Lesson video

Hi there.

I'm Mr. Tazzyman and I'm really excited to be doing some learning with you today.

If you're all ready, we can get started.

Here's the outcome for today's lesson.

By the end, we want you to be able to say, "I can use addition and subtraction strategies to solve problems in different contexts." I think it's really important to say that going into this lesson you might have learned a lot of different strategies for adding and subtracting mentally, and today you're gonna put them into use in different contexts.

Here are some of the key words that we might see during this lesson.

I'm gonna say them and I want you to repeat them back to me, so I'll say my turn, say the word and then your turn and you can say it back.

My turn menu, minuend.

Your turn.

My turn, subtrahend.

Your turn.

My turn, difference.

Your turn.

My turn, partition.

Your turn.

Okay, let's make sure we also understand what those words mean, as well as how we might say them.

The minuend is the number being subtracted from.

A subtrahend is a number subtracted from another.

The difference is the result after subtracting one number from another.

You can see an equation at the bottom, seven subtract three is equal to four.

In this equation, the number seven is the minuend, the number three is the subtrahend, and the difference is the number four.

We also have partition.

Partition is the act of splitting an object or value down into smaller parts.

Here's the outline for today's lesson on using addition and subtraction to solve problems in different contexts.

For the first part, we are going to think about how we might find and understand the structure of the question, how it's built? Then we'll look at solving the problems in the second part.

Ready to begin? Okay then.

Here's two friends you're going to meet along the way, Aisha and Laura.

They're going to help us by discussing some of the prompts that you'll see on screen that also reveals some of the answers and give some good bits of reasoning to deepen our understanding.

Below is the start of a maths problem.

June grows a sunflower.

After a couple of months it has grown 120 centimetres.

What could the question be? Hmm.

Well, Laura says, "I think it might grow some more." The question might be, how tall is it after three months? Aisha says, "That would be good.

I think that would need addition and you're missing some information." Laura says, "We'd have to say how much more the sunflower grew in the third month." Aisha says, "Jacob might have grown a sunflower too." It could be taller.

Then the question could be how much taller? "I like that," says Laura.

We'd need some extra information again.

I wonder what she means? Have a think.

Aisha says, "Yes, we'd need to know how tall Jacob's sunflower was." And Laura says, "Thinking like this helps to understand the structure of a problem, so I know how to answer it." Here are three maths problems. Aisha spies 10 birds in a line.

Three birds fly away.

How many birds remain? There are 10 slices of pizza.

Laura eats three slices.

How many slices of pizza are left? Crates of watermelon can fit 10.

This crate has three.

How many more watermelons can be put in? What is the same and what is different about all three of these maths problems? Look closely at them and have a think.

Laura says, "They all have the same structure." The equation is 10 subtract three is equal to an unknown.

That's what the problem is asking you to work out.

And Laura then goes on to say, "They all have different contexts." They are about different things.

Okay, it's your turn to check that you've understood what we've been through so far.

Here are three more similar maths problems. You can see they've actually got the same context, but we've changed something.

In the first one, Aisha spies eight birds in a line.

Four birds fly away.

How many birds remain? There are eight slices of pizza.

Laura eats four slices.

How many slices of pizza are left? And crates of watermelons can fit eight.

This crate has four.

How many more watermelons can be put in? Your task is to write down the equation that shows the structure of all three problems. Pause the video here and I'll be back in a moment to reveal the answer.

Welcome back.

Did you manage to find an equation that worked for all three of these contexts? Let's see.

Did you get eight subtract four is equal to four? Hopefully you did.

Okay, let's move on.

Here are two maths problems. Laura has baked 13 cupcakes.

She gives five of them to her friends.

She's very kind, Laura.

How many does she have left? At the first stop, five children get on the bus.

At the second stop, eight more children get on.

How many children are on the bus now? What's the same and what's different about these two problems? Have a think.

Aisha says.

"They both have similar structures, but one needs addition and the other subtraction." She says, "I can draw a bar model to show the structure.

And you can see it there, we've got two unknowns in this bar model.

We know that one of the parts that makes the whole is five and that's the same in both questions.

In the cupcake problem, the missing part is the minuend.

This is a subtraction problem.

So from that, she's been able to get the fact that the total is 13 because Laura had 13 cupcakes and she gave five away.

In the bus problem, the missing part is the total or sum.

This is an addition problem.

So you can see in the bar model now that the total has been replaced with a question mark, but one of the parts is eight and one of the parts is five, which need to be added together in the bus problem.

The structure is the same.

It can be represented with the bar model, but the question is different.

One of them is a subtraction question and one of them is an addition question.

