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 2-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 are going to be able to bring to this lesson, so if you're ready, let's make a start.

In this lesson, we're going to be thinking about identifying addition strategies to help us to calculate efficiently.

So we're going to look at lots of different additions, and we're going to see if we can pick the most efficient strategies to use, so that we can calculate the answers to our additions.

Let's have a look at what's in our lesson.

We've got two keywords.

We've got calculate and efficiently, and we're going to be learning about calculating efficiently.

Let's just practise those words 'cause we're going to be using them a lot in our lesson today.

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

Are you ready? My turn, calculate, your turn.

My turn, efficiently, your turn.

Excellent, I think we did that very efficiently.

We got to where we wanted to get to, and we didn't waste a lot of time in getting there, so well done.

Let's see what's in our lesson.

There are two parts to our lesson today.

In the first part, we're going to be using known facts to add efficiently, and in the second part, we're going to be using bridging ten to add efficiently.

So let's make a start on part one, and we've got Andeep and Izzy helping us in our lesson today.

The children go shopping.

They cannot write anything down, so they need to be able to calculate the total cost of sets of items efficiently.

There's that key word again, efficiently.

So that means getting to an answer relatively quickly and easily, but making sure that our answer is accurate as well.

So let's have a look at what they're shopping.

Oh, lots of different prices there, aren't there? What would you buy if you could? Izzy wants to find the cost of a football and the car.

So we can see the football and the car there on the end.

So what prices are those? Hmm, well, so they've got 5 pounds and 2 pounds and Izzy's remembered something.

She says, "When I add 2 to an odd number, I reach the next odd number." I wonder if you've learned about that before.

So if she adds 2 onto 5, 'cause 5 is an odd number, she'll get to the next odd number, and the next odd number after 5 is 7, well done, yes.

So she says, "I know that 5 plus 2 is equal to 7." "So the football and the car, it will cost me 7 pounds," she says, Andeep wonders how much a rocket and an astronaut will cost.

How can he calculate this efficiently, again, what strategy can he use? This time, the astronaut costs 20 pounds and the rocket costs 50 pounds.

Have you spotted something? Andeep says, "I can use my known facts to help me." Ooh, I wonder what fact he's going to use, can you think? Ah, Andeep spotted something, he's using the same fact that Izzy used, 2 plus 5 is equal to 7, and he's spotted that the astronaut at 20 pounds is 2 tens, and the rocket at 50 pounds is 5 tens.

So if he knows that 2 plus 5 is equal to 7, he says, "I know that 2 tens plus 5 tens is equal to 7 tens, and that's the same as 70.

So it will cost me 70 pounds." Wow, Andeep, I wonder if you've been able to save up enough money.

Maybe that's something to dream for at Christmas or a birthday or something.

What did you notice about the calculations that Izzy and Andeep did? So there is Andeep's astronaut and rocket, and Izzy worked out the total cost of the football and the car.

Is there something you spot? Ah, yes, Andeep says, "We both used the same known fact to help us to calculate efficiently." Izzy says, "I was adding ones, but you used the same fact to calculate with tens." That's right, Izzy knew about 5 plus 2, and Andeep was able to use that knowledge of 5 plus 2 to think about 5 tens and 2 tens.

Time to check your understanding.

Which known fact would each child use to calculate the cost of their toys? So Andeep is buying some pens and pencils this time, and Izzy is buying a robot and a dragon, or a dinosaur I think there, but which known fact would each child use? Have a look at those facts, A, B, and C, and decide which one would help Andeep and Izzy, pause the video, have a go, and when you're ready for some feedback, press Play.

What did you think? Ah, it was 3 plus 4, wasn't it? Andeep's pencils and pens cost 3 pounds and 4 pounds, so he can use 3 plus 4 equals 7 to help him to calculate the total cost of his items. But what about Izzy? She didn't have 3 plus 4, but she did have 3 tens and 4 tens, 30 and 40.

