Lesson video

Hello, my name is Mr. Tasuman, and I'm really excited to be working If you're ready, let's get started.

The outcome of today's lesson is for you to be able to say that you can add three-digit numbers by redistributing, and we're gonna use redistribution as a way of transforming our sums to make addition easier.

Here are some really important key words that you're gonna need to be able to understand to be able to access the learning slides.

I'm going to say them, and then you are going to repeat them back to me.

I'll say my turn, say the word, and then I'll say your turn, and you can say them.

My turn, redistribute.

Your turn.

My turn, inverse.

Your turn.

My turn, efficient.

Your turn.

Okay, let's have a look at what each of these words means, and you can try to understand them and use them as you're learning.

Redistribution is a way of transforming a sum to make it easier to calculate mentally.

The inverse is the opposite or reverse operation.

For example, subtraction is the inverse operation of addition.

Being efficient means finding a way to solve a problem quickly whilst also maintaining accuracy.

Okay, here's an outline then of what we're going to do in the lesson today.

We're adding two- and three-digit numbers by redistributing, and the first part of the lesson's going to be about efficient mental addition with redistribution.

Then, we're gonna move on to redistributing with three-digit addends.

Are you ready? Let's get started.

Here's two friends that we'll meet in this lesson, Sophia and Andeep.

Now, these two are going to help us with some discussions, and some answers, and some thoughts that they might have in response to some of the prompts that we'll see on the slides.

They start by playing with some bucket scales.

Andeep puts 29 blue cubes into one side of a bucket balance.

Sophia adds 15 red cubes.

Andeep puts 30 blue cubes into the other side of the bucket balance, and Sophia adds 14 red cubes.

What do you notice? Well, Andeep helps us out here, and he says that he notices the bucket scale is balanced, so the number of cubes on each side must be equal, and Sophia also helps out because she says that both sides have an array of cubes with one missing, but the missing cube is a different colour in each bucket.

We can write this set of bucket scales and the cubes within them as an equation.

On one side, we have 29 plus 15.

On the other side, we have 30 plus 14.

The bucket scale is balanced, so we know that the totals are of equal value, so we put an equals sign in the middle.

Which of these two expressions would be easiest to solve? Andeep says he would prefer to solve 29 plus 15 because the first addend is lower.

Sophia says, "I would prefer to solve 30 plus 14 because it is easier to count on from multiples of 10." Who do you agree with and why? Have a think about it.

We can use redistribution to transform addition calculations, making them easier to solve mentally.

Base 10 can be used to represent redistribution.

We've got 29 plus 15 equals, and we've modelled that using base 10.

Sophia says, "This is the same as the bucket scales." She recognises that expression.

She says, "I'm going to transform this addition using redistribution.

First, I'll check which addend is closest to a boundary.

29 is 1 away from 30.

Then, I will subtract 1 from the other addend and redistribute it." There it goes.

She's taken 1 away from 15 to leave 14.

She sends that 1 over to the first addend to turn it into 30.

Now, she's got an easier addition.

She says, "I will combine the two addends to find the sum.

The sum is 44." Well done, Sophia.

What do you notice about the total number of cubes? Sophia says, "I transformed the addends to create a calculation I was more comfortable with.

The sum is the same because the total number of cubes is the same.

I didn't lose any by redistributing." Jottings can be useful to help with redistribution.

We've got the same sum on the right there with base-10 model underneath, and we're gonna go through the same process.

We take away 1 from the second addend, and you can see it in the jottings there.

We move it over to the first addend by adding on 1 there, and we replace that addend with 30.

We combine them, and that gives us 44.

Andeep says, "These jottings help me to calculate mentally.

I might not need them all of the time." Okay, now it's your turn.

We're gonna check your understanding.

I'd like you to use redistribution to calculate this addition, 39 plus 27, and Andeep gives us a helpful tip there.

He says, "Remember to start by finding the addend closest to a boundary." Pause the video here, have a go, and I'll be back in a little while to give you an answer so you can see how you got on.

Good luck.

Welcome back, let's see how you got on.

Now, you might have spotted that 39 was actually the addend that was closest to a boundary, so we needed to start by taking 1 away from 27 in order to redistribute it over to the first addend, which would turn 39 into 40.

40 plus 26 is an easier calculation to do mentally.

You should have got 66.

Did you get it? I hope so.

Okay, we're gonna move on.

Ready? Let's go.

Andeep wants to have a go at using redistribution.

He uses digit cards to create the following sum, 52 plus 26.

He says, "I'm gonna transform the calculation using redistribution so that it's easier to find the sum." He starts with 52, add 26 as a jotting, and this time, he says, "The closest addend is 52, which is 2 away from 50." So he subtracts 2 from 52.

He redistributes that 2 onto the second addend, transforming it from 26 to 28.

So now he's left with the sum 50 plus 28, which is 78.

Okay, your turn to have another go.

Use redistribution to calculate this addition, 32 plus 45.

