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Hello.
Welcome to today's lesson.
My name is Mr. Peters, and today we're gonna be thinking about using our knowledge and understanding of decimal place value and applying that to different contexts so we can solve different problems. If you're ready to get started, let's get going.
Hopefully, by the end of this lesson today, you should be able to say that you can use knowledge of decimal place value to solve problems in different contexts.
Here are the key words for today's lesson.
I'll have a go at saying them first and then you repeat them afterwards.
Are you ready? My turn, multiple.
Your turn.
My turn, common.
Your turn.
My turn, partition.
Your turn.
My turn, interval.
Your turn.
Let's think about what these mean in a bit more detail.
So the multiple is the result of multiplying a number by an integer.
For example, 2 multiply by 5 is equal to 10.
So 10 is a multiple of both 2 and 5.
Something is common when it is used frequently or it occurs regularly.
We can partition an object or a value into smaller parts.
And finally, an interval is the space between two values or parts.
So you can see here I've got two values of 0 and 10, and the interval is the distance between those two values.
Look out for this language throughout our lesson today, and use it where you can to reason and think about your understanding as well.
Okay, so this lesson today is broken down into two cycles.
The first part is going to be thinking about reading graphs with common partitions to 1, and the second part is going to be thinking about reading scales with common partitions to 1.
If you're ready, let's get started.
During this lesson today, Sam and Sofia are gonna join us, and they're gonna be sharing their thinking and their questions throughout the lesson to help us along the way.
Okay, so we're gonna start the lesson thinking about the common partitions to 1 and how we can use these to count upwards to 1.
So let's look at this example here.
A whole has been divided into five equal parts, and each part has a value of 0.
2.
We can now count up in multiples of 0.
2 up and beyond one whole.
Here we go.
Can you count with me? 0, 0.
2, 0.
4, 0.
6, 0.
8, 1.
Then if we move our bar model between the next two wholes, we can carry on in the same vein.
1.
2, 1.
4, 1.
6, 1.
8, 2.
"What would then come after 2?" Sofia's asking.
Take a moment to have a think for yourself.
That's right, it would be 2.
2, wouldn't it? You can see that after each whole number we get 2.
So, for example, 0 and 1.
The next multiple straight away is whole number 0.
2, isn't it? So we've got 0.
2, 1.
2, and then it would be 2.
2.
Here's another example.
This time our whole has been divided into four equal parts.
Each part has a value of 0.
25.
And again, we can then use our multiples 0.
25 to count up on our number line.
Let's do that together again.
0, 0.
25, 0.
5, 0.
75, 1.
And if we move along between 1 and 2, 1.
25, 1.
5, 1.
75, 2.
Another question, what would be after 2? That's right, it would be 2.
25 again.
And again, you'll notice that straight away after each whole number we have 0.
25.
So 0.
25, 1.
25, and then it would be 2.
25.
Have a look at this example.
What do you notice this time? Our bar model isn't horizontal.
Now it's vertical, isn't it? Let's see what that does to our number line.
The whole has been divided into two equal parts, and each part has a value of 0.
5.
So that means we can now count up in multiples of 0.
5.
So it goes from 0, 0.
5, to 1.
And again, if we extend that above and beyond one whole, we would have 1, 1.
5, and 2.
And then Sam's asking, "Well, what is it that we notice this time?" Well, everything else that we've been working with has been horizontal, whereas this time, it's vertical, isn't it? And that's what Sofia is saying.
We can rotate the number line and count vertically too as well.
So once we've been familiar with counting, using our multiples of common partitions to 1 above one whole, we can then start applying this to understanding graphs.
Here is a graph.
What type of graph is this? That's right, it's called a bar chart or a bar graph, isn't it? And our bar graph is showing us the distance in kilometres travelled to school.
So we've got four children here.
We've got Izzy, Jun, Sofia, and Sam, and they all travel a certain distance to get to school.
Sofia's asking us, "Can you spot where the number line is on our bar chart?" That's right.
