Lesson video

Hello, my name's Mrs. Cornwell, and I'm going to be helping you with your learning today.

I'm really looking forward to today's lesson.

I know you're going to work really hard and will do really well, so let's get started.

Welcome to today's lesson, which is called Know That Addition and Subtraction Are Inverse Operations.

And it comes from the unit, Additive Structures, Addition and Subtraction.

So in our lesson today, we're going to recognise addition and subtraction as the inverse of each other and we'll find out a little bit more about what that means, and we will practise using addition and subtraction and seeing the link between them, okay? So let's have a look at what we're going to do.

So our keywords for today are add.

My turn, add, your turn.

And subtract.

My turn, subtract, your turn.

And inverse.

My turn, inverse, your turn.

Well done, excellent.

So in the first part of our lesson, we're going to use subtraction to undo addition stories and equations.

In this lesson, you will meet Aisha and Alex.

They will help us with our learning today.

Alex is putting some pens on the table.

So he tells a first, then, now story to explain what he's done.

First there was one pen on the table.

Then I put three more pens on.

Now, there are four pens on the table.

Alex represents it as this equation.

One plus three is equal to four.

Aisha takes some pens back off the table.

Aisha tells this first, then, now story.

First there were four pens on the table.

Then I took three pens back off the table.

Now, there is one pen on the table.

She represents it as this equation.

Four minus three is equal to one.

How did each story change? What was the same and what was different? That's right, there were three pens in the then part of each story, but Alex added three pens and Aisha subtracted three pens.

The children place their first, then, now boards side by side to represent their stories.

What do you notice about the start and end of each story? That's right, the addition story starts with one pen and the subtraction ends with one pen, doesn't it? "The subtraction looks like the addition done backwards," says Alex.

Let's represent this with cubes.

So one plus three is equal to four.

One, we can put an arrow, draw an arrow a bit like on a number line, to represent the plus three, is equal to four.

So four minus three is equal to one.

So to undo that change, we have to take off the three that were added, don't we? Four minus three is equal to one.

When you change your number with addition, you can undo the change with subtraction.

Alex tells this addition story.

First I had two books on the shelf, then I put six more books on.

Now I have eight books on the shelf.

Two plus six is equal to eight.

And there we can see the equation.

What number do you think must be subtracted to undo that change? Let's have a look.

So first I had eight books on the shelf, then six books fell off, didn't they? Eight minus six.

Now, I have two books on the shelf.

Eight minus six is equal to two.

To undo the change, the amounts added and subtracted must both be the same.

So now it's time to check your understanding.

Use cubes to find the number which will undo the change and complete the story and equation.

So we've got six plus three is equal to nine, and then you need nine minus, mm, is equal to six.

Okay, and we will tell a story as well, okay, to represent the addition, so let's have a look at our story.

First I had six conkers in my tin.

Then I collected three more conkers.

Now I have nine conkers in my tin.

So you need to tell the story to that to undo the addition and complete the equation as well, okay? So pause the video now while you try that.

Okay, and now let's see how you got on.

So first I had nine conkers in my tin.

Then I gave away three conkers, okay? 'Cause we had to subtract three, didn't we, because three had been added.

Okay, nine minus three is equal to six, and now I have six conkers in my tin.

To undo the change, the amounts added and subtracted must both be the same.

Let's tell the subtraction story to undo the addition story here.

So we've got five plus four is equal to nine, and then we need nine minus, mm, is equal to five.

Think carefully about the then part in each story.

First there were five pencils in the pot, then I added four more pencils, now there are nine pencils in the pot.

So how are we going to undo that addition? First there were nine pencils in the pot.

Then, I subtracted four pencils, that's right.

Now there are five pencils in the pot.

So to undo the change, we had to subtract the same amount that was added, didn't we? So now it's time to check your understanding again.

Tell a subtraction story to undo this addition story, so we've got seven plus two is equal to nine.

