Lesson video

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

It's from our unit, Adding and Subtracting ones and tens to and from two-digit numbers.

So we're going to be looking at two-digit numbers and we're going to be thinking about adding and subtracting, and hopefully using our known facts to help us.

So if you're ready, let's make a start.

So in this lesson, we're going to be adding and subtracting a single-digit and a two-digit number, and we're gonna be using lots of different ways of thinking about this and using our known facts to help us work out new ones.

So if you're ready, let's make a start.

We've only got one keyword in our lesson today, and that's equation.

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

My turn, equation.

Your turn.

Well done.

I'm sure you know what an equation is.

We're going to be using them a lot to help us record our work in our lesson today.

So watch out for it as we go through.

There are two parts to our lesson today.

In the first part, we're going to be using known number facts to add.

And in the second part, we're going to be using known number facts to subtract.

So let's make a start on part one.

And we've got Alex and Sam helping us in our lesson today.

Sam represents this story using Base 10 blocks on a part-part-whole model to here's the story.

It took Alex four minutes to walk to his friend's house and another three minutes to walk to school.

His journey took seven minutes all together.

So our parts were four and three and our whole was seven.

Let's write an equation to represent the story and remember to say what each part of the equation represents.

So there's our equation.

So the four represents the four minutes it took Alex to walk to his friend's house.

The three represents the three minutes it took them to walk to school.

And the seven represents how long his journey took altogether.

And we can see the four, the three and the seven in the part-part-whole model as well.

Sam represents another story using Base 10 blocks on a part-part-whole model.

Ooh, got a bigger part this time, haven't we? It took Alex 24 minutes to walk to his friend's house and another three minutes to walk to school.

His journey took 27 minutes all together and we can see that now on the part-part-whole model.

One part is 24, the time it took him to walk to his friend's house.

One part is three, the time it took him to walk to school and the whole is how long it took all together, 27 minutes.

Now let's write an equation.

So 24 was the number of minutes it took Alex to walk to his friend's house.

Plus three, the number of minutes it took him to walk to school is equal to 27.

The number of minutes the journey took altogether.

Let's look at the equations that represent the stories and think about what's the same and what's different.

Did you spot something that was the same? Alex says, "Each representation has four ones with three more ones added." We can see that in the first part-part-whole model.

And in the second we can see that 24, there are four ones in that part and then another three ones.

But the number of tens in the equations are different.

There are no tens in the first equation, four ones plus three ones.

And in the second we've got 24, which is two tens and four ones.

So let's look at this on a number line.

Ooh, in both equations we add on three ones to four ones.

In the first equation it's four ones plus three ones.

And in the second equation it's 24 plus three ones.

Three plus four is equal to seven.

So there will be seven ones in the sum in each equation.

And there we can see the sum is seven, the sum is 27.

But in the second equation there are two tens in the first addend and no tens are added.

So there are still two tens in the sum.

What do you notice about the ones digits here? Can you spot any patterns? Have a look.

What did you notice? Let's continue the pattern on the number line.

What's changing and what's staying the same? Sam says, "I noticed that the number of tens changed each time, but the ones in the addends stayed the same." So in the top number line, we've got 34 plus is equal to 37.

The next one we've got 44 plus 3 is equal to 47.

And the final one we've got 54 plus 3 is equal to 57.

So the tens change each time, but the ones in the addends stay the same.

What do you notice about the ones digits? Can you spot any patterns there? And Sam says, "The sums all have a seven in the ones because there are three ones added to four ones each time." And we know that three ones plus four ones is equal to seven ones.

Can you think about any other equations that would belong in this pattern? Well here we've got a rather strange looking number line with blanks before all our ones digits, haven't we? But we've got a something four plus three is equal to something seven.

And Sam says, "Any part of the number line where the addends had three ones added to four ones would be in the pattern." It wouldn't matter which decade we were in, how far along the number line we were.

If there's a four in the ones and we're adding a three, then there will be a seven in the ones of the sum.

Time check your understanding.

Which number line A, B, or C uses the same number fact as the one shown on the left of the screen? Pause the video, have a go and when you're ready we'll come back for some feedback.

