Lesson video

Hello, I'm Mrs. Proechel.

and I'm here to do some math learning with you today.

I can't wait to learn lots of new things and hopefully have lots of fun.

So let's get started.

Today's lesson is called Addition and Subtraction Involving Zero and it comes from the unit Addition and Subtraction Facts Within 10.

By the end of today's lesson, you should be confident in adding and subtracting zero and knowing when zero is the difference.

Here are today's key words, zero, add, subtract, and same.

My turn, zero.

Your turn.

My turn, add.

Your turn.

My turn, subtract.

Your turn.

My turn, same.

Your turn.

Well done.

Now that we can say them, we get to use them.

This is today's lesson outline.

You can see that there are three parts to this lesson today.

The first part, we will be adding zero to a number within 10.

The second part, we will be subtracting zero from a number within 10.

And in the third part we are gonna be looking at subtracting a number from itself within 10.

Let's get started with adding zero to a number within 10.

In this lesson, you are going to meet Sam and Jacob.

They're gonna help us with our learning today.

Let's get started.

Some children catch a bus to school.

I wonder if you can see the children on that bus.

There are six children on the bus when it first arrives.

They stop at a bus stop and two more children get on the bus.

So how many children are on the bus now? Let's write this as an equation to help us.

I can see that there are six children at the start.

We add two more children.

So our number sentence must be six plus or add two, six add two.

I know that two more than an even number is equal to the next even number.

So there must be eight children on the bus because eight is the even number after six.

Now there are eight children on the bus.

Well done if you got that correct.

The next morning there were four children on the bus and when they arrived at the bus stop, there was no more children to get on.

So how many children are on the bus now? Let's write that equation again to help us.

I can see that there are four children at the start of the story.

No more children or zero children get on at the bus stop.

So I know that we are adding four and zero.

Four plus zero equals.

Hmm.

I wonder if I'm adding no more onto that bus.

No more children get on.

How many will there be? Four.

There will still be four children on the bus because no children have got on.

Let's practise adding zero.

I've got this equation here, seven plus zero.

I'm going to use a tens frame to help me with this.

I'm gonna put my seven counters on my tens frame and we're going to add zero.

I'm gonna add zero counters to how many will I have now? Seven plus zero is seven.

Five plus zero.

There's my tens frame with my five counters I add no more counters to how many will I have at the end? Five still.

Nothing will have changed.

How many counters do I have now? Five.

Well done.

Do you notice anything? So when I add zero to seven, it is equal to seven.

When I add zero to five, it is equal to five.

Jacob has noticed that when we add zero to a number, the number does not change.

Well done Jacob.

That's a good spot.

Let's repeat that after Jacob.

When you add zero to a number, the number does not change, your turn.

Well done.

Let's try and remember that for the rest of our learning.

Let's have a go at this one then.

Jacob places six counters onto his tens frame.

He adds zero counters.

How many counters will he have now? When you add zero to a number, the number does not change.

There must still be six counters because the amount will stay the same.

Six plus zero is equal to six.

Well done Jacob and well done to you if you got that correct.

Now on the way home there are no children on the bus.

They stop off at the bus stop and they pick up five more children.

How many children are on the bus now? Let's write the equation to help us to solve this.

I know that we have no children at the start and we're adding five.

So that must be zero plus five.

Zero plus five is five.

There are five children on the bus at the end of this story.

Sam has noticed something zero plus five is equal to five and five plus zero is equal to five.

They are the same addends, but they are written in a different order.

Can we remember what that's called? Some has noticed that it doesn't matter which order we add them that they still equal five.

We are still adding that zero.

If we change the order of the addends, the sum remains the same.

Can we remember what that's called? That's right, Sam.

Addition is commutative.

It means that we can swap the addends around, but the sum will still be the same.

So let's have a go at this one then.

Zero add nine.

I have zero and I add nine more.

How many do I have now? Zero plus nine is equal to nine.

So if zero plus nine is equal to nine, what is nine plus zero? I've swapped the ad ends around.