Let's check that you've understood all of that.

Here are two more maths problems. Identify which involves addition and which involves subtraction.

Then represent the structure using a bar model.

Let me read the questions for you.

Laura sees four squirrels on the way to school.

On the way home she sees seven more.

How many squirrels did she see altogether? Aisha has a go at archery.

She scores seven on her first turn and 11 on her second.

How much did she improve? Which one is addition? Which one is subtraction? And can you draw a bar model to show the structure of both? Pause the video here, have a go at that and I'll be back in a minute to reveal what the answer is.

Welcome back.

How did you get on? Were you able to identify an addition and a subtraction and draw a bar model? Well, let's check.

This one was the addition.

The squirrel question, you needed to do four added to seven.

So the archery question was subtraction.

You needed to do 11, take away seven because we were trying to work out how much Aisha had improved.

And here's the bar model.

Our total was 11 and our two parts were seven and four.

How did you get on? I hope you got it.

Okay, let's go to the next part.

Problems can sometimes look different.

Below is an addition number pyramid.

The two adjacent bricks add together to make the total above.

So two bricks next to one another add together and they make the brick above them.

There are three missing numbers.

You can see we've represented those with question marks.

They are our unknowns.

What is the equation for each? So we're not necessarily looking for just the number.

We're looking for what the missing equation is.

Aisha says, "I will start with the bottom left." This is a subtraction.

250 subtract 120 equals an unknown.

Now I will do the middle right, an addition.

120 plus 70 is equal to an unknown as yet.

Aisha says, "I can't do the equation for the top yet." I know 12 plus seven equals 19.

So 120 plus 70 is equal to 190.

Aisha's used the known fact there and unitizing.

Well done, Aisha.

Now she can do the equation at the top.

She says it's addition and she knows both of the addends.

It's 250 added to 190 is equal to an unknown.

In order to get that, she had to work out one of the other equations so that she had a value to make an addend.

Okay, practise time.

For your practise, number one, I want you for each of these worded problems to write down the equation in the question, represent 'em as a bar model and then solve them.

For A, 42 penguins escape from a zoo.

Zookeepers managed to catch 30, but the rest is still not found.

How many penguins are still not back in the zoo? And for B, a tenpin bowling team score 120 points in the first half of a match and then 200 points in the next half.

How many points did they score altogether? For number two, I want you to write the equations for the missing numbers In this addition number pyramid.

You do not need to solve.

You can see the letters A and B are nestled within this pyramid.

I'd like you to write an equation that represents that brick.

Pause the video here, have a go at these and I'll be back in a little while for some feedback.

Good luck.

Okay, ready for some feedback? Be ready to mark.

Here's one A.

So the question, the equation, the structure was 42 subtract 30.

You might have drawn it out as a bar model looking like this.

We have 42 as the total.

One of the parts is 30 and then we have a missing value for our next part.

You might have used the number line to clarify your thinking.

Started on 42, counted back 30 to give you 12.

Okay, let's look at B.

In B, the structure was 120 plus 200.

Again, you might have drawn a bar model that looks something like this.

This time the unknown was the total and we had two paths of 120 and 200.

Here's a number line and you might have started on 120 and made a jump of 200 to get to 320, which was the answer.

Okay, let's move on to looking at this addition pyramid.

We are asking you to find the equations.

A, was 110 subtract 90.

B, was 90 add 70.

How did you get on? I hope you did well.

It's time for us to move on to the second part of the lesson now, solving problems in different contexts.

We'll be able to use our learning from the first half to analyse the problems and find their structure and then we'll use a range of different methods to solve them.

Aisha looks back at this pyramid.

She wants to solve the rest of it.

She says, "I'll start with the subtraction using partitioning." I'll partition 120 to 120 and she's written a jotting above just to clarify her thinking.

She uses a number line to help.

She starts on 250 and she's going to count back.

First with a jump of 100 to get to 150 and then she's gonna subtract the 20 to give her 130.

She fills in the brick, then looks towards the top.

She says, "The last one." And she decides she's going to use a technique called redistribution.

She writes out her jotting, but she decides she'll take 10 from 250, the first addend, and then she's going to redistribute it to 190, the second addend.

It transforms the calculation and she says, "Now I have an easier calculation." 240 plus 200.

She knows that's 440 and she pops that into the top of the brick.

The puzzle is complete.

Well done, Aisha.

Here are two maths problems. Laura has 450 football cards.

Aisha has 210.

How many more cards does Laura have? And here's the second one, Laura has 450 football cards.

Aisha has 210.

Laura gives away 230 to June.

How many more cards does Laura have now? What is the same and what is different between these two maths problems? Have a look and have a think.

