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 the quotient is affected when the divisor is equal to the dividend, 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 the quotient is affected when the divisor is equal to the dividend.

Let's have a look at this lesson's keywords: dividend, divisor, and quotient.

Let's practise them.

Are we ready? My turn.

Dividend.

Your turn.

My turn.

Divisor.

Your turn.

My turn.

Quotient.

Your turn.

Fantastic.

Words that we've definitely heard before.

So let's get started and exploring this lesson.

In the first part of our learning, we're going to be looking at when the number in each group is equal to the dividend.

And in the second part of our learning, we're going to be looking at when the number of groups is equal to the dividend.

Are we ready? Let's get started then with exploring when the number in each group is equal to the dividend.

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

Are you ready guys? Let's get started.

Jacob and Sofia are discussing this array.

Sofia knows that when one of the factors is equal to one, the product will be equal to the other factor.

So one times by five will be equal to five.

We can see this as one group of five is equal to five.

Or Jacob notices that we could also see this as five one time is equal to five.

Remember, multiplication is commutative so we can change the order of the factors, but the product will still remain the same.

Jacob and Sofia now explore this problem as a division.

I'm putting cookies into bags of five.

If we have five cookies, how many bags of five can we make? We can see that in this problem, we are putting cookies into bags of five, so that's going to be our divisor because that's the number in each group.

We can say that they have five cookies that are being put into the bags of five.

So that must be our dividend because it's our whole, so five divided by five.

We have five cookies, so that means that we can make one bag of five cookies.

So five divided by five will be equal to one.

Five divided into groups of five means that we can make one bag.

So that's equal to one.

Well done Jacob and Sofia, but I have to admit, looking at those cookies is making me feel a little bit hungry right now.

Let's have a look at those equations that we've just created.

Five divided by five is the related division problem to one times by five, which is equal to five.

Yes, the product of one and five becomes the dividend in our division.

And when we divide it by five, it is equal to one, which is actually the other factor.

So we can say that these are related facts.

Well done, a lovely thing to notice there guys.

Over to you then.

Let's have a look at another problem.

Solve this problem and record it as an equation.

I'm putting cookies into bags of two.

If I have two cookies, how many bags of two can we make? Record this as a division equation and then use the stem sentence to help you explain the problem.

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

Welcome back.

Let's have a look then.

We can see that there are two cookies being put into bags of two.

So we can see this as two divided by two.

Two divided into groups of two is equal to one.

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

So your equation should have looked like this.

Two divided by two is equal to one.

Well done to you if you got that correct.

Now let's use that knowledge to fill in the missing numbers and complete these equations.

One times by two is equal to something.

So two divided by two is equal to something.

Think about what we have looked at already in our learning.

Pause this video, have a go at completing both of those equations and then come on back to see how you've got on.

Welcome back.

Let's have a look there.

One of the factors is one in our multiplication, so we can see this as one group of two.

If we have one group of two, we have two.

So one times by two is equal to two.

Now we can create this related division problem.

If one times by two is equal to two, then we know that two divided by two must be equal to one.

That's our other factor in our multiplication log, so it is our related division problem.

Well done to you if you managed to complete both of those problems. Let's continue with our lesson.

Jacob and Sofia notice something about the problems that they have just solved.

We know that when one of the factors is equal to one, the product will be equal to the other factor because one times by five is equal to five or one times by two is equal to two.

Let's have a look at that division then.

What do we notice with the division equation? Jacob has noticed that when the dividend is equal to the divisor, the quotient is equal to one.

So it is, five divided by five is equal to one and two divided by two is equal to one.

We were able to make one group in each of those problems, weren't we? So what we've noticed is that when the dividend and the divisor are equal, the quotient will be equal to one.

So let's use that knowledge to solve 10 divided by 10.

Come on then Jacob, show us what you know.

We know that 10 divided by 10 will be equal to one because the dividend and the divisor are equal.

So it will.

Well done, Jacob.

So we have three examples there that all follow the same rule.

When the dividend is equal to the divisor, the quotient will be equal to one.

Let's have an explore of a few more problems just to confirm.

Help Jacob to complete some more equations that involve the same divisor and the same dividend.

Six divided by six is equal to what? Four divided by four is equal to what? And something is equal to nine divided by nine? Pause this video, have a go at finding all the missing quotients and then come on back when you're ready to see how you've got on.

