Lesson video

Hello everyone, welcome back to another maths lesson with me, Mrs. Pochciol.

I can't wait for us to have lots of fun together and hopefully learn lots of new things.

So, let's get started.

This lesson is called explain how a divisor of one affects the quotient, and it comes from the unit doubling, halving, quotative, and partitive division.

By the end of this lesson, you should be able to explain how a divisor of one affects the quotient.

Here are this lesson's key words: dividend, divisor, and quotient.

Let's practise them.

My turn, dividend, your turn.

My turn, divisor, your turn.

My turn, quotient, your turn.

Fantastic, let's get started then and have a look at our lesson outline for today.

In the first part of our learning, we're going to be looking at when one is the number in each group, and in the second part of our learning, we're going to be looking at when one is the number of groups.

So, let's get started with our first learning cycle.

Jacob and Sofia are here again to help us with our learning.

Are you ready to get started guys?

Let's do this.

Jacob and Sofia return to this array.

We can see this as five ones is equal to five.

We know that when one of the factors is one, the product is equal to the other factor.

So, five times by one is equal to five.

Or we could also see this as one five times is equal to five.

One times by five is equal to five.

Sofia and Jacob now look at this problem as a division.

I am putting cookies into bags of one.

If we have five cookies, how many bags of one cookie can I make?

They are putting the cookies into bags of one.

So that is going to be our divisor, the number of cookies in each group.

They have five cookies all together that are being put into the bags of one.

So, this is going to be our dividend, or the whole five cookies.

If we have five cookies that means that they can make five bags with one cookie in each.

That means that five divided by one is equal to five.

So, we can say that five divided into groups of one is equal to five.

Now it's over to you to have a go at a problem similar to this.

Solve this problem and record it as an equation.

I am putting cookies into bags of one.

I have two cookies.

How many bags of one cookie can I make?

Record this as an equation and use the stem sentence to explain what you find.

Pause this video and come on back when you're ready to see how you got on.

Welcome back.

Let's have a look then.

Here we can see that they have two cookies that are being put into bags of one.

So, we can see this as two divided by one.

With two cookies, we will be able to make two bags with one cookie in each.

So, two divided into groups of one is equal to two.

That's because we have two cookies, so we can make two groups of one.

So well done to you if you completed that equation and managed to find out that two divided into groups of one will be equal to two.

Sofia and Jacob now look at the equations that they have just solved, and they notice something.

We know that when one of the factors is one, the product is equal to the other factor.

But similarly, when the divisor is one, the quotient is equal to the dividend.

Look, it's the same pattern.

Sofia makes a connection with something that she has learned before.

She noticed that when the divisor is equal to the dividend, the quotient was equal to one.

But this time, when the divisor is equal to one, the dividend and the quotient are equal.

Look at that.

What a connection to make there, Sofia.

Well done to you.

We can see there that the number of groups that we are sharing between and the number in each group have swapped places.

We've looked at this before, haven't we?

What a great thing to notice there, Sofia.

Well done.

So, we can see that if the divisor is equal to one, the quotient will be equal to the dividend.

So, use this knowledge, Jacob.

What would 10 divided by 1 be?

We know that 10 divided by 1 would be equal to 10.

Because the divisor is 1, we know that the quotient will be equal to the dividend.

Well done, Jacob.

You are correct.

Now it's over to you.

Have a look at three more equations.

Can you help Jacob to complete some more equations using what you know?

Make sure to explain after each one how you knew that that was the missing number.

Pause this video and come on back when you're ready to see how Jacob solved them.

Welcome back.

Let's have a look then.

Here we can see that in each problem the divisor is 1.

So that means that the quotient will be equal to the dividend.

So, 6 divided by 1 will be equal to 6, and 4 divided by 1 will be equal to 4.

Well done if you got those.

Now the final one, we can see that the equals symbol had changed position, but that doesn't change what the equation says.

9 divided by 1.

The divisor is still 1, so that means that the quotient will be equal to the dividend, which is 9.

Well done if you managed to complete all three of those problems.

Let's continue to practise this in task A.

Task A is to fill in the missing numbers.

So, you can see that you have some multiplications, and some divisions with missing factors and missing quotients.

So, use your knowledge to find the missing numbers.

Part 2 is to fill in the missing numbers of these equations.

You will notice that there are different parts of the equations missing, so make sure you look carefully at what information you know and use that to help you to work out what those missing numbers must be.