Aisha says, "Well, we can write the first one as an equation, which would be 450 subtract 210." Well done, Aisha.

You are putting our learning into practise by immediately trying to find the structure of the problem.

But Laura says, "Yes, but the second one has two parts to it.

First we have 450 subtract 230.

Then we would take the answer from that and find the difference with 210.

So there's two parts here.

Aisha says, "The first problem is a bit easier because it has one step." And Laura says, "Yes, the second one has two steps, so it's harder." Have a look at this problem.

In one year, the local council plants 360 trees.

The next year they plant 270 more.

How many trees have been planted over the two years? How can this problem be represented? "I am going to represent this as a bar model," says Laura to help me think about it.

And there it is.

She's got two parts and a missing total.

It's an addition and the addends are multiples of 10.

So she decides she's going to use partitioning and bridging.

That's her most efficient strategy.

She starts on 360, adds on 200 to get to 560.

Then she adds on 40 and then 30.

Those last two jumps were 70 partitioned again, and that's because she needed to bridge through 600.

Now, the most important part really does the answer solve the problem? She says, this seems a reasonable answer because it won't be greater than 700.

The council planted 630 trees.

She says, "That's amazing.

I agree." Okay, time to check your understanding on the things we've just learned about.

In a science experiment, Aisha makes 280 grammes of slime.

Laura makes 130 grammes of slime.

They mix their slime together.

How much slime is there now? Have a go at this problem and I'll be back in a little while for some feedback.

So pause the video here.

Welcome back.

Let's see how you got on.

We know that the structure of the problem was 280 grammes plus 130 grammes.

You might have decided here to use partitioning and bridging.

First of all, you might have added 100 to 280 to get to 380.

Then partitioned the second part into 20 and 10, leaving you on 420 grammes.

How did you get on? I hope you got it.

Okay, let's move on.

Aisha pulls herself 250 millilitres of squash.

Laura, kindly, I told you she was kind, kindly pulls in 102 millilitres more before Aisha drinks 47 millilitres.

How much squash does she have left? Let's start with how can the problem be represented.

Aisha says, "There are two steps here, which I need to show." First, is 250 plus 102.

She draws that there as two parts next to one another.

Then she says we can subtract 47 from that sum.

So she's drawn that as a bar underneath in which she's got the total at the top of 250 plus 102.

Then she's got a subtraction of 47 with a missing part.

Which strategy is most efficient? She says, "I'm going to use adjustment for the first part that top bar." So she subtracts two from one of the addends, 102, so that then she's got an easier calculation, 250 plus a hundred, that's 350, but she's not finished.

Now she's got to adjust that sum.

She took two away from one of the addends, so now she needs to add two to that sum.

That gives her 352, and you can see she's very sensibly changed the bar at the top of the bar model to 352.

Now we're down to only one step to go.

She says, "Now I have the equation, 352 subtract 47.

I'll use partitioning and bridging." She draws out her number line and starts on 352.

She subtracts 40 to begin with to get to 312.

She has seven left over.

She knows she's gonna have to bridge through 10, so she partitions the seven into two at first to get to 310, an easy number to work from.

Then she subtracts five and finishes on 305 millilitres.

Two steps in that question.

Well done, Aisha.

Let's think though whether the answer solves the problem.

She says, "The answer is 305 millilitres." That seems reasonable as I didn't drink loads.

You can see she only drank 47 millilitres.

Well done, Aisha.

Problems can sometimes look different.

This is a magic square.

The rows sum to the same number, 15.

The columns also sum to 15.

The diagonals also sum to 15.

Magic.

Aisha and Laura are looking at a magic square.

All the rows, columns, and diagonals add up to 300 this time.

Last time it was 15.

This time it's 300.

They want to find the missing number.

Can you see it in there? We've represented the unknown as a question mark.

It's top right.

Aisha says the missing number is the top right.

What's the equation? Well done, Aisha.

Look for that underlying structure to begin with.

Laura says, "I think it will be 160 plus 20 equals question mark or 140 plus 40 equals question mark." Aisha says, "I think there are two steps to this.

I think it will be either of your sums subtracted from 300." Whom do you agree with? Hmm.

Well, let's see.

Laura agrees.

She says, "I see you are right.

I'll draw a bar model." There it is.

300 is our total.

We have a part of 160, a part of 20 and an unknown.

And if you look at the magic square, that's the top row.

All the values have been put in as parts to make 300.

Laura says, "I know that 16 plus two is equal to 18, so I know that 160 plus 20 is equal to 180." Great use of unitizing.

Well done, Laura.

