Lesson video

Hello, my name's Mrs. Hopper and I'm looking forward to working with you in this lesson.

This lesson comes from our unit on the order of operations.

I wonder if you've come across that before.

Any ideas what it's about? Well, let's get going with this lesson and explore more about the order of operations.

In this lesson, we're going to be combining division with addition and subtraction.

By the end of the lesson, we should be able to explain which order to complete the division and additional subtraction elements of a problem, and to know how to write this as an equation.

There's one key word and a key phrase in our lesson today.

We've got brackets and order of operations.

I'll take my turn to say them, then it'll be your turn.

My turn, brackets, your turn.

My turn, order of operations, your turn.

Well done.

They may be words you've come across.

Let's just remind ourselves what they mean.

Brackets are symbols used in pairs to group things together.

So here we've got 12 plus 16 divided by four.

You might have used brackets in English as well.

And the order of operations is a set of rules that tell you which operations have priority over others in an equation.

Sometimes we can tell this order from the problem that we are solving, but when there's no problem attached to it, we need to know which order we should complete the different elements of an equation.

There are two parts to our lesson, in the first part, we're going to be combining division with addition, and in the second part we're going to combine division with subtraction.

And we've got Jun, Aisha, and Sam in the lesson with us today.

Jun and Sam both have some coins in their wallets.

One of them has 35 p in five Ps, and the other has 20 p in two Ps.

Jun says, "How many coins do we have altogether?" Sam says, "I could count in 5s and then in 2s, and I could work this out, couldn't I?" "You could," says Jun, "But I think there could be a more efficient method we could use." Sam says, "Perhaps we could use division to help us." "Great idea," says Jun.

"My divisors will be five because I have 5-pence coins." so Jun's gonna be dividing by five.

And Sam says, "My divisors is different.

I have 2-pence coins, so my divisors is two." So she's going to be dividing by two.

Jun says my dividend is 35, the number I'm starting with my whole because that is the total amount of money I have in my wallet.

So Jun is looking at 35 divided by five.

Sam says my dividend is 20 because that is the total amount of money I have in my wallet.

So Sam's looking at 20 divided by two.

Now we can find the quotient for each division.

So that's the result of the division and it'll tell us how many coins they each have.

35 divided by five is equal to seven, and 20 divided by two is equal to 10.

To find out how many coins we have altogether, we can add our quotients together.

So Jun has seven 5-pence coins, giving him a total of 35 pence, and Sam has ten 2-pence coins, giving her a total of 20 pence.

So they have seven plus 10 coins altogether, which is 17 coins.

"We have 17 coins altogether," says Jun.

Jun says, "We could write this equation to record how we solve the problem." 35 divided by five plus 20 divided by two, so that was equal to seven plus 10.

Seven and 10 were the quotients, the results of the divisions and we need to add those together to find the total number of coins.

Now, Jun and Sam have different coins in their wallets.

We've got 60 pence in 10 p coins and 80 pence in 20 p coins.

Jun says, "Let's find out how many coins we have altogether this time using division and addition again." Sam says, "I'll start by writing the division expressions for each group of coins." So we've got 60 divided by 10, that'll tell us how many 10 p coins we have in 60 P.

And 80 divided by 20, that will tell us how many 20 p coins we have in 80 p.

"Now we can calculate the two quotient and add them together to find our total number of coins," says Jun.

60 divided by 10 is equal to six, 80 divided by 20 is equal to four.

Six plus four is equal to 10.

"We have 10 coins altogether," says Sam.

"How could we write this as an equation?" Jun says, "We could write this equation to record how we solve the problem." 60 divided by 10 plus 80 divided by 20 is equal to six plus four, which is equal to 10.

Time to check your understanding.

Which expression represents how to find the total number of coins in these wallets? Is it A, B, or C? Pause the video, have a go.

When you're ready for some feedback, press play.

Which one did you reckon? We had 30 P in two pence coins, so 30 divided by two and 80 P in 10 pence coins, so 80 divided by 10.

So it's C.

The division expressions you could write for this problem are 30 divided by two and 80 divided by 10 because there is 30 pence in two pence coins and 80 pence in 10 pence coins.

A has divided each dividend by the wrong divisors.

We've got the 30 P divided by 10 to find out how many 10 p coins and the 80 divided by two.

And B, has the divisor and the dividend written the wrong way around? Two divided by 30 and 10 divided by 80.

We need to make sure that we record our dividend first and then divide by our divisor.

Jun and Sam are going to explore more equations that combine division and addition.

So here we've got 12 plus 16 divided by four is equal to something.

Jun says, I know that 12 plus 16 is equal to 28, so I need to calculate 28 divided by four to solve this equation.

Does that sound right? Sam says, "I'm not sure whether we need to add or divide first.

