Lesson video

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

This lesson comes from the unit on addition and subtraction of two digit numbers.

Is this new for you? Have you done anything like this before? I'm sure you've got lots of skills about numbers and addition and subtraction that you're going to be able to bring to this lesson.

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

So in this lesson, we're going to be combining and partitioning tens and ones in the context of equations.

Oh, what does that mean? Well, we're going to be solving some equations, so doing some calculations, and we're going to be combining and partitioning tens and ones as we do it.

So are you ready? Let's make a start.

We've got two key words.

We've got calculate and efficiently, and hopefully, that's what we're going to do, calculate efficiently.

Let's practise saying those words and then we can look out for them as we go through the lesson.

I'll take my turn, then it'll be your turn.

So my turn.

Calculate.

Your turn.

My turn.

Efficiently.

Your turn.

Fantastic.

I hope you've been working efficiently today getting things done in reasonable time and being quite accurate as you go.

So let's get in and see what our lesson is all about today.

There are two parts to our lesson.

In the first part, we're going to be combining groups of tens and ones within an equation.

And in part two, we're going to be finding missing tens or ones within an equation.

So let's make a start on part one.

And we've got Andeep and Izzy helping us in our lesson today.

The whole is missing in this bar model.

Izzy writes an equation to help her find the missing number.

What do you think the equation's going to look like? What calculation are we going to do? Ah, so she's going to add, but she says it's easier to add if I rearrange the numbers.

So at the moment, we've got two and 30 and four and 50, making up our whole.

How could she rearrange them do you think? Ah, she says, "I will put the tens together and the ones together to add them." That sounds like a good idea, Izzy.

So she's got 30 + 50, those are our two multiples of 10.

Plus 2 + 4.

And that is equal to the whole, which is unknown at the moment.

Izzy wants to calculate the sum of this equation efficiently.

Let's see what she does.

So efficiently means she's going to do it quite quickly and in a relatively straightforward way that works for her.

She says, "I will use Base 10 blocks to represent the numbers." Good idea, Izzy.

So can you see? She's got 30 represented with three tens, and 50 represented with five tens.

And two represented with two ones and four represented with four ones.

So she's got her 30 add 50 add two add four.

She's going to combine her tens first and then the ones.

So combining her tens, she's got three tens and five tens, which is eight tens, so she's got 80.

And she's rewritten it just with the digits to give the number 80.

What about those ones? Well, she's got two ones and four ones and 2 + 4 = 6.

So altogether she's got six ones.

So she's written her equation much more efficiently.

We had 30 + 50 + 2 + 4.

And now because we've combined our tens and combined our ones, we've got 80 + 6.

And that's equal to 86.

So her whole is worth 86.

Andeep's arranging the numbers differently.

What's he done this time? He says, "I think I'll add the ones first." So he's rewritten the equation.

2 + 4 + 30 + 50.

The same four numbers that he's adding, the same four addends, but he's written them in a different order.

So he's going to add the ones first.

2 + 4 = 6.

Now he's going to add the tens, 30 + 50 = 80.

So now he can combine the tens and the ones.

80 + 6 or 6 + 80 = 86.

So he's just redrawn the bar, two and four first then 30 and then 50.

But still the whole is 86.

He says, "If we change the order of the addends, the sum remains the same, so the sum will still be 86." It's time to check your understanding.

Can you match the expressions which have the same total value? So can you find the ones where the numbers have been written in a different order within the expression? Pause the video, have a go.

And when you're ready for some answers and feedback, press play.

How did you get on? So the one on the top at the left is 60 + 5 + 3 + 20.

Can you see another expression that's got 60, 5, 3 and 20? There it is, it's the middle one.

We've rewritten it in a different order.

5 + 60 + 3 + 20.

But the four addends are still there.

What about 20 + 2 + 50 + 6? Can you see that one anywhere? That's right.

2 + 50 + 20 + 6.

The same for addends but written in a different order.

So they'll have the same total value altogether.

And then finally, let's just check 20 + 5 + 30 + 6.

Yes, we've got a 20, a 30, a six and a five, but in a different order.

6 + 5 + 30 + 20.

