Lesson video

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

So, if you are ready to work hard, let's make a start and see what this learning is all about.

Hello, and welcome to this lesson.

Today's lesson is all about adding and subtracting one from any number, and it comes from our unit Addition and Subtraction Facts Within 10.

So by the end of this lesson, you should be able to add and subtract one from any number.

So let's make a start.

We've got some keywords in this lesson.

You may have heard them before, but let's try them out and look out for them as we go through the lesson.

So I'll take my turn and then it'll be your turn.

So my turn, one more, your turn.

My turn, one less, your turn.

Well done.

As I say, they may be phrases you've used before, but they're going to be really useful to us in our learning today, so look out for them as we go through the lesson.

There's two parts to our lesson today.

First of all, we're going to think about adding one to any number within 10.

And then in the second part of our lesson we're going to subtract one from any number within 10.

So let's start with adding one, and we've got Sam and Jacob helping us in our lesson today.

So Sam and Jacob are counting along the number line.

We can count on from any number, so let's have a go.

We're going to start our count at three, and we count four, five, six, seven, eight, nine, 10.

We could start our count at seven, couldn't we? Let's have a go.

I think Sam's gonna help us again.

So we start our count at seven, and we count eight, nine, 10.

Excellent, you might want to choose some other starting numbers to practise from as well.

Sam thinks she can find one more than any number on the number line, and she's got some beads there to help her as well.

Let's have a think.

Sam says, "To add one more, I just count on one more number." Hmm.

Do you think Sam's right? You have a think about that.

"To add one more, I just count on one more number." So what is one more than three? Can you see we've got three beads there on the left-hand end of the string? The number after three is four.

So one more than three is four.

So we said we could count on from any number.

If we count on from three, the next number we say is four.

So Sam is right.

"To add one more, I just count on one more number." The number after three is four, so one more than three is four.

So what is one more than seven? Can you think about using Sam's counting on strategy to help? Can you see the seven beads there? What is one more than seven? The number after seven is eight, so one more than seven is eight.

And now we can see the extra bead and we can see that jump on the number line counting on from seven to eight.

Jacob has hidden some numbers on the number line.

I wonder if we can find the missing numbers.

Can we use Sam's strategy to help us, I wonder.

So we can use the numbers that are there already to help us.

So we can see that there's a missing number after four.

So what is one more than four? Remember Sam's counting strategy.

Can you count to find the next number? Jacob says, "I know the number after four is five." So one more than four is five.

We count on one more and we get to five.

What about the next missing number then? What is one more than six? Jacob says, "I know the number after six is seven." One more than six is seven, so the missing number must be seven.

We're counting on one more from six.

Sam wants to find one more than eight.

So what is one more than eight? We've got a stem sentence there.

One more than eight is hmm.

"Sam says I will start my count at zero." Ooh, do we need to start count at zero? Jacob says, "We can start our count from any number, so start your count at eight." We know we have to count on one more to find the next number.

One more than eight is nine.

That's right, we count on from eight, and we get to nine, so one more than eight is nine.

Our missing number was nine.

Sam says, "I don't need all the numbers on my number line." Because as Jacob said, we can start our count at any number, so we started our count at eight.

So Sam's drawn just a little bit of the number line showing eight and one more.

And when we add one more onto eight, we count on one more, we get to nine.

Time to check your understanding.

Can you use the parts of the number line like Sam did to find one more each time and complete the stem sentence? The number after hmm is hmm.

So Sam's challenging you to find one more than two is hmm and one more than seven is hmm.

So use the number lines, use Sam's strategy, pause the video, and then we'll talk about it.

How did you get on? Did you manage to use Sam's strategy to help you? Let's have a look at them together.

So the first one was asking us to find out what one more than two is.

Did you count on? One more than two is three.

And if we use the stem sentence, the number after two is three.

What about the next number line, finding one more than seven? That's right, one more than seven is eight.

