Lesson video

Hi everyone, It's Ms. Jones here.

And welcome to today's lesson on shading regions to satisfy a set of inequalities.

So it's building upon what we've looked at in the previous lesson around inequalities and how to plot them and solve them on a graph.

Before we begin however, please make sure that you have a pencil and some paper, you remove any distractions from around you and you try and find a quiet space to work.

Please pause the video now to make sure you've got all of that ready to go.

Now you have all of that ready, let's start.

So the first question is asking you to sketch the following lines.

So when we say sketch, the reason that's in bold is you don't have to plot it exactly on graph paper, or on a really strict set of accurate axes, it's as a sketch.

It still needs to be accurate but, less so.

Once you've sketched all three of these equations, I would like you to tell me what shape is bound by the three lines.

I would also then like you to try and create another set of lines that the forms the same shape, but in a different position.

So if you think that might be a bit challenging, maybe try a shape that is the same type of shape, but a different size or different orientation.

But if you want a challenge, try and make exactly the same size shape, that would be brilliant.

Pause the video to have a go at that.

This is what you should have found.

You should have found that it makes a triangle.

As I said, it didn't need to be quite as accurate as this.

If you just sketched it, you should have been able to see that we would have formed a triangle with those lines.

So really well done if you got that.

And amazing job if you managed to create some more equations of lines to form other triangles and even exactly the same triangle of the same size, well done.

Very good job.

How could we alter the equations to create this region? So just to make sure it's very clear that we're talking about this inside part here, what could we do with these equations? So if we take the first equation, y equals two, it's not underneath y equals two it's above y equals two.

So we could change this to an inequality to show we're talking about the part above y equals two.

So y is greater than or equal to two.

And that's going to show us everything above that line, but we've still got these other two parts to show as well.

So if we take the next one, of x equals negative three, now you have a good, how could we change that to make it clear that we're talking about this side of x equals negative three.

Hopefully you said x greater than or equal to negative three, that shows it's this side, which is the side that has the triangle in.

And finally slightly trickier.

What about x add y equals five.

What can we do to change that? To make it clear we're looking at everything this side of x add y equals five.

Hopefully you said that we're going to use that inequality so x add y is less than or equal to five.

You can think about that.

That second one, that third one sorry is slightly trickier, and it also does help to think about the rearrangement of that.

So x is less than or equal to negative x, add five.

So we're looking for all of the y values underneath this line.

This line is y equals negative x add five, and we want all the y values underneath it.

So we're going to be less than or equal to negative x add five.

Well done if you managed to get those ones.

Can you now pause the video please, to complete your independent task, which I'll be showing on the next slide.

So the first question is asking to draw the following inequalities on a set of axes.

So you've been asked to draw x is greater than or equal to negative one.

So you need to find on your axes x equals negative one, and then it's everything that's larger than that.

So all the x values are larger than that.

So that's what you should have shaded it, and it should look something like this.

We then had x add y is greater than two.

So again, it's quite often easiest to rearrange these into a form you're used to, like y equals mx plus c.

Remember that inequality sign.

So you're drawing y is equals to negative x add two as a line, and then shading in everything that's above that because the y value is greater than negative x add two.

Then we've got y is less than or equal to six, which is a nice simple one.

And then you've got y subtracts to x is less than one, which we can again rearrange to y is less than x add one, to make it easier for us to draw.

So y is negative x add one.

And then it's all the y values underneath it, so we shade underneath it.

Then we are asked to do similar but in reverse.

So what inequalities are drawn on the following graphs.

Remember those dotted lines, and well done if you did the dotted lines and the full lines correctly for question one.

You've got a dotted line here, which means it's just going to be less than or greater than.

And we are looking at the y values, 'cause it's all the x values, but it's specifically the y values that less than four.

Here is the x values that are greater than or equal to negative one.

Actually it matched up with that one there, well done if you noticed that.

The third one, again we're going to have to find the equation of this line.

So we should know that this is, y equals, you can see the gradient is negative one, so it's negative x and it's going through negative two.

So we could either write y is and it's going to be all the y values greater than 'cause it's above it, greater than negative x subtract two.

Or we could have rearranged that to be y add x is greater than negative two, which we can see.

And similarly for the other two.

So check your answers, and really well done if you managed to get at least some of them correct.

and extra well done if you managed to get most of them and or all of them correct, using the dotted lines and the full lines and recognising which way that inequality sign is going to go.

'Cause that sometimes tricks some people.

So really well done for that.

The final task is your explore task.

Similarly to the try this task, that we saw some equations and we changed those into inequalities in the connect task that formed shapes.

I would like you to try and do the same yourself.

So can you form or create sets of inequalities to form the following shapes, a rectangle, a triangle, a trapezium, and a parallelogram.

And if you want to be creative, what other shapes can you make? Pause the video now to have a go at that.

So hopefully you managed to create all of these shapes.

You've probably noticed that for a rectangle.

I'm sure a lot of you actually just used horizontal and vertical lines.

So y is less than or greater than something, and x is less than or greater than something.

Well done if you managed to do one that's a little bit on its side, that's brilliant well done.

The triangle we did quite a few in the try this, the trapezium we needed to make sure.

And hopefully you notice with the gradients that we had two parallel lines.

With the parallelogram, we needed to have two sets of parallel lines, two pairs of parallel lines.

So really well done if you've noticed those extra bits as well.

Well done if you managed to create any extra shapes, that's absolutely brilliant.

And I really look forward to seeing them.

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

You've done absolutely brilliantly today.

So a massive well done from me.

And I'll see you next time.