Lesson video

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

Are you ready to work hard? Are you ready to remember perhaps some things that you've learned before? Well, if so, let's make a start.

So in this lesson, we are going to be using column addition with regrouping to solve problems. We've got two keywords.

They are estimate and regroup.

So I'll have my turn at saying them, and then it'll be your turn.

So my turn, estimate, your turn.

My turn, regroup, your turn.

They may be words you're familiar with, but let's just take a look at what they mean just to remind us they're going to be useful today.

Estimation means to find a value that is close enough to the right answer, usually with some thought or calculation involved.

So we're going to be looking at the numbers today and thinking, "Well, what number is that close to? Can I use that number that's close to get a rough idea of the answer that I'm going to be getting when I do my calculation?" It's often really useful as part of the way of checking that we've got the right answer.

And the process of unitizing and exchanging between place values is known as regrouping.

For example, 10 tens can be regrouped for 1 hundred, or 1 hundred can be regrouped for 10 tens.

And you're going to see some of that as we go through today's lesson.

There are two parts to our lesson.

We're going to be using two addends to make a sum in the first part.

And then in the second part, we're going to be finding two addends to make a given sum.

So let's make a start on part one.

And in this lesson, we've got Alex and Lucas helping us with our learning.

And Alex says, "Elephants are my favourite animal." Hm, I wonder if that's a clue to what we're going to be looking at.

I wonder what your favourite animal is.

Alex and Lucas are completing a project together.

Alex says, "Let's do a project about elephants." Oh, he did tell us elephants are his favourite animal, didn't he? And there is an elephant.

Lucas says, "Good idea.

But can we have lots of maths in our project?" Ooh, I like that.

"Sure!" says Alex, "There are lots of elephant facts that we can use." Ooh, I'm excited about this.

Are you? Alex shares some elephant facts.

He says, "Did you know elephants can be over 300 centimetres tall?" Wow! That's quite tall.

Do you know what that would be in metres? Hm, how many metres would that be? And their trunks can be up to 200 centimetres long.

That is a very long trunk.

Lucas says, "That's amazing! They must be able to reach a long way up." Alex says, "This is Edward." Edward is an elephant.

"He's 337 centimetres tall and has a trunk 185 centimetres long." Wow! So there is his height, 337 centimetres, and his trunk is 185 centimetres long.

Alex says, "Each of his tusks are 167 centimetres long." Can you see those? His tusks sticking out on either side of his trunk.

And each of his tusks is 167 centimetres long.

Wow! That's quite long, isn't it? Lucas says, "Let's work out the total length of both of Edward's tusks." So he's going to work it out.

How do you think he's going to do that? Alex says, "Well, each of Edward's tusks are 167 centimetres long." So Lucas says, "To work out the total length, I would have to add 167 centimetres and 167 centimetres together." I wonder what strategy he's going to use.

Ah, he's gonna do a column addition to add them together.

Ooh, Alex says, "I can estimate the answer.

167 is close to 150.

150 add 150 is 300.

So I estimate that the sum will be close to 300 centimetres." Let's see if he's right.

So Lucas is starting with the ones.

7 ones add 7 ones is equal to 14 ones.

I'll regroup 10 ones as 1 ten, and we'll add it into the tens column.

6 tens add 6 tens add the regrouped ten is equal to 13 tens.

So we can regroup 10 of those as 1 hundred.

So we've got 10 tens regrouped as 1 hundred, and the extra 3 tens in our tens column.

And 1 hundred add 1 hundred plus the regrouped hundred is equal to 3 hundreds.

So we've got our answer of 334.

The sum is 334 centimetres, which is close to Alex's estimate of 300 centimetres.

And so Lucas says, "My answer could be correct, not completely sure, but it could be correct." So Alex says, "Edward's tusks have a total length of 334 centimetres." Lucas wants to work out how far Edward can reach.

Remember, we talked about his height and how long his trunk was.

Edward is 337 centimetres tall and has a trunk 185 centimetres long.

To work out Edward's reach, I would have to add together 337 centimetres and 185 centimetres.

So that's Edwards height, plus the length of his trunk that he can reach up with.

Oh, Alex is going to estimate again.