But remember addition is commutative, so the sum will remain the same.

Nine plus zero is equal to nine.

Jacob's notice something when zero is one of the addends, the number added to will not change.

So we can see that there zero plus nine is equal to nine and nine plus zero is equal to nine.

Let's use that knowledge to help us solve this then.

The children are going to solve these equations.

They use what they have learned to help them, but we can see that there are some missing number problems. Jacob has reminded us that when zero is one of the two addends, the number added two will not change.

So let's have a look at this first one.

Zero plus something is equal to one.

I can see there that I am adding zero, which means the number it is being added to does not change.

So if the sum is one, that means the missing number must also be one.

The missing number plus zero is equal to two.

When we add zero, the number that you add it to does not change.

So the sum is two.

So the missing addend must also be.

Two.

Something plus zero is equal to four.

So if I'm adding zero to that number and the sum is four, the starting addend must also be four.

well done if you got those correct.

Right then, over to you.

So which of these equations would have zero as the missing number? Look carefully.

Remember that Jacob told us when zero is the addend, the number that it's added to will not change.

So have a look.

Can you see any where the addend and the sum haven't changed? We can see that A, 10 plus zero is equal to 10 and C, four plus zero is equal to four.

The starting addend and the sum is exactly the same amount, which tells me that zero has been added.

So well done if you spotted those.

Let's have a little look at B.

B, Jacob said he knew that that one couldn't be zero because the sum had increased from the addend that we are adding it to.

Seven is more than six.

So zero could not have been added here.

Some great learning there.

So let's now hand it over to you.

Task A is for you to find the missing numbers to complete these equations.

So we've done lots of practise within our lesson today, so this should be nice and simple.

Remember that when we add zero, the addend that we are adding it to does not change and the sum will remain the same.

So have a little go at these and come back when you've had a go.

So pause this video and come back when you've had a little go.

Welcome back.

I hope you had lots of fun figuring out those missing number problems. Let's see how we've got on.

Two plus zero equals? I know that when we add zero to an addend it does not change.

So two plus zero must be equal to two.

10 plus zero must be equal to 10.

It hasn't changed.

Nine plus zero must be equal to nine.

Or what do we notice about D zero plus four? Zero is the first addend in this problem, but remember it doesn't matter which order it is.

Whatever it is added to will remain the same.

So zero plus four must be equal to four.

Well done.

Zero plus three must be equal to three.

One plus zero is equal to one.

Zero plus six.

Remember, it doesn't matter which order must be equal to six because the amount stays the same.

Or what's happened here? What's we notice with this one? My equals has been swapped around.

Does that matter? No.

Seven plus zero is still equal to seven.

Seven equals seven plus zero.

Four plus zero is equal to four.

Five plus something is equal to five.

So here we know the sum and we know the addend and because those two are the same, we know that zero must have been added.

Let's have a look at this next one.

Something plus zero is equal to zero.

Hmm.

I know that zero must also be the missing addend because zero plus zero is equal to zero.

And finally the sum is eight.

So what have I added to zero to get eight? Eight.

Fantastic.

Eight is equal to the sum because zero doesn't change it.

Okay, let's move on to our second part of today's lesson, which is subtracting zero from a number within 10.

Now what we've just done might give you a little clue about what's to come.

We have some strawberries here and we have a representation of an equation.

So let's have a look.

First, there were eight strawberries in a box.

Four of them were eaten.

So how many strawberries will be in the box now? Hmm? Let's write this as an equation to help us.

We know that there were eight strawberries at the start.

We know that four of them were eaten.

So we are going to subtract four to find out how many strawberries are left at the end.

So eight subtract four is equal to? Four.

Well done if you've got that, there will be four strawberries in the box.

Let's have a look at another problem.

There were six strawberries in the box.

Now none of them were eaten.

How many strawberries are in the box now? Let's write this as an equation to help us.

Six subtract zero is equal to.

Hmm.

So if I had six strawberries and none of them were eaten, how many would be left? That's right.