Well done if you spotted those.

The expressions that match have the addends in a different order, but they will have the same value because we're still combining the same four addends.

Andeep adds these numbers without using Base 10 blocks.

He's got 30 + 5 + 40 + 2.

He says, "I will use my known facts to help me." He says, "I'll add the tens first." Which known fact do you think he's going to use? Ah, that's right.

He says, "I know that 3 + 4 = 7, so three tens plus four tens will be equal to seven tens or 70." So those two addends have a total value of 70.

"Now I will add the ones." He says, "5 + 2 = 7." So his tens have a total value of 70.

His ones have a total value of seven.

So what is his sum? Ah, that's right.

70 + 7 = 77.

We can use our knowledge of place value, seven tens and seven ones, 77.

Izzy says, "I will check by adding the ones first.

5 + 2 = 7." She says.

"Now I'll add the tens.

3 + 4 = 7, so three tens plus four tens is equal to seven tens or 70." 7 + 70 is also equal to 77.

It doesn't matter which order we add the addends, the sum will be the same.

Izzy uses Base 10 blocks to find the missing whole in this bar model.

She says the missing whole is 59.

What mistake has she made? You might want to stop and have a look before we share our thinking.

Can you see what's happened? Oh, she says, "I forgot to think about what the digits in each number represents." Can you see she's got two tens and three tens next to the two ones and three ones in the bar model.

And she's got six ones and three ones next to the six tens and the three tens.

She says, "I represented the tens as ones and the ones as tens." We've got to think really carefully about what those digits represent, haven't we? Before we start to represent them ourselves with something like our Base 10 blocks.

She says, "I will correct my mistake." Can you visualise what's going to happen? That's right.

The two and the three are ones, so they need to be represented with ones blocks.

But the 60 and the 30 are six tens and three tens.

So we need to represent those with the 10 sticks.

So our ones have a total of five.

And our tens have a total of 90.

So all together we have a whole of 95, don't we? Nine tens and five ones.

And it's time to check your understanding again.

Can you rearrange the tens and ones, and then find out which equation is correct? Remember you can have the tens first or the ones first.

So we've got some completed equations there, but they're not all correct.

So pause the video, rearrange the tens and ones, and find out which equation is correct.

And when you're ready for some feedback, press play.

How did you get on? Which one was correct? That's right, it was B, wasn't it? So we've got our tens, we've got 40 and 50, four tens plus five tens is nine tens, which is 90.

And then the 2 + 3 = 5.

So we've got a sum of 95.

What went wrong in the other ones? Well in A, we've got five tens there.

So I think we've added the wrong way 'round.

We've used the three and the two to make the five, and then the five and the four of the five tens and the four tens to equal nine.

That's not right, is it? And what about the last one? Well here we've added three and five to give us eight, but we're adding three ones and five tens.

So that's not giving us eight tens, is it? So we've got to be really careful when we identify our tens and our ones that we add them and give them the right place value as we complete our equation and our calculation.

Andeep arranges these digit cards in the equation below.

When he solves the equation, he reaches a total of between 70 and 80.

Ooh, that's interesting.

So his total is going to be between 70 and 80.

So he's adding two multiples of 10 and two one's digits.

And he's got to be between 70 and 80.

Hmm.

You might want to have a think about this.

Andeep's arranged them.

Izzy's going to talk us through what the thinking might be.

So let's work out how he arranged the cards.

Izzy says, "The total is between 70 and 80, so it must have a tens digit of seven." Well that's right, it's between 70 and 80, so it's got to have a seven.

How could we make a seven as our tens digit using those cards? There is our seven.

What could we use? Ah, Izzy says, "3 + 4 = 7.

So the digits three and four must be the tens digits in our equation." So there we go.

We've got 30 and 40, and that's going to give us an answer of 70 something, isn't it? What have we got left? She says, "The other digit cards must be the ones." One and seven.

Could we have used the seven in the tens? That would've given us 70, but we've got to add something onto it.

So even if we'd had 10 as our other number, we'd have had a number greater than 70 as our answer.

So Izzy was right.

Three and four were the only digits we could have had as our tens digits.