It sits here on the Y axis, doesn't it? The Y axis is the axis that goes vertically, and the X axis is the axis that goes horizontally.
If I leave you to have a think for a moment, what information can we gather from the graph? Take a moment to have a think for yourself.
Before we can identify what information this graph is showing us, we need to be able to read the graph, don't we? So in order to read the graph, we need to understand the size of each interval on the number line.
So let's put our number line back into place.
So let's look at the distance between 0 and 1.
Here we go.
One whole has been divided into how many equal parts? That's right.
It's been divided into four equal parts.
So each part has a value of 0.
25.
That means we can use our understanding of multiples of 0.
25 to count up and identify what each of the intervals would be.
Let's count up using those intervals, shall we, just to double check they're correct.
0, 0.
25, 0.
5, 0.
75, 1, 1.
25, 1.
5, 1.
75, and 2.
Great.
So they're all correctly in place.
Now we can start reading the values, can't we? So the question is, how far does each pupil travel to get to school? Well, let's look at Izzy's purple bar first of all.
That goes up to the line, which is equal to 1.
5, and the 1.
5 would be represented in kilometres because the title for the axis is distance in kilometres.
So the purple bar would represent 1.
5 kilometres.
So Izzy travelled 1.
5 kilometres to get to school.
Jun travelled 0.
75 kilometres to get to school.
Sofia travelled 1.
25 kilometres to get to school.
And Sam finally travelled 0.
5 kilometres to get to school.
Can you see how understanding our common partitions to 1 has helped us to read this graph? Well done if you managed to do that as well.
Okay, have a look at this graph here.
What'd you notice this time? That's right, the bars are going horizontally this time rather than vertically.
And can you spot where the number line would be this time? Ah, so the bars are going horizontally, so the number line is actually on the X axis, isn't it? And again, the X axis is the one that goes horizontally, and the Y axis is the one that goes vertically.
If I give you a moment to have a look, can you see if you can understand and gather any information from our graph already? What's it telling us? As always, in order to be able to read and understand the information on this graph, we're going to need to identify the intervals in between each of our whole numbers on the number line.
So let's have a look between 0 and 1.
The whole has been divided into five equal parts this time.
That must mean each part has a value of 0.
2.
So again, we're gonna be counting up in multiples of 0.
2 here, aren't we? Let's that to our number line now.
Let's count up as well just to double check that they are correct.
0, 0.
2, 0.
4, 0.
6, 0.
8, 1, 1.
2, 1.
4, 1.
6, 1.
8, 2, 2.
2, 2.
4, 2.
6, 2.
8, and finally 3.
So now that we've got our number line in place and we know it's going up in multiples of 0.
2, we can start thinking about some of the questions, can't we? So let's have a think about what our graph is showing us.
The title of our graph is company value, and this is in trillions of dollars.
So it's telling us how much each company is worth.
On the left hand side of the Y axis tells us the company name.
And you may be familiar with these companies.
We've got Apple, Amazon, Meta, and Microsoft.
And then on the X axis we've got the value in trillions.
This is telling us the value that that company has, the worth of that company in trillions of dollars.
So our first question is, what is Microsoft's company value? Have a look.
Can you spot Microsoft on the bar chart? Find Microsoft, and maybe draw a line along from the bar down to the number at the bottom on the X axis to find out how many trillions Microsoft is worth.
And there you go, Microsoft is worth $1.
6 trillion.
And you can see at the bottom of the page the date at when that value was correct for Microsoft, because the values do fluctuate up and down every so often.
So Microsoft has a value of $1.
6 trillion.
How much more is the value of Amazon compared to Meta? Gosh, right, how are we gonna calculate this then? Well, let's find out the values of both Amazon and Meta, shall we? Let's draw a line down from both of their bars.
We can see that Amazon has a value of $1.
4 trillion, and Meta has a value of $0.
8 trillion.
And the arrow on our chart now is showing us the difference between those.
It's showing us how much more Amazon has in comparison to Meta.
So we can see, if we counted on in multiples of 0.
