Lesson video

Hi, everyone.

It's me again, Ms. Jones.

And today we are looking at Inequalities.

Inequalities, that sounds similar to what we've looked at so far, maybe it's linked with equations, equality.

What do you think inequality means? And where do you think it comes up? That's what we'll be looking at today.

But before we do, please make sure you have a pen and some paper.

You have a nice quiet space to work, if you can find one and you remove all distractions away from you.

Pause now to make sure all of that is ready so that we can make start.

Okay, the first thing I would like you to do is to tell me, which of the cards below could you place in the inequality? So inequality is essentially just not equal, isn't it? So here it says zero is.

And this means less than something subtract something.

And that's what you need to fit in using these cards here.

So zero is less than something subtract something.

Which ones, which of those cards, and which of those integers are going to work in this inequality here? Pause the video to have a go at that.

If for example, there were loads you could have had, you could have had just starting with 12, we could have had all of these 12 subtract one, 12 subtract negative three.

All of those would be greater than zero, and there are loads of others you could have got.

So really well done for getting lots of those.

We can use greater than, and less than, to express an inequality.

You can draw bar models to demonstrate an inequality involving positive numbers.

Here, this model is showing us that five is less n, 'cause we can see is smaller than, and we don't know how much more than, but we know it's smaller than some where somehow that end, which inequalities can you see in this image here? So we see in this image, the equations, which inequalities can you see? However, Xavier can see that P, which remember is that purple one is greater than three w's.

And if you almost draw that little line up there, you can see that those three w's are less than p.

Have a go at creating some other inequalities, pause the video to do that.

But then there were loads that you could have got.

So for example, we've got p is greater than g.

Which we've demonstrated with this bar model here.

You've got g is greater than w and you've got g, green add 2w is less than 3r.

If you want something a little bit more complex, and there's loads you could have got, you could have written an endless string of algebraic terms. That's brilliant, well done for those.

Pause the video now to complete your independent task.

For your independent task, the first question asks you to just get used to the using these different symbols.

And you can see, we have got an equal sign as well as are greater than, or less than.

For question number two, you needed to write an algebraic inequality from the description.

So n is greater than negative three, again, we're just practising using our inequality symbols.

Then we were asked to take the inequalities that are true when a equals four.

So we need to substitute in, a equals four here.

Remember 2a would not be 24.

It would be two lots of four, which is eight.

So actually this symbol should have been an equal sign to improve it.

So that one was not in accord.

That was not true, when an a equals four.

Here are your answers.

Really well done if you've got all of those correct, or even some of those correct, great job.

Finally for our explore task, we have three facts up here, a equals four, b equals two and c equals nine.

Given that those are the values of a, b and c, which of the following inequalities are true? Is it true? That 2a is greater than c.

The ac is less than 17b and I'll let you read the rest of them.

So I don't give away what the symbols mean.

Once you have answered that question about which are true.

Create your own examples of true inequalities.

Pause the video here to have a go at that.

.

So, actually none of those were true, really well done if you've got that.

two lots of a be eight, which has in fact less than c, which was nine.

Ac means, remember a multiplied by c, so four lots of night, it was greater than 17 lots of b or two.

b subtract c got us negative two, which is not greater than three lots of four.

a squared got us a 16 and b to the power four also got us to 16, so those two were equal.

Remember b to the power of four does not mean be multiplied by four, it means b multiply by b, multiply by b, multiply by b.

Absolutely loads of examples of true inequalities, here are just some I created, a squared is less than c squared, negative b is greater than negative c.

So extra points and extra well done done, if you use some negative or even some decimals and fractions, that really good job.

Hopefully you now have a really good understanding of what inequalities are and how we can use them, especially with algebraic terms. Remember to complete your quiz at the end of this lesson and an amazing job, well done.