But now we've got 1 + 7.

So what have we got in our ones? Well, 1 + 7 = 8, so the ones digits in the total must be eight.

So there we've got our equation.

30 + 1 + 40 + 7 = 78.

And it's time for you to have a go.

You're going to use the digit cards to make some different totals in our equations.

We've got the digit cards two, three, four and five, and we're going to make equations that add to two multiples of 10 together and two ones digits together.

So for A, you need to find a total that is greater than 80 and is odd.

For B, your total's got to be greater than 80, but it's got to be an even number.

For C, it's got to be less than 70 and odd.

For D, it's got to be less than 70 and even.

And for E, you're going to find a number where both the tens and ones digits are odd.

So you've got to think about how you can arrange those digits in different ways so that you can create those different totals.

That looks like an exciting challenge.

I hope you have fun.

Pause the video, have a go.

When you're ready for some feedback, press play.

How did you get on? I hope you enjoyed that.

Let's have a look.

A was challenging you to make a total that's greater than 80 and odd.

How do we get an odd to total then? Well, we've got to have a ones digit sum that is an odd number.

So how could we do that? Well, there's one way we could do it.

So 2 + 3 will give us an odd total, an odd number plus an even number gives us an odd number total.

So 2 + 3 = 5.

And then we've got the four and the five left.

And they become our tens numbers.

Four tens plus five tens is equal to nine tens, which is 90.

So that will give us a total of 95, which is greater than 80 and it's odd.

Well done if you spotted that one.

For B, you had to make a total that was greater than 80, but it had to be even this time.

So we couldn't have our 2 + 3.

We need two odd numbers or two even numbers.

So what could we have as our even digits? Well, we could have the three and the five.

3 + 5 = 8, but oh dear, I don't think we've got enough tens then, have we? Remember, it's got to be greater than 80.

So I think we might need to have.

There we go.

If we use the three and the five as our tens digits, then that means we've got eight tens, three tens plus five tens is eight tens.

And that leaves us two and four as our ones, and two and four are going to add to be an even number 'cause they're both even and they have a sum of six.

So we've got eight tens and six ones, which gives us a sum of 86, which is greater than 80 and it's an even number.

So C said, can you make a total less than 70 and odd? So we've got to have an odd number and an even number in our ones this time.

Hmm.

And we've got to be less than 70.

So we could use the four and the five as our ones digits.

I wonder if you did that.

Ah, there we go.

So 4 + 5 = 9.

So that gives us an odd number in our ones.

Two tens plus three tens is equal to five tens, 20 + 30 = 50.

And 50 is less than 70, even with the nine added on.

So our sum is 59.

It's less than 70 and it's odd.

For D, we had to have a total that was less than 70 and even.

Hmm.

So we think about those one digits.

So this time we need either two even numbers or two odd numbers, but we've got to keep those tens down, haven't we? What about.

Ah yes, we could use the five and the three, two odd numbers they will sum to be an even number.

5 + 3 = 8.

So that gives us an eight in our ones that will be an even number.

And we've got two tens and four tens, which is six tens.

68 is our total.

Oh, it's just less than 70 and it's an even number.

And finally, we had to make a total where both the tens and ones digits are odd.

So this time we'd to have one odd and one even number as our tens, and one odd and one even number as our ones.

It didn't matter how big our total was.

So we could have 24 + 35.

And that's we've got.

Oh, here we've got 24 + 53.

So as long as one of our tens numbers is odd and the other is even, we will have an odd number of tens.

And as long as one of our ones digits is odd and the other is even, we will have an odd number of ones as well.

So in this case we've got 77.

Seven is an odd number of tens and seven is an odd number of ones as well.

Well done, and I hope you enjoyed reasoning your way through those problems. And on into the second part of our lesson.

Let's find some missing tens and ones within an equation.

Andeep hides one of the addends in this equation.

Izzy uses Base 10 blocks to help her to find the missing addend.

So we've got 30 +4 + something + 5 and it's equal to 69.

Izzy says, "The whole has six tens and nine ones.

So 4 + 5 = 9, so we don't need any more ones." So it's obviously not a ones digit that we're missing.