2, we'd find out how much more there is.
So there is three intervals there, aren't there, and each one of those intervals has a value of 0.
2, so altogether that's three lots of 0.
2.
So the difference between Amazon and Meta's worth is $0.
6 trillion.
Right, onto some checking of our understanding now.
The number line is increasing in intervals that are A, B, or C.
Take a moment to have a think.
That's right.
It's C.
They're going up in multiples of 0.
25, aren't they? How do we know that? Well, the distance between 0 and 1 is the whole, and it's been divided into four equal parts, so each part has a value of 0.
25.
That means we're gonna be counting up in multiples of 0.
25.
Here's a bar graph showing the distance in kilometres cycled at the weekend.
Again, you can see the children who have done the cycling.
And at the bottom on the X axis you can see the distance that they've cycled in kilometres.
Question is, how far does Sofia cycle at the weekend? Take a moment to have a think.
That's right, Sofia cycled 2.
4 kilometres, didn't she, overall.
Well done if you managed to get that.
Okay, onto our first task for today.
What I'd like to do is fill in the missing numbers for each part on the number line.
And then once you've done that, I've given you a graph here and I'd like you to answer some questions about this graph.
The graph shows the litres of water drunk during the school day by Sam.
Have a go answering the questions from A to C.
Good luck with that, and I'll see you back here shortly.
Okay, I'm gonna fill in the numbers now on our number lines.
Here we go.
The first number line was going up in multiples of 0.
25.
The second number line was also going up in multiples of 0.
25, but you may have noticed the numbers starting at the number line and finishing at the number line were different.
And finally, the bottom number line is also going up in multiples of 0.
25.
But I didn't give you the interval in the middle between 23 and 25, did I? So you needed to find where 24 would be as well.
The first vertical number line was going up in 0.
5s.
The second vertical number line was going up in multiples of 0.
2.
And the third vertical number line was going up in multiples of 0.
1.
Well done if you've got all of those.
Okay, so the first question asks, what was the most amount of water that Sam drank in one day? Well, that happened on Friday, and he drank 3.
25 litres of water on that day.
The second question was how much did he drink on Tuesday? And Tuesday, he drank 1.
75 litres of water.
And the last question was, how much more water did he drink on Wednesday than he did on Monday? And the answer to that was 0.
5 litres of water.
Well done if you managed to get that and realised that each of the intervals were going up in multiples of 0.
25.
Okay, onto the second part of our lesson now.
Reading scales with common partitions to 1.
So far we've been looking at graphs, haven't we, and thinking about how our common partitions can be applied to those, whereas now we're gonna start thinking about scales.
We often use scales when we're thinking about measuring the weight of something.
So, for example, when you are measuring out ingredients for something that you might be baking.
Have a look at these weighing scales below.
What do you notice that's different about them? In order to see the differences, let's look a little bit more detail between 0 and 1 on each one of the scales.
Here you can see that we've partitioned the wholes into different amounts of intervals here, haven't we? So the first one's been split into two equal parts.
So that interval would be going up in multiples of 0.
5.
The second one has been divided into four equal parts.
That must mean we're working in multiples of 0.
25.
And the last one has been divided into five equal parts.
So again, that must mean we're working with multiples of 0.
2 each time.
It's really important for us to identify the value of each of those intervals in order for us to be able to read the scales as we go.
So now that we've identified, we can do that between 0 and 1.
We can then extend this beyond 1, can't we? Let's count up using these intervals on our scales.
Let's start with the left hand scale first of all.
Starting at 0, we go 0.
5 kilogrammes, 1 kilogramme, 1.
5 kilogrammes, 2 kilogrammes, 2.
5 kilogrammes, 3 kilogrammes, 3.
5 kilogrammes, 4 kilogrammes, 4.
5 kilogrammes, 5 kilogrammes, 5.
5 kilogrammes, 6 kilogrammes, 6.
5 kilogrammes, 7 kilogrammes, 7.
5 kilogrammes, 8 kilogrammes.