And we can think the number after seven when we count, the number after seven is eight, so one more than seven is eight.

Ooh, Sam's going even further.

Sam thinks she can find one more without the number line.

(gasps) I wonder what she's going to do.

Oh, I think she's going to use her counting 'cause she's really good at counting all the numbers up to 10 and she can start at any number, and she knows that one more is the next number that we say, so she thinks she can fill in what one more than six is without a number line at all.

She says, "We can start our count from any number, so I will say six and count one more." So if we start our count at six, one more is seven.

Ooh, what about one more than seven? Can you think? Sam says, "I will say seven and count one more." Can we do that? Seven, eight.

Eight is the next number after seven, so one more than seven is eight.

Sam says one more is the next number we say when we count, when we're counting in ones.

Time to check your understanding.

Can you find the number that is one more than seven? Is it six, is it nine, or is it eight? Use your counting skills, pause the video, and then we'll talk about it together.

Did you use your counting skills? Did you start from seven and count on one more, and you found out that eight is the answer we were looking for? One more than seven is eight.

And Sam says, "I said seven, then I counted one more." I hope that's what you did as well.

One more is the next number we say when we count.

So let's think about that with a story.

So let's tell a first, then, and now story and write the equation to go with it.

We've got some pencils.

Can you see? So first, there were four pencils in the pot.

Then, one pencil was added to the pot.

Now I wonder how many pencils we have.

Let's think about the equation.

First, there were four pencils.

Then, we added one, so one pencil has been added.

And now there are five pencils.

One more than four is five.

What do you notice about the first addend and the sum? We've put a box around four, the first addend, and our sum, which was five.

What do you notice about those numbers, I wonder.

Hmm.

Did you notice that the sum is one more than the starting addend? Five is one more than four.

And we said that when we counted on, we got one more, so we've added one and we've now got one more than the number we started with.

Adding one gives one more, so like counting on one when we count or when we work with a number line.

One pencil has been added to our pot.

Time to check your understanding.

We've got some more pencils here.

And can you see that first we had some pencils and then one was added.

Can you write an equation to match the picture and to complete the bar model? So have a look at the picture, write an equation, and complete the bar model.

Pause the video and have a go and then we'll talk about it together.

How did you get on? Did you spot that we had eight pencils and then one more pencil was added? So we had eight pencils and then we added one more pencil, so eight add one, and that equals nine, and we can complete our bar model.

Did you spot that nine is one more than eight? We've added one more pencil, so our answer is one more than the number we started with.

Sam says she can use the first equation here to solve the second equation.

Hmm, let's have a look.

So that first equation says five add one is equal to six.

The second equation says one add five is equal to hmm.

And Sam says she can use the first equation to solve the second equation.

You have a think about that.

I wonder what she's doing there.

Let's look for a pattern to help us.

What do you notice about the addends in each equation, the numbers we are adding together? They're the same addends, aren't they? But they're in a different order.

In the first equation, we've got five add one.

And in the second equation, we've got one add five.

Oh, Sam's reminding us addition is commutative.

Do you remember that, addition is commutative? We can swap the addends around and the sum stays the same.

And as Jacob says, "If we change the order of the addends, the sum remains the same." Is that what we've done here? Do you think that's the difference between equation one and equation two? It is, isn't it? Five add one is equal to six, and one add five is equal to six.

Jacob says, "I wonder if this is the same in all problems." So he's got a first-then-now problem with some cakes this time.

So let's check.

First, there were three cakes, then one cake was added, and now there are four cakes.

Let's check it again.

Ooh.

First, there was one cake, and then three cakes were added, and now there are four cakes.

(gasps) Did you see? In the first example, we had three cakes and we added one cake.

This time, we started with one cake and we added three cakes.

Adding one gives one more, but it doesn't matter whether we start with the one or whether the one is the number we add on.

It doesn't matter the order.

If one is there, we are adding one to give one more.

