Lesson video

Hello, my name is Mr. Tasman, and I'm really excited to be working with you on this lesson today.

If you are ready, let's get started.

So let's get started with today's lesson.

By the end of the lesson, I want you to be able to say that you can adjust a number to make an addition easier.

Today's lesson is all about trying to make additions easier.

Here are some of the key words, and I'm gonna start by saying them, and then you are gonna repeat them back to me.

So I'll say my turn, and say the word, and then I'll say your turn, and you can say it back.

My turn.

Adjust.

Your turn.

My turn.

Inverse.

Your turn.

My turn.

Efficient.

Your turn.

Okay, let me take a little bit of time now to explain each of those keywords because they're gonna be really useful to us throughout these lesson slides.

Let's start with adjust.

When you adjust, you make a small change to a number.

This is done to make a calculation easier to solve mentally.

The inverse is the opposite or reverse operation.

For example, subtraction is the inverse operation of addition.

Working efficiently means finding a way to solve a problem quickly whilst also maintaining accuracy.

Okay, here's our lesson, our IM for today.

We're adding two three-digit numbers using adjusting strategies, and there's gonna be two parts to the lesson.

Firstly, we're gonna look at efficient mental addition with adjustment.

And secondly, we're gonna look at what we can do if we want to adjust both addends.

Let's get started.

In this lesson, we're gonna meet two friends, Jacob and Aisha.

Now these two are gonna be really helping us to discuss some of the mathematics that we come across, and also to give some valid answers to some of the maths prompts that we get.

Okay, let's start with this.

Jacob and Aisha are performing a dance.

They start by jumping forward three times.

There they go.

They turn around and jump three times.

Where do they end up? Well, this dance is an example of the inverse, and lots of you might have realised that they end up back where they started.

You can use a number line to show this.

Have a look below.

So, we've added three with their three jumps forward, then they turn around, and we are now going to use the inverse.

We're gonna subtract three, they end up exactly back where they started, or be it facing the other way.

Okay, now it's time to check your understanding.

We've got a statement here, and we need to know whether it's true or false.

The inverse of add two is subtract two.

I'm gonna ask you now to pause the video and have a chat with somebody next to you, what do you think? I'll be back in a moment to give you the answer as to whether it's true or false.

Welcome back, let's find out whether or not the statement is true or false.

This is true, I hope you got that.

The inverse of add two is subtract two.

Now, let's have a look at justifying the answer because we've got two options here that might justify that statement.

A says that they're different operations so they can't be related.

B says that if you add and subtract the same number, the process appears undone.

Your task now is to think about which one of those justifications is most likely to justify this statement? Pause the video and have a chat.

Welcome back, let's see which justification you thought.

B was the more applicable justification in this circumstance.

If you add and subtract the same number, the process appears undone, just like Aisha and Jacob doing their dance moves.

Okay, ready to move on? Let's go for it.

Here are two equations with missing numbers.

49 plus 15 equals something.

50 plus 15 equals something.

Aisha and Jacob are discussing which one they would find the toughest to solve.

Aisha says, "I would prefer to solve the first one because the first addend is smaller." So, she's looking at 49, and she realised that that's actually smaller.

Jacob says, "But the first one needs bridging! I'd find it much easier to add on from a multiple of 10." Who do you agree with and why? Here are two more equations with missing numbers.

15 plus 49 equals something.

15 plus 50 take away one equals something.

Which would you rather calculate? Well, Aisha says, "I would prefer to solve the first one because there are fewer operations." Whereas Jacob says, "But look at the numbers in the second one! I'd find them easier to work with." The second equation uses adjustment to transform the equation into something slightly different.

49 has been substituted with the expression 50 takeaway one, to create an equation that is easier to calculate.

49 becomes 50 takeaway one.

Then we can work it out as 65 takeaway one, which gives us 64.

Nice and easy to work out.

Aisha sets a challenge for Jacob.

She selects two pairs of digit cards and creates the sum, 22 plus 29 equals.

Jacob accepts the challenge.