What did you spot? So the number line on the left has four plus three is equal to seven.

And we've got some number lines on the right there.

So did A, B, or C use that number fact? It was C, wasn't it? 64 add 3 is equal to 67.

It doesn't matter how many tens we've got, we've still got four ones adding three ones which will equal seven ones in our sum.

So C was the correct answer.

The number of tens in the equation changed.

The ones in the addend stayed the same.

So the ones in the sum also stayed the same.

Four plus 3 is equal to seven.

So 64 plus 3 is equal to 67.

Alex represents the equation, five plus three is equal to eight on his bead string.

Can you see there five ones add three ones and there's eight ones altogether? He says, "I think I can use this to find some other facts." Let's see what he does.

What do you think he might do? He says, "I can change the tens and keep the ones the same." So we've got no tens at the moment.

Five plus three is equal to eight.

Ah, he's added in one 10.

So now he's got 15 plus 3 is equal to 18, and another one, 25 plus 3 is equal to 28 and 35 plus 3 is equal to 38.

Can you see what stays the same each time? So picture the beads to work out which of the following equations could also be made using Alex's pattern.

Time to check your understanding A, B, or C, which one is correct and could be made following Alex's pattern? Pause the video, have a go and then when you're ready we'll get together for some feedback.

What did you think? So we were looking for five ones, add three ones.

And can you see that C has 65 plus 3 is equal to 68? We know that five ones plus three ones is equal to eight ones.

If we add six tens to five ones and then add three ones, it's the same as 65 add 3 is equal to 68.

You might have seen a three add five in B as well, but this time the ones that we were adding on their own were five and not three.

So it is still sort of the same calculation, but our extra ones that we were adding in that case were five and the three ones were with the tens.

So it's similar but not quite the same.

So we can use the patterns in numbers to solve equations more efficiently.

So here we've got some equations and represented with part-part-whole models and we need to find the sum or the whole in each case.

Sam wonders which number fact she can use to solve these equations.

Can you have a look? See if you can help her.

So let's think about what changes and what stays the same.

Sam says, "I can see six ones and two ones in each equation that stays the same." Can you see that too? She says, "I can use six plus two is equal to eight to help me to solve the other equations." We can use Base 10 blocks to help us to understand what's going on here.

So we've got 36 plus 2, so there's 36 and we're adding two more.

So what's going to change? It's just the ones, isn't it? So our sum is 38, 36, add two more ones is equal to 38.

What about 46 add 2? Well all that's changed is the tens, isn't it? We know that six plus two is equal to eight.

So we know that 46 plus 2 must be equal to 48.

We haven't changed the tens.

So what do you think is gonna happen with the last one? Ha, we've got 56 add 2.

So we know that six plus two is equal to eight, so 56 plus 2 must be equal to 58 and we were able to use that fact to help us.

Sam says, "Each equation had one more 10 than the last, but the ones stayed the same." Let's continue the pattern together.

So we had that six plus two equals eight and we were just changing the number of tens each time.

So here we've got 56 plus 2 is equal to 58.

We need some more equations with the same pattern in the ones.

So we could have 66 plus 2 is equal to 68.

76 plus 2 is equal to 78.

86 plus 2 is equal to 88.

What did you notice about the tens digits in the first addend and in the sum? And Sam says, "Well no tens were added.

So the sum had the same number of tens as the first addend." Time to check your understanding.

Use Base 10 blocks to find and complete the next equation in the pattern.

So we'd looked at 86 plus 2 is equal to 88.

What will the next one in the pattern be? Pause the video, have a go and when you're ready for some feedback, we'll come back.

What did you think? Well, we could addend one more 10, couldn't we? So now we've got 96, add 2 is equal to 98.

We can use that same pattern in the ones, but just with the tens changing.

Sam says that you can use the known fact five plus one to solve this equation.

Do you agree? We've got 31 plus 5 is equal to 36, and Sam wants to use five plus one.

What do you think? Alex says 31 partitions into 30 and 1, and then you add 5.

So you need to use the fact one, add five.

And Sam was thinking about using five add one.

Hmm.