First I save seven pounds, then I save two more pounds.

Now I have nine pounds.

So you need to complete the subtraction story that will undo that, so pause the video now while you try that.

Okay, and now let's see how you got on.

First I had nine pounds.

That's right.

Then I spent two pounds, because you added two, so you need to take the two back off.

Now I have seven pounds, that's right.

And the equation will be nine minus two is equal to seven.

Okay, so now let's undo this addition equation.

So we can see we've got four plus three is equal to seven, okay? Think about what we're going to have to do to undo that change.

That's right, we'll say seven minus three is equal to four, won't we? We undid the change by subtracting the same amount that had been added.

Subtraction is the inverse of addition.

It will undo the change made when adding, so we can see seven minus three is equal to four.

Aisha tells an addition story and writes the equation.

First there four children at the table, then two more children sat down.

Now there are six children at the table.

I wonder what equation we would write to undo this addition.

Aisha's saying, "I think I would write six minus four "is equal to two." Is she right, do you think? Now we know you must subtract the same amount that was added, and in this equation we added two, didn't we? We started with four and added two to increase the amount.

So Aisha's realised her mistake, hasn't she? She says, "I must start with six and subtract two." That's right, and that will undo the change.

And we can see, that gets you back to four, doesn't it, when you subtract two? Six minus two is equal to four.

Okay, so now it's time to check your understanding again.

Alex represents a first, then, now story with cubes and writes this addition equation.

Six plus four is equal to 10.

And there's his six cubes.

When he adds four, it is equal to 10.

So have a look and think about which equation there will undo that change.

Pause the video now while you try.

Okay, and let's think about which equation that would be.

So which subtraction equation would undo this addition? That's right, it would be 10 minus four is equal to six.

So here's the task for the first part of your lesson.

Work with a partner, both get a first, then, now board and put your boards side by side.

And Alex is saying, "I will tell an addition story "for the first example given "and represent it with cubes on my first, then, now board." And then Aisha says, "I will use cubes on my board "to undo your edition story, "then fill in the missing number.

"Then, I will tell the addition story for the next example "so you can undo it." Okay, and you can see the first example is there next to Alex, isn't it? And there are some more as well.

So for each question, write the equations to represent your work, okay? And here are the examples to work through.

So pause the video now while you complete those.

Okay, so here's the second part of your task.

This time, the numbers at the start and end of the story are missing.

How many different ways could you complete this? So Alex is saying, "Use cubes to help you find out." And Aisha reminds us, she says, "You cannot start your story "with more than eight cubes." So you can only have eight or fewer cubes at the start of your story, okay? So pause the video now while you try that.

Okay, so let's see how you got on with the first part of your task.

So for the first example, you may have done this and you can see the first example below there, can't you? So Alex is telling us, "I represented the first example like this, "five plus one is equal to six." And then Aisha says, "I used subtraction "to undo your story." So she said, "Six minus one is equal to five." And there, she used that to complete the missing number to fill in the missing number, didn't she? Okay, you will also have completed these examples, so you would've said, "Five plus two is equal to seven," so you had to subtract two to get back to five again, and then your equations would be five plus two is equal to seven, seven minus two is equal to five.

And then if you look at the next one, you added three, so you needed to subtract three again, didn't you? And there are your equations.

And then for the final example, you added four, so you needed to subtract four.

And there are the equations to represent that, so well done.

Excellent.

Okay, so now for the second part of your task, you may have done this.

So you couldn't start with more than eight cubes, it was eight or fewer cubes.

So we could have had one, couldn't we? And if you added two, it would get you to three, and subtracting two would get you back to one, so you could have had one and three, and your equations would be one plus two is equal to three, three plus two is equal to one.

And there were lots of other examples you could have.

Let's have a look at some of the other examples.

So you could have added two, that would've got you to four, and there are the equations to represent that, you could have had three, that would've got you to five, and then you could have had four and the other number would've been six there, it would, could have had five, and then you would've reached seven, there are the equations again.