22 plus 29 equals something, and he says, "It looks tricky, but I can transform the calculation to make it easier.

I'll start by adjusting the second addend from 29 to 30." So he adds one to 29 to make it 22 plus 30.

"Hey, that's not fair! That's much easier!" Says Aisha.

"Don't worry! I'll adjust it later using the inverse to answer the challenge you set.

I'll represent the problem on a number line." So he's drawn out his number line, starting with 22, he adds 30 to give himself 52.

"Now I'll adjust the sum.

My addend was one too many, so I need to subtract one." Which he does, and he ends up with 51.

"Wow! So by transforming the calculation using adjustment, you can do it more efficiently." That's what Aisha concludes.

Okay, it's time to check your understanding of what we've just gone through.

I'd like you to solve the following sum using adjustment.

So transform that calculation to make it easier by adjusting one of those addends.

Pause the video here, have a go, and I'll come back in a moment to see how you got on.

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

So we start with 34 added to 39, they are our addends.

Then, we adjust 39 by adding one to it to make it 40, a much easier calculation.

34 plus 40 is 74, but of course we've adjusted one of those addends, so now we need to adjust the sum.

We take away one and we end up with 73.

How did you get on? Did you get it? I hope so.

Okay, ready to move on? Let's go.

Aisha decides to make the challenge harder.

She says, "I'm going to include an extra digit card for the first addend." She pops a four in the hundreds' column, making 422 plus 29.

Jacob says, "Okay, I'll try that that!" How do you think that this will change the calculation? Hmm, let's have a look.

Jacob looks back at his jottings.

He says, "I'll go back to my jottings and include the four extra hundreds in my calculation." So you can see he started putting it in where it should be appearing.

And you'll notice something.

Aisha says, "The extra hundreds didn't affect the adjustment." They didn't actually change any of the processes he went through to try to calculate this.

Aisha looks back at Jacob's jottings.

She says, "I think there's a more efficient way of setting it out." So she starts with 422 plus 29.

Then she says, "I'm going to write my adjustment differently.

I'll substitute 29 for 30 takeaway one." So she does that.

Then she says, "Now, I'm going to add the addends." She adds 422 and 30 to give her 452.

Then she says, "Lastly, I'll adjust the sum using the inverse, which is subtraction!" And you can see it there, she's taken one away, and she's got 451.

Now both of these are jottings.

Both of them get the correct answer, but you might have one that you prefer.

Why is that? Have a think.

Okay, now Jacob challenges Aisha, "Do you want three-digit addends? He says.

"Yes please! I like a challenge." Says Aisha.

Well done, Aisha, what a great attitude.

So, Jacob gives her 320 plus 299.

Aisha uses jottings.

She starts with the two addends, and she says she'll transform the calculation using adjustment.

She'll need to adjust one of the addends, but which one? Jacob helps out.

He says, "Look for an addend that is close to the next hundred boundary." So Aisha says, "Okay, I will adjust 299 by adding one to make it 300.

So I'll substitute 299 with 300 take away one to help." She writes that down.

You can see there, she's taken 299 and adjusted it.

And she's written it down as an expression, 300 takeaway one.

"Now, I'm gonna add the addends." She adds 320 and 300 to get 620.

She says, "Lastly, I'll adjust the sum using the inverse and subtracting one." So she gets 619.

Well done, Aisha, fantastic jottings.

Now it's gonna be your turn to have a go to see if you've understood that.

You've got 280 plus 199.

So you can start by writing it down, and then I want you to use some jottings to find the total.

Remember to use adjustment.

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

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

So, you might have adjusted 199 to make it 200, remembering that you'll need to subtract one at the end to adjust your sum.

Then you end up with 480 takeaway one, which gives you a total of 479.

How did you get on? I hope you got it.

Alright, are we ready to move on? Let's have a look.

Aisha and Jacob select new digit cards, 290 plus 340.

Again, they discuss which addend they would like to adjust.

Aisha says, "It's got to be 340 because it's always the second addend." It has been so far, we've only adjusted the second addend.