He says, "I can estimate the answer.

337 is close to 350 and 185 is close to 200.

350 add 200 is equal to 550.

So I estimate that some to be about 550 centimetres." Hm.

So Lucas is going to do the column addition.

7 ones add 5 ones is equal to 12 ones.

So we regroup 10 of those ones into 1 ten.

"3 tens add 8 tens is add the extra regrouped ten is equal to 12 tens.

I'll regroup 10 of those tens into 1 hundred," he says.

And then 3 hundreds add 1 hundred plus the regrouped hundred is equal to 5 hundreds.

So the sum is 522 centimetres, which was close to Alex's estimate of 550 centimetres.

So Lucas says, "My answer could well be correct." And Alex says, "Edward can reach up 522 centimetres.

That's amazing!" That is a long way up.

I wonder if you could imagine how far up that is.

What is 522 centimetres up? Perhaps outside in your playground or in your garden.

Alex and Lucas look at a problem together.

Ellie wants to reach up and get to the apple in this tree.

So there's Ellie, another elephant, and there's an apple in the tree.

Ellie is 289 centimetres tall and has a trunk 173 centimetres long.

The apple is 480 centimetres high.

Can Ellie reach it? So can Ellie get her apple treat? Alex says, "Let's estimate the answer." So Lucas says, "289 is close to 300, and 173 is close to 200.

300 at 200 is equal to 500.

So I think that Ellie can reach the apple." 'Cause the apple, remember, was 480 centimetres up.

So over to you.

Can Ellie reach the apple? You need to add together Ellie's height and the length of her trunk, 289 centimetres and 173 centimetres.

And can Ellie reach the apple, which is 480 centimetres high? Pause the video, have a go at the addition, and see if you can work out whether Ellie can reach the apple or not.

How did you get on? Do you think Ellie can reach the apple? Well, here's our column addition.

289 add 173, so that's Ellie's height and the length of her trunk.

9 ones add 3 ones is equal to 12 ones.

10 ones are regrouped as 1 ten.

8 tens add 7 tens, add one more ten is equal to 16 tens.

And 10 tens are regrouped as 1 hundred.

And then 2 hundreds add 1 hundred plus the regrouped hundred is equal to 4 hundreds.

So Ellie's total reach is 462 centimetres.

"Oh, no!" says Alex, "Ellie cannot reach the apple.

She can only reach 462 centimetres and the apple is 480 centimetres high." Alex and Lucas think about their estimate.

Alex says, "I thought Ellie would be able to reach the apple.

The estimate for Ellie's reach was 500 centimetres." Lucas says, "I think I know what happened.

When I estimated, I made both numbers larger.

I changed 289 into 300 and I changed 173 into 200.

So my estimate would've been greater than the actual answer." So he made 289 into 300 and 173 into 200.

Both of those numbers were larger, weren't they? Alex says, "Maybe we should have made one number larger and one number smaller to give a more accurate answer." So how could you improve Lucas's estimate? You've got three options there, A, B, and C.

And remember, Ellie is 289 centimetres tall and has a trunk 173 centimetres long.

Which calculation would give the most accurate estimate? Pause the video, have a look, and then we'll talk about it together.

So what did you think? Let's start with C.

Both numbers have been made smaller so this estimate will not be very accurate.

289 has been taken all the way down to 200, and 173 all the way down to 100.

So not very accurate this time.

What about B? This estimate will not be very accurate because 100 is not very close to 173.

So 289 is quite close to 300, but 100 is a lot less than 173.

So again, not a very accurate estimate.

So that leads us with A, what do we think? This estimate will be very accurate.

One number has been adjusted slightly higher, so 289 has been adjusted up to 300, and one number has been adjusted slightly lower, so 173 has been adjusted to 150.

300 add 150 equals 450, or 450 is very close to Ellie's reach of 462, and it also wouldn't have given us too much hope that she might be able to get that apple.

Poor Ellie, we'll have to find her a lower apple, won't we? Time for you to do some practise.

So an apple tree contains three apples.

The apples are 470 centimetres, 485 centimetres, and 495 centimetres high.

Which apple should each elephant reach for so that they all one? One of these elephants might be able to reach all three, but we want to make sure that everybody can reach one.