Let's ask Aisha if she can help us." Aisha's been learning about the order of operations, a set of rules that tell you which operations have priority over others in an equation.

This diagram shows the order of operations.

Division has priority over addition.

So it needs to be calculated first.

The things that have the highest priority are at the top of our triangle.

And this triangle was devised so that we could, when we were just looking at an equation, always get the correct answer or get the answer that was intended.

So division has priority over addition, so it needs to be calculated first.

So even though 12 plus 16 is written first, the order of operations means that you need to calculate 16 divided by four first.

So 16 divided by four is equal to four, so we can now put that value in and it's 12 plus four is equal to 16.

So that means the solution to this equation is 16.

Aisha shows Jun and Sam another equation that combines division with addition.

Remember that the order of operations means that you need to calculate 10 divided by five first.

10 divided by five is equal to two.

So 10 plus 10 divided by five is equal to 10 plus two, which is equal to 12.

So that means the solution to this equation is 12.

Jun says, "Is it possible to write an equation where you would add before you divide?" "Good question, Jun.

It is possible.

You would need to use brackets," says Aisha.

So if we wanted to do the addition first, 10 plus 10 first, we'd have to put bracket around it because if you remember, in the order of operations, brackets has the highest priority.

Any part of an equation written in brackets should be calculated first.

Brackets have the highest priority in the order of operations.

So this equation is 20 divided by five, which is equal to four.

Let's compare these equations.

The numbers and operations are the same, but only one equation has brackets.

Including brackets in an equation can change the solution.

It's really important to record your equation correctly for this reason.

And Jun's reminding us, "In the order of operations, division has priority over addition.

Sam says, "When there are no brackets, you divide before you add.

Time to check your understanding.

Can you match the equations to the correct solutions? Pause the video, have a go.

When you're ready for some feedback, press play.

How did you get on? So the first one was six plus six divided by three.

There's no brackets, so we need to do the division first.

Six divided by three is two and six plus two is equal to eight.

In the next one, we've got the same numbers in our expression, but this time the six plus six is in brackets.

Six plus six is equal to 12, 12 divided by three is equal to four.

14 plus 12 divided by two.

There are no brackets, so we do the division first.

12 divided by two is equal to six, 14 plus six is equal to 20.

In the next one though, same values, but this time we've got brackets.

14 plus 12 is in brackets, so we need to do that first.

So that's 26, and 26 divided by two is equal to 13.

Aisha says, "Remember, that when there are no brackets, division needs to be calculated before addition." And time for you to do some practise.

So in question one, you're going to complete the equations and solve each problem.

And for question two, you're going to solve each equation.

And Sam says, "Remember, that when there are no brackets, division is completed before addition." Pause the video, have a go at questions one and two, and when you're ready for some feedback, press play.

How did you get on? Let's look at one.

So you were completing the equations and solving each problem.

Jun has 32 p in two pence coins and Sam has 70 p in five pence coins.

How many coins do they have altogether? So we're going to divide 32 by two because that we are finding out how many 2-pence coins and we're going to divide 70 by five to find out how many 5-pence coins.

32 divided by two is equal to 16, 70 divided by five is equal to 14, 16 plus 14 is equal to 30.

They have 30 coins altogether.

So in B, we're thinking about paint.

Sam has 10 litres of red paint, which she pours into five pots, and Jun has 20 litres of blue paint, which he pours into four pots.

They each give one pot of paint to Aisha.

How much paint does Aisha have? So we are thinking about 10 litres of red paint divided between five pots, so 10 divided by five, and we're adding that to 20 divided by four.

So 10 divided by five is two, so there'll be two litres in each pot there.

And 20 divided by four is equal to five, so there's five litres in those pots.

So Sam has two litres in each pot of the red paint and Jun has five litres in each pot of the blue paint.

So that's seven litres in total and they've each given a pot to Aisha, so that's one of each.

So Aisha has seven litres of paint.

Onto question two.

You were solving each equation looking carefully to see if there were brackets, and if there were no brackets, then division happens before addition.

So eight divided by four is equal to two, 12 plus two is equal to 14.

In B, we've got brackets this time.

12 plus eight is equal to 20, 20 divided by four is equal to five.

In C, there are no brackets.

So 18 divided by three is equal to six and six plus three is equal to nine.

But in D, we've got brackets.

18 is divided by three plus three, which is six.

18 divided by six is equal to three.

So you can see in those first examples and you'll see in the next, how important it is to make sure that if we need brackets, we put them in the right places because it can really change the result of an equation.

In E, 12 divided by three plus nine, we're going to divide first.

12 divided by three is four, four plus nine is 13.

And then in F, it's 12 divided by three plus nine or three plus nine is equal to 12.

12 divided by 12 is equal to one in G, 12 plus 18 divided by six.