Pause this video, have a go at part 1 and part 2, and then come on back when you're ready to see how you've got on.

Welcome back.

Let's have a look then at how we got on.

We can see that when one of the factors is equal to 1, the product will be equal to the other factor, so the missing numbers here were 7, 9, and 11.

When we look at the divisions, the divisor was 1 in each of our problems, so that means that the quotient would be equal to the dividend, so again, our missing numbers were 7, 9, and 11.

Well done if you completed part 1.

In part 2, we had to work out the missing numbers.

In the first problem, we can see that the quotient is equal to the dividend, so we know that that missing divisor must have been 1, because when 1 is the divisor, the quotient is equal to the dividend.

The second problem we are missing our dividend here, but we can see that the divisor is 1, so we know that the missing dividend will be equal to the quotient, which is 10.

Well done, some great explanations here, Jacob.

This last one, then let's have a look.

8 divided by 1.

Again, our divisor is 1, so that means that the missing quotient will be equal to the dividend, which is 8.

Well done for completing task A.

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

When 1 is the number of groups, so we've already explored 1 as the number in each group.

Now it's time to explore when 1 is the number of groups.

Let's have a look.

Jacob and Sofia are discussing this array.

We can see this as 5 one time is equal to 5, and we can record this as 5 times by 1 is equal to 5.

We know that when one of the factors is equal to 1, the product is equal to the other factor, or we could see this as 1 five times is equal to 5, and record this as 1 times by 5 is equal to 5.

Well done.

I love how you're using all of your prior learning here, Jacob and Sofia.

It's really helping us to make all of those great connections with our learning, isn't it?

We know that 5 times by 1 is equal to 5, so we can also write the related division fact.

If 5 times by 1 is equal to 5, then we know that 5 divided by 1 will be equal to 5.

It's the other factor.

Jacob has remembered, though, that when we are dividing, we can see this as grouping or sharing depending on what the problem is.

We've already seen in our grouping problems that when the divisor is equal to 1, the quotient will be equal to the dividend, but Sofia's wondering whether this is the same case when our division problem is a sharing problem rather than a grouping problem.

I think we can explore that, Sofia.

Let's do this.

Jacob and Sofia now explore the problem as a sharing worded problem.

We are sharing apples between one person.

If we have 5 apples, how many apples will that person get?

Our dividend is equal to 5, so we will have 5 apples, and the divisor is 1, so we are sharing them between one person.

Let's represent that.

There we go; there's our 5 apples, and there's our one person.

So, 5 apples are being shared between one person, so that one person will get all 5 apples.

So, 5 divided between one group is equal to 5, the original number, because we are going to give them all to that one person.

If the divisor is 1, the share in each group will be equal to the dividend.

Over to you then to have a go at this for yourselves.

Solve this problem and record it as an equation.

We are sharing apples between one person.

If we have 10 apples, how many apples will that person get?

Record this as an equation and then use the stem sentence to explain what you found.

Pause this video and come on back when you're ready to see how you've got on.

Welcome back.

Let's have a look then.

Here we can see that we have 10 apples being shared between one person, so our equation will be 10 divided by 1.

We know that when the divisor is equal to 1, the quotient is equal to the dividend, so 10 divided between one group is equal to 10.

That's because if we have 10 apples, that one person will get all 10 of the apples.

Well done to you if you got that correct.

Let's move on then with the next part of our learning.

Sofia and Jacob now use what they know to complete this equation.

We can see that we have a divisor of 1.

What numbers do you think could complete the boxes, Sofia?

Sofia knows that when the divisor is equal to 1, the quotient will be equal to the dividend, so as long as the dividend and the quotient are equal, these could be any number.

Yes, so, we could have 12 divided by 1 is equal to 12.

Oh, here he goes again, or it could be 168 divided by 1 is equal to 168.

Yes, Jacob, look at you using those larger numbers again, but you are correct because remember, when the divisor is equal to 1, the quotient is equal to the dividend, so 168 is our dividend, and the quotient is also 168, so you are correct, Jacob.

Time for you to have a go at this.

Can you create your own equation with 1 as the divisor?

Remember, when the divisor is 1, the quotient will be equal to the dividend.

So, pause this video, create as many different ones as you want to create, and make sure to share them with the people around you to see what numbers they can come up with, and then come on back when you're ready to continue with the learning.

Welcome back.

I hope you had lots of fun there creating all of your crazy equations.

Let's have a look.

I think Jacob went pretty simple this time.