Six, you would've reached eight, seven, you would've reached nine, and eight, you would've reached 10, wouldn't you? So well done if you did that.

Excellent.

And you may have noticed, I work systematically, starting at one and trying each number in order until I reached eight, so well done.

You've worked really hard in the first part of our lesson today.

So now, let's move onto the second part of our lesson where we use addition to undo subtraction stories and equations.

So let's use the pictures to tell this first, then, now story and represent it as an equation.

First there were five cats in the garden, then one cat left.

Now there are four cats in the garden.

Five minus one is equal to four.

What happened to the amount of cats at the start of the story? That's right, the amount of cats decreased because some were subtracted.

Now let's tell this story and think about what is different this time.

First, there were four cats in the garden, then one more cat came into the garden.

Now there are five cats in the garden.

Four plus one is equal to five.

The amount of cats increased because some were added.

This is an addition story.

How did each story change? What was the same and what was different? What do you notice? That's right, there was one cat in the then part of each story, but in the first story, one cat was subtracted, and in the second, one cat was added.

The children place their first, then, now board side by side to represent their stories.

Five minus one is equal to four.

Four plus one is equal to five.

What do you notice about the start and end of the each story? That's right, the subtraction story starts with five cats and the addition story ends with five cats.

"The addition has undone the subtraction," says Alex.

So addition must also be the inverse of subtraction.

Let's represent these stories using cubes.

So we start off with five and then we subtract one, don't we, five minus one.

And that's equal to four.

And then five, subtract one, equal to four, can be shown with an arrow like that, can't it? And then we could start with four and add one, so four plus one is equal to five.

And there we can show it again with the arrow there, can't we? When you change your number with subtraction, you can undo the change made with addition.

Let's use cubes to tell this subtraction story.

Eight minus six is equal to two.

First I had eight books on the shelf.

There's our eight, then six books fell off the shelf.

Now I have two books on the shelf.

What number must be added, do you think, to undo that change that was made? So first I had two books on the shelf, then I put, mm, books back on the shelf.

That's right, so we've got two, so we have to add to get to eight, we have to add our six back on again, don't we? Because we subtracted six from eight to reach two, so we need to add six back on to our two to get back to eight again and to undo that change.

So two plus six is equal to eight.

What did you notice about the numbers that were added and subtracted? That's right, they were both the same, weren't they? To undo the change, the amount added and subtracted must both be the same.

So now, it's time to check your understanding again.

Listen to the subtraction story.

First I had nine conkers in my tin.

There they are.

Then I lost three conkers.

Now I have six conkers in my tin.

Nine minus three is equal to six.

And there's the equation.

Now which number must you add to undo the change? So we've got six, three, or nine.

So pause the video now while you think about that.

Okay, and what did you think? That's right, it was three, wasn't it? Because we can see that we subtracted three from nine, nine minus three, to get to six.

So to get back from six, from six back to nine again, we have to add the three back on, don't we? That's right, well done.

So now, let's tell the addition story to undo the subtraction story here.

So we've got nine minus four is equal to five, and we've got a story.

First there were nine pencils in the pot, then I dropped four pencils, now there are five pencils in the pot.

So we've got nine pencils, we drop four, so we have to subtract four, and now there are five pencils in the pot.

So now, you have to undo the change that was made and complete by completing that story, don't you? So let's have a try at that together.

First there were five pencils in the pot.

Then, I put four pencils back.

That's the pencils that were subtracted before, isn't it? Now there are nine pencils in the pot.

So five plus four is equal to nine.

So now it's time to check your understanding again.

Tell an addition story to undo this subtraction story.

So our subtraction equation is nine minus two is equal to seven.

First I had nine pounds, then I spent two pounds, so that was subtracted, now I have seven pounds, okay? So you've got to tell the addition story to undo the subtraction story, okay? So pause the video now while you do that, okay? Okay, and let's see how you got on with that.