So she could do what Andeep did, and think about 3 plus 4 being 3 tens plus 4 tens is equal to 7 tens.

That's what we've got in B, isn't it? But I think the fact that we know is 3 plus 4 is equal to 7, and C, well, we've got a 3 and a 4 in there, but we've got 3 ones and 4 tens.

So it might be something that we can calculate mentally by using what we know, but it's not the fact that it's gonna help us this time.

So I think A was the fact that would help both and Andeep and Izzy.

Or it's a near double, so we could use a known fact that 3 plus 3 is equal to 6, so 3 plus 4 is one more and equal to 7, and then we can apply that to our tens.

If 3 plus 4 equals 7, then 3 tens plus 4 tens is equal to 7 tens or 70.

So Izzy would need 70 pounds to buy her two items. Izzy now wants to find out what these items will cost.

How can she calculate this efficiently? So she's got some pens and she's got a rocket, but this time, she's got something that costs 4 pounds and something that costs 50 pounds.

She says, "I have 4 ones and 5 tens.

I can imagine a Gattegno chart." Have you come across a Gattegno chart that helps us to organise our ones and our tens, and maybe our hundreds as well? So here's part of a Gattegno chart for Izzy to use.

So she can see 5 tens, which is 50, and 4 ones, which is 4.

"5 tens is the same as 50 and 4 ones is the same as 4," she says.

"I know that 50 plus 4 is equal to 54, 5 tens and 4 ones is equal to 54." Well done, Izzy, great strategy to calculate efficiently there.

So Izzy bought her pens and her rocket, but now she wants to buy some coloured pencils as well.

What would be the most efficient way to calculate the total cost of the items now? So she's got her pens for 4 pounds, her pencils for 3 pounds, and her rocket for 50 pounds.

She says, "There are 4 ones and 3 ones.

So I can use my known facts for this bit." So she's going to add together the 4 ones plus the 3 ones, plus the 50, which is 5 tens.

She's going to do the ones first.

"4 plus 3 is equal to 7." She may have known that as a fact or she may have used a near double.

So she says, 4 pounds plus 3 pounds plus 50 pounds is going to be equal to 57 pounds." She's added the cost of her ones, which was 4 plus 3, so 7 pounds, and she can now add that onto the 50, the 50 pounds, 57 pounds.

Time to check your understanding.

Can you find the most efficient strategy to calculate the cost of each set of items? What will you think about? Ans what will you do first? You've got Set A and Set B.

Pause the video, have a go, and when you're ready for the answer and some feedback, press Play.

How did you get on? What efficient strategies did you use? So for Set A, we had a 30-pound dinosaur or dragon, and 4 pounds for the pens.

So we've got a tens value and a ones value.

So we can use Izzy's strategy and think of the Gattegno chart.

So we've got 30 and 4, and we know that 30 plus 4 is equal to 34.

So Set A has a total cost of 34 pounds.

What about Set B? Ah, so for Set B, there were 4 ones and 2 ones, in our 4 pounds and 2 pounds.

So we could use our known facts to combine those single-digit numbers of pounds first.

4 plus 2 is equal to 6.

So now we've got 30 pounds and 6 pounds, and we know that 30 plus 6 is equal to 36.

So the total cost of Set B, was 36 pounds.

I wonder if those were the same strategies that you used.

If not, have a little moment to look at these strategies and talk about them with somebody near you.

Andeep wonders how much some pencils and a unicorn would cost.

How can he calculate the cost now? Oh, so this time we've got 3 pounds and we've got 56 pounds.

Hmm, I wonder how he's going to think about this.

He says, "I can imagine a part-part-whole model and I can partition the 56 into 50 and 6 or 6 and 50." So can you see we haven't got the circles round it, but that looks a bit like a part-part-Whole model, doesn't it? So he's partitioned his 56 pounds into 6 pounds and 50 pounds.