And she changes the bar model to make sure that she has noted that 180.

Now it looks a bit simpler.

Only one step to go.

"Great," says Aisha.

So now we can do 300, subtract to 180.

She's going to use a number line to help her thinking.

She starts on 300 counts back a hundred first because she's partitioned 180 into 180, so the next step is to count back 18, get to 120.

She says, "The missing number is 120." And she fills in the magic square.

Laura and Aisha, well done.

Okay.

It is time for you to have a practise.

We've got some worded problems here.

One A, Aisha and Laura organise a cake sale to raise money for charity.

They have 222 cupcakes for sale.

Their teacher gives them 48 more.

How many cakes do they have for sale now? One B, Aisha and Laura collect blackberries to make a lovely crumble.

Delicious.

Aisha collects 350 and Laura collects 107.

How many blackberries do they have? Here's number two.

Aisha and Laura are sorting crayons for the class.

They have 320 new ones and 198 old ones.

Their teacher throws away 102 of the old ones.

How many crayons do they have now? And their B, Aisha and Laura travel 252 miles by car to visit friends.

they travel 110 miles and stop for lunch.

Then they travel a further 98 miles before stopping again.

How many more miles do they need to go? Here's number three.

Find the missing numbers in this addition number pyramid.

Last time I was asking you to just write down the equations, but now I want you to solve it.

And number four, find the missing numbers in this addition magic square, the rows, columns, and diagonals add up to 450.

Okay, a lot to get through there.

Just remember, look for that underlying structure first, what is the equation? Does it have two parts? Pause the video here and I'll be back in a little while for feedback when you finished it.

Good luck.

Welcome back.

Let's now go through some of these problems. We've got the cake sale.

We know that the underlying structure was 222 plus 48.

That was our equation.

You might have solved it using redistribution.

Take two of the first addend and add it to the second addend to give you a much easier calculation, 220 plus 50.

That gives us 270 cakes altogether.

Okay, let's move on to look at B.

We've got the Blackberry collection.

This was an addition, so you might have used partitioning.

You might have started on 350, added 100 to get to 450 and then added seven to get 457 blackberries.

That's a lot of blackberries.

Here's number two A.

This was the question about crayons.

You might have spotted that to begin with, you can add together the number of new ones and old ones, 320 plus 198.

You might have used adjustment for this, turning the calculation into 320 plus 200 by simply adding two to the second addend.

That gives 520, but we know that we need to adjust that as well, so we'll use the inverse, subtract two and finish with 518.

And some people might think, right, the question's done now, but of course this has two parts to it.

We now need to take that and subtract to 102 because that's what the teacher threw away.

You might used partitioning for this, starting on 518, subtracting a hundred to get to 418, and then subtracting two to get to 416.

That was the answer.

416 crayons.

Here's B, the long car journey.

We'd start with 110 plus 98.

To do this, we might use redistribution.

Take two away from the first addend and add it onto the second addend, giving us 108 plus a hundred, a much easier calculation, 208.

But then we needed to take 252, which was the total journey and subtract 208 because that's how far they'd already travelled.

Again, we might well have decided to use partitioning here, but we might have counted on from 208 to 252.

Start by adding to get to 210, then add 40 to get to 250, and then add two to get to 252.

Altogether, we've counted on 44 that they have got 44 miles to go.

Okay, the missing numbers in this addition number pyramid, so for A, you had to do 180, subtract 120, that was 60.

For B, you had to do 120 plus 350, that was 470.

And for C, you had to do 180 plus 470, which was 650.

And lastly, number four, the missing numbers In this addition magic square, they all had to add up to 450.

So we started with 180 plus 60 equals 180 plus 20 plus 40, which gives us 240.

So in that top row we know we've got 240 and we've got A as another part.

So if we take 450 and subtract 240, we can use partitioning to do this.

If we count on from 240, we add 60 to get to 300, then add a hundred to get to 400, and then 50 to get to 450, which means that all together we've added on 60, a hundred and 50.

A hundred and ten plus a hundred.

If we combine the tens and a hundreds here gives us 210.

So there it is.

Let's look at B.

That was 30 and let's look at C, that was 120.

Okay, I hope you managed to solve those puzzles and find the missing values in those problems. Here's a summary of what we've learned today.

Problems can be shown as worded problems in lots of different contexts.

Problems can also look different.

Reading questions carefully can help you understand the steps and operations needed to solve the problem.

And sometimes there could be more than one step.

Looking carefully at the numbers and operations helps you choose the most efficient strategy.

My name is Mr. Taziman, and I've really enjoyed learning with you today.

I hope to see you again in the future on another maths lesson.

Take care.