Welcome back.

Let's have a look then.

In the first and the second equation, the divisor and the dividend are equal, so that means that the quotient must be equal to one.

In the third problem though, we can see that the equals symbol has changed position, but the dividend and the divisor are still both nine log nine divided by nine.

So we know that the quotient will still be one.

Well done to you if you managed to solve all of those problems there.

Let's continue to practise this and explore in task A.

Task A part one is to fill in the missing numbers.

So you can see that you have three multiplications and three divisions there with the missing factors and missing quotients.

Then part two is to fill in the missing numbers.

Each equation is missing a different part, so make sure you look really carefully to see which part of the equation is missing and then use your knowledge from this learning cycle to help you to fill in the missing number.

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

Welcome back.

I hope you enjoyed exploring those equations there.

Shall we see how you got on? Part one then was to fill in the missing numbers.

In the multiplication equations, we noticed that the product was equal to one of the factors, so that means that the other factor must be one because we can see one times something is equal to one.

Three times something is equal to three.

They are the same.

Five times something is equal to five.

So that means all of those missing factors must be one.

Let's have a look at the divisions then.

In each of the divisions, we can see that the dividend is equal to the divisor.

And I know that when this is the case, the quotient will be one.

So one divided by one will be equal to one.

Three divided by three, they are equal, so the quotient will be one.

Five divided by five, the dividend and divisor are equal, so all of those missing quotient will be one.

Well done if you managed to complete part one.

Let's have a look at part two.

Part two is to fill in the missing numbers from each equation.

In the first two equations, we can see that the quotient is equal to one, so that means that the dividend and the divisor must have been equal.

So that means the missing numbers are seven and four because seven divided by seven will be equal to one and four divided by four will be equal to one.

In the first one, we were missing our divisor.

And in the second problem, we were missing our dividend.

Now let's have a look at this last one.

We can see that the dividend and divisor are both eight.

They are equal.

So that means that eight divided by eight, we will be able to make one group.

So the missing quotient must have been one.

Well done to you if you got those correct.

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

When the number of groups is equal to the dividend.

Let's have a look.

Jacob and Sofia are now discussing this array.

We can see that when one of the factors is equal to one, the product will be equal to the other factor.

So one times by five will be equal to five.

We can see this as one five times is equal to five and that matches our array, but we may also be able to see this as five ones.

Five ones are equal to five.

Some beautiful equations there, Sofia and Jacob, thank you for that.

Let's have a look at them a little bit more in detail.

We know that one times by five is equal to five, so from this, we can create a related division problem.

If one times by five is equal to five, then five divided by five will be equal to one, the other factor.

Well done.

We know that the divisions can be seen as grouping or sharing.

We've already seen that when the dividend and the divisor are equal, it will make one group when we were grouping in the first learning cycle.

But Sofia would like to know whether this is still the case when we look at a sharing division problem.

So let's have a look.

Jacob and Sofia now explore five divided by five as a sharing problem.

We are sharing apples between five people.

If we have five apples, how many apples will each person get? Our dividend is five, so that means that we will have five apples.

And the divisor is also five, so that means we are sharing five apples between five people.

There we go.

Here we have five apples that are being shared between five people.

If the number of apples are equal to the number of people, that means that they are going to get one apple each.

There's just enough for all of them to get one.

So five divided by five is equal to one, or five divided between five groups is equal to one.

So again, Sofia has noticed that when we are sharing between equal groups, if the dividend is equal to the divisor, the share in each group will be equal to one.

Let's have an explore of another problem.

Solve this problem and record it as an equation.

We are sharing apples between 10 people.

If we have 10 apples, how many apples will each person get? So pause this video, record the equation, and then use the stem sentence to explain what you found 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 have 10 apples being shared between 10 people.

So we can see this as 10 divided by 10.

We know that when the dividend is equal to the divisor, the quotient is equal to one.

So we know that 10 divided between 10 groups will be equal to one.

That's because if we have 10 apples, each person will be able to get one apple each.

Well done to you if you managed to complete that equation and said that each person would get one apple each.

Let's have a look then at the two equations that we've solved so far.

Again, we can see that in all of the equations, the dividend and the divisor are equal.

And in both of our sharing problems, the quotient was equal to one.

Sofia noticed that in each problem, the numbers were different, five and 10, but because the dividend and the divisor were equal, that meant that the quotient would still be one.

