﻿Hello, I'm Mr Langton and today we're going to have a look at expressions and variables. So just take a minute to make sure you've got something to write with and something to write on and ideally try and find a quiet space where you're not going to be disturbed. When you're ready, let's go. So we'll start off with the try this activity. Xavier and Yasmin have both formed algebraic expressions using cubes. How could you represent their expressions with written algebra? Now Xavier says, I think my expression has a greater value than yours. Yasmin says no, mine has got a greater value. How could both their statements be correct? What I'd like you to do is pause the video and have a go for yourself, write out as many different expressions as you can for each person. See if you could work out how they could both be right. So pause the video in three, two, one, now. How did we get on? Let's have a look at the different expressions that they could've written. We'll start with Xavier's. Xavier has got three green cubes which is three A and he's got six yellow ones so he's got three A plus six. Now actually, they're grouped into the same amounts so we could say that Xavier's got three lots of A plus two. Cause each one is an A plus two. We could write that algebraically as well using a bracket, three lots of A plus two. So there's three ways you could've got, you might've got some more. Let's have a look at Yasmin, now, she's got two green cubes, two A, and she's got eight yellow ones. And again, hers can be grouped as well. All the groups are the same and she's got two groups so that's two lots of A plus four. Which can be written with brackets, two multiplied by A plus four. Okay, have you got those? Right, let's move on. Now let's try out some different values for A to see who's expression is the greatest. Let's start off by saying that A equals one so in this case, Xavier is going to have three plus three plus three. Xavier is going to have nine. Whereas over here Yasmin is going to have five plus five which is 10, so there's an example of how Yasmin's could be greater than Xavier's. What about if we said that A equals five? So in this case, if A is five, then that'd be worth seven plus seven plus seven which makes 21. Now for Yasmin, she's got five plus four, that's nine plus nine which is 18. So there's an example where Xavier's correct, where his expression is greater. But just out of interest, could they both be wrong? I was having a bit of a think about it and I found, if A equals two then Xavier's statement is worth four plus four plus four which is 12. And if A is worth two for Yasmin, then hers is worth six plus six which is 12 so it's possible that each of their expressions is worth the same amount. A number we don't know in an expression is called a variable as we can choose any number we like. If we know what the expression is equal to, then we call that number an unknown as we can work out what it is, we just don't know what it's value is yet. So Xavier has said, I can choose whatever value of A I like and we've shown that already by putting different examples in for A. Now Yasmin's expression is a little different this time because it's equal to 20, there's only one value that A can be, we've fixed it and made it into an equation. So what you're going to do now is pause the video and have a go at the task. When you've finished, resume the video and we'll go through the answers together. Good luck. How did we get on? Let's go through them together. So the first one, we've just got to say whether or not they're an equation or an expression. Question A has got an equals sign in it so 10 equals two X take away five so that means that that one's going to be an equation. Part B, six X plus five. Now we've got a variable in there but there's no equals sign it's an expression. Third one, negative four equals three A take one. That's going to be an equation cause once again it's got an equals sign. And the fourth one, negative seven C, that one's just an expression, not only is it just a term, but it's negative seven C. So what we're going to do now is look at these on the right hand side and do some substitution. What is the value of each of these if B equals three? So for the first one, B is three, we've got three subtract five which is negative two. Next one, B is three so we've got six multiplied by three and I'm adding two, six threes are 18 plus two is 20. For the third one, it's three subtract four lots of B, that's four times three. So three takeaway 12 is negative nine. And finally, for this last bit, we've got negative four B plus three so that's negative four lots of three, I'm going to add on three. And actually, that's going to be the same, isn't it? If we've got negative four times three, that's negative 12, plus three is negative nine. Have you noticed that these two are giving us the same answer? An awful lot of similarities between the two question there, actually. So finally, which expression has got the greatest value when C equals seven? If I substitute C equals seven in, I'm going to do 12 take away two lots of seven, two lots of seven is 14. 12 take away 14 is negative two. Over here, I'm doing seven take away five which is positive two, so this one here, C take away five gives us the greatest value when C equals seven. Look at the expressions below. Which is largest when M equals four? Should we do it together? If M equals four here, I've got 50 take away three lots of four, 50 take away 12 and 50 take away 12 is 38. This next one when M equals four. I've got three lots of four which is 12 and 12 plus 20 is 32. Finally, this third one. I've got four divided by two and adding on 25. Four divided by two is two plus 25 makes 27. So in this case, A is the largest one. Now what I want you to do next, I want you to try and find some more values of M so you can make A, B or C the lowest, the least value, make A, B or C the middle value, and A, B or C the greatest value. So we've already found an example where A is the greatest value, that's when M is four. What else can you find out? I'm going to let you pause the video and have a go. If you want a hint, don't pause the video just yet. I'm going to count you down so you can pause the video now. If you want a hint, just keep watching and I'll give you a little hint on the next bit. So pause now in three, two, one. Okay, so here's a little hint. If we draw a table like this we can start to work out some of the values and see where it's largest. We already did the M equals four, didn't we? So that, we found that that was 38, we found that that was 32, and we found that that was 27. So we can see that A is the largest one there and if you try out these other values for M, you might be able to work out where we've got the largest and the smallest ones for A, B and C. Good luck. I'll give you the chance to pause it now and have a go yourself. Three, two, one. So how did you get on? I've just got a little table on the side for you just to show you some of the answers that you could've got. I've highlighted in red where A, B or C give the lowest value, so for example when M is zero, B is the lowest, when M is eight, A is the lowest. I've highlighted in blue the ones that give the middle value, so if M is one, C will be in the middle and if M is four, B will be in the middle. And the one I've highlighted in green, where it gives the highest value. Have you noticed that C doesn't give you a highest value at all? And finally, if you'd like to share your work with Oak National, then please ask your parent or carer to share the work on Twitter, tagging Oak National and #LearnwithOak. Thanks, see you later, three.

Which of the following are expressions?

What is the value of the cubes if a = 4?

What is the value of this expression if a = 5?

Which expression has the greatest value when a = 7?

Which expression has the greatest value when a = 4?

Expressions and Variables

In this lesson, we will look at the different values that expressions can take, and how changing a variable can change the value of the expressions.

Maths

Y8 Maths

Key Stage 3

Year 8

Expressions and variables

Forming and solving equations

Algebra

THEME

UNIT

Equations and identities

Forming and solving linear equations 1

Forming and solving linear equations (Part 2)

Equating linear expressions

Solving further linear equations

Solving geometric problems using linear equations

Forming and solving equations from descriptions

If a = 3, which of the following is true?

Is the following an expression, equation, or identity?

If x=5, which symbol should go in the box

Which equation can be formed from the diagram?

I think of a number. I times it by 5 and subtract 3. The answer is 17. Form an equation to show this.

Zaki thinks of a number. He multiplies the number by 5. He then adds 3. His answer is 38. What number did Zaki think of?

What equation does this bar model show?

Solve the equation: 15 =  5 + 4e

Solve the equation:

Lesson overview:Expressions and variables

Core Content

Forming and solving equations: