Lesson video

Hi there, my name is Mr. Tilston.

I'm a teacher.

It's really lovely to meet you and it's lovely to work with you today on this lesson, which is all about unit conversions.

Unit conversions are really important and they're something you're going to come across a lot in your life.

For example, last night I was cooking dinner for my family and I had one kilogramme of chicken, but the recipe asked for grammes, so I had to use a unit conversion.

Today's lesson specifically will focus on graphs and charts.

So if you're ready, I'm ready.

Let's begin.

The outcome of today's lesson is I can use knowledge of measure conversions to interpret graphs and tables.

As always, we've got some keywords.

My turn bar graph or bar graph you might like to say.

Your turn.

My turn, interval.

Your turn.

What do those words mean? Let's have a reminder.

A bar graph is a graph drawn using rectangular bars to show how large each value is.

The bars can be horizontal or vertical, and we've got an example there and that has got vertical bars.

An interval is what is in between two values or points.

On a bar graph these may be marked, and you can see there the two interval is marked or unmarked, and you can see some unmarked intervals there in between zero and one.

Our lesson today is split into two cycles.

The first will be interpreting graphs and tables, and the second will be solving problems. So if you're ready, let's begin by interpreting graphs and tables.

In this lesson, you're going to meet Andeep.

Have you met him before? He's here today to give us a helping hand with the maths.

This table shows how much food is required for dogs of different masses.

So let's have a little look at the table.

How many columns can you see? I can see three columns.

One column says mass of dog.

One column says food intake daily, and another column says food intake weekly.

So we've got three columns with three different bits of information.

Let's see if you are good at interpreting that table and reading it.

What is the daily amount of food needed for a dog with a mass of around five kilogrammes? So which column do you think we'll need to look at first? We're trying to find a dog with a mass of five kilogrammes, but it's going to be the first column.

And you can see we've got some different dog masses.

Two, five, 10, 20, 50.

We want the five kilogramme ones in this case and that's that.

So we follow along from there and the question asked, what is the daily amount? Not weekly, daily.

So the column that we need now is the food intake daily.

So we'll go along from the five kilogramme row and we come down from the food intake daily column.

And that gives us this value 100 grammes.

So a dog with a mass of five kilogrammes needs 100 grammes of food each day.

Do you think you got that? Should we try another one? If a dog has a mass of approximately, so around about 20 kilogrammes might be a bit more, might be a bit less.

It's about 20 kilogrammes.

How much food does it need per week? Right again, think about which column we need, which row are we going to come from this time, the 20 kilogrammes.

Now this time it asked per week.

So which column are we going to come down from? The last one.

So the value that we've got there, a 20 kilogramme dog needs 1,750 grammes of food each week.

Should we try one more? Let's mix it up a little bit.

Let's go the other way around.

What is the mass of the dog if it needs 1,260 grammes of food per week, right? What can we do this time do you think? Well, we can look at the weekly food intake column and we can go down to 1,260.

That's what he was asking us.

And then we can come across from that to find out what the mass of that dog is.

And that is 10 kilogrammes.

It's time for a check for understanding what is the suggested daily food intake.

So that's daily food intake for a dog with a mass of around 20 kilogrammes.

Pause the video and give that a go.

Did you manage to do that? Well, let's have a look.

So we want daily and we want 20 kilogrammes and they meet just here.

So that's 250 grammes.

Well done, if you've got that.

Now we've got a graph, a bar graph.

This bar graph shows the heights of different dog breeds.

Now it's missing a bar, it's missing the Dalmatian bar.

We're going to include that later on.

So let's have a look at the graph.

We've got an x-axis that's going up in hundreds.

Wonder what the hundreds could be.

And then we've got a y-axis that's got the dog breeds.

So there's a type of dog, and this is height in millimetres.

Now what do you notice about the bars? Have a go look at the bars, look at the position of the bars, anything at all that you notice? Well, something I notice is that this look at the Chihuahua one, what could you say? The Chihuahua's height is an exact multiple of 100.