We divide first because there's no brackets.

18 divided by six is equal to three.

12 plus three is equal to 15.

And in H, we're going to do our addition first.

12 plus 18 is equal to 30.

30 divided by six is equal to five.

Did you remember that when there are no brackets, division is completed before edition.

I hope you did.

And on into the second part of our lesson, we are combining division with subtraction this time.

Jun and Sam are helping to prepare party bags.

Jun says I will put two lollipops in each of my party bags and Aisha says I will put six sweets into each of my party bags.

Jun has six lollipops, Aisha has 12 sweets.

Who can fill the most party bags and by how many? So Jun's putting two lollipops into each bag so he can fill 1, 2, 3 bags with his six lollipops.

Aisha has 12 sweets.

She's putting six sweets into each of her party bags.

Six sweets, 12 sweets, so she's only filled two bags.

Six divided by two is equal to three, that's three party bags.

12 divided by six is equal to two, that's two party bags.

So Jun says, "I can fill one more party bag than you." Aisha says, "We could write this equation to show our working out." Six divided by two, subtract 12 divided by six is equal to three, subtract two, which is equal to one.

This time Jun has four lollipops and Aisha has 18 sweets.

They still put two lollipops or six sweets in each bag.

Who can fill the most party bags this time? And by how many? "Let's write each division expression to help us write the equations," says Jun.

You are dividing four lollipops into groups of two.

Four divided by two is equal to two.

I'm dividing 18 suites into groups of six.

18 divided by six is equal to three.

"You can fill one more party bag than me this time," Jun says.

We could write this equation to show our working out.

18 divided by six, subtract four divided by two is equal to three subtract two which is equal to one.

The division expression that represents Aisha's party bags needs to be written first in the equation because it represents the greater amount.

So if we want a positive number as our amount, we'll write the greater value expression first.

Jun and Sam are pouring drinks into cups for the party.

Jun has 1,200 millilitres of black current that he pours into six cups.

Sam has 1,500 millilitres of orange that she pours into five cups.

Which cup of drink has the greater volume? Black current or orange.

And by how much? Jun says, "First I will write the division expressions." Can you think what these division expressions are going to be? 1,200 divided by six.

That's Jun's black current that he pours into six cups and then 1,500 divided by five.

That's the 1,500 millilitres of orange that samples into five cups.

So the result of Jun's expression is 200 what? 200 millilitres in each cup, isn't it? And for Sam, it's 300 millilitres in each cup.

Then says, Jun, "I can write and solve the equation for the problem." We know that Sam's Cup has the most amount of juice in it, the larger volume.

So we're gonna write that one first in the equation.

1,500 divided by five, subtract 1,200 divided by six.

We know that we do the division first, so it's 300, subtract 200, which equals 100.

The cup of orange drink has the greater volume than the cup of black current drink by 100 millilitres.

Time to check your understanding.

Which equation matches this problem? Jun and Sam are pouring drinks into cups for the party.

Jun has 1,800 millilitres of black current that he pours into six cups.

Sam has 2000 millilitres of orange that she pours into five cups.

Which cup has the greater volume? Black current or orange.

And by how much? So is it A, B, or C that represents that? Pause the video, have a go.

When you're ready for some feedback, press play.

What did you think? Which one was it? How did you spot that it was B? A has written the division expressions the wrong way around.

The expression with the greatest value needs to be written first if we want to find a positive difference.

We would find the difference here, but it would be expressed as a negative number and difference, we always think of as positive.

So B has the expressions written the right way round, doesn't it? And then C, this doesn't match the problem because it uses addition and that doesn't help us to find the difference.

So B was correct.

A was almost correct, but it wouldn't have given us a positive answer.

Sam and Jun explore more equations that combine division with subtraction.

So we've got 12 divided by six, subtract four divided by two.

And Aisha says, this time, there are two division operations.

They must both be completed before the subtraction.

So 12 divided by six is equal to two and four divided by two is equal to two.

Two subtract two is equal to zero.

Sam says that means the solution to this equation is zero.

Let's have a look at this.

Any part of an equation written in bracket should be calculated first.

Bracket have the highest priority in the order of operations.

So now we've got 12 divided by, six subtract four, and then divided by two.

Jun says, "I need to calculate six subtract four first because it is in the brackets." So this means our equation is 12 divided by two, divided by two.

Now I can solve each division from left to right.

Division is not commutative, so you cannot divide in any order, which is why you need to work from left to right.

12 divided by two is equal to six and six divided by two is equal to three.

So the solution to this equation is three.

Let's compare this equation to another with the same numbers and operations but without brackets.

So this was where we started.

12 divided by six, subtract four divided by two had a value of zero.

Aisha says, "Brackets can change the solution.