Can you see that It looks a bit more like some of the calculations we've done already, where we had two prices that were a single number of pounds, and then a number of tens? Ah, so now he's going to add the 3 pounds and the 6 pounds from the 56 pounds.

He says, "There are 3 ones and 6 ones, so I can use known facts now.

3 plus 6 is equal to 9, so 3 pounds plus 56 pounds must be equal to 59 pounds." He's dealt with his ones first, and then he's added in his tens.

3 plus 6 is equal to 9, plus the 50 is 59.

So the total cost is 59 pounds.

So we've got some sets of items here.

Calculate efficiently to find the total cost of each set of items and explain what you notice.

So we've got a penguin and some pencils, we've got some pens, pencils, and an astronaut, and we've got a basketball, and an astronaut.

So pause the video to calculate the cost, see what you notice, and when you're ready for the answer and some feedback, press Play.

How did you get on, and what did you notice? So for the penguin and the pencils, ah, that was a bit like the calculation that Andeep did, wasn't it? So we can think about partitioning our penguin cost 24 pounds into 4 pounds and 20 pounds.

Now we can add the 4 pounds and the 3 pounds, which is equal to 7 pounds, and add them onto the 20, so we've got 27 pounds.

What about the next set, the pens, the pencils, and the astronaut? Well, here we've got our ones separately, haven't we? So we can add our ones together and then add on our tens.

So 4 pounds plus 3 pounds is equal to 7 pounds, plus our 20 pounds is 27 pounds.

Hmm, what about the last set, are you spotting something here? Well here, we've got that idea of the Gattegno chart that Izzy used.

We've got one value that's a set of ones and one value that's tens.

So 7 pounds plus 20 pounds, and we can think of our Gattegno chart, 20 and 7, 2 tens and 7 ones is equal to 27 pounds again.

That's right, each set of items cost 27 pounds because in each set there were 2 tens and 7 ones.

It's just that we'd partitioned them and arrange them differently.

In the first one, the 4 of our 7, was linked to our 20 pounds.

In the middle set, the 4 pounds and the 3 pounds were separate.

And in the final pair of items, the basketball and the robot, the 7 pounds was all in one place, the cost of the basketball, but all of them had a total cost of 27 pounds.

Izzy buys a dinosaur and a unicorn.

Will they cost more or less than Andeep's items? So the dinosaur is 30 pounds and the unicorn is 52 pounds.

And for Andeep's set, he's got a unicorn, which is 52 pounds, and the pencils which are 3 pounds.

Can you see something there? Izzy says, "I know that they will cost more than Andeep's items because I'm adding 3 tens to 52 rather than 3 ones." Oh, well spotted, Izzy, the dinosaur costs 30 pounds, so that's lots 3 of 10 pounds, isn't it? But the pencils cost 3 pounds, 3 lots of 1 pound, so it's going to be more expensive to buy Izzy's items, they will cost more than Andeep's items, I hope you worked that out.

Izzy says, "She can imagine a part-part-whole model and partition 52 into 50 and 2," and then she can add, this time, she's going to add her tens first "50 plus 30 is equal to 80 and plus the 2 is 82." So the dinosaur and the unicorn will cost 82 pounds altogether.

Each child buys another item.

Let's estimate the total cost of each set and then find the most efficient way to calculate their total cost.

So estimating means giving a rough idea, that is fairly close to the real answer, but we haven't calculated it.

So Andeep has added in an eraser to rub out any mistakes he might make, I'm sure you don't make mistakes, Andeep, and anyway, mistakes are something to be proud of because we learned from them.

But it costs 1 pound.

Izzy has bought an aeroplane and that costs 10 pounds.

Ooh, what do you notice? Andeep is adding ones to 50, so the total will still be in the fifties or at most, in the sixties.

So he's got 52 plus 3 plus 1, so he's added small numbers, so I think he's answer's still going to be in the fifties, and we can partition our 52 into 50 and 2.