So it's easy to read.

Is that true of any of the other dog heights? Are they exact multiples of 100? No they're not.

The other heights are somewhere between the marked interval, so that's a marked interval.

The others are between the marked intervals as you can see.

So we must use estimation and reasoning to work them out.

It's a little bit more tricky.

What can you say about the Terrier's height? So there's a Terrier.

So we've come across from the Terrier and down to the height.

What could you say about that? Think about the position of that.

I think it's fairly easy to work out what the height could be because it's exactly halfway between 200 millimetres and 300 millimetres.

What's exactly halfway between those values? 250 millimetres.

That's the height of the Terrier.

Let's have a look at the Bulldogs height.

What could we say about that? Is that exactly halfway? No, it's not.

It's less than halfway in fact, between 300 millimetres and 400 millimetres.

So we could probably say it's more than 300 millimetres.

It definitely is in fact, and it's less than 350 millimetres going to be somewhere in between those values.

If the space between 300 millimetres and 400 millimetres were split into four equal parts, see if you can do that with your mind, can you visualise it? Can you imagine four equal parts of new intervals on there? It would take up one of them.

The Bulldog's height is approximately 325 millimetres because it would go 25, 50, 75, 100.

So let's do a little check for understanding, shall we? Can you estimate the height please of the Great Dane? Good luck.

Let's have a look at that Great Dane.

So it's the tallest of all the dogs on this gravel.

Let's have a look.

It's somewhere in between 700 and 800.

I would say it's exactly halfway between 700 and 800.

So I would say that's 750 millimetres.

Maybe a little more, maybe a little less, but I think we're definitely in the right neck of the woods if we say 750 millimetres.

So well done, if you said that or a value close to that.

We've got a different graph.

John has a West Highland White Terrier puppy.

Have you ever seen one of those? Maybe you've even got one of those.

So this is Snowy.

and this graph is showing the mass of Snowy from birth to two months.

What do you notice? Have a good look at the graph.

The first thing I notice is that the axis aren't labelled.

He's been tracking her mass since birth using a bar graph.

How could we label those axis? What do you think? What could the zero one and two mean on the y-axis? What could the zero one and two mean on the x-axis? They mean different things.

Let's have a look.

So this zero one and two is the month.

So zero is the month that she was born in.

And then we've got one month and two months.

And this is the mass in kilogrammes.

So we're going up to two kilogrammes.

What do you notice about the intervals on the y-axis showing them mass? What sorts of things can you see there? I can see we've got some marked intervals.

Zero, one and two.

I can see we've got some unmarked intervals as well.

Is there anything you notice about the unmarked intervals? There are 10 equal parts between zero and one, and the same number of equal parts between one and two.

So 10 between those two.

You might have had some recent experience at looking at 10 equal parts.

What could each of those parts be worth? So what is one kilogramme split into 10 equal parts? Do you know a useful unit conversion that might make that a bit easier? Well, each unmarked interval is worth 100 grammes because 1,000 split into 10 equal parts is 100 for each part, 100 grammes.

So now we know that, what was her maths at birth? So remember the zero is the birth month coming across from zero.

So we're going up in 100s.

What can you see there? 100, 200, that's 200 grammes.

What about her mass at one month? So again, we're going to come across from the bar for one month.

And if you've got a ruler when you are doing this, that's my top tip.

Use a ruler to form that straight line.

Now I'm not going to count 100, 200, I'm going to go 100 less than one kilogramme or 1,000 grammes, which is 900 grammes.

What's about at two months? So let's do a line coming across from the two month bar.

I think there's two different ways you could say this.

I think you could say it in grammes and in kilogrammes and grammes.

So we could say it's 1,800 grammes because one kilogramme is 1000 grammes, two kilogrammes is 2,000 grammes and it's 200 grammes less than that.

So we could say that.

Or it's gone past one kilogrammes.

So it's one kilogramme something and it's an extra 800 grammes.

So it's one kilogramme 800 grammes and they're both perfectly acceptable.

This graph is similar in some ways and different in others.

So I wonder if you could spot what's the same and what's different.

This it is a graph about Andeep's dog.

He's got a Cavalier King Charles Spaniel.

Have you seen one of those before? Very cute.

So let's have a look.

Do you notice anything the same, anything different? I've noticed that the same is the same number of months.

So it's got the same x-axis and the same, it's showing the mass in kilogrammes, but something different.

Look at the unmarked intervals.

What do you notice? Are they split into 10 equal parts this time? No they're not.

How many equal parts can you see? Can you count them? The scale's definitely different.

This time there are five equal parts between zero and one, and the same number between one and two.

So five equal parts.

So we're splitting that one kilogramme or 1,000 grammes into five equal parts.

What would each one be worth? What's one kilogramme split into five equal parts? That's 200 grammes.

So each unmarked interval is worth 200 grammes.

So we could count up in steps of 200 grammes.

So what was a mass at birth? So that's zero a month.

Let's go across from that bar using that horizontal line.

What have we got? So remember we are counting in steps of 200.

200, 400, 600.

That's 600 grammes.

What was a mass at one month? What do you think? Let's have a look.

Let's create the bar, the horizontal bar.

So it's gone over one kilogramme or you could say it's gone over 1,000 grammes.

So I think we've got two ways that we could say this in grammes and in kilogrammes in grammes.

So we could say it's 1,200 grammes and it's gone past one kilogramme.

It's one kilogramme 200 grammes, both perfectly fine.

Let's do a quick check for understanding.

Let's see if you are on track.

Same graph, what was her mass at two months? Can you say it in two different ways? Pause the video and have a go.

Let's have a look.

Well, each interval was worth 200 grammes and 200 grammes less than 2000 grammes, which is two kilogrammes is 1,800 grammes.

So you could have said that or you could have said one kilogramme, 800 grammes.

Well done, if you got that.

It's time for some independent practise.

So we've got a graph here, a bar graph.

Have a good look at it before you start, make sense of it.

And then you've got some questions.

So number one A, which dog is taller? Bulldog or Terrier? B, what's the height of the Cockapoo? And C, the Dalmatians height, that missing bar is 550 millimetres.

Can you draw a bar to show this? Use a ruler for that.

A ruler is really handy for this task.

Number two A, give the mass of the Cockapoo at each age in months.

So this is showing the massive Cockapoo newborn one month, two months, and three months.

And then B, at four months a Cockapoo has a massive of 2,750 grammes.

Can you draw a bar to show this? And a little tip, think about what each unmarked interval is worth.

So look at the space between zero and one.

How many equal parts can you see? And therefore what's each unmarked interval is worth? That will help with that.

Alright, very best of luck and I'll see you soon.

Welcome back.

How did you get on and would you like some feedback? Let's have a look.

So which dog's taller Bulldog or Terrier? Well, that's the difference between the Bulldog and the Terrier.

So the Bulldog's slightly taller than the Terrier because the bar's longer.

The height of the Cockapoo, we go to draw a bar coming down from the Cockapoo and that's where it is.

Now I can picture that being split into four equal parts between 300 and 400, making each part worth 25 millimetres.

So I would say that's approximately 375 millimetres.

You might have got little more or less than that and that's fine too, but something around that.

The Dalmatians height is 550 millimetres.

Draw a bar to show this.

Let's do that.

So here we go.

So that bar needs to be halfway between 500 millimetres and 600 millimetres.

So it needs to look just like that.

Well done if you got that.

And let's have a look at the next one.

So one kilogramme has been partitioned into four parts.

So each part is worth 250 grammes here.

So the newborn's 750 grammes.

At one month it's 1,250 grammes.

And you might have said one kilogramme, 250 grammes.

At two months, 1,750 grammes or one kilogrammes, 750 grammes.

And at three months, 2,500 grammes or two kilogrammes, 500 grammes.