Six.

There would still be six strawberries in the box.

Let's practise subtracting zero.

So here we can see four subtract zero.

If I have four counters and I subtract no counters, how many counters will I have left? Four.

Hmm.

Are we noticing something here? Two counters subtract no counters, I will still have two counters.

Do we notice anything? How can we link this with the adding of zero that we've just done? Well done, Jacob.

That's right.

When you subtract zero from a number, the number does not change.

Just like when we added zero, the addend we were adding it to didn't change.

Jacob now has a little turn for himself.

He creates a first, then, now story for this equation.

First I had four cookies, then I gave no cookies to my friends.

Now I still have four cookies.

You might like to now create your own first, then, and now story to explain this equation or a problem similar to this, right over to you then.

Which of these equations are correct? Let's have a look at the first one.

10 subtract zero is equal to 10.

I can see that the amount has not changed.

So that is correct.

Seven subtract zero is equal to seven.

Again, the starting amount has not changed at the end.

So that is correct because when zero is subtracted, remember, it does not change the amount that we start with.

C, four subtract zero is equal to zero.

Hmm.

My starting amount and my end amount is different.

So that means something must have changed, but I am subtracting zero.

So we know that that one is incorrect.

Let's have a look at this problem in a different way.

So let's use our knowledge to find this missing number in a part-part-whole model.

I can see that the whole is nine and one of my parts is zero.

So what do we think could be the missing in this other part? Sam has said that to find the missing number, we have to subtract the part that we know from the whole.

So that means nine is the whole and zero is the part.

So nine subtract to zero will give me the other part.

When we subtract zero, the amount does not change.

So nine must be the other part.

Well done if you spotted that.

Let's have a little practise of that.

So what are the missing numbers in these equations? 10 subtract zero is equal to? Something subtract zero is equal to zero Jacob is reminding us that when we subtract zero from a number, the number does not change.

Use that tip to help you.

10.

Subtract zero.

10 subtract zero.

So that amount will not change.

So my missing number must be 10 So my missing number must be 10.

B, something subtract zero will leave me with zero.

So five subtract zero from an amount, I still have zero.

So that starting amount must have been zero to start with.

Well done.

That was a tricky one that one.

So well done if you got that one correct And C, something subtract zero is equal to three.

I can see that my end amount is three.

So that means the zero hasn't changed it.

So the start amount must be three.

Well done.

Jacob's explaining that he knew that it had to be three, for C, because the difference was three after nothing had been subtracted.

Okay, over to you then.

Task B is to find the missing numbers to complete these equations.

So you'll see that we have got a range of equations with missing numbers and also some part-part-wholes.

Remember when we subtract zero from an amount, the amount does not change.

Welcome back.

Let's see how you got on.

One subtract zero, so zero will not change the starting amount, so that must be equal to one.

10 subtract zero.

Nothing has changed.

So this must be equal to 10.

Have a look at C.

I can see that the equals has been moved to the start of my equation.

That does not change anything.

We can still work out nine subtract zero.

So the difference must be nine.

Zero subtract zero.

If I have nothing to start with and I subtract nothing, I will still have nothing at the end.

Four subtract zero is equal to four.

Three subtract something is equal to three.

I can see that that amount has not changed.

So I must be subtracting zero.

Something subtract zero is equal two.

So I know that starting amount must be the same as the difference because the zero hasn't changed it.

Two is the missing number for that problem.

Similarly to that one, this next one is something subtract zero is equal to six.

Again, I know that the difference is six.

Zero does not change the starting amount.

So I know that the starting amount must be six.

Let's have a look at these part-part-wholes.

So five is my whole, five is a part.

I can see that my parts and my whole are the same.

So I know that the other part must be zero.

Let's have a look at this one.

Then four is the whole and zero is a part.

I can subtract the part from the whole to find the other part.

So four, subtract zero.

I know it does not change that starting amount.

So the other part must be four.

Well done for completing that task.

Let's have a look at the third part of our lesson now.