But Jacob says, "I disagree.

It's 290 because it's 10 away from 300." Who do you agree with, and why? Well, Aisha realises that she's learned it doesn't always have to be the second addend.

And Jacob says, "The addend to adjust is the one nearest the next boundary, most likely the next hundred when you're adding three-digit numbers." Great reasoning, well done, Jacob.

Jacob chooses addends which are both multiples of 10.

He says, "I've got another one for you! How might you adjust this time?" Aisha accepts the challenge and says, "Okay, I'll give it a go!" Aisha uses her jottings again.

She writes down 320 plus 290, and she says, as ever, "I'll transform the calculation using adjustment.

I'll need to adjust one of the addends, but which one?" Jacob pipes in with, "Look for the addend that is closest to the next a hundred again." "Okay, I'll adjust 290 by adding 10 to make it 300.

So I will substitute it with 300 takeaway 10." And she does that.

You can see that this time she's adjusted that addend by 10.

Then she adds the addends, and lastly, she adjusts using the inverse to give her 610.

Okay, it's time to check your understanding of what we've just been through.

For each of these, I would like you to choose the addend that you would adjust, and explain why.

Pause the video, have a go, and I'll be back with an explanation in a moment.

But just have a look at Jacob's advice.

He says, "Remember, you're looking for the addend closest to the next nearest hundred boundary." Welcome back, let's see how you got on.

For the first one, A, 190 would've been the addend to choose.

Jacob says, "It's 10 away from 200." Aisha says, "399 for the second one because it's one away from 400." Jacob says, "899 for C because it's one away from 900." And lastly, "290 on D because it's only 10 away from 300." Okay, let's get going.

Jacob draws a new set of cards for Aisha to calculate, 195 plus 318.

What do you notice about the adjustment needed? Aisha says, "The addend closest to a hundred number is five away this time." And Jacob says, "Also the addend that needs adjusting appears first in the calculation." Aisha uses her jottings again, she transforms the calculation using adjustment, but she wonders, "What can I do about the order of the addends?" And Jacob says, "Well, you can swap them! Remember, addition is commutative so it won't affect the sum." "Oh yes, I will rewrite the addends and swap them." So she does just that.

"Now to adjust 195.

It's five away from the nearest a hundred, so I'll substitute it for 200 take away five." And she does just that.

You can see the adjustments she's made there.

Now she adds the addends together and then adjusts using that inverse, this time by subtracting five and she gets 513.

Okay, it's time to check your understanding.

I'd like you to find the sum below using adjustment, 298 plus 170.

Pause the video here and I'll be back in a moment to give you the answer so you can tell how you got on.

Welcome back, let's see how you did.

You may have written out the addends to begin with, and Jacob says, "Remember, you can swap the addends around if it makes it easier." Then you've got 170 added to 300 takeaway two because you've adjusted 298.

470 takeaway two, which gives you 468.

Did you get it? I hope so.

Let's move on.

Now we're gonna have a go at some practise.

For number one A and B, you'll see that there are some jottings with adjustment written out, but some of the numbers are missing.

Can you fill in the numbers? And for number two, I'd like you to have a go at calculating the sum of each of these pairs.

Pause the video here, have a go, and then I'll be back with some feedback in a little while.

Good luck! Okay, let's have a look and see how you got on.

This is one A and one B.

There are the answers, pause the video should you need to in order to mark yours.

Okay, let's have a look at the answers for number two.

On the first one, you can see the jottings there, and you should have got 406.

For the second one, Jacob tells us that you can swap the addends if it helps.

How did you get on? Hopefully you got them.

I'll give you a moment to mark them and then I'll be right back to carry on the lesson.

Let's get going with the second part.

We're now looking at what happens if you adjust both addends.

Jacob creates a new sum, 199 plus 399.

What do you notice? Jacob says, "Both the addends are near the next a hundred.

But which ad ends should I adjust?" Aisha says, "Why don't we try adjusting both?" Good thinking, Aisha.