So we can do 50 pounds plus 2 pounds plus 3 pounds plus 1 pound, and 2 plus 3 plus 1 is equal to 6, so 56 pounds in total.

What did Izzy add on? Ah, Izzy's adding tens to 50.

So she started with her 52, the unicorn is the same, but this time, she's added on 30 pounds and 10 pounds, so her total will be somewhere around 90 pounds because we know that 5 tens and 4 tens is equal to 9 tens or 90.

So this time, we've got that 2 pounds from the unicorn, that's our only value of ones.

So 50 plus 30 plus 10, so that's 50 plus 40, which is 90, and then the other two.

So the total cost of Izzy's items is 92 pounds, a lot more than the total cost of Andeep's items. And it's time for you to do some practise.

There are items in a shop, you're going to use an efficient strategy to calculate the total cost of some sets of items. So those are the items and these are the sets that you're going to be calculating.

So in A, you've got a car and a T-shirt, in B, and aeroplane and some sunglasses, and then so on, C, D, E, and F.

So what strategies will you use and which known facts will help you to calculate the total cost of these items? 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 for A, the car costs 4 pounds and the T-shirt costs 5 pounds.

4 plus 5 is a known fact, it's near double as well, so you might know that 4 plus 5 is 9 or you might have worked it out because 4 plus 4 is 8 and another 1 is 9.

However you worked it out, 4 pounds plus 5 pounds is equal to 9 pounds.

In B, the aeroplane this time costs 20 pounds and the sunglasses cost 40 pounds.

So we've got multiples of 10 that we're adding this time.

Again, we can use known facts.

If we know that 2 plus 4 is equal to 6, then 2 tens plus 4 tens is equal to 6 tens or 60 pounds.

What about C? Well, our little figure there was 53 pounds, and our teddy bear was 30 pounds.

This time, we're going to think about partitioning our 53 into 50 and 3.

So 53 plus 30 is the same as 3 plus 50 plus 30.

We can add our tens, which is 80, 5 plus 3 is 8, so 5 tens plus 3 tens is 8 tens or 80, add on the extra 3 and we get 83 pounds.

So the total cost of those items is 83 pounds.

What about D? The teddy bears back with some pencils, 30 pounds plus 3 pounds, and we can think of the Gattegno chart here and use our knowledge of place value.

3 tens plus 3 is equal to 33.

This time, for E, we've got the teddy, pencils, and a T-shirt, so we've got 30 plus 3 plus 5.

So this time, we can think about our ones first.

There are 3 ones and 5 ones and we can use known facts.

3 plus 5 is equal to 8, so 30 plus 3 plus 5 will be equal to 38 pounds, the total cost.

And finally for F, we've got our princess and our car, 42 pounds plus 4 pounds.

Again, here, we can partition our 42 into 40 and 2, and then use known facts.

So 42 plus 4 is like 40 and 2 plus the 4 pounds.

So we can add our pounds together, 4 pounds plus 2 pounds is equal to 6 pounds, add on the 40 is equal to 46 pounds, so the total cost is 46 pounds.

I hope you were able to find your efficient strategies to calculate those total costs.

So let's look into the second part of our lesson.

We're going to be using bridging 10 to add efficiently.

Now the children go to the clothes shop, and Izzy wants to calculate the cost of some gloves and a T-shirt.

So can you see there, a pair of gloves is 7 pounds and a T-shirt is 43 pounds? There we are.

She says, "I can use known facts." So she's going to partition the 43 into 40 and 3, "3 and 7 sum to 10, so the total cost will be equal to the next multiple of 10.".

Ah, so 7 pounds plus 3 pounds is another 10 pounds.

So this time, we're adding 10 pounds onto 40 pounds.

So the total cost is 50 pounds.

So we've bridged two, the next 10, haven't we? Andeep wants to buy a T-shirt and some socks.

Can he calculate using known facts as well? So he's got to calculate 43 pounds plus 8 pounds.

