Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you in our maths lesson today from the unit reviewing column addition and subtraction.

Hopefully, there'll be things in here that are familiar to you and you'll be able to revisit some ideas that you've learned about before.

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

So, in this lesson, we're going to be using column addition to solve problems in different contexts.

We've just got one keyword and that's column addition.

So I'll have a go and then it'll be your turn.

So my turn.

Column addition.

Your turn.

I'm sure you've come across column addition before.

You've possibly been practising it quite a lot recently, but let's just remind ourselves what it means 'cause it's going to be really important in this lesson.

So column addition is a way of adding numbers by writing a number below another one.

It's a way of organising the numbers, making sure that the digits are lined up in the correct columns to make it easy to keep track of what we are doing.

So we've got two parts to our lesson today.

In the first part, we're going to be solving problems involving two digit numbers.

And in the second part, we're going to solve problems involving three digit numbers.

So let's make a start.

Oh, we've got lots of people helping us in our lesson today.

We've got Alex, Jun, Laura, and Lucas.

Alex is playing a game with some friends.

He says, "I throw five bean bags at this target.

I score points depending on where they land." Laura says, "I'm going to say the points as Alex scores them." So good luck, Alex.

Off you go with your bean bags.

(gasps) He scored 10.

Laura says, "10.

A 5.

10.

One.

Oh, and zero." He got outside the target that time.

So he had a 10, a 5, another 10, a 1, and a 0.

And Laura says, "10, add 10, add 5, add 1 is equal to 26.

Alex scored 26 points altogether." Alex throws the bean bags again.

What score does he get this time? Oh, you did well this time, Alex.

You scored with all five bean bags.

He says, "The first time, I scored 26 points.

This time, I scored 32 points." 3 tens and 2 ones.

Yep, 32.

Well done.

Laura says, "How many points did Alex score altogether?" You might be able to work this out in your head, but we can use a column addition to make sure that we've got the answer correct.

So he's going to work out the sum of 26 and 32.

He says, "I'm going to use column addition to add the numbers together.

I'll write one addend above the other.

I'll put the digits with the same value in the same column." So he's written 26 as his first addend and 32 as his second addend.

And you can see that he's got the 6 and the 2, the ones digits lined up, and the 2 tens and the 3 tens lined up as well.

And Laura is reminding him, "Start by adding the numbers with the smallest place value first." So we're gonna start with the ones.

"6 ones add 2 ones is equal to 8 ones." And we record that in the big equal sign at the bottom to show that that's our equation.

That's where our sum goes.

And 2 tens add 3 tens is equal to 5 tens, or we could think of it as 50, but it's represented with a 5 in the tens column.

"So 26 add 32 equals 58.

Alex scored 58 points altogether," says Laura.

Laura's been having a go as well.

She scored 41 points and 45 points.

What's her total? Now, you may be able to work it out mentally, but set it out as a column addition again just to check.

Alex says, "Use column addition to add the numbers together.

Make sure you write the digits in the correct columns." And Laura is reminding you, "Start by adding the numbers with the smallest place value first." So pause the video, have a go at working that out using a column addition and we'll get together for some feedback.

How did you get on? So one addend was 41 and the other was 45.

And we can make sure they're lined up so that the ones digits, the 1 and the 5, are above each other or are in the same column.

And the 4 tens and 4 tens are also in the same column.

So we start by adding the smallest value digits.

So that's our ones.

So 1 one add 5 ones is equal to 6 ones.

And then in the tens, 4 tens add 4 tens is equal to 8 tens or 80.

And 80 is represented with an 8 in the tens column.

So 86.

41 add 45 is equal to 86.

So Laura scored 86 points altogether.

Jun throws next.

He scores 25, 31, and 32 points.

Jun says, "I had three goes altogether.

Now I'm going to use column addition to add the numbers together." I'll write one addend above the other and I'll put the digits with the same place value in the same column.

So his first score was 25, then 31, and then 32.

And he set them out very neatly with the ones all in the same column and the tens all in the same column.

And Lucas says, start by adding the numbers with the smallest place value first.