We're missing a number of tens.

We've got the nine ones already.

We need to find the missing tens.

Three tens plus some tens is equal to six tens.

Have you worked it out? Three tens.

Oh Izzy says, "I know 3 + 3 = 6.

So three tens plus three tens is equal to six tens.

So we must need another three tens.

And now we've got six tens and nine ones, which is our 69.

So the missing addend had to be 30.

We were missing three tens.

This time, Izzy hides one of the addends in her equation and Andeep thinks he can find it.

We've got 20 + 40 + something + 3 = 68.

Can you work out what's missing? Is it a tens or a ones number? Andeep says, "The whole has six tens and eight ones.

Two tens plus four tens is equal to six tens.

Well that's our 20 + 40, so we don't need any more tens." 20 plus 40 is equal to 60.

So we've got all the tens from our sum.

So we must be looking for a missing ones digit.

That's right, something + 3 = 8.

Do you know what the missing number is? Something + 3.

Andeep says, "I know that 5 + 3 = 8." There we go.

Five ones add three ones is equal to eight ones.

There are our eight ones.

So the missing addend was a five.

20 + 40 + 5 + 3 = 68.

Time to check your understanding.

Can you use some Base 10 blocks perhaps to find the missing addends here? 10 + something + 2 + 4 = 56.

And 50 + 30 + something + 5 = 87.

Pause the video, have a go.

And when you're ready for the answers and some feedback, press play.

How did you get on? So here we had 10 + something + 2 + 4.

Well the whole has five tens and six ones.

We've already got the ones, haven't we? Two ones plus four ones is equal to six ones, so we don't need any more ones.

But what about those tens? Ah, I know that 1 + 4 = 5.

So one ten plus four tens is equal to five tens.

We've already got the one ten so we must be missing four tens.

So the missing addend must be 40.

And there we are.

10 + 40 + 2 + 4 = 56.

What about the next one? So we've got our 50 + 30 + something + 5, and we have a sum of 87.

So the whole has eight tens and seven ones.

Well 50 + 30, five tens plus three tens, is equal to eight tens or 80.

So we don't need any more tens.

We've already got the tens we need.

So there they are, the eight tens from our 80.

What about our ones? We've got five ones.

So I know that 2 + 5 = 7.

So the missing addend must be two.

2 + 5 is equal to the seven ones we need.

So our equation was 30 + 50 + 2 + 5 = 87.

Well done if you've got both of those.

Andeep thinks he can find the missing addend without using Base 10 blocks.

So we've got 2 + something + 1 + 50 = 73.

Hmm.

Can you see what's missing there? Can you tell what size of number it is? Andeep says, "I will draw a bar model." So we know that our whole is 73, and we're missing one of the parts.

We've got a two and a one and a 50, but we're missing another number.

So that number's got to be quite big, hasn't it? It's got to be a number of tens.

He says, "I will look to see if I need to add tens or ones." I think it's tens, do you? He says, "The whole has seven tens and three ones.

2 + 1 = 3, so I do not need any more ones." We've got all the ones there, haven't we? "To find out how many tens are missing, I will think something + 50 = 70." 'Cause we know we need seven tens in our answer.

So what plus 50 is equal to 70? Oh well he says, "I know 2 + 5 = 7, so two tens plus five tens must be equal to 70." So our missing addend must be 20.

So the missing addend is two tens or 20.

2 + 20 + 1 + 50 = 73.

Well done, Andeep.

Well done for doing that without the Base 10 blocks.

Time for you to have some practise.

Can you find the missing addend? And can you use the bar model to help you? Think about what our sum is.

Think about how many tens and how many ones, and see if you can work out what the missing addend is, maybe without using Base 10 blocks this time.

Pause the video, have a go.

And when you're ready for the answer and some feedback, press play.

How did you get on? So this time our whole has eight tens and six ones.

We've already got six tens and two tens, which is equal to eight tens.

So we don't need any more tens.

So our missing number is not a number of tens.

We've got 80 already.

There they are.

So we need to find out how many ones are missing.

So I'm going to think something + 2 = 6, 'cause I know I've got a two ones in my equation already.