He says, "When I look at the one digits, I know they will cross the tens boundaries." Yes, 8 plus 3 is going to be greater than 10, isn't it? So we know we've got an answer in the fifties.

He says, "I can bridge 10." So we can partition our 8 pounds into 7 pounds and 1 pounds.

Why have we done that? Ah, that's right, because we know that 43 plus 7 will get us to the next 10.

So we've got 43 pounds plus 7 pounds, which takes us to the next 10, plus another pound, 43 plus 7 is equal to 50 pounds, and another 1 pound, gives us a total of 51 pounds.

Izzy says, "I found a different way." She says, "The socks were 1 pound more than the gloves, so the total would be 1 pound more as well." Izzy's gloves and a T-shirt cost 50 pounds, but the socks are 1 pound more, so they'll cost 51 pounds in total.

Over to you to check your understanding, can you match each set of items to the most efficient calculation strategy? So we've got gloves and shoes, and we've got sunglasses and shoes.

So which one can we solve using known facts and which one will bridge 10? Pause the video, have a think, and when you're ready for the answer and some feedback, press Play.

What did you think? Yes, that's right, if we look at the ones digits, 7 pounds plus 5 pounds, that's going to bridge 10, isn't it? So the ones digits when added, crossed the tens boundary, so we can bridge 10.

What about the sunglasses and the shoes? Well, we've got 45 pounds and the 3 pounds, so we can use known facts there, can't we? The ones digits do not cross the tens boundary so we can use a known fact, and we know the fact of 5 plus 3.

The children wonder about the most efficient way to calculate the total cost of the T-shirt and the sunglasses.

So this is 9 pounds and 43 pounds.

They must decide whether to use known facts or the bridge 10 strategy.

What would you use? You might want to have a think before they share their ideas with us.

Izzy says, "The ones sum to greater than 10, so I'm going to use bridge 10." We've got 9 ones in the price of the sunglasses for 9 pounds, and 43, we've got 3 ones there, 9 plus 3 is greater than 10.

So we're going to think about how we can partition our 9, so that we can bridge through 10.

So we can partition the 9 into 7 and 2.

So 43 plus 7 is equal to 50, and then we're going to add another 2 pounds, so 50 plus 2 is equal to 52 pounds.

So they've bridged 10 by taking the cost of the sunglasses and partitioning it.

so they can make the next 10, and then add on the rest to bridge through.

Andeep says, "I didn't need to calculate." Oh, go on, Andeep, tell us.

Oh, he says, "The sunglasses cost 1 pound more than the socks, so the total will be 1 pound more again." Do you remember when Izzy bought the T-shirt and the gloves that was 50 pounds, and then the socks were 1 pound more and now the sunglasses are 1 pound more again? Well done, Andeep, I think because that check for understanding was in the way, I had forgotten about that bit, but thank you for reminding me.

Izzy thinks both of these sets of items will have the same total cost, is she right? Have a look at them, you might want to pause and have a think before we share our thinking.

So the sunglasses with the T-shirt costs 9 pounds, and the T-shirt costs 43 pounds, but the other sunglasses cost 3 pounds, and the boots cost 49 pounds.

Hmm, do you spot something there? Let's think about the total number of tens and ones in each equation.

So we've got 9 plus 43, which is 9 pounds plus 40 pounds, plus another 3 pounds, so we've partitioned the 43 into 40 and 3.

What about the other equation? We've got 3 plus 49, so let's partition the 49.

So we've got 3 plus 40 plus 9.

Do you spot something there? Izzy says, "Both sets add 40 to 3 plus 9, so the total will be the same." Andeep's gonna check that Izzy's right? "43 plus 9," he says.

So we can partition our 9 pounds because we're going to bridge through 10.

So 43 plus 7 plus 2.

43 plus 7 is equal to 50 pounds, plus the other 2 pounds, and we get a total of 52 pounds.