So he's gonna start with the ones.

5 ones add 1 one add 2 ones is equal to 8 ones.

And then 2 tens add 3 tens add 3 tens is equal to 8 tens or 80.

So 25 add 31 add 32 is equal to 88.

Jun scored 88 points altogether.

Lucas has had 3 goes as well.

What's his total score? So he scored 24, 35, and 40 points.

So Jun says, "Use column addition to add the numbers together.

Put one addend above the other and put the digits with the same value in the same column." And then Lucas is reminding you, "Start by adding the numbers with the smallest place value first.

So pause the video, record this as a column addition, and work out what Lucas's total score was, and we'll come back for some feedback later.

How did you get on? So, our first addend was 24 and then 35 and then 40.

And you can see all our ones digits lined up and all our tens digits lined up.

And we're gonna start with the smallest value, which is the ones digits.

So 4 ones add 5 ones add 0 ones is equal to 9 ones.

And then in the tens, 2 tens add 3 tens add 4 tens is equal to 9 tens or 90.

And 90 is represented with a 9 in the tens column.

So our total score this time is 99.

24 add 35 add 40 is equal to 99.

Lucas scored 99 points altogether.

Alex made a total of 48 points, which two bean bags show his scores.

So there are five bean bags there each with a different score on them.

Two of them are Alex's scores and he made a total of 48 points.

So which two bean bags show Alex's scores? Hmm, I wonder.

Laura says, "I know 4 ones add 4 ones is going to equal 8 ones.

So I'm going to add together 14 and 24." So there we've got our 14 and 24.

4 ones add 4 ones is equal to 8 ones.

That's correct.

"2 tens add 1 ten is equal to 3 tens.

That's not right," she says.

"It isn't equal to 48." So that one's not going to work.

Hmm.

She says, "I did not choose the correct addends, but I can learn from my mistake." Oh, well done, Laura.

That's a really good attitude to have.

So can we learn from Laura's mistake as well? Which two bean bags show Alex's scores? Can you have a think? Laura had made a mistake, but what mistake had she made? And can we learn from that and make this correct score? So pause the video, have a go, and we'll come back for some feedback.

How did you get on? Oh, Jun said, "I'm going to add together 14 and 34." Now, what did Laura choose? She chose 14 and 24, and she didn't have enough points.

So Jun is still thinking about that 4 and 4 is equal to 8, but he's got more tens this time.

Let's see if that works.

So he's got 14 and 34.

"4 ones add 4 ones is equal to 8 ones.

3 tens add 1 ten is equal to 4 tens.

Alex's two scores were 13 and 44." Well done, Jun.

Did you get that too? Did you use Laura's working to help you to see how you needed to adjust one of those scores to make the correct total? Time for you to do some practise.

You are going to use column addition to find the total scores.

So we've got Lucas's points, Laura's points, Alex's points, and Jun's points.

Can you work out how much each of them scored in total? And who scored the most points in total? Then again, they've played the game again and they've scored some more scores.

This time they had three goes each.

So can you add up Lucas's scores, Laura's scores, Alex's scores, and Jun's scores and find out who scored the most points when they had a three-round game.

And for part three, we know the total that they scored and we know that they each had two goes.

So which two bean bags show each child's scores? Use column addition to show your answers.

And you can use the bean bags in more than one solution.

So more than one person might've scored 21 points, for example.

Pause the video, have a go, and we'll come back for some feedback.

How did you get on? Here was the answer to the first round where each of them had had two goes.

So our column additions were 45 plus 14 for Lucas, and he scored 59 points.

35 plus 32 for Laura.

She scored 67 points.

50 and 11 for Alex.

He scored 61 points.

And 23 and 36 for Jun and he scored 59 points in total.

So who scored the most points in total? It was Laura this time.

Well done, Laura.

You won that round.

In question two, they'd all had three goes.

So who had scored the most this time? So you can see there, you can check your additions with the ones that are there on the screen.

I hope you got everything lined up in the right columns.

Who scored the most points this time? It was Jun.

Jun got 89 points.

So he beat Alex by 2 points this time.

