Lesson video

Hello, my name is Dr.

Shorrock, I am really happy that you have chosen to do your math learning with me today.

We are gonna have a lot of fun as we deepen our understanding of all things maths.

Today's learning is from our unit, measuring length and recording in tables.

The lesson is called Use Graphs to Represent Lengths and Heights.

And we are going to deepen your understanding of how we can represent lengths and heights on a graph.

We're gonna deepen your understanding of what a graph is and we're gonna use them then to solve problems. Now remember, sometimes new learning can be a little bit tricky, but I am here to guide you and if we work really hard together, I know we can be successful.

So what is a graph and how do we represent length and heights on them so that we can then solve the problem? Shall we find out? Our key words that we will be learning today are graph and axis.

Let's practise those words together, shall we? My turn, graph, your turn.

Fantastic.

My turn, axis, your turn.

Lovely.

So listen out for those words as we progress through our learning.

A graph may be new to you, but it's just a visual way of showing some information.

We are going to be looking at bar graphs today.

Sometimes you hear them called bar charts and you can see one represented here to give you an idea of what it is we will be looking at.

Our other key word is axis, and these are lines that run horizontally, so that's left to right, and vertically up from zero.

Let me show you an image.

So let's have a practise of this.

Show me horizontal.

Fantastic.

Show me vertical.

Brilliant.

So horizontal going across and vertical up and down.

And we are going to be using those words when we talk about the axis on our graphs throughout the lesson today.

Our lesson is all about using graphs to represent lengths and heights.

And we are going to start by representing lengths or heights on a bar graph.

We will then move on to solving problems related to a bar graph.

And these are the characters who are going to help us with our learning today.

We've got Izzy, Laura, Jacob, and Andeep.

Say hello.

This table shows the length of some objects that I have measured today.

In the first column, you will see the objects that I measured, a conker, a leaf, a pebble, and a twig.

In the second column, you can see the lengths that I measured them to be.

The conker was three centimetres, the leaf eight centimetres, the pebble five centimetres.

And yes, I know you've got it already, the twig was nine centimetres long.

We can represent this information that is presented here in this table as a bar graph.

And a bar graph is a way of making things really visual to help us interpret the information a lot easier.

This is an example of a bar graph for the data that we have collected in our table.

I wonder, what do you notice? Maybe pause the video, find someone to tell.

What do you notice about this bar graph? When you've told someone what you notice, press play.

Okay, what did you notice? Did you notice it's got a title there? Bar graph comparing the length of objects, the title's really important, it tells us what the graph is about.

Oh, look what Laura's noticed.

Laura has noticed that the objects are labelled on that vertical axis.

Can you see how it's got conker, leaf, pebble, twig? So the objects are there.

Ooh, what else has she noticed? That's right.

The length of the objects are labelled on the horizontal axis.

Can you see the length of the objects? Yes.

Ooh, Laura has also noticed and I wonder if you notice this, that the bar show the length of each object.

Can you see? Can you see the bar for conker goes across three and the length of the conker is three centimetres.

What about for the pebble? Can you see the length of that bar goes across five? And the length of the pebble was five centimetres.

What else can you tell from this graph do you think? Yeah, straight away you can tell what the longest object was 'cause it's got the longest bar, the twig.

Well done if you notice that.

Oh, Laura has noticed something that's also really important when we do a bar graph, she's noticed there are gaps between the bars.

Can you see they're not all together, are they? There are gaps between the bars and that's really important.

Did you also notice that the information in the table and the graph match, they are showing the same thing.

We've got the data in a table, but also we're showing it more visually on this bar graph.

Let's look at some different data, shall we? So today Laura found out the heights of some trees and recorded her findings in a table.

You can see there that she's found the height of the oak tree, a beech tree, an apple tree, a maple tree, and a cherry tree.

And she has recorded their heights.

So the oak tree was 20 metres, the beech tree was 30 metres.

I wonder if you can tell me how tall the apple tree was.

That's right, the apple tree was five metres.

The maple tree, 15 metres.

And what was the cherry tree? That's right.

The cherry tree was 10 metres tall.

So we can represent this information as a bar graph and make it more visual.

Here is my bar graph and you can see from my title it's a bar graph that compares the height of the trees.

Maybe pause the video and have a discussion with someone near you about what you noticed about this bar graph.

Think about what we noticed about the previous bar graph.

Can you notice the similar things? When you've told someone what you noticed, press play.

What did you notice? Did you notice that height is labelled on that vertical axis? So the height in metres.

Did you also notice like Laura, that the trees are on that horizontal axis? Did you notice that the bars represent the height of each object? And what do we notice about the numbers on the vertical axis? Jacob is asking us.

I've got 10, 20, 30.

