 to it, what expression do I get?

I'm thinking of a number (call it x). If I multiply it by 3 then add 4 to it, my answer is less than 19. What range of values can my number take?

Given that x > y, is the following inequality always, sometimes or never true? x + 2 > y + 2

Solve the inequality 2x - 11 ≤ 21

If a + b = 10 , which of the following is also always true? Select one.

Lesson overview:Representing inequalities

Forming and solving inequalities: