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 we'll do really well.

So let's get started.

So welcome to today's lesson, which is called Represent the Inverse Relationship between Addition and Subtraction.

And it comes from the unit additive structures addition and subtraction.

Okay, so in our lesson today we're going to interpret and represent the inverse relationship between addition and subtraction.

And we're going to spot those links between the two and use them to help us to find missing numbers and to complete stories.

So let's get started with that.

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.

Excellent, well done.

Okay, so in the first part of our lesson we're going to undo an addition story in a range of contexts.

In this lesson, you will meet Aisha and Alex.

They'll help us with our learning.

Okay, so here's Aisha and Alex.

First, Aisha has five sweets.

Then Alex gives her three more sweets.

Now she has eight sweets.

If she gave the three sweets back to Alex, how many sweets would she have then? How do you know? Aisha would have five sweets again, wouldn't she? I know, says Alex, because if you add an amount and subtract the same amount again, it will undo the addition.

Subtraction is the inverse of addition.

Alex tells a first, then, now addition story.

First I found five conkers.

Then I found two more conkers.

Now I have seven conkers.

Five plus two is equal to seven.

Then Aisha tells a subtraction story to undo it.

First I had seven conkers, then I lost two conkers.

Now I have five conkers.

Seven minus two is equal to five.

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

So we've got five plus two is equal to seven.

Seven minus two is equal to five.

I added two says Alex, then Aisha subtracted two again.

If you add a number to the start of your story, you can subtract the same number to undo the addition.

Alex thinks he can make the two stories into one.

Let's try.

First I had five conkers, then I found two more conkers.

So I had seven conkers, then I lost two conkers.

Now I have five conkers.

What do you notice about the number at the start and end of the story? They are the same, that's right because Alex undid the addition using subtraction.

He used the inverse.

What do you notice about the then parts of the story? That's right.

The amount added and the amount subtracted were the same, weren't they? Okay, so here's a different story.

First, there were three children in the line and they're represented by those counters, aren't they? Then four more children joined the line.

So there were seven children in the line.

Then, hmm, children left the line.

Now there are three children in the line.

So Alex is saying, I think if I subtract three, I will undo the change.

What mistake has been made? That's right.

If we change an amount by adding to undo the change, we must subtract the same amount.

So we added four, four more children joined.

So we needed to subtract four to undo the change, didn't we? There, okay, so well done if you spotted that.

Okay, so we can show that subtraction is the inverse of addition on a number line.

First I had seven pencils in my pot.

There they are.

Then I put three more pencils in.

So I had 10 pencils in my pot.

So 10, then I took three pencils from my pot.

So 10 subtract three is equal to seven or 10 minus three is equal to seven.

To undo the change, we must subtract the same amount that was added.

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

The first part of a story is shown on the number line there.

Use the inverse to undo the addition and write the equation to represent this.

Okay, so we can see the story that's been represented is an equation here, has represented as an equation here.

Seven plus three is equal to 10.

Okay, so pause the video now while you use the inverse to undo that addition.

Okay, and let's see how we got on.

So we know that we had seven and we added three to get to 10.

So to undo the change we needed to start at 10 and subtract three to get back to seven.

So well done if you did that.

And there's the equation to match it, look, well done.

Okay, so Aisha writes these equations to represent the story shown.

Four plus two is equal to six and six minus two is equal to four.

And if we tell the story we can, that will help us, won't it? So first I had four pounds, then I added two pounds.

So I had six pounds, then I spent two pounds.

So now I have four pounds again.

Okay, so let's have a look at that.

Which part of the equations represents the end of the addition story? That's right, it will be six.

So I had six pounds, that was after two had been added.

So four plus two is equal to six.

Which part of the equations will undo the change made in the first part of the story? That's right, it will be when we subtract two, won't it? Because that undoes the change made.

You added two and then you subtracted them again.

So well done if you noticed that.

So we can use pictures to show that subtraction is the inverse of addition.

And here's a picture.

Look, first there were five cubes, then I added three more cubes.

So there were eight cubes, then I subtracted three cubes.

Now there are five cubes again.

We can write equations to represent this picture.

Five plus three is equal to eight.

Eight minus three is equal to five.

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

Which pair of equations represents what has happened in this picture? Okay, so look carefully at the equations and pause the video now while you try that.

Okay, and let's see how we got on then.

So we can see first in the picture there are six cubes.

Okay, so we need six and then we added two.

So we'll need six plus two is equal to eight, won't we? And then if we have a look, we had eight in the middle picture when the two cubes have been added and we subtracted two cubes again to get back to six.

So it will be the first one, A.

Well done if you spotted that.

We can use pictures to help us complete equations, can't we? So let's have a look and see how this picture can help us.

The two represents the two white counters, three red counters were added.

So we've got two plus three is equal to, and then we know that two is a part and three is a part.

And the, so the whole is five.

Three were added, so to undo the addition, we had to subtract three, didn't we? So five subtract the three red counters got us back to two again.

Okay, so now it's time for another check.

Use the picture to complete the equations.

Okay, so we've got four plus one is equal to hmm and five subtract hmm is equal to four.

So pause the video now while you try that.

Okay, and let's see how we got on.

So four is the four white counters represented by the four white counters.

And we can say plus one, the red counter is equal to five, which is the amount in the whole group.

And then five, and we subtract the red counter again to get back to the four white counters, don't we? Five subtract one is equal to four.

We can see that one was added.

So one needed to be subtracted again to undo the change.

Alex tells an addition story, then undoes it with a subtraction and represents it as the equations shown.

Six plus three is equal to nine, nine minus three is equal to six.

The pictures show his story.

Look carefully what's the same and what's different.

What do you notice? With the number line and cubes, you can see that we change six by adding and subtracting three.

With the counters we could have added and subtracted three, but we could also have added and subtracted six 'cause we don't know which way round they were ordered in, do we? Which picture could represent the same story as these equations? So we've got four plus three is equal to seven, and seven minus three is equal to four.

Okay, and then when you found out, write the equations for the other pictures as well.

So pause the video now while you try that.

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

So did you spot it? The number line had four and then plus three is equal to seven.

And then because three were added, we had seven subtract three is equal to four.

What did we think about the counters? That's right.

That possibly could have also been represented by those equations because we don't know which order the counters were added and subtracted in.

So we could have had the four red counters and then the three white counters could have been added and then they could have been taken back off again.

So that could also have been represented by that couldn't it, by those equations.

And for the cubes, let's have a look at what equation we would write to represent those.

So we've got three and then we can see four was added.

So three plus four is equal to seven, and then the four was taken back off to get back to three.

Seven minus four is equal to three.

So well done if you did that.

Okay, so now here's the task for the first part of today's lesson.

Use the pictures to find the missing numbers.

Okay, so you'll be looking very carefully, okay? And thinking about how you will undo that change.

All right, pause the video now while you try that.

Okay, and then let's see how we got on with that then.

So we have five plus two is equal to seven, that's right.

So seven, we knew that we'd added two.

So we needed to subtract two again, didn't we? To undo the change.

Seven minus two is equal to five.

The next one we had five plus three is equal to eight.

So eight minus three must get you back to five again.

That's right.

And then six plus two is equal to eight.

So if you had a number line, you would have start at six and do one step of two to reach eight, wouldn't you? Eight minus two would get you back to six again.

And then finally on your number line, you would start with six and jump three to get to nine.

Nine minus three would get you back to six again.

So well done if you did that.

You've worked really hard in that first part of today's session.

Okay, so now let's look at the second part of our lesson where we're going to undo a subtraction story in a range of contexts.

So this time, instead of starting with addition, we're starting our story with a subtraction.

First I had seven conkers, then I lost two conkers.

So I had five conkers, then I found two conkers.

Now I have seven conkers.

What do you notice about the number at the start and end of the story? That's right, they're the same because two were subtracted, then two was added.

So the change was undone.

What do you notice about the then part of the story? That's right.

The amount subtracted and the amount added were the same, weren't they? Okay, so here's a different story.

First, there were seven children in the line, then four children left and there there's the counters are showing the four children that left.

So there were three children in the line.

Then hmm, children returned to the line.

Now there are seven children in the line again.

So Alex is saying, I think if I add three, I will undo the change.

What mistake has been made do you think? So, that's right.

Did you spot it? Four were subtracted from the number at the start of the story.

So to undo the change, we must add four again.

So there we can see we needed to put the four children that left back on again, didn't we? If we change in amount by subtracting to undo the change, we must add the same amount.

And there we can see it was four.

We can show how to undo a subtraction on an number line.

First I had 10 pencils in my pot.

Then I took three pencils from my pot.

So I had seven pencils in my pot, 10 minus three is equal to seven.

Then I put three more pencils in my pot.

Seven plus three is equal to 10.

So now I have 10 pencils in my pot again.

We undid the change, didn't we? We can undo a subtraction equation with an addition equation.

To undo the change we must add the same amount that was subtracted.

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

The first part of your story is shown on the number line.

Show how you undo the subtraction and write the equation to represent this.

So we've got 10 minus three is equal to seven, and you have to show how you undo that subtraction with an addition, don't you? So pause the video now while you do that.

Remember to write the equation as well, won't you, when you've represented it on the number line.