What do you notice about those numbers? Yeah, they go up to 30 metres, which is the height of the tallest tree.

Did you spot that? The height of the tallest tree is 30 metres and my last number on my vertical axis is 30 metres.

It is the same and that's really important.

We need our vertical axis to go at least as high as the highest object.

Jacob has noticed the numbers on the vertical axis are increasing in tens and he's explaining is because the greatest value 30 metres is in the 10 times table.

And Jacob is letting us know that increasing in tens makes the data easier to draw and read.

So we've looked at two bar graphs so far and I've shown you both of them here.

Can you let me know what you notice about the bar graphs? And by that I mean what is the same about them and what is different about them? You might like to pause the video whilst you have a look and then press play.

Did you notice that bar graphs can have bars that are on horizontally or vertically? Did you notice that both bar graphs have gaps between their bars? Did you notice the numbers labelled on the horizontal axis of the first graph are increasing in ones? Whereas the numbers labelled on the vertical axis of the second graph are increasing in tens? And it is okay to increase in different amounts depending on the data that you are trying to represent.

Let's check your understanding.

This table shows how far different children hopped at break time.

I'd like you to use the data in the table to complete the sentence.

The maximum value needed for the numerical axis is hmm.

Press pause and when you've had chance to have a go, press play.

Okay, did you say the maximum value needed for the numerical axis is 45? Brilliant.

Well done.

Another question to check your understanding, to represent this data in a bar graph, what should the numbers labelled on the axis increase by? In ones, in fives, or in tens? Have a look at the data presented in the table and see what you think.

Can you spot anything about those numbers in the table? Are they in a particular times table? Have a look at the data, press pause, and when you're ready, press play.

Okay, did you suggest that representing this data in a bar graph, we should increase our axis in fives because all the numbers in the table are in the five times table.

Well done.

Okay, your turn to practise now.

Question one for Task A, I'd like you to complete the table and bar graph using the data given.

So there are some missing parts of the table and missing parts of the graph.

Use each of them to complete the other.

For the second question, I'd like you to use the data in the table, spot and circle the mistakes in the bar graph and then explain the mistakes.

Have a go at both questions and when you are ready to hear the answers, press play.

Okay, how did you get on? Should we have a look at how you completed the table and the bar graph? So hopefully you drew on those bars for the pencil for 10 centimetres and the pen for 15 centimetres.

You can see the eraser is five centimetres.

And the book, oh, there was no number on the axis for that, was there? We had to work that out.

That's right, it was 20 centimetres.

So the book is 20 centimetres.

How did you get on? Well done.

And for question two you're asked to spot the mistakes by circling them and then explain them.

So I made a mistake with the salmon, the carp, and the trout, and you were asked to explain the mistakes.

The salmon is 90 centimetres in the table, but 100 in the bar graph, the carp is 40 centimetres in the table, but 50 centimetres in the bar graph, the trout is 50 centimetres in the table, but 40 centimetres in the bar graph.

Well done if you spotted all my mistakes.

Let's move on to the second part of our learning.

We are going to look at solving problems related to a bar graph.

So we're gonna show you a bar graph and ask some questions about it and we're gonna use that bar graph to help us answer those questions.

So we can solve problems related to information that has been represented as a bar graph.

Let's look at this bar graph.

I tell you what, let's start with the title.

It's a very good place to start.

The title says bar graph comparing the lengths of objects.

So already that's telling us that this graph is going to show us some objects and how long they are.

So a title is a very good place to get some information from.

And Laura is asking what questions could we ask about this bar graph? Maybe you'd like to pause the video and see if you can find someone and come up with a question that you could ask about this bar graph.

Did you come up with any questions? We could ask, how long is the conker? Can you see a conker on the graph? Wonder how we can work out how long it is.

Hmm.

Ah, thank you, Laura.

Laura is saying we can use those bars to help us answer this.

Can you see we've drawn a line on at the end of the conker and all the way down to that numerical axis and we can see straight away how long that conker is.

The conker is three centimetres long.

Now let's check your understanding, which object is the longest in this graph? So again, let's read the title, bar graph comparing the length of objects.

Ah yes, we've just looked at this graph, but now we're being asked which object is the longest.

And Laura is reminding us to use the bars to help us.

So pause the video, have a go at working out which object is the longest, and when you are ready, press play.

Okay, did you notice that the twig is the longest? How did you know the twig was the longest? That's right, it's got the longest bar, so it had to be the longest object.

It's really nice, isn't it, when we see data presented in a bar graph, we can tell something straight away because it's so visual.

Here is another bar graph.

This is the bar graph comparing the heights of trees.

What do we notice? Hmm.

Maybe pause the video.

Tell someone what you notice about this graph.

