Lesson video

Hi, everyone.

I'm Ms. Jones, and I am really, really excited to introduce the topic of algebra to you in these lessons.

It's one of my favourite things, and it's going to be great.

Today's lesson is all about algebraic expressions, but before we can begin, you need to make sure you've got pen and some paper, you have removed any distractions from around you, and if you can, try and find a nice, quiet space to work.

Pause the video here to make sure you've got all of that ready for today's lesson.

So let's begin.

Your first task is to have a go inputting each of these numbers here, five, 10, eight, and negative two, into both of the function machines, A and B.

Once you have done that, I would like you to think about which of these numbers at the top had a greater output, so what comes out of it, from the first function machine.

I would also like you to find a number that has the same output from both function machines.

So for example, if I put 11 in here and 11 in here, I would get the same output, the same number coming up.

Pause the video to have a go at that.

This is what we should have got.

The numbers that had a greater output from the first function machine and the second were five and negative two.

So if you put five into both of them, came out with 29 in the first one and 21 in the second one.

If you put negative two into both of them, it came out with eight in the first one, and it came out with negative 28 in the second one.

So to find a number that has the same output from both function machines, hopefully you tried a few different numbers, and the answer was seven.

Seven multiplied by three and 14 gets you 35.

Seven subtract two multiplied by seven also gets you 35.

Really, really well done if you had an experiment with those, and extra well done if you managed to find that it was five and negative two, and that it was seven that has the same.

You can leave out the multiply symbol when using algebraic notation.

For example, four multiplied by N can be written as four N.

So if I was to look at this function machine here, I'm starting with instead of a specific number, I'm starting with N, which just means any number.

We don't know what the number is.

Starting with N, I'm multiplying it by two, and then I'm adding three.

So if this was a specific number, I would write two multiplied by that specific number add three, but we are using N instead, so I have two multiplied by N add three, which can be written and should be written as two N add three.

Two N add three is a mathematical phrase, which is called an expression.

That word is going to be used an awful lot in the next few lessons, so make sure you remember what an expression is.

It's a mathematical phrase.

What I would like you to do now is have a go at filling in the gaps in the trios below.

So the first one is these three boxes, and the second one are these three boxes.

To do this, you need to use that function machine to try and produce something similar to what you can see above.

Remember, you might need to use brackets in order to show the order of the operations that you are doing, 'cause you're doing N add three first, remember, and you need to make sure it's clear that that's what you should do first, thinking about your order of operations and your priorities.

So pause the video to have a go at that.

So this is what we should have got.

We should have got N add three multiplied by two.

Now if you wrote N add three multiplied by two without the brackets, which part would you have to do first? The multiplication.

That's why we need brackets, to make sure we can, it's really clear that the N add three is the thing we do first.

This can be written as two N add three.

Remember, we said we didn't need that multiply sign when we have an algebraic expression.

That two actually goes at the front.

Just like if I had N multiplied by two, I would put the number first, two N.

Well done if you did that.

For this one, three N add two, I would do three, lots of N first, and then add two, which is written here, so I'd be multiplying by three first and then adding two.

We can substitute numbers into an expression.

For example, we can substitute the number four into the expression to check that our trios are correct.

So for that first one that we did, we could have a go at substituting four in to check that we get the same answer no matter what we're doing.

So for example, if I put four into this expression, I would do N becomes four.

So I do four, add three, and then multiply it all by two, which gets me 14.

And I can check that I did that correctly in my diagram here by doing four, then adding three, then multiply them by two, which equals 14, so I did that right.

So substituting is really helpful for checking our answers.

Pause the video here to complete your independent task.

Your first question involved matching cards.

So you had to match the cards below into pairs of equivalent expressions, and this is what we've done here, so we've got these ones that match together.

Well done if you got that.

You then had to do some substitution, so work out the value of each expression when N equals three.

Hopefully, now some people do this.

They write, if it's two N, they'd write 23.

That's not correct 'cause remember, two N actually means two multiplied by N, so I had to do two multiplied by three, which is six.

With something like this, remember your priorities and your order of operations.

I'd need to do the multiplication first.

Even though you can't see that the multiply sign is there, we know this is multiplication, so I do 10 multiplied by three first, and then subtract it from 100, which is 70.

For question three, it involved you substituting in a few different values to find, to make this inequality true.

So, four X.

In order for it to be less than three X add five, essentially we needed an X value that was four or less, or less than five, in fact.

For this one, we needed an X value that was greater than five, and remember, greater than five could also include a decimal, so well done if you got any decimals, 5.

5, 5.

1, et cetera.

And for them to be equal, X needed to equal five.

So an extra well done if when you were doing this, you got some values of X that were negative, and/or decimals or fractions.

That's really brilliant.

Well done.

So now onto the explore task.

Carla and Xavier have written expressions using the variable B.

So, Carla's expression is B add four, and Xavier's expression is two B.

What does two B mean? Two lots of B.

Well done.

What I would like you to do is compare their expressions, so to find a value of B that makes her expression, Carla's expression greater, and to find a value for B that makes Xavier's expression greater, and then also to find a value of B that makes the expressions equal.

So pause the video now to have a go at that.

So for Carla's expression to be greater, we needed B to be less than four, so for example, B equaling 3.

5.

If B is 3.

5, then this would be 7.

5, and this would be seven, so that would make Carla's expression greater.

For Xavier's expression to be greater, or Carla's expression to be smaller, we'd need B to be greater than four, so for example, 4.

5 or five.

So if B was five, for example, then Carla's expression would be nine, and Xavier's expression would be 10.

For B add four to equal two B, so for those two expressions to be equal, then B needed to equal four, because both of those expressions would equal eight if that were the case.

Amazing job if you managed to get some examples, again, especially amazing if you managed to include some negatives and some decimals.

That's great practise for you, so really well done for that.

And that brings us to the end of the first lesson on algebra, and an amazing, amazing job.

If you'd like to, please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

I'm really looking forward to seeing you again.

An extra well done from me.