Lesson video

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Hey everyone, Ms. Jones here.

And today we are going to be looking at inequalities but in even more detail, especially in an algebra context, which I'm really looking forward to.

But before we can start, please again, make sure that you've got a pen and some paper as well as removing all distractions and making sure you have a nice quiet space to work if you can find one.

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

Okay, the first thing we are going to do is have a look at what's on the screen now.

A student looked at a bar model drawn to represent.

what does that say? Good N is greater than three.

So we can see here that we've got N and its clearly greater than three and that's why it's been drawn that way.

This person here is saying that they think that N is less than six.

I would like you to have a think about whether that student is correct, is N less than six? I would also let you think about how else the bar model could have been drawn to show that N is greater than three? Give some examples and some non-examples.

So where non-example would be if we had three here? Then obviously you'd be drawing this with a nice ruler and you had N here Again, if you were drawing this with a nice ruler, not like me.

And that's a non-example because N clearly isn't greater than three here.

So have a go at all three of those things and pause the video to do that now.

So from the way that that bar model has been drawn, it appears that we can deduce the N is less than six, because three was here and N was here and it looks like if we were to add on another three to make the six, it looks like N is less than six.

However, the key information that we were given was that N is greater than three, and that's why it was drawn like it was.

The proportions are not important only that we've got N larger than three.

So if N is greater than three, sometimes that means that N is greater than six.

Sometimes it could mean that N equal six and sometimes it means, that N indeed is it less than six.

But essentially that pink bar or whenever we've got an algebraic term being represented by a bar, it should be visualised as being allowed to vary.

So your examples could, you could have drawn three here and you could have drawn N all the way out here to show the N is greater than three.

And that doesn't mean that N is less than six necessarily, you just need to make sure.

You imagine that pink bar being as big or as small as you want it, as long as it meets the conditions in the original question.

Well then, if you got that.

You can use an established inequality to form a related inequality.

For example, if we know that N is a number where N is greater than three, we can deduce that N add five is greater than eight.

So if I was to add five, on to N, I would know if I did exactly the same thing here, that N add five is still greater than eight.

Two variables are related by the equation, Q equals three M.

So now we have an equation, but we are still looking at in a qualities related to that equation.

But the first thing I would like you to do is generate some examples of M and Q that satisfy that equation.

So make it true.

So, for example, if I decided that M equals three, for my example, Q would equal nine.

So that is an example of M and Q that satisfy that equation so come up with some more examples.

When you have done that, I would like you to decide whether these two statements here are always true, sometimes true or absolutely never true, no matter what number you choose or value you choose.

So pause the video, to have a go at those two questions there.

So here are some examples of what Q and M could be, well done if you've got any of those and if you've got any extra ones, brilliant, especially well done if you use decimals, fractions and negatives to get some answers there.

Follow these two statements, Q add one will always be greater than the three M if I add one onto Q, so if I made this 10 now that is greater than three M which is not.

So if you add one onto this side, it's always going to make it larger.

So it makes it therefore larger than three M.

This one however, is never true.

If I subtract two from three M, that is now smaller than it was, and it is now smaller than Q.

So actually if you change that inequality sign to that way around, it would be always true.

So that's what I want to remember, that if you add a positive integer on something is always going to increase and if you subtract a positive integer for something it's always going to decrease.

Really well done, if you got those right.

Pause the video now to complete your independent task.

So for the first question you were asked to tick the inequalities that are true when A equals three and B equals negative three.

So we're just using some substitution here.

So for example, for the first one, I will substitute in three here add negative three, Which actually equals zero, which is not greater than one, so that's not true.

The question two, it says, given that X equals three Y, add in the correct symbol equals, greater than or less than into the following.

So if I have X add one, is that greater than, less than or equal to three Y? What if I've added one to this that makes it larger, so it's going to make it larger than three Y.

Well done if you've got that correct.

As another example, let's have a look at C, says three Y is something X subtract one.

Similarly, if I was just subtract one to this one, it makes it smaller.

So three Y is going to be greater than X, subtract one.

Well done, if you got those right.

And here are the rest of your answers, really good job with that.

Finally, for the explore task, use the cards to form inequalities that are always true.

So you're given the equation that A equals B, add two.

I would like to know, what is always going to be greater than what? So for example, A, add one is always going to be greater than A, that's quite a nice and easy one.

See if you can use A's and B's in the same inequality.

Pause the video to have a go at that.

So there are a lot that you could have chosen from using any two of these.

So, you know, that A add one is always going to be greater than A, which is greater than A subtract one and it forms a nice pattern there.

Similarly, with the B's.

Now you can see here that we've got a bit of a combination, A add one is greater than B add two because A equals B add two, so A add one is going to be greater than B add two.

And there were loads you could have chose, you could have chosen from.

So really, really well done, if you've got any of those, maybe if you even got any extra ones, I don't think there were any but really good job today.

And that brings us to the end of this lesson.

Make sure you complete your quiz.

And I hope you've had a really fun time 'cause I have.

See you next time.