Is there some question that you could answer by looking at this graph? Such as how tall is the apple tree? Can you see the apple tree on our bar graph? Yes, it's in the middle, isn't it? It's the third one along.

How can we work out how tall the apple tree is? Hmm, I've spotted something.

Have you? Yes.

Hmm, it's not quite as easy this one, is it? We can use the bars to help us, Laura is saying, and I'm gonna draw my line on and then what have we noticed? Yeah, it's not next to a number, is it? It's halfway between zero and 10.

We know that half of 10 is five.

So the apple tree is five metres tall.

Let's check your understanding then.

How tall is the maple tree? Let's have a look at the graph.

Still a bar graph comparing the height of trees.

Okay, and where is the maple tree? That's right, it's fourth along.

And I want you to use the bars to help you work out how tall the maple tree is.

You might like to work with someone if you've got someone near you, press pause, and when you've worked out how tall a maple tree is, press play.

How did you get on? Did you realise that the maple tree is halfway between 10 and 20, so it's 15 metres tall.

Well done.

We can also solve comparison problems using a bar graph.

So how much taller, how much longer, how much shorter, questions like that.

We can do that.

We can answer those by using a bar graph.

We might say, how much taller is the oak tree than the apple tree? So what do you notice here? It's always good to stop and think about questions.

I've noticed that it talks about an oak tree and an apple tree.

So I'm gonna have to use two bars to help me and I can see where the oak tree bar is and I can see where the apple tree bar is.

So those are the two bars that I'm going to be needing to focus on and Jacob is reminding us or helping us by saying we need to find the height of both trees and then we need to find the difference.

Why are we finding the difference? That's it, because we need to know how much taller one tree is than the other.

And to do that, we find the difference.

So the oak tree, that's quite straightforward, that's 20 metres tall.

Now we need to find the height of the apple tree.

And it's the shortest, it's got the shortest bar and the apple tree was between zero and 10 metres.

It was five metres tall.

So the oak tree is 20 metres, the apple tree is five metres.

So now we need to find how much taller the oak tree is than the apple tree.

And to find the difference between their heights, we need to subtract.

And Laura is doing that subtraction for us.

20 metres subtract five metres is equal to 15 metres.

So that tells us then that the oak tree is 15 metres taller than the apple tree.

So when we are doing comparison problems, we need to work out the heights of both trees and then subtract the smaller height from the larger height.

So let's check your understanding on this.

This is a bar graph comparing the length of objects.

I want you to tell me how much longer the twig is than the conker.

The twig is hmm centimetres longer than the conker.

So the key words there you're hearing are twig and conker.

So those are the two bars to focus on and then we need to find the difference in their length.

So we need to subtract, have a go, pause the video, and when you're ready to check your answers, press play.

How did you get on? Did you work out the length of the conker was three centimetres, the length of the twig was nine centimetres, then we had to find the difference.

So nine centimetres, subtract three centimetres is equal to six centimetres.

So the twig is six centimetres longer than the conker.

Well done if you got that right.

So your turn to practise now in Task B, we're gonna solve some problems related to a bar graph.

In question one, I would like you to write down what you notice about this bar graph.

So what does it tell you? What are the bars showing you? This is a bar graph comparing how far children hopped.

So what can you notice? For your second question, I would like to answer the following questions about that bar graph.

How far did Laura hop, how far did Jacob hop? Which child hopped the furthest? How much further did Izzy hop than Andeep? What's the total distance that Laura and Jacob hopped? Have a go at questions one and two, press pause, and when you've had a go, press play.

Shall we see how you got on? For question one, you might have said something like this.

I noticed that there were four bars each with a gap between, so maybe you describe something about what you could see.

Maybe you noticed that Jacob hopped the least distance because his jump is represented by the shortest bar.

I wonder what else you might have noticed.

For question two, maybe you noticed Laura hopped 30 centimetres.

Jacob hopped 25 centimetres.

Izzy hopped the furthest, she had the longest bar, and then Izzy hopped 45 centimetres, Andeep hopped 35 centimetres.

If we found the difference by subtracting, we notice Izzy hopped 10 centimetres further than Andeep.

And for part e, we had to find out the total distance that Laura and Jacob hopped by adding their distances together, 30 centimetres added to 25 centimetres is equal to 55 centimetres.

So that total distance that Laura and Jacob hopped was 55 centimetres.

How did you get on? Well done.

Amazing learning today, everybody.

I hope you have really deepened your understanding on how we can use graph to represent lengths and heights and how we can then go on to solve problems. We know we can represent information about length and height from a table in a bar graph and we know that makes it really visual and really easy for us to explain and spot patterns.

We know we can solve problems related to information represented in a bar graph.

Thank you ever so much for learning with me today.

I've had a lot of fun and I hope you have too.

I'll see you another time.

Bye.