So something + 2 = 6.

What do we have to add to two to equal six? Oh well we know that 4 + 2 = 6, so the missing addend must be a four.

4 + 60 + 2 + 20 = 86.

Well done if you've got that.

Izzy uses the digit cards shown to complete the missing numbers in the equation.

So this time we've got a number of tens plus some ones plus a number of tens plus some ones is equal to 37.

So we've got to have a total which has three tens and seven ones.

Andeep says he knows which digit cards are needed for the tens digits and which are needed for the ones digits.

But how does he know? Do and have a quick think before he tells us.

How do you know Andeep then? Share your thinking.

He says, "The tens digits must sum to three, so the tens digits must be one and two." 'Cause it's the only way we can make a sum of three with those cards.

Well done, Andeep.

So 10 and 20 are our tens numbers.

And he says, "They can be written in any order." So we could have 10 and then 20, or we could have 20 and then 10, because we know that addition is commutative.

We can change the order of the addends and the sum stays the same.

"The ones digits must sum to seven.

So the ones digits must be the three and the four." So there we are.

So we could have 20 + 3 + 10 + 4.

Or 20 + 4 + 10 + 3.

Again, we could change the order of the digits and the sum stays the same.

Haha, time for you to do some practise.

How many different ways can you complete each equation using the digit cards shown? So we've got one, two, three and four again.

And you're going to complete those equations using those four digit cards.

Each one just use once each time.

And then you're going to think about how many different ways you could write that equation with the sum staying the same? So how could you change the orders? Pause the video, have a go at those three questions, and when you're ready for the answers and some feedback, press play.

So for A, we were looking for a sum of 73.

So the tens digits must sum to seven.

So they could be 30 and 40 or they could be 40 and 30.

What about our ones digits? Well, the ones digits must sum to three, so they've got to be the one and the two.

But we could have one and two or they could be two and one.

So what are the different equations you could write? We could have 30 + 1 + 40 + 2.

We could have 30 + 2 + 40 + 1.

Or we could have 40 + 2 + 30 + 1.

Or 40 + 1 + 30 + 2.

All of those have a sum of 73 because the addends are always 30, one, 40 and two that's just written in different orders.

And we know that addition is commutative.

So if the addends are written in a different order, the sum will stay the same.

What about B? How are we going to make a sum of 46? Well the tens digits must sum to four, so they could be, well 10 and 30.

That's the only way we're going to get a sum of four out of one, two, three and four, isn't it? So 10 and 30 or 30 and 10.

And the ones digit must sum to six.

We've used the one and the three, so the two and the four.

2 + 4 = 6.

So we could have four and two or two and four.

So our equations could be 10 + 2 + 30 + 4 = 46.

But so is 30 + 2 + 10 + 4.

And so is 10 + 4 + 30 + 2.

Or 30 + 4 + 10 + 2.

All of those equations have a sum of 46 because it's the same four addends written in a different order.

And finally, C.

We had a sum of 64 this time.

Ooh, did you see we had 46 before, haven't we? So the tens digits must sum to six.

So they could be 20 and 40.

Or 40 and 20.

And the ones digits must sum to four.

So they could be three and one or one and three.

So the four equations would be these.

20 + 1 + 40 + 3.

Or 20 + 3 + 40 + 1.

Or 40 + 1 + 20 + 3.

Or 40 + 3 + 20 + 1.

All of them have a sum of 64 because it's the same four addends just written in a different order.

Well done if you found all of those.

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

We've been combining tens and ones within equations.

What have we learned about? Well, we can use strategies we already know to help us to prepare for the addition of two digit numbers.

We're getting closer, but we're not quite there yet.

But we've been using known facts and we've been using our place value to help us.

And we've been using our knowledge that we can add the addends in a different order and the sum stays the same.

And sometimes that helps to make an equation easier to solve.

And it's important to be able to calculate mentally before adding two, 2-digit numbers.

So using those known facts and being able to apply those to solve calculations is really helpful.

Thank you for all your hard work and your mathematical thinking, and I hope I get to work with you again soon.

Bye-bye.