Lesson video

Hi, I'm Miss.

Kidd-Rossiter, and I'm going to be taking today's lesson on density as rate.

Before we get started, please make sure you're in a nice, quiet place, free from any distractions, and that you've got something to write with and something to write on.

If you need to pause the video now to get any of that sorted, then please do.

If not, let's get going.

So, on your screen, you've got a graph that's telling us something about honey.

On the X-axis, we've got litres.

On the Y-axis, we've got kilogrammes.

Pause the video now and think about what is the graph telling us about honey? And what rate can you see here? Pause now.

Excellent, what did you think? What does kilogrammes measure? What does litres measure? What is the graph telling us? Let's talk about it together.

Well, the first thing that we need to understand is what kilogrammes and litres are representing.

So, kilogrammes is mass, okay? So, kilogrammes is mass, and when people talk about how much they weigh, what they're talking about is their mass there, okay? And litres is a measure of capacity.

So that's how much of something can fit somewhere.

So, a water bottle might have a capacity of one litre or two litres.

From the graph, we can see that five litres of honey has a mass of seven kilogrammes.

So, five litres of honey has a mass of seven kilogrammes.

What does that mean? What's our rate here then? So, can we work out what one litre would be? So, five litres has a mass of seven kilogrammes.

What would one litre have a mass of? Pause the video now and think about that.

Excellent, it would be seven divided by five, wouldn't it? Kilogrammes.

So, one litre is 7/5 of a kilogramme, or we could say one litre is 1.

4 kilogrammes.

So, this is what we call the density.

So we use the word density to describe the mass of a substance per, for example, litre.

So that's what density is.

So, we can see here, that the density is the constant of proportionality, and the density is the rate here.

So, the rate of kilogrammes per litre.

So, our rate is 1.

4 kilogrammes per litre.

You're now going to apply your learning to the independent task.

So, pause the video here, navigate to the independent task, and when you're ready to go through the answers, resume the video.

Good luck! Well done on that independent task.

Let's go through some of the answers.

So, what is the mass of two litres of fruit juice? So, if we read up from our X-axis and then across, we can see that the mass is eight kilogrammes.

So, let's draw ourselves a little table where we have litres and then kilogrammes.

We know that eight kilogrammes is two litres, so that must mean that one litre is how many kilogrammes? Excellent, four.

So, we can see here that our constant of proportionality is four, so that means that our density must be four kilogrammes per litre.

How many litres of fruit juice have a mass of nine kilogrammes? So, we know if we're going this way, we multiply by four.

So if we're going in the opposite way, we can either times by the reciprocal, which is 1/4, or divide by four.

They're equivalent calculations, aren't they? So, that gives us 9/4, which is 2.

25 litres.

If you left it as 9/4, that's absolutely fine as well.

And then finally, how many litres of fruit juice have a mass of 50 kilogrammes? So again, we multiply by the quarter or divide by four, so 50/4 gives us 12.

5 litres.

It's fun then.

10 litres of sparkling water have a mass of nine kilogrammes.

So, let's draw our table again, litres and kilogrammes.

We've got 10 and nine, so that means that this way, our constant of proportionality or our density is 9/10, so the density of sparkling water will be 0.

9 or 9/10 kilogrammes per litre.

How many litres of sparkling water have a mass of five kilogrammes? So, if we're going back the other way, we'd be multiplying by 10/9, which will give us 50/9, which is equivalent to 5.

5 recurring litres.

And then finally, what is the mass of 200 litres of sparkling water? Well, we're multiplying by 9/10, so that gives us 180 kilogrammes.

Use the previous two graphs to help with this section.

So, 10 litres of sparkling water are mixed with one litre of fruit juice.

So all together, we've got how many litres then? Excellent, 11 litres.

And if the mass of 10 litres of sparkling water is nine kilogrammes, and the mass of one litre of fruit juice is four kilogrammes, what's the mass of the total mixture? Excellent, 13 kilogrammes.

So, we've just worked out that one, haven't we? So that's the answer to that.

What's the density of the mixture? So, I'm just going to do this one up here, where I've got a little bit more room.

Density.

Then we know, we draw our table, litres and kilogrammes.

11 litres is 13 kilogrammes, so that means that we must multiply by 13/11, so that means that our density must be 13/11 kilogrammes per litre, which is equivalent to 1.

18 recurring kilogrammes per litre.

So we know that for every 11 litres, we have 13 kilogrammes.

So, hopefully you've managed to do this really accurately on your graph.

So, I know that for 11 litres, I've got 13 kilogrammes.

That means for 22 litres, I must have 26 kilogrammes.

Which means for 44 litres, I must have 52 kilogrammes.

For 66 litres, I must have 78 kilogrammes.

And so on.

Then you will have drawn with a ruler, a line that goes through these points, a straight line that goes through these points all the way through to zero.

But like I say, yours will be done with a ruler.

A little task then.

How many different sentences can you write to compare densities of vegetable oil, water, and honey? If you're happy to give this a go, pause the video now and get going.

If you need a little bit of support, there's some sentence starters here to help you out.

So, pause the video now and give this task a go.

Excellent.

There were so many different responses here, so I'm sure that you've written loads down.

If you're really interested in this topic, it might be good for you to go and research and draw some of your own graphs to represent density.

That's the end of today's lesson, so thank you very much for all your hard work.

I hope you've enjoyed it.

Don't forget to go and take the end of the lesson quiz so that you can show me what you've learned, and hopefully I'll see you again soon.

Bye!.