Sam says, "I know that addition is commutative one plus five is the same as five plus one." Ah, good thinking Sam.

So 31 add 5, once we've partitioned our 31 into 30 and 1 and we know we've got a five to add, we might think of five and one more as six to help us to solve the equation.

If I change the order of the addend, Sam says the sum remains the same, so I can use one plus five or five plus one to help solve the equation.

So which single-digit fact could be used to solve the following equation? So we've got 42 plus 3 is equal to 45, so is A, B, or C, the single-digit fact that you would use to help you to solve that equation.

Pause the video, have a go and when you're ready we'll get back together for some feedback.

What did you reckon? Did you spot that we had four tens, but then we had two ones and three ones that we needed to sort out and add.

So two ones plus three ones is equal to five ones that would definitely help us to solve this equation.

Ah, but did you spot that C was three ones plus 2 ones.

So just the addends in the other order.

And we know that two plus three equals five, so we know that 42 plus 3 is equal to 45 and we can change the order of the addends and the sum remains the same.

So if two plus three is equal to five, then three plus two is equal to five.

So B matched the calculation exactly, but C was the same fact, but just with the addends written in a different order.

So that could have helped us as well.

Well done if you spotted both of those.

Time for you to do some practise.

You need to use some known facts to find the missing numbers.

So think carefully about the known facts you're going to use to work out the missing numbers in these equations.

And then for question two, you're going to use the known fact to find some new facts and you could use Base 10 blocks, a bead string or a number line to help you.

And the known fact that Sam has is I know that three plus six is equal to nine, so I also know that.

Pause the video, have a go at your tasks and when you're ready we'll get together for some feedback.

How did you get on? There were lots to look at here.

Let's look at A first.

We had eight is equal to six plus two.

So could you see that helping you? We've got 18 is equal to 16 plus 2.

So 28 is equal to 26 plus 2.

38 is equal to 36 plus 2.

Now we've got a different part that's missing.

48 is equal to 46 plus 2.

58 is equal to 56 plus 2.

And now did you notice we'd switch from having a missing part to having the missing whole? So something is equal to 66 plus 2, well that's 68 and something is equal to 76 plus 2 and that must be 78.

Let's look at B.

Here we had 53 plus 4 is equal to something, so we've only got tens to deal with in our first addend.

So we know it's going to be 50 something and we know that three plus four is equal to seven so our sum must be 57.

Can we use that same fact? We've got a 34 plus something is equal to 37.

Well if we know three plus four is equal to seven, then four plus 3 is equal to seven.

So 34 plus 3 is equal to 37 and we've just turned it around.

So our whole is first here, 97 must be equal to 93 plus 4.

27 is equal to 23 plus 4.

37 is equal to 34 plus 3.

48 is equal to ooh, something plus 3.

I think we might have a different number fact here.

What plus 3 is equal to eight? It's five, isn't it? So 48 is equal to 45 plus 3.

58 is equal to 55 plus 3.

And then we're back to our six and twos and our ones here.

So something is equal to 66 plus 2, so that must be 68 and something is equal to 76 plus 2, so that must be 78.

Let's look at C, 45 plus 4 is equal to something.

While five ones plus four ones is equal to nine ones.

So 45 plus 4 must be equal to 49.

Oh.

Can you see here we've got equals 49? So our sum is the same for all of them, but can you see that our addend is changing? So 45 has become 46.

So one addend is one more, so we must have to add one less.

So 46 plus 3 is equal to 49.

And then carrying on that pattern, it must be 47 plus 2 and 48 plus 1.

So by thinking carefully about our known facts, we can solve these equations really quite easily.

Well done if you've got those right.

And for part two, we were told that three plus six is equal to nine.

So what else did we know? Well, we could know that 13 plus 6 is equal to 19.

23 plus 6 is equal to 29.

33 plus 6 is equal to 39.

43 plus 6 is equal to 49.

53 plus 6 is equal to 59.

63 plus 6 is equal to 69.

73 plus 6 is equal to 79.

83 plus 6 is equal to 89 and 93 plus 6 is equal to 99.