And Sophia reminds us, "Remember to start by finding the addend closest to a boundary." Pause the video here so you can have a go, and I'll be back in a moment to give you the answer.

Good luck.

Welcome back, let's see how you got on.

You might have spotted that the addend that was closest to a boundary was 32, so we needed to subtract 2 from that addend, making it 30, and we needed to redistribute that 2 onto 45, creating 30 plus 47, again, a much easier sum to complete.

You should have got 77.

Well done if you did.

Ready to move on? Let's go.

We're gonna now have a go at doing some practise tasks.

For Number 1A and B, you'll see there are some jottings there that have been partly completed.

They have some missing numbers.

You can see where there's underlines without a number above them.

Your task in 1A and B will be to fill in those missing numbers.

And for Number 2, you're going to use redistribution to calculate the sums you can see that have been drawn using digit cards.

Pause the video here, have a go at the practise tasks, and then I'll be back in a little while to give you some feedback.

Enjoy.

Okay, it's time to give you some feedback.

I'm gonna reveal the answers for 1A and B.

You can see that, in 1A, you should have got 93, and in 1B you should have got 96.

Pause the video here so you can mark them carefully if you need to.

All right, let's move on to Number 2.

The answers for Number 2A was 72, and B was 68.

Again, pause the video here if you'd like to mark your answers carefully.

Okay, well done.

We've completed the first part of the lesson, and now we're going to move on to looking at redistributing but with three-digit addends this time.

Let's get ready, and let's go for it.

Andeep has another go at redistribution.

He creates three-digit addends this time, 320 plus 190.

What is different about the redistribution this time? Hmm.

Well, Sophia says, "The addends are multiples of 10.

Maybe it's best to look for the addend nearest to a hundred boundary." Andeep says, "Good thinking.

That's 190, which is the second addend.

I wonder if it will still work?" Andeep uses jottings just like before.

"Okay, I'm still gonna transform the calculation using redistribution so that it is easier to find the sum," he says confidently.

Let's see how he gets on.

He sets it out using jottings to help, and he realises that 190 is the addend closest to a hundred boundary.

It's 10 away, so he subtracts 10 from 320, and he redistributes the 10 onto 190, making 200.

Now, his sum is 310 plus 200, much easier to calculate mentally, so he adds together the new redistributed addends to get 510.

Top work, Andeep, well done.

And he concludes that it doesn't matter which addend you use for redistribution, and Sophia says, "Also, we redistributed 10s instead of 1s this time, and that works just as well." Great, so it's your turn now.

I'd like you to add together these three-digit numbers using redistribution, 440 plus 290.

Andeep gives us a little clue here.

He says, "Don't forget, look for the addend closest to a hundred boundary." Pause the video here, have a go, and I'll be back in a little while to give you the answer so you can see how you got on.

Welcome back, let's see how you did.

You've got 440 added to 290, and you might have spotted that the addend that was closest to a hundred boundary was 290, so we needed to start by subtracting 10 from 440 to make 430, redistributing it onto 290 to make 300.

Now, we've transformed our sum, and we should get 730.

Well done if you did.

Okay, let's move on.

Sophia changes one of the digit cards in Andeep's sum.

You can see it there.

Which addend should they redistribute? Have a look and have a think.

Well, Sophia says, "Hmm, the addends are no longer both multiples of 10, but I still think we should look for the addend nearest to a hundred boundary." And Andeep says, "Yes, I agree.

That's 196 this time.

We will have to redistribute some 1s instead of 10s." Andeep uses jottings just like before.

He wants to transform the calculation again using redistribution.

So he starts out with writing out the sum.

He realises that 196 is the addend closest to a hundred boundary.

It's four away, so he decides he's going to redistribute using four.

He subtracts 4 from 320, redistributes it over to the other addend to make 200.

He's got a much easier sum now.

He's transformed that addition to 316 plus 200.

He adds together the new addends, and he gets 516.

Well done, Andeep, brilliant.

He says, "You can still redistribute using multiple 1s," and Sophia says, "Yes, and it it works with three-digit numbers.

We can still transform the calculation." Okay, your turn again.

I'd like you to add together these three-digit numbers using redistribution, 440 plus 296.

And Andeep tells us, "Don't forget, look for the addend closest to a hundred boundary." Pause the video here, have a go, and I'll give you the answer in a little while.

Welcome back, let's see how you got on.

Did you write the addends out like this? You might well have done and seen that 296 was closest to a hundred boundary.

It was 4 away, so you might have then taken 4 from the first addend and redistributed it to the second one, giving you a new calculation of 436 plus 300, much easier, and the final answer was 736.

Did you get it? Well done if you did.

Let's move on.

Andeep has one last go at creating a new sum, and he creates 280 plus 450.

Which addend should they redistribute? Hmm.

Sophia says, "Well, they're both multiples of 10, which means that we are going to be redistributing 10s." Andeep says, "Yes, but this time, it will need to be more than one 10 because both addends are more than 10 away from a hundred boundary." Look at the numbers.