And Jacob says, "When one addend is one, we can think one more." But it doesn't matter whether it's the first addend or the second addend.

Let's have a look at another example.

Jacob has one pound.

Sam has six pounds.

How many pounds do they have altogether? Hmm.

Let's write an equation to help us solve the problem.

So Jacob has one pound, and Sam has six pounds.

So we are adding together the one pound and the six pounds, those are our two addends, and we've got to work out what that is equal to.

Jacob says, "There is a one in the equation.

I can think one more." Doesn't matter that the one is the first addend, we can still think one more because we know we can swap the order.

And Jacob says, "I know that one more than six is seven." So Sam and Jacob have seven pounds altogether.

One more than six is seven.

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

So the order in the problem was Jacob had one pound and Sam has six pounds.

But Jacob knew that because there was a one there, he could change the order around and think about one more than six to give him the answer.

Time for you to check your understanding.

So let's write an equation to help us solve this problem.

Jacob walked one kilometre on Monday and eight kilometres on Tuesday.

How far did he walk altogether? Pause the video, have a go at writing the equation to help solve that problem.

How did you get on? Let's have a look.

So he walked one kilometre on Monday, and he walked eight kilometres on Tuesday.

How far did he walk altogether? So he walked one add eight, and one add eight, aha, what's Jacob spotted? "When an addend is one, I can think one more." So he can swap the order of the addends around, and he can think one more than eight.

One more than eight is, he knows that it's nine.

So altogether he walked nine kilometres.

That's a long way, isn't it? Have you ever walked nine kilometres? If we change the order of the addends, the sum remains the same.

So we can use Jacob's idea of saying that when one addend is one, we can always think one more.

So, thinking about what Jacob knows, the children want to solve these equations.

They're going to use what they've learned to help them.

I wonder if you can use what we've been learning about to help you to solve them as well.

Jacob says, "When one addend is one, you can think one more." So can you see, are there some addends of one that can help us there? And Sam says, "If we change the order of the addends, the sum remains the same." So it might be easier to say two and one more rather than one and two.

So you can change the order so that you can think one more when you see a one in your equation.

So one plus one, one and one more is two.

And the same there.

We don't need to worry about changing the order when the addends are the same, do we? What about the next one, two add one? Well, we've got two, and we know when we add one, it's one more, 'cause Jacob says when one addend is one, you can think one more, so one more than two is three.

Let's look at the next one though, one add two.

We've changed the order of the addends, but as Sam says, the sum remains the same, and we can still think two and one more.

So we've still got a sum of three.

And what about the last one? Three plus one.

So when one addend is one, I can think one more.

So I've got my three and one more, one more than three is four.

And as Sam says, we've swapped the order of the addends but the sum remains the same.

One add three is the same as three add one, same as one more than three, it's equal to four.

I hope you use Jacob's idea that when he sees one is an addend, he can think one more.

Ooh, now this is interesting.

This time we haven't got a missing sum, we've got a missing addend.

We can see an addend of one in all of those equations.

So what is our missing number going to be? Hmm, I wonder.

They're still going to use what they've learned to help them.

And Jacob is still saying when one addend is one, I can think one more.

And Sam's reminding us, "If we change the order of the addends, the sum remains the same." So let's look at that first one.

One add hmm is equal to two.

We know we've got an addend of one, so we can think one more.

So one more than hmm is equal to two, or we know that one more than one is equal to two.

This time we've got hmm add one is equal to three, so hmm add one, so one more than hmm is equal to three.

We can change it round and think about our one more then.

One more than what is equal to three? One more than two is equal to three.

And we've got hmm add one is equal to four.

So, again, we can change the order, we can think one more than hmm is equal to four, so our missing number must be three.

I hope you were able to use what Sam and Jacob had learned about swapping the order of the addends and the sum remaining the same, and spotting that when one is an addend, we can think one more to help you to solve those problems. Time for you to do some practise.