And you can see how that would continue all way round up to 10 kilogrammes.
Have a look at the second scale.
Let's count some of the way around here.
0.
25 kilogrammes, 0.
5 kilogrammes, 0.
75 kilogrammes, 1 kilogramme, 1.
25 kilogrammes, 1.
5 kilogrammes, 1.
75 kilogrammes, 2 kilogrammes, 2.
25 kilogrammes, 2.
5 kilogrammes, 2.
75 kilogrammes, 3 kilogramme.
And again, that would continue all the way around up to 10 kilogrammes.
And then finally the last one.
We're going up in multiples of 0.
2 here.
So 0, 0.
2 kilogrammes, 0.
4 kilogrammes, 0.
6 kilogrammes, 0.
8 kilogrammes, 1 kilogramme, 1.
2 kilogrammes, 1.
4 kilogrammes, 1.
6 kilogrammes, 1.
8 kilogrammes, 2 kilogrammes, 2.
2 kilogrammes, 2.
4 kilogrammes, 2.
6 kilogrammes, 2.
8 kilogrammes, and again, 3 kilogrammes.
And that would also continue all the way around up to 10 kilogrammes.
Okay, now that we can identify the value of each interval marker on our scale, we can then think about solving problems. Sam was buying cheese from the supermarket.
What is the mass of the cheese? Take a moment for yourself to have a think.
That's right, the scale has moved around from 0 up to 2 and a bit, hasn't it? How are we gonna work out what the extra bit is? Well, the distance between 2 and 3 kilogrammes is 1 kilogramme, and that 1 kilogramme has been divided into four equal parts.
So each one of those parts has a value of 0.
25 kilogrammes.
And the arrow is pointing to the first one of those interval markers, isn't it? So the total would be 2.
25 kilogrammes, wouldn't it? And that's been shown here on our digital scales as well.
Sam then spotted a large pineapple that he wanted to buy.
What was the mass of the pineapple? Well, again, the arrow is moved from 0 round to 1 and the bit, hasn't it? And Sam is saying here.
And we can see that the distance between 1 and 2, that makes 1 kilogramme, and that's been divided this time into five equal parts.
So the value of each one of those parts is 0.
2 kilogrammes.
That means we're counting up in multiples of 0.
2.
So we can see here that it would be 1.
4 kilogrammes as it's moved on two interval markers after the 1 kilogramme, isn't it? On our digital scales, that could be recorded as 1.
4 or 1.
40.
Okay, time for us to check our understanding for the last time today.
True or false, the weighing scale shows 2.
5 kilogrammes.
That's right.
It's false, isn't it? Which justification can we use to help us answer that? That's right, we can use B, can't we? 2.
5 is not a multiple of 0.
2, which is what the scale is going up in.
So therefore it cannot be 2.
5 kilogrammes.
It's actually 2.
6 kilogrammes.
Okay, on for our task then.
What I'd like you to do is give the value provided on the scales.
And then for question two, what I'd like to do is draw the correct arrow on to represent each one of these numbers on each scale.
Good luck with that, and I'll see you again shortly.
Okay, welcome back.
The first scale is showing 5.
25 kilogrammes.
The second scale is showing 9.
75 kilogrammes.
The third scale is showing 6.
5 kilogrammes.
And the fourth scale is showing 3.
8 kilogrammes.
Well done if you've got those.
And then hopefully here you can see where I've recorded the arrows for each one of these now.
Give them a tick if you manage to get all of those.
Brilliant.
That's the end of our lesson for today.
Hopefully you're feeling a lot more confident again now about using your understanding of common partitions of 1 to help us solve problems in a range of different contexts.
So to summarise our lesson today, you should be able to say that using our knowledge of common partitions to 1, you can identify intervals on graphs to help you understand the data.
And again, the same is applied to identifying intervals on scales to help us understand the data.
Thanks for learning with me today.
Hopefully you've taken something from this today and you're feeling a bit more confident with it all.
Take care.
I'll see you again soon.
