Lesson video

Hello everyone.

Welcome back to another maths lesson with me, Mrs. Pochul.

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 each part of a division equation and know how they can be interchanged and it comes from the unit doubling, halving, quotative and partitive division.

By the end of this lesson, you should be able to explain each part of a division equation and know how they can be interchanged.

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

Let's practise them.

My turn, dividend.

Your turn, my turn, devisor, your turn.

My turn, quotient, your turn.

Fantastic, now that we've said them, let's get using them.

Here is this lesson outline.

In the first part of our learning, we're going to be labelling division equations and linking this to multiplication.

And in the second part of our learning, we're going to be finding errors in equations.

So let's get started with the first part, labelling division equations and linking to multiplication.

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

Are you ready guys? Let's get started.

Sophia and Jacob discuss what they can see here.

Sophia thinks that she can see this array as a multiplication.

She can see two groups of five, which is equal to 10, and she records this as the equation, two times by five is equal to 10.

Jacob thinks that he can see this as a division.

He can see this as 10 divided into two groups is equal to five and he records the equation, 10 divided by two is equal to five.

They explore Jacob's division a little bit further.

The whole in the division is known as the dividend.

So here we can see that 10 is our whole or we can say 10 is the dividend.

Let's explore Jacob's division.

Sofia notices that 10 is the whole in this division, we call this the dividend.

The divisor is the number that we are dividing by.

So in our equation two is our divisor because we are dividing by two and the result of a division is known as the quotient.

This could be the number of groups or the size of the group.

Let's have a practise of our new words.

The dividend is the whole, your turn.

The divisor is the number we are dividing by, your turn.

The quotient is the result of the division.

Your turn, have a little practise of saying these for yourselves until you are feeling really confident at the new names of the numbers in our equation.

So 10 is our dividend, two is our divisor, and five is the quotient.

Fantastic, these words we're going to be using throughout our lesson.

So it's really important that you are confident in what they mean.

Let's have a practise of this, label the different parts in each of the equations.

What is the dividend? What is the divisor and what is the quotient? Look really carefully at these equations to label each of them.

Don't fall into any traps.

Pause this video.

Have a go at labelling each part of the equations and then come on back when you're ready to see how you got on.

Welcome back, let's have a look then.

we can see that in the first two equations our dividend is at the start of the equation, eight and 20.

Our divisors are after the division symbol.

So here you can see two and 10 are our divisors and the quotient follows the equal symbol.

So in these equations we can see that four is the quotient and two is the quotient.

But what was different about this third equation? This third equation, we had to think a little bit more carefully because the equal symbol has changed places in the equation.

So now let's have a think about this.

We're going to look for the division symbol because the number before the division symbol will be our dividend and the number after our division symbol will be the divisor.

So in this equation here we can see that 15 is our dividend.

It comes before the division symbol and the divisor is five, that comes after the division symbol.

Then the quotient is equal to this.

So we can see here that in this equation, three is our quotient.

Well done if you managed to correctly label all of the parts of those equations.

Now let's explore this a little bit further.

Sofia notices another equation that can be represented by this array.

We could also see this array as five groups of two, which is equal to 10, and she records the equation as five times by two is equal to 10.

Jacob now decides to also do the same with his division and he decides that the division will also be two divided by 10 is equal to five.

Hmm, I'm not sure about that one, Jacob.

Yes, I agree Sofia, how did you get that division Jacob? Jacob changed the order of the numbers just like Sofia did.

Is that correct? We know that we can change the order of the factors in a multiplication because multiplication is commutative.

It doesn't matter which order you'd multiply the factors, they will still equal to the same product, but division isn't commutative, so we can't just change the order.

Of course, Jacob's realised we can't actually divide two by 10, so that cannot be an accurate division for that array.

Jacob decides to use Sofia's new multiplication to help him to create his own division.

Five groups of two are equal to 10, so we can see that the dividend is still going to be 10 because that's the whole, but this time we have five groups of two.

We can see that the hole has been divided into five groups here, so the divisor must be five.

Then we can see that once we've divided into those five groups, there are two in each group.

So that means that two must be are quotient.

So here is the new division.

Well done Jacob.

That division looks a lot better than the first one.

10 divided by five is equal to two.

10 divided into five equal groups and there's two in each group.

That makes a lot more sense.

Well done Jacob, and well done to Sofia for spotting Jacob's error.

Jacob now explores his division equations.

He's noticed that in both equations, the dividend has remained the same, but what's different about our equations? Jacob notices that the divisor and the quotient have actually changed places.

Look, that's the same with the multiplication equation.

We can see that the whole or the product remains the same, but the factors have changed positions.

That means that the number of groups and the size of the group can be interchanged in our equation.

Look, 10 divided by two is equal to five or 10 divided by five is equal to two.