So we've got to find the missing numbers to complete the equations.

And remember, if one addend is one, you can think one more.

We can swap the order of the addends and the sum remains the same.

So pause the video, have a go at these, and then we'll look at the answers together.

How did you get on? Did you remember to spot those addends of one and think one more? So let's have a look.

A, three plus one, three and one more, one more than three is four.

B, two plus one.

Two and one more is equal to three.

And then for C, one and one more is equal to two.

And for D, ooh, zero and one more, one more than zero is one, well done.

Can you spot something with the next row? Hmm, I wonder if you spotted that we'd swap the addends so the sum will remain the same.

So we will still have four, three, two, and one as our sums. One plus three is equal to four, one plus two is equal to three, one plus one is equal to two, and one plus zero is equal to one.

Now for our final column, we've got four add one is equal to.

We've got one as an addend, we can think one more.

Four and one more, so one more than four is five.

Now, what do you notice about J? Five plus hmm is equal to six.

Do you notice we've got five as an addend and our sum is six? And six is one more than five, so we must be missing an add one.

So five add one is equal to six, one more than five is equal to six.

Can you spot the same in K? We've got one addend is six and our sum is seven.

Seven is one more than six, so our missing addend must be one.

And for our final question, again, our sum is one more than the addend we know.

Eight is one more than seven, so our missing addend must be one.

Well done if you got those right, and well done if you used Jacob and Sam's ideas about adding one being one more and being able to change the order of the addends and the sum remaining the same.

Let's move on to part two of our lesson.

So in this part of the lesson, we're going to be subtracting one from any number within 10.

So we can count back from any number, says Sam.

So we start our count at seven and we count back.

Can you count with me? We start our count at seven, and we count six, five, four, three, two, one, zero.

Excellent counting.

Should we try another one? (gasps) Let's start our count at nine.

So we start our count at nine and we count back.

Eight, seven, six, five, four, three, two, one, zero.

Great counting back.

You might want to choose another couple of starting numbers and have a go at doing some more counting back together.

Jacob thinks he can find one less than any number on the number line, and he's got some beads to help him here.

So let's have a go.

What is one less than three? Hmm.

Jacob says, "To find one less, I just count back one number." So there's three, he's counted back one to two, and there it is on the number line.

We started on three, we counted back one, and we landed on two.

One less than three is two.

We know the number before three is two, so one less than three is two.

What is one less than seven? Can you have a think? Jacob says again, "To find one less, I just count back one number." So can you count back one from seven? Remember we could start our count anywhere.

So if we count back one from seven, we get to six.

Seven, six, and there we can see it on the number line.

We know the number before seven is six, so one less than seven is six.

Jacob has hidden some numbers.

Let's see if we can find the missing numbers using our counting back strategies.

So we can use the numbers that are there already to help us.

We could use numbers and count on, but this time we're going to use a number and count back.

So, Jacob says, "I know that the number before eight is seven when I count backwards." So that missing number there, one less than eight, is seven, so there's our seven.

What about the other gap? Ah, Jacob says, "I know the number before four is three." So there we go, counting back one, so one less than four is three.

Again, you might want to try some other numbers, see if you can find some other missing gaps on the number line.

Jacob wants to find the missing number.

So one less than two is.

Oh, he says, "I'll start my count at 10." Oh, Jacob, I thought you could count back from any number! Let's see.

Does he need to do that? Sam says, "No, you can count back from any number, so you should start to count from two." So let's count back, one less than two is one, that's right.

Jacob says, "Hang on, I don't need all the numbers on my number line then." Do you remember Sam doing this in the first part when we were counting on? So Jacob's going to do the same for counting backwards.

So he's spotted he doesn't need all the numbers.

He can start at two, and he can count back one, and he knows that if he counts back from two he will land on one.

So one less than two is one.

Let's check your understanding.

You've got some parts of number lines here to work out numbers that are one less.