This shows why it is really important to record your equation correctly and think carefully about if you need brackets and where they should go.

Time to check your understanding.

Can you match the equations to the correct solutions? Remember the order of operations.

Pause the video, have a go.

When you're ready for some feedback, press play.

How did you get on? So in the top one, we have no brackets, so the divisions will be done first.

16 divided by eight is equal to two, and four divided by two is equal to two.

Two subtract two is equal to zero.

For the next one, there is a bracket around the eight subtract four.

So we've got 16 divided by four, which is four and four divided by two, which is two.

In the next one we have no brackets so the divisions happen first.

36 divided by six is equal to six.

Subtract three divided by three, which is equal to one.

So that's six subtract one, which is equal to five.

And then we do have brackets this time.

36 divided by six subtract three, we do that bit first.

Six subtract three is three.

36 divided by three is equal to 12.

And 12 divided by three is equal to four.

And is just reminding us, remember that when there are no brackets, division needs to be calculated before subtraction because it comes higher up in the order of operations.

And time for you to do some practise.

For question one, you're going to write a whole number in each box to complete the equations.

How many different answers can you find? And Aisha again, reminding us, remember that when there are no brackets, division is completed before subtraction.

And in question two, some of these equations needs to include brackets to make them correct.

Check each equation and add brackets where they are needed.

So pause the video, have a go at questions one and two.

And when you're ready for the answers and some feedback, press play.

How did you get on? So in question one, there are lots of different solutions.

But here are some examples of how you could complete each equation with a whole number in each box.

So 35 divided by seven, subtract something divided by seven is equal to.

Well, the first empty box needs to be filled with a multiple of seven because the divisors is seven.

And we wanted whole number answers, didn't we? Did you notice that the second empty box was always a five? Because the first division expression, 35 divided by seven did not change.

So it was always going to be five subtract and then whatever the result the quotient of your second division expression was.

So we could have had 28 divided by seven, so subtracting 4, 21 divided by seven, 14 divided by seven and so on.

So in B, the first empty box needed to be filled with a multiple of six because the divisors is six and we wanted whole numbers.

You could have chosen a number greater than 30 so that you could subtract the quotient to find a positive difference.

So we needed any multiple of six that was greater than 30.

So we could have had 36 divided by six, six subtract 5, 42 subtract six, giving us seven to subtract the five from, 48 subtract six and so on.

We could have carried on.

So for C, this time, you could choose the dividend and the divisor.

You could choose any division expressions that would have the quotient of 10 and six.

So we could have had 40 divided by four, subtract 24 divided by four.

We could have had 60 divided by six, subtract 36 divided by six.

We could have had 90 divided by nine, subtract 30 divided by five.

The possibilities were endless.

And for question two, some of these equations needed brackets to be included.

Check the equation and add brackets where they're needed.

So whether are no brackets, we do the division first.

So eight divided by four is equal to two, 20 subtract two is not equal to three.

So we needed brackets here.

What if we do the 20 subtract eight.

20 subtract eight is equal to 12.

12 divided by four is equal to three.

So we needed brackets around the 20 subtract eight to do the subtraction first.

Aisha says, "I knew that a needed brackets because you need to calculate 20 subtract eight first and then calculate 12 divided by four to get the solution of three." What about B? B does not need brackets because when there are no brackets, you calculate the division first.

Eight divided by four is equal to two and 20 subtract two gives the correct solution of 18.

What about C? Again, C is correct as it is.

It doesn't need any brackets.

We can do the division first.

What about D? D needs brackets around the five subtract two.

30 needs to be divided by three to equal 10, doesn't it? Five subtract two is equal to three.

What about E? Well, we are thinking about five as our solution.

50 subtract 25 divided by five, which is what we would do first, does not equal five.

So 50 subtract 25, we need 25 divided by five to give a solution of five.

So for F, we've got a solution of 45.

Well, that is 50 subtract five and 25 divided by five is equal to five.

So that one is correct as it is.

30 subtract five is equal to 25 and 25 divided by five is equal to five.

So that is correct as it is as well.

But 30 subtract five is not equal to one.

So this time we need to do the subtraction first.

30 subtract 25 is equal to five and five divided by five is equal to one.

Well done if you've got all of those right.

And we've come to the end of our lesson.

We've been combining division with addition and subtraction.

What have we learned? We've learned that when solving problems that combine division with additional subtraction, you can think about the context of the problem and choose which element of the problem to complete first.

When you write out your solution as an equation, you need to know the order of operations.

Division has priority over addition and subtraction.

If you solve the problem by adding or subtracting first, you need to use brackets to show that this part of the equation needs to be calculated first.

Thank you for all your hard work.

I hope you enjoyed exploring some more about the order of operations this time with division.

And I hope I get to work with you again soon.

Bye-bye.