Did you work systematically? No wonder if you use the Base 10 blocks to help you as well, but well done if you've got all of those possibilities.

And on into part two of our lesson where we're going to be using known number facts to subtract.

So the children wonder if they can use known number facts to solve subtraction problems. So Sam says, "I had 6 p and I spent 4 p.

I have 2 p left." and Alex says, "I had 46 p, I spent 4 p.

I have 42 p left." Ooh, can you see something there? Let's have a look.

So let's find out by looking at Sam's problem first.

So Sam had 6 p and she spent 4 p and she has 2 p left.

6 p, subtract 4 p is equal to 2 p.

And we might have known that six, subtract four is equal to two.

So let's look at Alex's problem and Sam says, "I think we can use my problem to help solve your problem." Ooh, let's have a look.

Alex says, "I had 46 p and I spent 4 p.

So I have 42 p left." Can you see what happened there? 46 p subtract 4 P is equal to 42 p.

Can you see that six subtract four is equal to two in there? The four tens haven't changed.

So that 40 p has stayed the same.

So what's the same in both problems? Sam says, "We're taking four ones away from six ones in both." What's different? Alex says, "My problem has some tens but yours doesn't." So I wonder what other equations we could solve using the known fact, six minus four is equal to two.

And you can see that represented on our first number line.

What do you notice about the second number line? Let's look at the patterns to find out.

Alex says, "I know that six minus four is equal to two.

So I also know that 16 minus 4 must be equal to 12." That one 10 stays the same, but we've had six ones and we've subtracted four ones.

16 subtract 4 is equal to 12.

And he says, "I know that 26 subtract 4 will be equal to 22." The two tens haven't changed, we've just subtracted four from the six.

What do you notice about each equation in the pattern? And Alex says, "Only the tens digit is different in each equation.

The ones digits stay the same." Which other equations would belong in this pattern do you think? Well Alex says, "Any equation where the whole has six ones and four ones are subtracted will follow this pattern." So which of the following equations could you solve by using the subtraction fact six minus four is equal to two.

Is it A, B or C? Pause the video, have a go.

And when you're ready we'll come back for some feedback.

How did you get on? Did you spot that 56 minus 4 equals 52 followed the pattern? We know that six minus four is equal to two, so we know that 56 minus 4 will be equal to 52.

What about C though? If we know that six minus four equals two, we also know that six minus two is equal to four, so we could think of the same fact or a very similar one to help us to solve this equation as well.

So B followed the pattern exactly, but C was a related fact that we might have been able to use.

So let's look at some subtraction patterns without using a number line.

Let's look on the bead string.

I know that eight minus three is equal to five.

So I know that 18 minus 3 is equal to 15.

28 minus three is equal to 25 and 38 minus 3 is equal to 35.

I can see that known fact in my ones being repeated and all that changes is the number of tens and the number of tens in the whole and in the difference is the same because we haven't touched the number of tens, we've only touched the ones.

So time to check your understanding.

Which of the following equations could also be made using the pattern on Alex's bead stringing that we were just looking at? Eight minus three is equal to five.

Pause the video, have a think and when you're ready we'll get back together for some feedback.

So how did you get on? Did you spot that it was B that followed Alex's pattern? We know that eight ones minus three ones is equal to five ones.

68 has six tens and eight ones.

If we subtract three ones from the eight ones, it will leave six tens and five ones, 65.

So which of the following equations can be solved using the known fact, nine minus five? Hmm.

Well we've got nines and fives in both of those equations, but are they in the right places? Sam says, "I will partition the numbers and use Base 10 blocks to represent them." Good thinking, Sam.

So here's 98 and 59.

Remember we are looking for one where we can use the known fact nine minus five.

Well she says, "Both equations are subtracting five but only one has nine ones." She says, I" can solve 59 minus 5 using 9 minus 5." We might be able to use a related fact for the other one, but there aren't nine ones for us to work with in the first equation.

98 is nine tens and eight ones.

So Sam says, "Nine minus five is equal to four.

So 59 minus 5 must be equal to 54." And there we are.

We've sold the equation.

Time to check your understanding.