So the children use a number line jottings this time.

Jacob says he'll try and adjust both the addends.

Aisha agrees, and she adjusts them both by one.

You can see that there.

Jacob says, "I'll represent this on a number line." He starts with 200, and adds 400.

Then he adds his addends together, which gives him 600.

Then he says he'll adjust the sum using the inverse, but this time by two, because we adjusted both addends by one.

So he takes two away to give him 598.

Aisha says, "Wow! You can adjust both addends if they're both close to the next hundred's boundary." Aisha looks back at Jacob's jottings.

And again she says, "I think there's a more efficient way of doing it." She's gonna write her adjustment differently.

She's gonna write in the adjusted addends and then jot down the total adjustment altogether.

You can see she's done it there.

She's got takeaway two, which is what she's adjusted both the addends by in total.

Then she adds the addends together, takes away the two to give her 598.

Now, which of those do you prefer, and why? Hmm, time for you to have a go.

I want you to solve the following sum using adjustment, 299 plus 199.

Pause the video here, have a go, and I'll be back in a moment to let you know how you got on.

Okay, let's see how you did.

So we've got Aisha's way of doing the jottings here, and you can see that she ended up with 498.

How did you get on? Hopefully you got it.

Ready to move on? Let's go.

Aisha replaces the ones digit with placeholders.

So, you've got 190 plus 390.

What do you notice? Jacob says, "Both the addends are still near a multiple of a hundred, but now they are 10 away." Aisha says, "Let's try and adjust both again." She starts with 190 plus 390, and Jacob says, "Let's adjust both addends by 10, making them 200 and 400." There they are.

And Aisha says, "We'll need to subtract 20 because I've made two adjustments of 10." "Let's add the addends together, which is easy because I know two plus four." We've got 600.

"Finally, we can adjust the sum using the inverse by subtracting 20." We get 580.

Your turn.

I'd like you to solve the following sum using adjustment, 290 plus 190.

Pause the video, have a go, and I'll be back in a moment to let you know how you got on.

Welcome back, let's see how you did.

So, here are the jottings, and if you work them through, you should have ended up with 480.

Hope you got it.

Ready to go? Let's move on.

Aisha selects some different digit cards.

298 plus 197.

What do you notice? Well, Jacob says, "Both the addends are different amount away from a boundary." And Aisha says, "I still think we can use adjustment." So they work together to find the sum.

Jacob says that we can adjust 298 by two, and 197 by three.

So we end up with 300 plus 200 much easier.

Aisha looks at what we might need to do to adjust those, subtracting two and three.

They work it through together, and they end up with 495.

Okay, it's your turn.

Find the sum below using adjustment on both addends.

You've got 398 plus 196.

Pause the video, have a go, and I'll be back with the answer soon.

Welcome back, let's see how you did.

We'll cycle through the jottings again, and you can see that the answer should have been 594.

Did you get it? I hope so.

Let's move on.

Now it's time for you to have another practise.

For number one, you can see it's very similar to our first practise.

There are some missing numbers in these sets of jottings.

Can you complete them? For number two, I'd like you to have a go at adding these pairs together.

Pause the video here, complete the practise, and I'll be back with some feedback in a little while.

Welcome back, let's see how you did.

I'll reveal the answers, and now I'm gonna ask you to pause the video again to mark carefully.

Okay, welcome back again.

Let's do number two.

Here are the two sums that you were asked to fill in, and here are the answers.

495 for two A.

And 892 for two B.

I'll give you a moment just to mark those.

Okay, thanks very much for joining me today to learn about adding two three-digit numbers using adjusting strategies.

Here's a quick summary of what we've done.

Adjusting is where we transform an addend to make an addition easier and use the inverse to adjust the sum.

It works best when an addend is close to the next hundred boundary.

It can be used on both addends if they're close to the next hundred boundary, and adjusting isn't always the most efficient method.

It is sometimes partitioning.

My name's Mr. Tasman, and I've really enjoyed the lesson today.

I hope to see you again soon.