Lesson video

Hi everyone! Ms. Jones here! And today's lesson we're going to be looking at collecting like terms. But before we do so, please make sure you have a pen and some paper as well as getting rid of any distractions and making sure that you have a quiet space to work if possible.

Pause the video now, to make sure you've got all of that ready so that we can begin.

Okay so let's start.

"What is the same and what is different about the expressions below?" Think back to what expression means.

"Which of the expressions do you think is written the simplest?" So you're looking at these expression here in the boxes.

"How could I represent the expressions?" So that's something you can also think about.

Could you represent them using blocks? Or could you maybe get some things in your house to represent these objects or numbers or terms? So pause the video to have a go at these two questions here.

So there's lots of things that you could have said.

For example, you might have noticed that these four here all have exactly the same value if you were to actually work out what they equated to, you would find they all have the same value of 45.

Similar with this one, you'd find they all have the same number of a's all together, same value.

You might've said that, these two are represented in a similar way.

You might've noticed that, these two are are represented in a similar way.

They have the same.

they both have five in for example, there's lots of things that you could've said.

"Which expression do you think is written the simplest?" Now you could have picked any of these and as long as you justify your answer that was fine.

I would say personally that these two for me are written the most simply as they have the least amount going on in these numbers of integers or these numbers of terms. And I think there most simple but I know that before some people have said maybe they think this is the most simple because they've just got nines and they can see them all and they can see how many there are.

There's lots of way you could've said this so, well done if you managed to do that.

"We can collect together like terms of variables and constants in order to simplify algebraic expressions." Now there's lots of language there, so variables our are terms like the "a" just means it could vary, if that makes sense, it could be something different.

Our constants are our numbers so one, five, three point five they are constants.

"Binh has represented two add b add three add two b." And we want to collect those like terms of variables and constants.

But in order for her to visualise that, she has represented them like this.

So you can see the yellow square represent ones, and the green blocks represent b's.

So she's got two plus b plus three plus two b.

So all together, she has got one, two, three, four, five ones.

And she's got three three b's.

And she has written that as three b add five.

And that has been simplified.

It really helps to represent these using blocks and ones or whatever you have around your house you might want to use spoons and forks, whatever you want to use, because it helps to recognise that this isn't just.

so the first time if you looked at this you might think "Oh, there's eight b's there or eight things there.

So I'm going to put eight b." But that's not what it is.

They've got to be separated out.

And for example, if I had blue block, let's say here I wouldn't have four ba.

I would have three b's and one a.

So what I would like you to do now, is have a go at simplifying the expressions at the bottom here.

It might help you to imagine them, using these representations here so you know how to draw these out if that helps you.

Pause the video now to do that.

Okay, so I simplified the expressions.

I really like this one, because a lot of people make a mistake with that one "Three a subtract a." Actually quite a lot of people would just write three, but if you did what I suggested, and you drew out three a's and you took away an a.

You'll notice that we've got two a's left, we don't got three left that not what we've got.

So really well done if you managed to get those answers.

Pause the video now to complete your independent task.

We have these questions here.

The first question was asking you rewrite these expressions as simply as possible by collecting the right terms. So for example, I would have potentially drawn out two a's and three a's and maybe five ones and subtract two ones.

And as my answer I would end up with five a add three.

Cause that would be after the five a's and three ones.

For the second question, you were asked to fill in the pyramid.

And the pyramid can be filled in by summing the two bricks below it.

So, for example, to find this brick here, I would have to add these two bricks together.

And so in here would go two b and 13.

Then you do the same with these two bricks to get the top one.

And to get this one we'd have to subtract 13 from 13 and b.

And these are the answers that you should have got.

Well done if you managed to do those.

Building on this idea of the pyramids, "How can you complete these addition pyramids?" So its the same principle as before, with your independent task, you're going to add the two at the bottom to get the one directly above it.

"What could the value of the missing bricks be in this addition pyramid?" So we've got a lot more gaps in this one.

So actually there might be more than one possibility.

And there are because its asking "How many different possibilities you can find for the bottom row?" So I'd really like you to experiment with this.

Use some algebraic terms, use some negatives, use some decimals, fractions, whatever you can think of that would be brilliant.

So pause the video to have a go at that.

And these are the answer we should have got.

So the top two, fairly straight forward hopefully, you just add these together.

Remember this, two add a, it's no two a.

You wouldn't get two a's by adding two ones and an a, you would get two and a.

And that's actually, it's something you need to get used to.

It's that this can be an answer a and two, you don't need to try to squash them together somehow.

It's fine to have that addition sign in your answer.

These ones here with representations.

Hopefully you managed to draw these out.

And then with our final pyramid, there were loads and loads of different solutions that we could have had.

So actually we've written this algebraically here because we can have any number for a and any number for b, as long as they add together to make four.

You may have noticed that as you were trying things out and maybe you got a few more different solutions.

So actually there's infinitely many possibilities for this because we just need two numbers that add together to make four.

We can go into decimals, fractions, etc.

, negatives.

It's interesting that four.

it is four and the reason that is, is because you'll notice that when we've got a three here, were going to have two three's here, which means were going to have these two adding up to make something add six.

And that missing something has got to be four.

four add six makes 10.

So a and b must equal to four.

Amazing job again.

Today you've done really, really, well.

This is quite new for some people I'm sure, algebra can look a little bit intimidating, but hopefully you're seeing that it can be quite simple.

So, really, really, well done today.

And make sure you complete your quiz at the end.

Well done.

See you next time.