Can you match the correct single-digit fact to the equation that it would help solve? Pause the video, have a go and when you're ready we'll get back together for some feedback.

How did you get on? Did you spot that eight minus 2 would help us to solve 68 minus 2? 3 minus 2 would help us to solve 93 minus 2 and 8 minus 4 would help us to solve 78 minus 4.

Well done if you spotted all those related facts.

Time for you to do some practise now.

You're going to find the missing numbers in these equations and record the known fact that you use to solve each equation.

So really think hard about which known fact you're going to use to help make solving that equation easier and filling in those missing numbers.

And for question two, Alex thinks he has discovered something.

Can you use Base 10 blocks a bead string or a number line to show whether it is true or false? This is what Alex has found out.

When a number with a six in the ones has two ones subtracted, the answer always has four in the ones.

So can you use the resources you have around you to see if you can find out whether Alex is right or not? Pause the video, have a go at your tasks and when you're ready we'll get back together for some feedback.

How did you get on? So you had lots of missing boxes to fill in here.

So can you think what facts you might have used? I think all of the calculations in A, nine minus three equals six was a useful one to know in order to solve them.

So nine minus three equals six.

19 minus 3 equals 16.

29 minus 3 equals 26.

39 minus 3 equals 36, and then 49 minus 3 equals 46 and 59 minus 3 equals 56.

So each time we had a different part or the whole missing, but that fact of nine minus three equals six helps us to solve all of those.

Oh, can you see something again in B? I think we might be looking at the same fact here.

59 minus 3 is equal to 56.

79 minus 3 is equal to 76.

69 minus 6 is equal to 63.

So that 9 minus 3 equals 6.

We are now thinking about it the other way around, nine minus six is equal to three.

So 79 minus six is equal to 73.

89 minus 6 is equal to 83 and 83 is equal to 89 minus 6.

We just changed the order of the way we'd written the equation for that last one, hadn't we? And what about C? Well, I've got a five and I've got a minus two.

Hmm.

I wonder, are we thinking seven here, perhaps? I've got something minus two is equal to something five.

I think we might be looking at seven minus five equals two or seven minus two is equal to five to help us here.

So 25 is equal to 27 minus 2.

27 minus 2 is equal to 25.

37 minus 2 is equal to 35.

32 is equal to 35 minus 3.

oh slightly different factor using there.

So our three plus two is equal to five, helped us there.

What about this one? 41 is equal to 46 minus something.

Six minus something equals one six minus five equals one.

41 is equal to 46 minus 5.

And then 56 minus something is equal to 51.

Again, six minus five is equal to one.

So 56 minus 5 must be equal to 51.

So nine minus three equals six helped us nine minus six equals three.

Seven minus two equals five and then six minus five equals one were useful facts in all of that.

And we also had a three plus two is equal to five thrown in there in C just for good measure.

Well done if you spotted all those useful facts.

And finally, we were trying to prove whether Alex was right or not.

So he said, "When a number with a six in the ones has two ones subtracted, the answer always has a four in the ones." So let's see, this beads stringing I think shows what Alex says is true.

So he knows that six minus two is equal to four.

So there it is.

It doesn't matter how many tens we keep adding.

If he subtracts two, the answer will always have a four in the one.

So here we can see 26, subtract 2 is equal to 24.

And you could have tried that with lots of different numbers and it didn't matter how many tens you had that as long as you had six ones and we were subtracting two ones, the answer would always have four ones.

Well done if you were able to show that using Base 10 or a bead string or a number line.

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

We've been using number facts to add or subtract a single-digit number and a two-digit number.

What have we learned about? We've learned that we can use known facts to help us solve equations with larger numbers.

Those one-digit facts up to 10 are really useful when we're working even with larger numbers.

We've learnt that partitioning a two-digit number into tens and ones can help us to see the pattern in the ones.

And we've learned that when we add to or subtract from the ones without crossing the tens boundary, the tens digit does not change.

In all of the examples we had, we didn't have to cross a tens boundary, maybe that'll come up later.

Well done for all your hard work and all your mathematical thinking today.

I hope you've enjoyed it as much as I have and I hope I get to work with you again soon.

Bye-Bye.