Lesson video

Hello, I'm Mr. Langton, and today we're going to look at the differences between equations and identities.

Make sure you've got something to write with, something to write on, and try and find a quiet place to work where you won't be disturbed.

Pause the video if you need to get ready, and in a moment, we'll begin.

We'll start us off with a try this activity.

Look at the statements Xavier and Yasmin have written.

Try out some different values for x.

What's the same and what's different about them? If you can, write some additional statements which are similar to Xavier's and Yasmin's.

What I'd like you to do is pause the video now and have a go.

You can pause in three, two, one.

Okay, so what did you find? Did you try the different values for x? I found with Xavier that most of the values I tried didn't work, unless I used x equals three, I couldn't get the answer of six.

Yasmin's statement though, no matter what I tried, whichever values of x I used, I always got it to work.

Now if this statement is true for any value of x, then we call it an identity, and we use a slightly different symbol, which I've highlighted here.

An equation has got an unknown, and we can solve an equation to find the value of that unknown.

Okay, what I'd like you to do now is look at each pair of statements, and see if you think that they're an equation or an identity.

You can pause the video and have a go, and when you unpause it, we'll go through it together.

You can pause the video in three, two, one.

So do you think this one is an equation or an identity? Well let's see.

What happens when x equals one? That gives me three plus six which is nine, and that gives me two plus seven which is nine.

So that works.

Now if it's an identity, it will work for any number.

So let's try another one, let's try x equals two.

That gives me six plus six which is 12, that's going to give me four plus seven which is 11, and they're not the same.

So this is an equation, not an identity.

What about this one? Let's start off by trying x equals one.

That's going to get me four plus 12, which is 16.

It's going to give me two plus two times one is two, times that by a two is four, and two times five is 10, and that gives me 16, so that works again.

That's a good start.

Now let's try x equals two.

That's going to give me four times two is eight, eight plus 12 is 20.

Now over here I've got two plus, I'm going to have to have the brackets this time, it's getting a bit confusing, two lots of two times two is four.

So two lots of four plus five, four plus five is nine.

Two nines is 18 plus two is 20.

That's the same as we got there.

So that seems to be working, and actually I can tell you that whichever value of x you use, you will always get the same answers each time.

That makes it an identity.

All right, last one.

Let's try x equals one.

If x equals one, I'll get three times one is three, three plus six is nine.

Go over here, if x equals one, I've got two lots of one plus five, two lots of six is 12, so it doesn't work for x equals one, so it's definitely not an identity.

We've found somewhere it doesn't work, and that's why I can tell you is it will only work if x equals four.

That gives me three, four is a 12, 12 plus six is 18.

And two lots of four plus five, four plus five is nine, so two lots of nine are also 18.

So it only works when x is four, so it's an equation.

Now I'm going to ask you to pause the video so you can have a go at the independent worksheet.

Once you've finished, unpause the video, and we'll go through it together.

Good luck, and pause it in three, two, one.

So how did we get on? Let's have a quick look at the answers.

The first one, a, is the symbol for an identity.

It tells you it's an identity, and in actual facts it's not.

That second one, b, yes, that is an equation, that does work.

There's only one value of x that you can use to make it work out, and that's the same for c as well, that's also an equation.

Now d is not an identity, it's a rather strange one, actually, because there isn't really a value that you can find that makes it work.

And e is a little bit similar as well, that's also not an equation either or an identity.

So both of those are also false.

Move over to the right hand side, we're looking for the missing values that will make these three statements into identities.

So on the left hand side, we've got six lots of x plus one, and multiply that with brackets, and then we'll get six x plus six.

One the right hand side, I've already got six x, so I'm going to need to add six onto that to make them equal identities.

For the second one, I've got two x plus three x, that makes five x.

And since I've only got one x there, I'm going to need four more x's to make them equivalent.

Finally, two lots of something take away one, is the same as four x take two.

Now that's actually going to be two x.

See if I multiply out those brackets, two lots of two x is four x, and two times negative one, there we go, and that makes them the same.

Okay one last thing.

Here we've got a magic square.

In a magic square, every column, every row, and every diagonal always adds up to the same value.

I'd like you to have a go and see if you can complete the magic square.

Pause the video, and when you've had a go, we'll go through it together.

So pause now in three, two, one.

Okay, let's have a go at this one.

We're told that every column, row, and diagonal is identically equal, they add up to the same amount.

So let's find the total of this right hand column.

You've got a, plus two a take four, plus one.

Let's write that down.

A, plus two a take four, plus one.

So that's going to give me three a take away three.

So now if we go along the bottom here, we've got two a take two plus one, that makes two a take away one.

Now we need three a's, so I'm going to need an extra a.

And we've got subtract one there, we need subtract three.

So we're going to need to subtract another two to make that work.

Okay, I'm going to start going down this left hand column.

We add the two that we've got together there, we've got two plus a take two, that just makes a.

All together, we need three a take away three, so we're going to need two more a's, and we're also going to need to subtract three from that.

So, let's go along the top now, from left to right.

So two a take three, I've got a on the right hand side, that's going to give me three a take three.

Now that should be the total of the whole thing, so that means that that one there needs to be zero.

Now let's go across this middle one, and get the last answers.

So we've already got two, and we've got two a take away four.

So all together, that's two a take away two, which means that we need another a to get our three a, and we need to subtract one.

So that makes three a take away three.

Let's just check, just going down, just to make sure we've not made any mistakes.

We've got zero plus a take away one plus two a take away two.

So now I've got three a's and I'm taking away three, so yes, I can be very very happy, we got it right.

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