You can see that neither of those addends are within 10 of a hundred boundary.

So Sophia says, "280 is the closest.

It's 20 away from 300." Andeep replies, "Okay, let's try redistributing with 20 then, see if it works." Great attitude, Andeep, okay, let's go.

He uses jottings just like before, and he sets out to transform the calculation using redistribution.

He knows 280 is the closest addend and that it's 20 away, so he decides to redistribute that one.

He takes 20 from 450 and redistributes it over to 280, giving him a new calculation of 300 plus 430.

He adds those together and gets 730, nice and simple.

Well done, Andeep.

Sophia says, "You can still redistribute using multiples of 10." Okay, it's your turn to have a go.

I'd like you to add together these three-digit numbers using redistribution, 440 plus 280.

Andeep says, "Don't forget, look for the addend closest to a hundred boundary." Pause the video here, have a go, and then we can see how you got on in a moment.

Welcome back, let's see how you did.

You may have spotted that 280 was the the addend that was closest to a hundred, so we needed to redistribute 20 from 440 and move it over to 280, giving us a new calculation of 420 plus 300, which was 720.

Did you get that? I hope so.

Okay, let's move on.

Andeep and Sophia are making fruit drinks.

They choose two fruit juice flavours and mix them together.

Andeep says, "I'll pour in 305 millilitres of orange juice." There it goes.

Sophia says, "I'll add 180 millilitres of pineapple juice." In it goes, it's mixed together.

Andeep wants to pour the content into a drinks bottle but doesn't know if the capacity is great enough.

He says, "This looks yummy, but my drinks bottle is only 500 millilitres.

Will it have a big enough capacity?" Sophia says, "Let's work it out.

If we add together the quantity of each juice, then we will know." Andeep and Sophia write this problem as an equation, 305 millilitres plus 180 millilitres.

Andeep says, "Which addend is nearest a hundred boundary?" Sophia replies, "I think 305 because, even though it's greater than 300, it's only 5 away." Great reasoning.

So Andeep says, "Let's take 5 away from 305 millilitres, leaving 300 millilitres," and then Sophia says, "Then, redistribute the 5 to make 185 millilitres." They've transformed the calculation, much easier.

They add together the redistributed addends to give them 485 millilitres And Andeep realises that will fit in the bottle because 485 millilitres is less than the 500 millilitres of his bottle's capacity.

Great, pour away, Andeep.

Okay, it's your turn, a similar kind of problem here, Sophia and Andeep make another fruit drink.

We start with Andeep pouring in 204 millilitres of apple juice, and Sophia pours in 282 millilitres of mango juice.

Will Sophia be able to pour all of it into her bottle with a capacity of 500 millilitres? I'm gonna ask you to pause the video here and have a go.

I'll be back in a little while to see if you've got it right.

Welcome back, let's see what you got.

So we start by writing it out as an equation, 204 millilitres plus 282 millilitres.

Then, we recognise that 204 is close to a hundred boundary, so we remove 4 from that and redistribute it over to the other addend, giving us 200 millilitres plus 286 millilitres.

In total, that's 486 millilitres.

Great news, yes, she can pour all the juice into a bottle because 486 millilitres is less than 500 millilitres.

All right, it's time for you to have some practise.

1A and B are jottings that have been written out with missing numbers just like you did in Task A.

Your job will be to try to write in those missing numbers.

For 2A, B, C, and D, you're going to add together those pairs of addends.

They're three-digit this time, and for Number 3, we've got a worded problem for you to have a go at.

I'll read it to you now.

"Sophia is off to visit cousins who live a long way away.

She travels with her family by car.

They travel 156 kilometres before stopping to get some lunch.

Then, they drive a further 203 kilometres without stopping.

How many kilometres did they travel on the journey?" Okay, pause the video here and have a go at those practise questions.

I'll be back in a little while to give you some feedback.

Good luck.

Okay, are you ready to do some marking and to see how you got on? Let's go for it.

Number 1A and B are displayed there.

You've got lots of the missing numbers there.

The answers were 550 and 557.

Pause the video here and do some marking.

Okay, let's do Number 2.

2A was 720.

2B was 727.

2C was 810.

And 2D was 372.

Pause the video here so you can mark accurately.

Finally, Number 3, you had to add together 156 kilometres and 203 kilometres.

You would've redistributed by taking 3 from 203 and adding it to 156, transforming the calculation into 159 plus 200 kilometres.

The final answer was 359 kilometres.

Did you get it? I hope so.

Thanks very much for participating in today's lesson.

Here's a summary of the things that we have learned or practised.

Redistribution can be used to transform a calculation to make it a more efficient mental addition.

It can be achieved by subtracting 1s or 10s from one addend and redistributing them to the other addend to create a multiple of 10 or 100.

That's easier to count on from.

It works for two-digit and three-digit numbers where one of the addends is close to a 10 or 100 boundary.

Thanks again for enjoying this lesson with me.

My name's Mr. Tasuman, and I hope to see you again soon for another maths lesson.

Bye.