Lesson video
In progress...Loading...
Hello there, my name is Mr. Tilstone, it's great to see you today, and I hope you are having a lovely day.
I'm having a great day.
Would you like to know why? Because I get to spend this lesson talking to you about one of my favourite things in the world, which is maths.
So I hope you enjoy the lesson as much as I know I will.
If you're ready, let's begin.
The outcome of today's lesson is this.
I can understand that dividing a number by 10 makes it one-tenth times the size.
And we've got some keywords, if I say them, will you say them back, please? My turn.
Scaling.
Your turn.
And my turn, inverse.
Your turn.
Those are very important words in today's maths lesson, they're not necessarily common words, so let's have a look at what they mean.
Scaling is when a given quantity is made (hums) times the size.
So two times the size, 10 times the size, a hundred times the size.
Inverse means the opposite in effect, the reverse of.
Our lesson today is split into two parts or two cycles.
The first, one-tenth times the size.
And the second, the inverse of 10 times.
Let's begin by focusing on one-tenth times the size.
In this lesson, you're going to meet Sam and Lucas.
Have you met Sam and Lucas before? They're here today to give us a helping hand with the maths.
Have you ever squashed or shrunk something? Hmm, what can you squash or shrink? Well, Lucas says, "Ice melts over time and shrinks in size." Yes it does.
That's the example of shrinking.
And Sam says, "I like squashing recycling" "to fit into the recycle bin." Have you ever done that? Squash that recycling right down.
That's squashing.
Let's have a quick check.
Make a list of things that you can squash or shrink, be imaginative.
Pause the video.
What can you squash? All sorts of things.
Well, Lucas says, "I like squashing sheets of tinfoil." Have you ever done that? It's very satisfying, squashing that foil right down.
And Sam says, "Sometimes clothes can shrink in the wash." Yes, that's happened to me before.
Scaling down is when we find a fraction times the size of a number, making it smaller.
Lucas and Sam explore scaling down by comparing base 10 blocks.
You may have some of these in your classroom, and you can explore along with them.
Here we go.
So Lucas says, "1 ten is 10 times the size of 1 one." And hopefully you've explored that quite recently with base 10.
But Sam says, "We can also say that 1 one" "is one-tenth times the size of 1 ten." "Let's start with 1 one," says Lucas.
Here's 1 one.
"To find 10 times the size multiply by ten." There we go, 10 times the size multiplied by 10.
"We had 1 one," says Sam.
"Now there are 10 ones or 1 ten." "We have found 10 times the size." "What about one-tenth times the size?" Hmm, Lucas says.
"We need to use the inverse." So there's our key word in action, the inverse, the opposite.
"To find one-tenth times the size, divide by 10." So we're going the other way to find one-tenth times.
So there we go.
And that is one-tenth times the size.
We've divided it by 10.
Sam says, "How about starting with a greater multiple of ten?" "Let's start with 20." Okay, let's do that.
"The process is still the same," he says.
"To find one-tenth times the size, divide by 10." So finding one-tenth the size is the same as dividing by 10.
So there we go.
Let's find one-tenth times the size, just like that.
So draw, or use, base 10 blocks to show the result of making 30, as shown below, one-tenth times the size.
What would that look like after making it one-tenth times the size? Pause the video and give that a go.
How did you get on? Let's have a look.
Well, here's the answer.
That's 30 made one-tenth times the size.
The same as dividing it by 10.
So one-tenth times the size of 30 is 3.
Let's do some practise, I think you're ready.
Number one, complete the labels and the sentences below.
So you've got some stem sentences there to fill in.
And some more here, so you can notice.
Number two, complete the following ratio table by filling in the missing numbers.
So you're making these numbers one-tenth times the size.
Be careful, because the blanks are in different parts of the table.
Number three, match the numbers to the numbers that are one-tenth times the size.
Number four, match the quantities with the quantities that are one-tenth times the size.
Right here, you pause the video, and away you go.
Welcome back, how did you get on? Would you like some answers? Let's do that.
So number one A, this one has been multiplied by 10 to make 10 ones or 10.
So we can say 10 is ten times the size of 1, but what about the inverse? Well, this time we're dividing by 10.
So multiplying by 10 is the inverse of dividing by 10, and dividing by 10 is the inverse of multiplying by 10.
So we're dividing by 10 this time.
And this time we can say 1 is one-tenth times the size of 10.
So dividing by 10 and multiplying by one-tenth are the same thing.
And for B, this time we've got 2 ones, and we multiply them by 10 to get 2 tens.
20 is ten times the size of 2.
And the inverse, we're dividing by 10, and we can say 2 is one-tenth times the size of 20.
And the missing numbers are as follows.
So one-tenth times the size of 60 is 6.
And then 50, one-tenth times the size of that is 5.
One-tenth times the size of 30 is 3.
One-tenth times the size of 20 is 2.
And then one-tenth times the size of 10 is 1.
And match the numbers to the numbers that are one-tenth times the size, 50 and 5.
So 5 is one-tenth times the size of 50.
9 is one-tenth times the size of 90.
2 is one-tenth times the size of 20.
And 4 is one-tenth times the size of 40.
Well done if you've got those.
Number 4, match the quantities with the quantities that are one-tenth times the size.
7 metres is one-tenth times the size of 70 metres.
7 kilogrammes is one-tenth times the size of 70 kilogrammes.
6 centimetres is one-tenth times the size of 60 centimetres.
And 12 millilitres is one-tenth times the size of 120 millilitres.