You might have said 8 divided by 1 is equal to 8.

Wow, that was a very calm number for you there, Jacob.

I hope you had lots of fun with that activity there.

Let's have a look then at where Sofia and Jacob go next with their learning.

Sofia and Jacob now use their knowledge to fill in the missing numbers in these equations.

In each row, find a dividend and a divisor that will be equal to the given quotient.

And in each column, the dividend and the divisor should also be equal to the given quotient.

How are we going to solve this one?

This is a new problem, isn't it?

I wonder how Jacob and Sofia are going to tackle this problem.

Let's join them and see what they're up to.

Sofia knows that this dividend must be zero because both quotients in each of those equations are equal to zero.

So, let's pop that one in there and see if that works.

Zero.

Now what are we going to do, though?

Jacob now looks at this equation.

Here, we need the quotient to be five, and we know that five divided by one is equal to five, so he places those numbers in there.

Now we have one number left to find, so let's work out what that number could be because then we can check as to whether all of our equations will work.

We know that the divisor here is one, so the dividend will be equal to the quotient.

The quotient that we need here is two, so the missing dividend must also be two, so let's pop two in there.

Right, we've got a number in each of our boxes.

Now let's check to see if it is correct.

Zero divided by two is equal to zero.

Yes, that equation is correct.

Five divided by one is equal to five.

Yes, that is correct.

Now let's check the vertical problems.

Zero divided by five is equal to zero.

It is, or it's looking good guys, and finally, two divided by one is equal to two.

Yes, you did it, Jacob and Sofia.

Well done.

All of those equations are now correct, so those numbers that you placed in those empty boxes must have been the correct numbers.

Well done to you.

That problem took a lot of thinking there, but you were able to use everything that we've learned.

I'm very impressed.

Now it's over to you to have a go at task B.

Task B part one is to complete the equations and fill in the missing numbers using what you know.

Make sure that you read each equation really carefully to see what part of the equation is missing or what knowledge you might have to use, and part two is to fill in the missing numbers to make these equations correct.

Remember, the equations must be correct both horizontally and vertically, so make sure to check as you go along that they are still correct.

Pause this video, have a go at part one and part two, and then come on back when you're ready to continue the lesson.

Welcome back!

Let's have a look at how we got on then.

Part one was to fill in the missing numbers.

One times by two is equal to two.

Zero times by five is equal to zero.

Ten is equal to something times by ten.

Here we can see that the factor is equal to the product, so that means that the other factor must be equal to one.

Well done if you got those three multiplications correct there.

Now let's have a look at the divisions.

Five divided by one is equal to.

I can see that the divisor is equal to one, so the quotient will be equal to the dividend.

Five divided by one is equal to five.

Ten divided by ten.

I can see that the dividend is equal to the divisor there, so that means that the quotient must be equal to one.

And finally, something is equal to two divided by one.

When the divisor is equal to one, the quotient will be equal to the dividend, so the missing quotient here must be two.

Well done if you managed to get all of those correct.

Let's have a look then at part two.

I hope you enjoyed solving this problem.

Let's have a look at how Sofia and Jacob solved it.

Again, we can see that both of the quotients are equal to zero, so this missing number here must be zero because that's the dividend for both of those equations.

Next up, Jacob had a look at this equation here.

He can see that the quotient needed to be five.

He knows that five divided by one is equal to five, so he places those numbers in there.

Let's fill in that last number, and then we can check whether they are correct.

Here we have one as our divisor, and ten is our quotient.

Ten divided by one is equal to ten, so ten must be the final number because the dividend will be equal to the quotient.

Now let's have a check at each of those equations to check that they are correct.

Zero divided by ten is equal to zero because zero is our dividend.

Five divided by one is equal to five because when one is our divisor, we know that the quotient will be equal to the dividend.

Now let's have a look at those vertical problems.

Zero divided by five, again that dividend is zero, so the quotient will also be zero.

That is correct.

And finally, ten divided by one.

We know that when one is the divisor, the quotient will be equal to the dividend, so ten divided by one is in fact ten.

Yes, you did it!

Well done, Jacob and Sofia, and well done to you if you managed to complete this table too.

And well done to you for completing task B.

Let's have a look at what we've covered in our learning today.

If the divisor is equal to one, then the dividend and the quotient will be equal.

Any number divided by one is equal to itself.

Thank you so much for all of your hard work today.

As always, I can't wait to see you all again soon for some more learning.

Goodbye!

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