So we counted in 250.

And here's our bar to show 2,750 grammes or two kilogrammes, 750 grammes.

Let's move on to the next cycle, which is solving problems. Are you ready? So we've got that same table again from before.

And a question, is a one kilogramme bag of dog food enough to feed a dog with a massive 10 kilogrammes for a week? Okay, so what information do you think we need to get first from this table? A dog with a mass of 10 kilogrammes.

How much food do they need per week? Well, let's go across from the 10 kilogrammes that tells us how much food they need per week.

That's 1,260 grammes.

Is that more than a kilogramme or less than a kilogramme or one kilogramme equals 1,000 grammes.

And I bet you knew that already.

And 1,000 grammes is less than 1,260 grammes.

So it's actually not enough for a dog of that mass.

They need a little bit more.

Let's have a little check.

How much food should a five kilogramme dog eat in five days? So in this case, you need to get some information from the table and then do something to that information.

Have a really good think about it and off you go.

Let's have a look.

So that's a five kilogramme dog.

So in one day they eat 100 grammes, but that's not what it was asking.

It was asking five days.

So what do you need to do for that 100 grammes, do you think? Times it by five or add it five times and that will give you 500 grammes.

That's how much they need in five days.

Well done, if you got that.

Okay, let's have a look at this chart again, this bar graph.

So this is a height of dogs in millimetres.

And the question is, which dogs have a height under 300 millimetres? Which ones do you think? Because some are over that and some are under that.

Let's have a look.

Which ones are under though? That's a question.

Well, a good start would be to draw a line coming up from the 300 millimetres and that's split the bar graph into two parts.

You can see then we can see some bars are shorter than that and some are longer than that.

And the Chihuahua and Terrier bars are shorter than that.

So they've got a height of under 300 millimetres.

What about this question? Which dogs have a height between 300 millimetres and 500 millimetres? What could I do to make that question a bit easier? What did I do last time? Well, I could draw another line, couldn't I? Coming up from what this time? 500 millimetres.

So there we go.

And the question was, which ones, which bars fall between those? Can you see? I can see two.

I can see the Bulldog and the Cockapoo where they've got a height between 305 millimetres.

And the last question, which dogs have a height greater than 500 millimetres? Well, I've already got my 500 millimetre line drawn, I just need to see which ones are longer than that and I can see two again, can you see them? Dalmatian and Great Dane.

Let's have another question.

By how much does the Terrier's mass increase between birth and one month? So what do you think we could do to work this one out? What information do we need to start with? Well, we need the mass of the Terrier at birth.

Can you see what that is? At birth she has a mass of 200 grammes.

What else do we need? What other piece of information? The mass at one month.

What's that said? It is 100 grammes less than one kilogramme, which is 900 grammes.

Now we've got two numbers, two values, we've got 200 grammes and 900 grammes.

And the question was how much does the Terrier's mass increase? What could we do with those two numbers? Need to find the difference between them.

You could do that in two ways, I think.

You could work out the difference by counting the unmarked intervals on the chart in steps of 100.

That's one way to do it.

It would take a little bit of time.

It's quicker and more efficient to work out the difference between 200 grammes and 900 grammes.

You could think 200 grammes plus something equals 900 grammes.

So what do you add to 200 to make 900? And I'm using my knowledge of what you would add to two to make nine to help me with that one.

That's 700 grammes.

Alternatively, you could have done a subtraction.

By how much does a Terrier's mass increase between one month and two months? Well, we've already got the one month value, haven't we? We need to find the two month value and then we need to work out the difference once again between those two.

So let's have a look.

This time then we've got 900 grammes plus something equals one kilogramme, 800 grammes.

I think we could do something to that one kilogramme 800 grammes to make that a little bit simpler, little bit more straightforward.

What could we do? We could convert it.

So now the question is 900 grammes plus something equals 1,800 grammes or 1,800 grammes.

Now again, you could use your knowledge of what you add to nine to make 18 to help with this one.