So Edmond is 326 centimetres tall and has a trunk 165 centimetres long.

Eva is 287 centimetres tall and has a trunk 186 centimetres long.

And Elsie is 298 centimetres tall and has a trunk 198 centimetres long.

So can you use this information to work out which apple each elephant should go for? And now we've got some thinking to do here.

Three elephants each take an apple from a tree.

The apples are 470 centimetres, 480 centimetres, and 510 centimetres high.

And again, we want each elephant to be able to get an apple.

So we know that Emmett is 307 centimetres tall, Erin is 275 centimetres tall, and Ezra is 292 centimetres tall.

And we've got three trunks there, but we are not sure whose trunk is whose.

Hm.

So we know the lengths of three trunks.

So you've got to try and work out which trunk belongs to which elephant so that each elephant will be able to reach an apple.

Lots of thinking to do there.

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

How did you get on? So we could work out the total reach of each of these elephants.

So Edmund has a reach of 491 centimetres, Ava has a reach of 473 centimetres, and Elsie has a reach of 496 centimetres.

So Edmond should go for the apple that's 485 centimetres high, Ava should go for the apple that's 470 centimetres high, and Elsie should get the apple that's 195 centimetres high.

So they each have an apple that they can reach.

And for two, these were the calculations that gave you the right trunk with each elephant.

So Emmett has a trunk 205 centimetres long, so that he can get the apple that's 510 centimetres high because his reach is 512.

Erin has a trunk 195 centimetres long, that means she can reach 470 centimetres, just enough to get that 470 centimetre apple.

And Ezra has a trunk 189 centimetres long, so he can reach 481 centimetres and get the 480 centimetre high apple.

I'm really glad that all the elephants got their apples.

Well done if you managed to think your way through those problems and solve the problems with the elephants.

So let's move on to the second part of our lesson.

We're going to be finding two addends to make a sum.

Alex has more facts about elephants to share.

He says, "Did you know that baby elephants hold their mother's tail so they don't get lost?" I'm pleased they do.

I wouldn't like to think of a baby elephant getting lost, would you? And there we have an elephant and baby elephant holding onto the mother's tail.

Lucas says, "I didn't know that, but I think I can make up a maths problem about it." Oh, well done Lucas.

Let's see what you come up with.

This is Elodie and her baby, Eli.

They have a total length of 545 centimetres.

So there we go.

Their length when Eli is holding onto Elodie's tail is 545 centimetres.

Lucas's challenges Alex to solve a problem.

Eli has let go of his mum's tail.

Oh no! Can you help reunite Eli and Elodie? So here are some elephants, but we don't know which is Elodie and we don't know which is Eli, but we do know how long each elephant is.

Alex says, "I know that Eli and Elodie have a total length of 545 centimetres." So can we find out which mother and baby elephant we're looking for? Alex says, "I'm going to look at the ones numbers.

I know that 9 and 6 have a sum of 15." And remember, there was a five in the length of Elodie and Eli together.

He says, "I'm going to add together 379 centimetres and 146 centimetres." So he's already thought about the ones digits, and that they're all give him the correct ones digit.

Let's hope the others work out too.

Let's try.

So 379 centimetres and 146.

That's those two elephants.

So he adds them together.

And he knows that Eli and Elodie have a total length of 545 centimetres.

So he's going to use column addition.

He's going to estimate first though.

379 is close to 400 and 146 is close to 500.

500 at 150 is equal to 550.

So 550 is a good estimate and it's close to that 545 we're looking for.

So let's see if we're right.

9 ones add 6 ones is equal to 15 ones.

10 ones are regrouped as 1 ten.

7 tens add 4 tens add the regrouped ten are equal to 12 tens, and 10 tens are regrouped as 1 hundred.

3 hundreds add 1 hundred add the regrouped hundred is equal to 5 hundreds.

Oh! So our answer is 525.

The sum of 379 and 146 is 525, which is 20 less than the sum you are looking for.

We were looking for 545 centimetres, weren't we? Those weren't the right elephants.

"Oh!" says Alex.

"These two elephants are not Eli and Elodie." Alex tries again to solve the problem.