They've swapped places.

Jacob and Sofia decide to explore this with a new array.

What related division facts could represent these arrays? The first multiplication is two times by 10 is equal to 20.

So let's have a go at writing the related division fact here.

We can see that the dividend, the whole is 20 because that's how many counters we have altogether.

In this array, there are two groups, so we can see that the divisor is going to be two 20 divided into two groups.

Then the quotient.

What will the quotient be in this? The quotient will be how many counters are in each group and we can see that there are 10 counters in each group.

So the quotient here must be 10, 20 divided by two is equal to 10, two times 10 is equal to 20.

So 20 divided by two is equal to 10.

Can you see how those facts are related there? Let's have a go at another one.

Jacob now looks at the array as 10 times by two is equal to 20.

He knows that the dividend is still going to be 20 because our whole hasn't changed.

This time though, he has divided the whole into 10 equal groups.

So this time the divisor is 10.

20 divided by 10.

Our quotient will be the number of counters in each group.

Here we can see that there are two counters in each group.

So in this equation, the quotient must be two.

10 times by two is equal to 20.

So 20 divided by 10 is equal to two.

Wow, well done there Jacob and Sofia, I love how you used our mathematical language there of quotient, divisor and dividend to help you to explain your divisions.

I'm really impressed, well done.

Over to you then, let's see if you can create your own division fact from this array.

You can see that Sophia has already recorded the multiplication for you.

So what is going to be the related division equation? Make sure to use the language of dividend, divisor and quotient to help you to explain how you work this one out.

Pause the video and come on back when you've managed to create your division equation.

Welcome back, let's have a look then.

Here we can see that the dividend, the whole is still 20, so that's going to be the first number in our division.

We can see that the array has been grouped into four groups.

So we can say that our divisor is going to be four, 20 divided by four.

Remember, the quotient will be the number of counters in each group.

We can see here that there are five counters in each of those four groups.

So the quotient in this division is equal to five.

We can see that four times by five is equal to 20.

So 20 divided by four is equal to five.

Welcome to you if you managed to get that related division fact.

Let's continue to practise this skill of finding related division facts with task A.

Task A is to draw a line to match each multiplication with the related division equation.

Make sure to look really carefully at the numbers in the equation because that's going to help you to see the different parts of each equation.

You might also like to use an array like Jacob and Sofia did to help you to visualise each of the problems. Jacob realises that he could use his stem sentence, times is equal to, so divided by is equal to, so you might also like to use that to explain what you found after each one.

Pause this video, have a go at task A and then come on back when you are ready to see how you've got on.

Welcome back.

I hope you enjoyed using that stem sentence there and exploring those equations.

Should we see which ones are related? Three times by 10 is equal to 30, so 30 divided by 10 is equal to three.

Well done if you've got that one.

Here, the equal symbol had moved, but 20 is still our whole, so our division is going to have 20 as the dividend.

So two times by 10 is equal to 20.

So 20 divided by 10 is equal to two.

Well done if you spotted that one, six times by 10 is equal to 60.

So 60 divided by 10 is equal to six.

50 is equal to five times by 10 or 50 divided by 10 is equal to five.

Eight times by 10 is equal to 80.

So 80 divided by 10 is equal to eight and finally, four times by 10 is equal to 40.

So 40 divided by 10 is equal to four.

Well done if you managed to match all of those related equations.

Let's continue with the second part of our learning, finding errors in equations.

This is going to let you apply what we've just learned in learning cycle one into some new problems. So let's get started.

Sofia solves this worded problem using her knowledge of multiplication and division facts.

What advice would you give to her? Jacob shares 40 stickers between 10 of his friends.

How many stickers will they get each? Sofia notices that four times by 10 is equal to 40.

So 10 divided by 40 is equal to four so that each child will get four stickers each.

Is that correct? I'm not sure about that one.

Hmm, you might like to have a think about this before we move on.

We can see that Sophia is correct.

Each child will get four stickers and she used the correct multiplication fact to help her, but the division equation that she's recorded is incorrect.

Let's have a look.

She's recorded 10 divided by 40.

We know that the dividend is our whole, so how many stickers does Jacob have altogether? Does he have 10 stickers? No, he has 40 stickers.

We know that the dividend has to go first in our equation, so it won't be 10 divided by 40.

What's it going to be Sofia? Sofia has noticed that 40 is the dividend and the divisor is 10, so she's recorded them the wrong way around.

That looks a lot better.

Four times by 10 is equal to 40, so 40 divided by 10 is equal to four.

Each of the friends will get four stickers.

Well done for correcting that, Sofia.

Okay then, let's have a look at these then.

Which of these equations are an accurate related division fact of three times by two is equal to six.

Think about the different parts of that equation and which parts will they become in our division.

Pause this video, have a look at the equations and decide which ones are correct.