So first I had, that's right, seven pounds, okay? Then I added, or I earned two pounds, and now I have nine pounds again, don't I? So the the two that we subtracted were added back on.

And our equation will be seven plus two is equal to nine.

Okay, so now, let's use the inverse to undo this subtraction equation.

So we've got seven minus three is equal to four.

So how will we undo the change that was made? Which part of the equation tells us that something has changed? That's right, it's a minus three, so to undo the change, we would say four plus three is equal to seven.

We'd add the three that had been subtracted to undo the change, wouldn't we? We undid the change by adding the same amount that had been subtracted.

Addition is the inverse of subtraction.

It will undo the change made when subtracting.

Okay, so now it's time to check your understanding again.

Alex represents a first, then, now story with cubes and writes this subtraction equation.

10 minus four is equal to six.

And you can see he's subtracted the four then.

So you need to think about which addition equation would undo this subtraction.

So you've got some options there, haven't you? So pause the video now while you select the correct equation to undo that subtraction.

And let's see how we got on.

So did you spot it? That's right, six plus four is equal to 10.

We knew that 10 minus four was equal to six, so six plus four would be equal to 10.

To undo the change, you had to add the four back on that had been subtracted, didn't you? Well done.

So now it's time for your task for the second part of our lesson.

Work with a partner each with a first, then, now board and put your boards side by side.

And Alex is saying, "I will tell a subtraction story "for the first example given "and represent it with cubes on my first, then, now board." And then Aisha says, "I will use cubes on my board "to undo your subtraction story, write the equation, "then fill in the missing number.

"Then I will tell the subtraction story "for the next question so you can undo it." And for each question, write the equations to represent your work, okay? And the examples, you can see the first one there is next to Alex, but we've got some more here as well.

So here are the examples for you to complete, okay? Pause the video now while you try that.

Okay, now the the second part of our task is here.

Tell your own subtraction story and represent it with cubes on your board, okay? So Alex is telling us, "I will write the subtraction equation "to represent my story," and Aisha's saying, "Then I will undo your story using addition "and write the addition equation." Okay, so have a try at that with your partner and pause the video now while you do that.

Okay, so let's have a look at the first example here then.

For the first example shown, you may have done this.

So six minus one is equal to five, and then five plus one was equal to six again.

Alex told the subtraction story and represented it with cubes and wrote the equation, and Aisha undid it, didn't she, using addition, and it would've been plus one there.

So well done if you did that.

Okay, so let's have a look then.

So you will also have completed these examples, won't you? So seven minus two was equal to five, so five plus two would get you back to seven, wouldn't it? And there are the equations to represent that.

Then the next example, eight minus three was equal to five, so five plus three would get you back to eight again.

And there are the equations to represent that.

And then finally, we can see that it had to be plus four because we had subtracted four before, so we had to add four, put the same four back on again, didn't we? And there the equations to represent that, so well done.

Excellent.

Okay, and then the second part of our task, you may have done this.

So Alex is telling us, "I told my own story "and represented the first part like this." He said, "Four minus three is equal to one." And then Aisha used addition to undo his story.

So she said, "One plus three is equal to four," so it would be plus three 'cause she had to add the same amount that had been subtracted, didn't she? So well done if you did that.

Okay, so you've worked really hard in our lesson today and hopefully now, you understand how addition and subtraction can undo each other, because that can be really useful.

Okay, so well done with that.

So now let's have a look at what we've learned in our lesson today.

Addition is the inverse of subtraction.

Addition can undo subtraction.

Subtraction is the inverse of addition.

Subtraction can undo addition.

When a given amount is added to the start of a story, to undo the change, we must subtract the same amount.

And when a given amount is subtracted from the start of a story, to undo the change, we add the same amount.

So well done.

You've worked really hard with that.

Excellent work today.