So can you think about what the number before is each time to work out what is one less than 10 and one less than five? Pause the video, have a go, and then we'll look at them together.

How did you get on? Did you use that the number before hmm is hmm? So let's think about 10.

The number before 10 is nine.

That's right.

So the number before 10 is nine, one less than 10 is equal to nine.

What about the number before five? The number before five when we count backwards, the number before five we get to is four.

That's right, so one less than five is four.

So, let's think about a first-then-now story and think about our subtracting one from any number.

So first, there were five pencils in the pot, then one pencil was taken out of the pot, now there are hmm pencils in the pot.

Let's write the equation that goes with it.

First, there were five pencils in the pot, then one pencil was taken away, one pencil has been subtracted, and now there are four pencils in the pot.

What do you notice about the first number, the number we started with, the minuend, and the number that we were left with at the end, the difference? Can you see we've got a five and a four? Ooh, that's like counting backwards, isn't it? Five, four.

And what have we done? We've taken away one pencil.

The difference is one less than the minuend.

Four is one less than five.

Subtracting one gives one less.

So one less than five is four.

We took away one pencil and we've now got four in our pot.

So subtracting one gives one less.

One pencil has been subtracted.

Jacob's going to use the counters to represent a different story.

Let's write the equation to represent it.

There are eight balls in a box.

One ball is a football.

How many balls are not footballs? There are eight balls in the box.

One of them is a football.

We need to work out how many are not footballs.

So if we take away the football, we will know how many are not footballs.

So there's our one football.

So how many are not footballs? Seven.

What do you notice again about the minuend, the number of balls we started with, and the number that were not footballs, the difference? If you notice that they're eight and seven, eight is one more than seven, seven is one less than eight.

The difference is one less than the minuend, the number that are not footballs is one less than the total number of balls in the box.

Subtracting one gives one less.

And we can look at that on the bar model as well.

There were eight balls in total, one of the balls is a football, so seven balls are not footballs.

So can you use the counters to solve the equation and represent it on a bar model? So we've got six subtract one is equal to hmm.

So, can you use the bar model and the counters to help you? And have a think about what we've been doing with our counting as well to help.

Pause the video, have a go, and then we'll talk about it together.

How did you get on? So six is our whole, six counters in total.

One counter is white.

We've taken away one of the counters to find out how many are red, and we've got five red counters.

Six subtract one is equal to five.

And did you spot that we've got one there as one of our parts? So if one is a part, the other part is going to be one less than the whole.

Subtracting gives one less.

Six subtract one is equal to five.

One less than six is five.

Jacob thinks he can find one less without the number line.

Ooh, I wonder how he's going to do that.

I think he's going use his counting, isn't he? He says, "We can start our count from any number.

I will say seven and count back one number." He's finding one less than seven.

So he's gonna start at seven and count back, and he gets to six.

Excellent.

So six is one less than seven.

What about eight? Can you work out what one less than eight is without the number line? He says, "I will say eight and count back one number." Can you do that? Eight and count back one number is.

Eight, count back one, and we get to seven.

So seven is one less than eight.

So, which of the following is the missing number? We need to work out what one less than nine is.

So you've got 10, eight, and seven.

Pause the video, decide which is the missing number, and then we'll talk about it together.

How did you get on? Did you count back like Jacob? If you count back one from nine, we get to eight.

So, eight is one less than nine.

And as Jacob said, "I said the number nine, and I counted back one number." There's our little bit of number line, count back one, and we get to eight.

The number before nine is eight.

Jacob says he can use what he knows about subtracting one to solve this equation.

Hmm, this time we've got a different missing part, haven't we? Eight subtract hmm is equal to seven.

What do you notice about the minuend and the difference? What do you notice about the number we're starting with and the number we're left with after we've made our subtraction? That's right, they're one apart, aren't they? They're next door on the number line.

Eight is one more than seven.

Seven is one less than eight.

So the difference is one less than the minuend.