Well done, Jun.

And for part three, you had to work out who had scored what? The bean bags represented total scores and each of our players had had two goes.

So Lucas had scored 66 points.

So his individual scores were 45 and 21.

Laura had scored 77 points, so her individual scores were 44 and 33.

Alex had scored 54 points, so his individual scores were 21 and 33.

And Jun had scored 89 points, so his individual scores were 45 and 44.

So I think Jun won that round again.

I think Jun's quite good at the bean bag game, isn't he? Maybe you can have a go at playing some bean bag games and adding up your scores as well.

Time to move on to the second part of our lesson.

This time we're going to be solving problems involving three digit numbers.

Ah, he's gone indoors this time.

Alex is playing a computer game where he has to collect coloured gems. And here are the coloured gems. And you can see they're all worth a different number of points.

"So the gems are worth a number of points depending on their colour." "In his first game, Alex collects these gems." Laura tells us.

So the ones at the top are to tell us what they're worth.

So underneath we've got Alex's collection of gems. So he got two 100 gems, one 50, and two 10s, and three 1s.

So 100 plus 100 is equal to 200.

50 add 10 add 10 is equal to 70.

And three 1s is equal to 3.

So he scored in total 273 points.

He plays the computer game again.

He says, "How many points have I scored this time?" Is he gonna make Laura do the adding up again? Can we help her out? So he scored four lots of 100 points.

So 100 add 100 add 100 add 100 is 400 points.

He had two 20 gems, which is worth 20 points.

And he had five 1 gems, which are worth five points.

So what's he scored, Laura? That's right.

This time, he scored 425 points in his second game.

Laura says, how many points did Alex score in both of his games in total? Hmm.

So Alex is going to work out the sum.

He scored 273 points in his first game and 425 points in his second game.

He says, "I'm going to use column addition to add the numbers together.

I'll write one addend above the other.

I'll put the digits with the same value in the same column." So there's his 273 points and his 425 points.

And Laura says, "Start by adding the numbers with the smallest place value." So we're gonna start in the ones.

3 ones add 5 ones is equal to 8 ones.

Enter the tens.

2 tens add 7 tens is equal to 9 tens or 90.

9 tens.

And 2 hundreds at 4 hundreds is equal to 6 hundreds.

So what was his total score? 273 add 425 is equal to 698.

Alex scored 698 points altogether.

Laura's had a go at the game.

She scores 321 and 266 points.

Can you use column addition to calculate her total? "Write one addend above the other.

Put digits with the same value in the same column." And remember to start by adding the digits with the smallest place value first.

Pause the video.

Have a go at working out what Laura's total score was.

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

So we had 321 points add 266 points.

All nicely lined up so that the ones, the tens, and the hundreds are all in the correct columns.

Then we can add them really easily.

And then we're gonna start with the smallest value digits.

So that's the ones.

So 1 one add 6 ones is equal to 7 ones.

2 tens add 6 tens is equal to 8 tens.

And 3 hundreds add 2 hundreds is equal to 5 hundreds.

So what was Laura's total score? 321 add 266 is equal to 587.

Laura scored 587 points all together.

Well done, Laura.

Jun played the computer game twice.

He adds his scores together and gets a total of 757.

So that's the sum of his scores.

He says, "Which of these numbers were my two scores?" Ooh, so we've got to pick two of those scores that will have a total of 757.

Laura says, "Jun's total has a 7 as its ones digit and I know that 4 and 3 have a sum of 7." Hmm.

Can you think which numbers you'd pick? "One of the numbers has 3 as the ones digit and the other number has 4 as the ones digit." She says, "I'm going to add 324 and 423." So 324 add 423.

So let's have a look.

So we're gonna start with the ones.

4 ones add 3 ones is equal to 7 ones.

Good start.

2 tens add 2 tens is equal to 4 tens.

Hmm.

Is that going to work? And 3 hundreds add 4 hundreds is equal to 7 hundreds.

Well, we've got the hundreds and the ones correct, but not the tens, have we? 324 add 423 is equal to 747.