I don't think you are ready for the next cycle, I know you are, and that is the inverse of 10 times.
So Lucas has 1 pencil, Sam has 10 times as many.
How many pencils does Sam have? Let's have a look.
So, "For every 1 pencil I have, you have 10." So here's Lucas's 1 pencil.
And here are Sam's 10 pencils.
So 1 there, and Sam says, "I have 10 times as many pencils." So one, 10 times as many as that is 10.
One pencil multiplied by 10 is equal to 10 pencils.
What if we look at the inverse? Could we go the other way around, the inverse of multiplying by 10, or 10 times? "Okay, let's turn the arrow around," she says.
That would give us the inverse, or help us to give the inverse.
So turn the arrow around.
Okay, how can we express it now? How can we go from 10 to 1? What could we say? "What's the operation?" One is one-tenth times the size of 10, so it's divided by 10.
So we can say 10 divided by 10 is equal to 1.
So let's have a little check.
So true or false, the inverse operation to undo "multiply by ten" is "divide by ten".
Is that true or false? Pause the video.
True or false? It is true.
Multiplication and division are inverse processes, therefore, multiplying by ten is the inverse of dividing by ten, and dividing by ten is the inverse of multiplying by ten.
Now, Sam has 20 pencils in total.
How many pencils does Lucas have? So Lucas says, "For every 1 pencil I have, you have 10." How many does Lucas have? "I have 20, which is 10 times as many as you." So something multiplied by 10 is equal to 20.
But let's look at the inverse.
20 divided by 10 is equal to something.
What is 20 divided by 10? "I know that 20 divided by 10 is equal to 2." "You have 2 pencils." And so he does.
This time, Sam has 30 pencils in total.
How many pencils does Lucas have? Hmm, what do you think? Again, he says, "For every 1 pencil I have, you have 10." And Sam says, "I have 30, which is 10 times as many as you." So something multiplied by 10 is equal to 30.
Can we use the inverse? Yes, we can.
30 divided by 10 is equal to something.
The inverse of 10 times as many, is divide by 10.
"I know that 30 divided by 10 is equal to 3." "You have three pencils." Yes, he does.
What do you notice here? What's happening? What's going on? What could you say? Lucas says, "I notice that for all of them," "for every one pencil I had, you had 10 pencils." And Sam says, "I notice that to find the inverse" "of 10 times as many you have to divide by 10." So 1 is equal to 10 divided by 10.
What could we say about the next one? 2 is equal to 20 divided by 10.
What about the next one? 3 is equal to 30 divided by 10.
Let's have a really quick check.
Complete the missing numbers to finish the equation describing the images.
Something is equal to something divided by 10.
Pause the video.
Did you get this? Did you get 6 is equal to 60 divided by 10.
If you did, very well done.
You are on track.
And you are ready for some final practise.
Number one, complete the missing numbers below.
1 is equal to something divided by 10.
2 is equal to something divided by 10, and so on.
And number two, fill in the missing numbers on the images, showing the inverse of 10 times as many.
Number three, which of the characters below do you agree with? Can you explain your reasoning? Well, let's see.
Lucas says, "To find the inverse of 10 times as many" "of a whole number, you have to divide by 10." And Sam says, "To find the inverse of 10 times as many" "of a whole number, you have to count back in tens" "until you get to 0." Hmm, who's right? Is it Lucas? Is it Sam? Is it both? Is it neither? What do you think? And when you decide, see if you can explain that as clearly as you possibly can using mathematical language.
Okay, pause the video, if you can work with somebody else by the way, I always recommend that, and I'll see you soon for some feedback.
Welcome back, how did you get on? Let's have a look.
Let's give you some answers.
So number one, complete the missing numbers below.
So 1 is equal to 10 divided by 10.
2 is equal to 20 divided by 10.
3 is equal to 30 divided by 10.
4 is equal to 40 divided by 10.
5 is equal to 50 divided by 10.
6 is equal to 60 divided by 10.
7 is equal to 70 divided by 10.
8 is equal to 80 divided by 10.
9 is equal to 90 divided by 10.
10 is equal to 100 divided by 10.
11 is equal to 110 divided by 10.
And 12 is equal to 120 divided by 10.
And fill in the missing numbers on the images showing the inverse of 10 times as many.
So with A, we've got, that's divided by 10, so 3 is equal to 30 divided by 10.
B, again, we divided by 10, so 4 is equal to 40 divided by 10.
And C, again, we're dividing by 10, 5 is equal to 50 divided by 10.
And which of the characters do you agree with? Well, both characters are actually saying similar things here.
Lucas is using tens as a group size in a division, or as Sam is using repeated subtraction.
Lucas has a more efficient method, because it's quicker.
So we could agree with both of them, but perhaps we'd prefer Lucas's method.
We've come to the end of the lesson, and my goodness, you've been amazing today.
Today we've been understanding that dividing a number by 10 makes it one-tenth times the size.
And that's perhaps a way of expressing it that you're not used to, but hopefully you're getting really confident with it, now I'm really good at it.
Scaling down is when we find a fraction times the size of a number, making it smaller.
And in this case, we've focused on one-tenth times the size.
to find one-tenth times the size, divide by 10.
Those two are exactly the same.
One-tenth times the size of something is the same as dividing by 10.
To find the inverse of 10 times as many, you divide by 10.
Very well done on your accomplishments and your achievements today.
You've been incredible, and I hope to get the chance to spend another maths lesson with you again at some point in the near future.
Until then, take care, have a great day, and goodbye.