We're going to move on to subtracting a number from itself within 10.

First there were three cakes on the plate.

Then how many were taken? Have a look at that picture.

Can you see how many have been taken? That's right.

Three.

Three were eaten.

They weren't just taken, they were eaten.

So how many are left on the plate now? Let's write this as an equation to help us.

Three subtract three is equal to how many? Hmm? I had three cakes and all three of them were eaten.

Oh no, there's no cakes left.

There are now no cakes on the plate.

Jacob is inspired by this story and decides to write his own first, then, now subtraction story.

First, I had seven watermelons in my box.

Then I dropped and smashed seven of them.

Now I have no melons left.

Oh no boy, Jacob.

Can we write an equation to match this problem? So first, Jacob had how many melons? Seven.

Jacob had seven melons.

What happened to his melons? He's dropped and he smashed seven of them.

So I know that we are subtracting seven.

So how many does he have now? Seven subtract seven is equal to zero.

He has no melons because he is dropped and smashed all of them.

Jacob and Sam are now discussing the equation that we've just looked at.

If you have an amount and subtract the same amount, you will have nothing left.

Sam agrees with Jacob.

The numbers subtract the same number will be equal to zero.

So if we think back to our cakes, we had three to start with.

We subtracted three and that left us with zero.

Thinking about our watermelons, we had seven watermelons.

Jacob dropped all of those melons, all seven of them.

So we subtracted seven and that left him with zero melons.

Jacob has noticed that he can say when we subtract a number from itself, it gives a difference of zero.

Let's have a go at this.

So which of these will have a difference of zero? Remember when you subtract a number from itself, it has a difference of zero.

Well done if you said A and C.

Five subtract five, I can see that five is being subtracted from itself, which gives us the difference of zero.

And in C, I can see that zero is being subtracted from it itself, which gives the difference of zero.

Sam noticed that in B, although zero was in the equation, it was not the difference.

The difference here would be nine because remember when we subtract zero from an amount, the amount does not change.

So that one would be nine, not zero.

Let's practise this a little bit more.

In task C, can you find the missing numbers to complete these equations? You will see that we've got a mixture of missing number equations and also some partial number line representations.

Pause the video and come on back once you've had a go.

Welcome back.

I hope you had a fun time solving those equations and finding all those missing numbers.

Let's see how you got on.

10 subtract 10.

I can see that it's being subtracted from itself.

That means my difference must be zero.

Six subtract six.

I can see that I had six at the start.

I have lost six, so that means I've got none left or they swap that equals sign, but that's not gonna trip us up, is it? Nine subtract nine.

The difference is zero because the numbers are the same.

Zero subtract zero.

The difference is zero.

One subtract one.

The difference must be zero.

Because the amounts are the same.

Now we can see with F that zero is the difference.

So what must I have subtracted from three to equal to zero? Three.

Well done.

Three is the missing number there.

Something subtract seven is equal to zero.

That must mean the missing number must be seven.

The same amount that we are subtracting.

Again, my difference here is zero and something subtract four is equal to zero.

So I know that when we subtract a number from itself, the difference is zero.

So the missing number must be four.

Well done.

With this partial number line here, we can see that they are showing us what has been subtracted and what number we have ended up on.

So two, I can see that I'm subtracting two.

So that must be that missing number and I can see that when I subtract two from two I will end on zero on my number line.

So two, subtract two is equal to zero.

Now here we have our partial number line and no information in our equation.

So let's look what number are we starting on? I can see that we are starting with eight.

So that must be my first number.

What must I subtract from eight to get to zero on my number line? I know that if the difference is zero, we have subtracted a number from itself.

So if the starting amount is eight, that means that we must also be subtracting eight to find the difference of zero.

Well done.

If you completed all of those tasks, you should be very proud of yourself for the work that you've done today.

Let's have a look at a summary of our learning.

When zero is added to a number, the number does not change.

When zero is subtracted from a number, the number does not change and subtracting a number from itself will give the difference of zero.