The total of the two numbers I added was 10 less than Jun's actual total of 757.

Laura's going to try again to get a total of 757.

She only needs 10 more, doesn't she? Again, Jun says, "Which of these numbers were my scores?" And Laura says, "I added 324 and 423 and got a sum of 747." Can you see another number that she might choose to use? She says, "I know that one number has 3 as the ones number and the other has a 4 as the one." So I've got to keep that 3 and that 4.

324 and 423 have a sum 10 less than 757.

So she says, "I think Jun's two scores are 334 and 423." She's kept that 4 plus 3 for 7, but she's got 10 more in her tens.

324 has changed to 334.

Let's see if she's right.

334 add 423.

4 ones add 3 ones is equal to 7 ones.

3 tens add 2 tens is equal to 5 tens.

And 3 hundreds add 4 hundreds is equal to 7 hundreds.

That's right, isn't it? 757.

"334 add 423 is equal to 757.

Jun had scored 334 points and 423 points." Great thinking, Laura.

Well done.

Over to you to check your understanding, Laura plays the computer game twice as well.

She adds her two scores together, and she gets a total of 556 points.

Which of these numbers were Laura's scores? And Laura says, "Look at the ones digit in 556.

Which two ones numbers could add to equal 6?" Have a look at the numbers carefully.

Have a go at the column addition.

Pause the video and we'll get together later for some feedback.

How did you get on? Did you take Laura's advice and look at the ones digits? Laura says, "The numbers must be 232 and 324 because the ones digits add to equal 6.

And that was the only way we could do it.

We've got one with a ones digit of 6, but we haven't got one with a ones digit of zero to add on.

And the 323, well, we'd need something with a ones digit of 3 to give us 6.

So it's got to be 232 add 324.

Let's just double check.

2 ones add 4 ones is equal to 6 ones.

3 tens add 2 tens is equal to 5 tens.

And 2 hundreds add 3 hundreds is equal to 5 hundreds.

556.

That was Laura's score, wasn't it? Laura says, "232 add 324 is equal to 556." So I scored 232 points and 324 points.

Well done if you've got that right.

Time for you to do some practise.

So, you're going to use column addition to find the total scores for Lucas, Laura, Alex, and Jun and find out who scored the most points in total.

Ooh, can you predict whose score will be the largest? Can you look at the numbers involved and make an estimate to see if you can predict whose score is the largest? For part two, who scored what? Can we use column addition to find the two different scores that add to make each total? So there are the possible scores.

So which of those two make Lucas's total score? Which of those two can make Laura's total score? And which for Alex and which too for Jun? So Lucas says, "Which two scores have a total of 769?" Laura's saying, "Have a look at the ones.

Which ones numbers add to equal 8?" Alex and Jun aren't gonna give you any clues, but see if you can use the thinking that Lucas and Laura have suggested to help work out Alex's and Jun's total points.

Pause the video now and we'll come back for some feedback later.

How did you get on? Here were the answers to the first question.

We had to work out the total scores for each of our players.

So Lucas had a total of 695 points, Laura, 689 points, Alex, 694 points, and Jun, 696 points.

So who scored most points in total? It was Jun again.

He seems to be good at bean bags and at computer games.

Well done, Jun.

And I hope you did lots of thinking around this, but these were the pairs of scores that each child got to get their total score.

So Lucas scored 518 and 251.

Laura scored 444 and 324.

Alex scored 533 and 245.

And Jun scored 513 and 154.

So we've come to the end of our lesson using column addition to solve problems in different contexts.

It's useful to remember that we've got column addition to use when the numbers are perhaps too big for us to calculate within our heads.

But remember, if we can calculate in our heads, we don't always have to use column addition.

So what have we learned about today? We've learned that when we're using column addition, the addends and the sum are recorded in columns with the same value digits in the same column.

And that when we're using column addition, we start by adding the numbers with the smallest place value first.

This may not seem as important now, but as we move on with our column addition, that will become really important.

Thank you again for all your hard work in this lesson and all your good thinking, and I hope I get to work with you again soon.

Bye-Bye.