What about 49 plus 3? Well again, we can bridge through 10, can't we? So we're going to partition the 3 pounds, this, time into 1 pound and 2 pounds, "49 pounds plus 1 pound plus 2 pounds.

The 49 plus 1 is equal to 50 pounds, and I've got another 2 pounds to add on.

So yes, my total crossed again is 52 pounds." Izzy was right.

And you remember, you can add the ones digits in a different order and the sum will remain the same, I'm sure you've heard of commutativity before.

so time to check your understanding.

Can you match the equations, which will have the same sum, and then solve them using the most efficient strategy? 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 52 plus 9 is going to give us the same sum as 59 plus 2, and in both of those, we could bridge through 10 to solve our equation, and our total would be 61.

78 plus 4 and 74 plus 8.

Again, we've got the same number of tens, 7 tens, and we've got an 8 ones and a 4 ones, we've just swapped their positions, and again, we can bridge through 10, and the sum would be 82.

And so these last ones must match, 89 plus 3 and 83 plus 9.

And again, we can bridge through 10 by partitioning our ones digit, and our answer will be 92.

So in each equation, when the ones are added, the tens boundary will be crossed.

So the most efficient strategy is to bridge 10.

And it's time for your final task.

You're going to use each digit card to complete the equation, and then solve each one using the most efficient strategy to calculate.

Can you predict which ones will bridge 10? So we've got 35 plus something is equal to something, and you are going to use the 1, 2, 3, 4, 5, 6, 7, 8, and 9 cards in that gap, and use the most efficient strategy to solve it.

So 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 did you do it like this? Aha, I predicted that when I add the digit cards 1 to 4 to 35, so 35 plus 1, 35 plus 2, 35 plus 3, and 35 plus 4, I will not cross the tens boundary, so I'm going to use my known facts to add the ones.

So 35 plus 1 is 36 'cause 5 plus one is 6, 5 plus 2 is 7, so 35 plus 2 is equal to 37.

35 plus 3 is equal to 38 because 5 plus 3 is equal to 8,.

and I know that 4 plus 4 is equal to 9, so 35 plus 4 is equal to 39.

So I might have thought about partitioning my 35 into 30 and 5, and then adding on my extra 1 digit, but I know that I can add up to 4 and I won't cross the tens boundary.

What happens next, though? Ah, I know that 5 plus 5 is equal to 10, so 35 plus 5 will be equal to the next multiple of 10, which is 40, because again, I can partition my 35 into 30 and 5.

5 plus 5 is 10, so I'm adding on another 10.

Now, what about the rest, 6, 7, 8, and 9? I predict that when I add the digit card 6 to 9 to 35, I will cross the tens boundary.

So I'll use a bridge 10 strategy to add the ones.

So 35 plus 6 is equal to 35 plus 5 plus 1, which is equal to 41.

35 plus 7 is equal to 35 plus 5 plus 2, so each time, I'm partitioning my ones that I'm adding into 5 and a bit, and the bit will be what goes past the next 10.

So 35 plus 5 plus 2 is equal to 42.

35 plus 8 is equal to 43, and 35 plus 9 is equal to 44.

I partitioned my 9 into 5 and 4, so that I could add it onto the 35 and bridge through 10.

Well done if you spotted those, and if you were able to predict when you would bridge through 10 and when you wouldn't.

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

We've been using efficient addition strategies to calculate.

So what have we been thinking about? Well, we can use strategies we already know to help us prepare for the addition of two 2-digit numbers.

We're not quite there yet, we're adding a 2-digit and a 1-digit number at the moment, but we can rehearse those strategies that are going to be really useful to us.

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

We've been practising our number facts, our pairs that make 10.

We've been practising known facts, and doubles, and near doubles, and some partitioning as well, and that's all going to be really useful, as we carry on with our calculation and we build up to adding and subtracting two 2-digit numbers.

Thank you for all your hard work today, and I hope I get to work with you in the lesson again soon, bye-bye.