So that tells us that if the dividend is equal to the divisor, no matter what the numbers are, the quotient will always be equal to one.

And as Sofia and Jacob have explored, we know that this is the case even when we are grouping or sharing.

Well done to Jacob and Sofia.

You've done a great job at investigating that.

Now let's use it in some problems. Jacob and Sofia now explore a range of equations.

Now this time, Jacob, we're going to read each question very carefully and not just assume what the answer is going to be.

We can see that six is equal to something times by two.

We know that three times by two is equal to six, so we can now use that to solve our division.

Six divided by two will be equal to three, the other factor.

Well done, Jacob.

Come on then, Sofia.

Have a look at the next one.

We know that two times by two is equal to four, so four divided by two will be equal to two.

Let's have a look at the next one.

We can see that the product is equal to the given factor two.

So that must mean that the missing factor must be one because the product and the factor are equal.

Let's have a look at the division then.

We can see that the divisor is equal to the dividend.

Two divided by two.

And what does that mean when we know that the divisor and the dividend are equal? We know that the quotient will be equal to one.

Well done, Sofia.

I love how you remembered that.

Finally, we can see that zero is the product here.

So we know that zero must be our missing factor because zero groups of two will be equal to zero.

And in our division, we can see that zero is our dividend.

So the quotient will also be zero because if we don't have anything to share or group, our quotient will also be zero.

Well done to Jacob and Sofia for solving all of those problems. Look how much we've learned together.

That's great, Jacob.

I'm so glad that you're feeling confident now at using your multiplication and division knowledge.

I'm very impressed.

Well done.

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

Now's your chance to show off, guys.

I can see that the quotient is one here.

So what could be our dividend and our divisor? Sofia thinks that she could put 10 in both of the missing boxes because when the divisor is equal to the dividend, the quotient will be equal to one.

Well done.

10 divided by 10 is equal to one, Sofia.

That's beautiful.

Well done.

Oh, Jacob thinks that he could put 263 in both of those boxes.

Oh, what do we think, Sofia? 263 is a huge number.

I think Jacob might be being a little bit silly there again.

What do you think? Oh, Jacob's done it again.

As long as the dividend is equal to the divisor, the quotient will be equal to one.

So 263 divided by 263 will be equal to one because as long as they are equal, they could be any number.

That is a great thing to notice there, Jacob.

So it wasn't a silly answer at all.

Jacob was correct.

Well done.

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

Let's continue to practise this learning with task B.

Task B part one is to fill in the missing numbers.

Remember to look really carefully at what parts you are missing and what numbers you have.

And in part two, add your own dividend and divisor to complete this equation and explain your thinking.

So pause this video, have a go at part one and part two, and then come on back when you're ready to see how you've got on.

Welcome back.

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

Let's fill in those missing numbers.

Something times by five is equal to five.

I can see that the factor is equal to the product here.

So the missing factor must be one.

Let's have a look at the next one.

We can see here that the known factor is one, so we know that the other factor is going to be equal to the product.

So that means the missing factor here is five.

Well done if you've got that one.

And finally, we can see that the product is zero.

So that means that the missing factor must also be zero because zero times by five is equal to zero.

Let's have a look at our divisions then.

We can see here that the quotient is equal to one, so the dividend and the divisor must be equal.

So our missing dividend must be five.

Well done.

Here we can see that zero is our dividend and we know that as soon as we see zero is our dividend, we know that the quotient will also be zero.

And finally, we can see here 10 divided by 10.

If the dividend and the di divide are equal, we know that the quotient must be equal to one.

Well done if you completed all of those equations for part one.

Now let's have a look at part two.

We know that in any equation where the dividend and the divisor are equal, the quotient will be equal to one.

So you might have said one divided by one is equal to one.

You might have said 20 divided by 20 is equal to one, or you might have said 684 divided by 684 is equal to one.

As long as your dividend and divisor were equal, then your equation was correct.

I hope you had a chance to share your equation there and to listen to some other people's ideas for that problem.

Unfortunately, we have come to the end of our lesson, so let's have a look at what we've covered.

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

Any number divided by itself is equal to one.

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

I'm hoping you're starting to build this really strong understanding of how to solve a range of division problems. I can't wait to see you all again soon to continue our learning.

Goodbye.