Come on back when you think you've got an answer.

Welcome back.

Let's have a look then, three times by two is equal to six.

So six is our whole, which means that six will be the dividend in our related division fact.

We can see that A and B both have six as the dividend and the quotient and divisor have changed places, but they are still using related numbers.

Both of these division facts are related to three times by two is equal to six.

In C, we can see that six is recorded as the quotient, which is incorrect as six is the whole in three times by two is equal to six.

Remember that whole, the dividend goes first in our division equation.

Well done if you said that A and B were related division facts.

Jacob now solves a worded problem using his knowledge of multiplication and division facts.

What advice can we give him here? Sophia shares 20 friendship bracelets she has made between 10 of her friends.

How many bracelets will they get each? We know that 10 times by two is equal to 20.

So 20 divided by two will be equal to 10.

They're going to get 10 bracelets each.

Have a little think about that problem.

Have a look at what Jacob has written.

Is he correct? What advice could we give him here? We know that Jacob has divided 20 by two, but actually, our bracelets are being shared between 10 friends, so he is not dividing by two.

He's actually dividing by 10 because there are 10 friends, not two.

That means that he should have divided 20 by 10 to find out how many bracelets each child will get.

Jacob has realised that 20 is our dividend, but we're dividing them by 10, not two.

So let's change your equation there Jacob.

20 divided by 10 is equal to two.

So each child will actually get two bracelets each, not 10, well done for realising your mistake there Jacob and correcting it.

So 20 bracelets shared between 10 friends will be equal to two each.

Each child can't get 10 each.

There's not enough bracelets for that Jacob.

Okay then over to you, have a look at this worded problem.

In a pack of cookies, there are 20 cookies, five people share them equally and get four cookies each.

Having a look at that division problem, can you identify the dividend, the divisor, and the quotient and record that as a division equation? Have a careful think about what each of those parts of the division tells us.

Read the problem carefully and record it as a division.

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

Welcome back.

Let's have a look then.

We can see that there are 20 cookies all together.

So 20 will be our whole in our equation, the cookies are being shared between five people, so that's the number that we are dividing by.

So that is our divisor, 20 divided by five.

Four is the number of cookies that each person gets after sharing.

So four is going to be our quotient.

So the correct division equation will be 20 divided by five is equal to four.

Well done to you if you got that correct.

Let's continue to practise this during task B.

Task B, part one is to explore each of the equations in the table and put a tick or a cross to show whether they are correct or not.

Two times five is equal to 10, so 10 divided by five is equal to two.

If you think that they are correct, you put a tick next to the box.

Five times by two is equal to 10, so 10 divided by two is equal to five.

10 is equal to two times by five.

So five divided by 10 is equal to two and 10 is equal to two times by five.

So five is equal to 10 divided by two.

The equal symbol has changed places in those bottom two equations.

But remember that does not change anything.

Have a look at all four of them and decide whether they are correct or incorrect.

Then part two is to circle the error that you find.

So when you find an incorrect answer, can you then explore why is that incorrect? Once you've explored why it's incorrect, can you then part B, rewrite the equations so that they are correct.

Pause this video, have a go at part one and part two of task B, and then come on back when you're ready to complete the learning.

Welcome back, let's have a look then.

Part one, let's explore all of those equations.

So two times by five is equal to 10.

So 10 divided by five is equal to two.

That's correct.

10 is my whole, my dividend.

We are dividing by five and the quotient will be two.

Five times by two is equal to 10.

So 10 divided by two will be equal to five.

Again, that is a correct related division fact, 10 is equal to two times by five.

So five divided by 10 is equal to two.

I'm not sure about that one.

That is not correct and we will see why in part two, 10 is equal to two times by five.

So five is equal to 10 divided by two.

That sounds good to me.

So there is our one incorrect equation.

Now let's look at part two, why is that not quite right? We noticed that in this equation that five divided by 10 was not correct.

10 is the product of two times by five, so that means in the related division fact, 10 would be our whole or our dividend.

Is 10 the dividend here, no, I can see that five is my dividend, five divided by 10.

We can't do that, so that must be incorrect.

Well done if you spotted that.

Now let's write them the correct way.

10 is equal to two times by five, so 10 is the dividend.

So this should be before the division symbol because that's our whole, 10 divided by five is equal to two.

Well done to you if you spotted that mistake and you were able to correct it.

Well done for completing Task B.

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

The dividend is the whole, it is what is being divided.

The dividend can only be the dividend in a division equation.

The divisor and the quotient represent the number of groups or the size of the group.

The divisors and the quotient can swap places and the equation remains correct.

Welcome for using our new mathematical language today, dividend, divisors and quotient.

I hope that you've been able to use that in lots of your explanations today.

Thank you for all of your hard work.

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

See you soon, goodbye.