Sam says, "Subtracting one gives one less." This means that the subtrahend, the number we've subtracted, is one, so eight subtract one is equal to seven.

And we can see that there on the number line.

Time to check your understanding now.

Which of these will have a subtrahend of one? The subtrahend is the number we subtract.

So for which of these will the number we subtract be one? Pause the video, have a look, and then we'll talk through them together.

How did you get on? What did you spot? Did you notice that there was something special about B, that the number we started with, the minuend, was five, and then we subtracted something, and then the answer, the difference, was four? And five and four are next to each other on the number line.

Five is one more than four, four is one less than five, so this is the one that must have a subtrahend of one.

The difference is one less than the minuend, so one must have been subtracted.

We can use what we know about adding and subtracting one to help us solve equations more quickly and accurately.

So shall we have a practise? Nine plus one is equal to 10.

Six plus one is equal to seven.

Are you thinking one more at the moment? Eight plus one, eight and one more is equal to nine.

Seven, ooh, we're in subtraction now.

Seven subtract one is equal to six.

We're thinking one less this time 'cause we're subtracting one.

10 subtract one is equal to nine.

Five, oh, five subtract something is equal to four.

Five subtract one is equal to four.

Well done, you might want to go through those again and have another look at them.

See how quickly you can work out those missing numbers.

Time for you to do some practise.

So this time, we are thinking about subtracting one from any number within 10.

So you're going to fill in the gaps, thinking about that idea of subtracting one each time.

Can you fill in those missing numbers? And then you've got some problems to solve, and you might want to use a 10 frame or a bar model to solve these problems. So pause the video now, have a go at the questions, and then we'll talk through the answers together.

How did you get on? Did you manage to fill in the missing numbers? Did you remember that if the subtrahend is one, the number we subtract is one, you can think one less? So 10 subtract one is equal to nine.

All of these, we're thinking, to begin with, one less because we're subtracting one each time.

So nine subtract one, one less than nine is eight.

Eight subtract one, one less than eight is seven.

Seven subtract one, one less than seven is six.

And you might've used your counting backwards to help you.

Did you spot something about the next four, E, F, G, and H? Did you spot that each time, the number we start with, the minuend, is one more than the number we finish with, the difference? So what must have happened there? We must have subtracted one from each of them because each time the number we end up with is one less than the number we start with.

So all of these are subtracting one.

I hope you spotted that.

Then we've got a bit of a mixture to finish.

Two subtract one is equal to, so one less than two is one.

Nine subtract something is equal to eight.

Nine is one more than eight, so we must have subtracted one.

What about one subtract one? If I've got one and I take it away, I'm left with zero, aren't I? And then six subtract something is equal to five, six subtract one is equal to five.

Well done if you spotted those patterns.

Then we had a couple of problems to solve.

So the first problem, Sam found a pencil in the classroom, and then she found four more pencils in the hall.

How many pencils has she found in total? So she found one and then she found five more.

But remember we can swap those addends around, we can think five and one more, and that means she found six in total.

And Sam says, "I drew a bar model.

One is a part, so I can think one more than five.

One plus five is equal to six." And in our second problem, Jacob wants to score seven goals.

He scored one goal so far.

How many more goals does he need to score? One plus hmm is equal to seven.

When one is the addend, I can think one more.

One more than hmm is seven.

It's one more than six, isn't it? One more than six is equal to seven.

And we can see that Jacob's used a 10 frame there to help him.

If he adds six more goals, he'll get seven in total.

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

You've worked really hard today.

I hope you've enjoyed thinking about those one more and one less to add and subtract one to and from any number within 10.

We've learned that adding one gives one more and that subtracting one gives one less.

So whenever we see one as an addend, we can think one more, and whenever we see one as the subtrahend, the number we're subtracting, we can think one less.

Well done for all your hard work today and all your good thinking, and I hope I get to work with you again soon.

Bye-bye!.