And Lucas reminds him the sum of 379 and 146 is 525, which is 20 less than the sum you're looking for.

We like the nine and the six, they were good, but our tens were not correct.

Alex says, "I'm going to add together 396 and 169 to see if they add to equal 545." So which elephants is he going to look at this time? That's right, it's those two on the end there.

So Alex adds 'em together.

He says he knows that Eli and Elodie have a total length of 545 centimetres.

So there's his column addition.

Do you think he's going to estimate first? He is.

396 is close to 400 and 169 is close to 500.

So 400 at 150 is equal to 550.

So 550 is a good estimate.

And again, it's close to that 545 we're looking for.

6 ones add 9 ones is equal to 15 ones, and 10 ones are regrouped as 1 ten.

9 tens add 6 tens add the regrouped ten is equal to 16 tens.

And 10 tens are regrouped as 1 hundred.

3 hundreds add 1 hundred add the regrouped hundred is equal to 5 hundreds.

565.

Oh the sum of 396 and 169 is 565, which is 20 more than the sum you're looking for.

So these two elephants are not Eli and Elodie either.

Oh my goodness.

Which of the two elephants are Elodie and baby Eli? It's your turn to have a go.

Can you find the two elephants that have got lost 'cause Eli let go of his mother's tail? Remember that Eli and Elodie have a total length of 545 centimetres.

So pause the video, have a go, and see if you can find Elodie and Eli.

Did you find them? This is the really important question.

Is this Elodie and Eli? Let's have a look.

396 add 149, let's see if that has a sum of 545 centimetres.

6 ones add 9 ones is equal to 15 ones.

10 ones are regrouped into 1 ten.

9 tens add 4 tens add the regrouped tens is 14 tens.

And 10 tens are regrouped into 1 hundred.

I like the look of this.

3 hundreds add 1 hundred add another hundred is equal to 5 hundreds.

Hits 545.

These are Eli and Elodie.

I'm so pleased we found them.

Well done for your calculating.

Time to do some practise.

We've got some more mother and baby elephants who've become separated.

So can you reunite the mother elephants with their babies? Erin and baby Enzo have a total length of 574 centimetres.

Amelia and baby Evan have a total length of 544 centimetres.

Ava and baby Ezra have a total length of 524 centimetres.

And Ella and baby Emmett have a total length of 554 centimetres.

Do you notice something about the ones digits in all those total lengths? Hm.

So have a look at the lengths of the elephants and see if you can find the mothers and their babies.

Pause the video, have a go, and we'll get together and see if we can find the mothers and babies.

So how did you get on? Here are our answers.

Erin and baby Enzo had a total length of 574 centimetres, so their lengths were 439 centimetres and 135 centimetres.

And that 9 ones at 5 ones is equal to 14 ones.

And then we regroup 10 of the ones to make 1 ten.

Amelia and baby Evan had the total length of 544 centimetres, so Amelia was 356 centimetres long and Evan was 188 centimetres long.

And if you did an estimate, 356 is close to 350 and 188 is close to 200.

So that gave us an estimate of 550, which was quite close to the 544.

And it was a good estimate for those two numbers.

And Ava and baby Ezra were 388 centimetres and 136 centimetres long.

And Ella and Baby Emmett had a total length of 554 centimetres, and they were 176 centimetres and 378 centimetres long.

I hope you enjoyed reuniting the mother and baby elephants so that they could grab their tails and go off walking again together.

Well done.

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

Lots and lots of facts and figures about elephants and elephants getting apples outta trees and mother and baby elephants together and lots of estimating and adding of three-digit numbers.

So well done.

You've worked really hard.

And I hope you've enjoyed it as much as I have.

So what have we learned about today? We've been using our knowledge of column addition to solve problems in a range of contexts.

We've learned that estimation gives you a value close to the correct answer, and it can help you to check that you've got your answer correct.

We start with the digits with the smallest place value so that we can represent the regrouping.

So in this lesson we always started with the ones digits.

And we need to look carefully at the ones number of a sum to find missing addends.

If we knew the ones number of the sum, we could start to reason about what our addends might be.

Again, thank you very much for your hard work and for working hard for our elephants today.

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

Bye-Bye!.