Okay, and let's see how we got on.

So, seven plus three would get you back to 10 again, wouldn't it? So we might need to write seven plus three is equal to 10.

So well done if you spotted that.

Now Aisha writes these equations to represent the story shown.

So we can see six minus two is equal to four and four plus two is equal to six.

Okay, and we can see the story, can't we? First I had six pounds, then I spent two pounds, so I have four pounds.

Then I earned two pounds more.

So now I have six pounds again.

Which part of the equations represents the end of the subtraction story? That's right.

So we can see the bit where after she spent the two pounds.

So she has four pounds left, doesn't she? And if we put it onto a number line, we can see six minus two is equal to four.

Which part of the equations will undo the change made in the first part of the story? That's right.

It's where we add two, isn't it? So we subtracted two, didn't we? So we had to add the two back on again to undo the change.

Four plus two is equal to six.

We can use pictures to represent subtraction and write equations to show the change that occurred.

So let's have a look at that.

So we can see here first there were eight cubes, then I subtracted three cubes.

So there were five cubes, then I added three more cubes.

Now there are eight cubes again.

Eight minus three is equal to five.

Five plus three is equal to eight.

It gets you back to eight again, doesn't it? It undoes the change.

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

Which pair of equations represents what has happened in the picture? Okay, so look carefully and have a look at each of this set of equations there and pause the video while you decide.

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

Okay, so what did you think? That's right.

We started with eight and we subtracted two, which left six.

And then when we had our six in the middle of the story, we added two back on to get back to eight to undo the change.

Well done.

We can imagine the changes that have occurred in the picture to help us to complete the equations.

So we can see we've got five minus three is equal to hmm.

And two plus hmm is equal to five.

So Aisha's saying three red counters were subtracted.

So we can see five minus three must be equal to two.

That's right.

And then Alex is saying three had been subtracted, so we added three to undo the change.

So two plus three, let's get you back to five, well done.

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

Use the picture to complete the equations.

So we've got eight minus two is equal to hmm, and six plus hmm is equal to eight.

So pause the video now while you try that.

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

So eight minus two is equal to six, isn't it? And it must have been the two white counters that were subtracted, I think there.

And then six plus two is equal to eight.

We subtracted two to reach six didn't we, from the eight.

So we need to add that two back on.

Two was subtracted.

So to undo the subtraction, we had to add two.

Well done if you did that.

Alex tells a subtraction story, then undoes it with an addition.

So he says eight minus two is equal to six.

Six plus two is equal to eight.

Okay, he wonders which picture tells the same story.

Which one do we think it is? So let's have a careful look.

Did you spot it? Each subtract and then add two.

But the number line is the only one that shows that the whole is eight, isn't it? So it must be that number line.

So well done if you spotted that.

Okay, so time to check your understanding again.

Which picture could represent the same story as these equations? We've got eight minus five is equal to three.

Three plus five is equal to eight.

Okay, so look carefully at the pictures to see which ones could be represented by those equations.

Pause the video now while you decide.

Okay, and let's see what we thought.

Okay, so did you see the cubes there? We can see that they started with eight and five.

The five pink ones were subtracted, weren't they? To get to three, the three blue ones and then we added those five back on to get back to eight again, didn't we? So well done if you spotted that.

The cubes show that eight is the whole and five has been added and subtracted.

So now here's the task for the second part of our lesson.

Make up your own story like the ones we have looked at.

Start with a subtraction story, then try again starting with an addition story and make up a story that includes zero in one of the parts.

Use counters on two first, then, and now boards next to each other or on a tens frame to represent it and draw one of your stories and write the equation to match.

Say what each part represents.

Okay, so pause the video now while you do that.

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

You may have done this.

First there were six children at the table, then two children left the table.

So there were four children at the table, then two children came back to the table.

So now there are six children at the table again.

Okay, and then you may have done this for your addition story at the start.

First I had four conkers, then I found two more conkers.

So I had six conkers, then I lost two conkers.

Now I have four conkers again.

And then for a story that used zero in the then parts of the story, this could be an example.

First I had four conkers, then I lost no conkers.

So I had four conkers.

Then I found no more conkers.

Now I still have four conkers because we know, don't we.

When zero is added and subtracted, the story looks the same in all parts.

Nothing changes.

So well done.

You've worked really hard in today's lesson.

You've found out lots about the inverse relationship between addition and subtraction, how to undo a change.

So well done.

Okay, so let's see what we learned in today's lesson then.

Addition is the inverse of subtraction.

Addition can undo subtraction.

Subtraction is the inverse of addition.

Subtraction can undo addition.

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

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

So well done, you've worked really hard in today's lesson and I've really enjoyed working with you.

Excellent work.