But there are other ways to do it as well.

We could use bridging.

So we've gone from 900 grammes to one kilogramme.

We're bridging through, we're partitioning that number, so that's 100 grammes, and then another 800 grammes takes us to 900 grammes.

So two different ways of working that one out.

But either way it's 900 grammes.

Let's have a check for understanding by how much does the Spaniels' mass increase between birth and two months? Have a go at that one.

Did you get the answer? Let's have a look.

Well, that's birth.

Now this time it's split into one, two, three, four, five equal parts.

So therefore each unmarked interval is worth 200 grammes.

So we could go 200, 400, 600.

At birth she's got a mass of 600 grammes.

And then at two months, well, it's 200 less than two or 2000, that's 1,800.

So we're looking at the difference.

You could count, you could go 200, 400 till you get there.

That will get you there.

It would take a little bit of time or you could do a little calculation.

You look into work out the difference between 600 grammes and 1,800 grammes or 600 grammes and 1800 grammes.

If you want to think of it that way.

Think about the difference between six and 18.

Or you could use bridging.

So we've got to find that difference.

Let's have a look at what bridging would look like.

So we're going up to the one kilogramme and then from the one kilogramme.

So from that bar to one kilogrammes is 400 grammes, then another 800 grammes takes us here.

Add them together.

And we've got 1,200 grammes.

Very well done, if you've got that.

You are on track.

Let's see how you get on with this.

Use the table to answer the following questions.

So we've got the same table from before.

We've got some questions.

And here are those five questions.

And we've got some questions about this bar graph.

Use the first bar graph to answer the following questions.

And we've got some questions here.

And number three, use a second bar graph to work out at what age in months, a Cockapoo's mass is above 2000 grammes? And then we've got some more questions about the Cockapoo's mass and how it increases over different periods of time.

In the final question, between four months and five months, a Cockapoo's mass increases by 750 grammes.

Draw a bar to show this.

Good luck with all that and I'll see you soon for some feedback.

Welcome back.

Let's have some answers.

So number one, that's less because 1,750 grammes is less than 2000 grammes.

B, 250 grammes multiplied by four is 1,000 grammes or one kilogramme.

C, 100 grammes plus 150 grammes.

That's the answer we're looking for equals 250 grammes.

D, you need to add 350 grammes to 100 grammes to make 450 grammes.

And E, it's very close to 250 grammes.

So either that much or maybe just a little tiny bit more.

And number two, that's 200 millimetres.

That's a difference.

B, you need to add another 175 millimetres.

So that's a difference.

And C, the difference is 370 millimetres.

So that's how much it's likely to grow.

And for number three, 2,000 grammes equals two kilogrammes.

So the bars at three months and four months are above two kilogrammes.

And then number four A, that's 500 grammes, B, 500 grammes, C, 750 grammes, D, 250 grammes.

And then the difference between birth and four months is 2,000 grammes.

And then the bar showing this increase would look just like this.

So well done if you got it in that position.

We've come to the end of the lesson.

Today's lesson has been using knowledge of measure conversions to interpret graphs and tables.

Information relating to measures such as length and mass can be presented in the form of tables or graphs just as it has been today.

Sometimes the marked intervals on a graph are split into two, four, five, or 10 equal parts and they become unmarked intervals.

The value of these can be determined by applying our knowledge of composition to 1,000.

I'm sure that by now you're getting really good at that.

I'm really confident.

It can be helpful to know some useful unit conversions such as one kilogramme equals 1,000 grammes to interpret the graphs and solve related problems. And if you know those unit conversions off by heart, you can recall them instantly, all the better.

You'll be all the better at solving that problem.

Well done on your achievements today.

Give yourself a little pat on the back.

You've been amazing.

I hope you've enjoyed the lesson.

I certainly have.

And I'm sure you've made lots of wonderful progress.

I really hope I get the chance to spend some more time with you in the near future doing another maths lesson.

Plus until then, enjoy the rest of your day.

Take care and goodbye.