Lesson video

Hi everyone and welcome to lesson eight in our series on addition and subtraction.

I'm Miss Tubman.

Now, the first thing you need to do, is make sure you have got any notes you made yesterday, any jottings and that you've got some paper and a pencil to help you today.

So if you haven't got those things just pause the video now and go and fetch them.

Welcome back.

Have you got everything you need? Brilliant.

Okay, so the practise questions I left you yesterday, started off by using a known fact to help you solve some calculations.

And that known fact was that 27 add 22 is equal to 49.

So let's see how we can use that to help us solve these equations.

Okay.

So my first one is 27 add 32 is equal to something.

So let's see, what's changed and what's stayed the same.

My first addend has stayed the same but my second addend has increased by one 10.

So my sum must also increase by one 10.

So my new sum will be 59.

Okay, next one.

What's changed, what's stayed the same.

So again, my first addend hasn't changed but my second addend has increased from 22 to 52.

That's an increase of three 10s or 30.

So I've added 30 to one addend and I've kept the other addend the same.

So I must add 30 to the sum.

So 49 add 30 is 79.

Is that what you got? I'm sure it is.

Last one then.

Okay, what's changed and what's stayed the same? Well, this time, my first addend has changed, hasn't it? So 27 has increased to 37.

So my ones digit hasn't changed at all but my tens digit has.

It's increased by one 10.

So I've added 10 to one addend and I've kept the other addend the same, so I must add 10 to the sum.

49 add 10 is equal to 59.

Let's just have a little look at all of those sums together, before we move on.

So I have got 59, 79 and 59 again.

Why do you think 59 appears twice? Let's see.

27 add 32 is equal to 59 and 37 add 22 is equal to 59.

That reminds me of some work that we did earlier on in this topic.

Does it remind you as well? This reminds me of the work that we did, where if we changed one addend by an amount and we changed another addend by the same amount, then we would keep the same sum.

So let's look at the change.

Ah, I have got 27 here and 37 here.

So I've increased one addend by 10.

I've added 10.

So I need to redistribute the other addend, don't I? So instead of 32, I'm going to subtract 10, which will give me 22 and that means my sum is the same.

So that's an interesting piece of learning that has linked us back to, work we did earlier in this topic.

I wonder if you spotted that connection.

Let's have a look at B then, Sam had 43 apples in one basket and 35 oranges in another.

Lots and lots of fruit.

Therefore he had 78 pieces of fruit altogether.

So my known fact is 43 add 35 is equal to 78.

Let's see what changes.

Sally gave him some more apples.

Okay.

So 43 represents my apples, so that addend is going to change.

He now has 63 apples.

So number of oranges hasn't changed.

How many pieces of fruit does he have now? Ah, and explain how you arrived at your answer.

Well, I'm going to look at how things have changed.

I can see that this addend has increased from 43 to 63.

So that's an increase of 20.

And I know that if I've increased one addend by an amount and I've kept the other addend the same, I must increase my sum by the same amount.

So 78 add 20 is equal to 98.

Is that what you got? I'm sure it is.

Okay, for your second challenge, you were making up your own question and everyone's going to have a question that looks slightly different.

And we'd love to hear about the questions that you came up with yourselves.

Here's mine.

I did, Abiir had 41 apples in one basket, 33 oranges in another.

Therefore she had 74 pieces of fruit altogether.

So that's my known fact.

Then I've increased the number of oranges, Mo gave her some more, so now she has 58 oranges.

How many pieces of fruit does she have now? Explain how you arrived at your answer.

And again, there's lots of ways of doing this.

I just used some jottings and I showed this change by starting with my known fact that 41 add 33 is equal to 74.

I knew that there was an increase of one addend from 33 to 58.

I looked at the value of the change, which was to add 25 and I knew that if I increased one addend by an amount, and kept the other addend the same, I need to increase the sum by the same amount.

So I added 25 to 74 to get 99.

So to sum up, the stem sentence we've been using to help us with our math so far, is that I've added something to one addend and kept the other addend the same, so I must add the same amount to the sum.

And that generalisation is that, when one addend is increased by an amount and the other addend is kept the same, the sum increases by the same amount.

Now just before we move on, I'd like you to have a little think about, how else addends could change.

We've talked about increasing one and keeping the other the same, what else might happen? So just have a pause to think about that before we move on to the next part of today's learning.

Okay, so we're going to start off with a number story.

Make sure you pay attention to what changes and what stays the same.

There were 62 children on a bus.

There were 32 girls and there were 30 boys.

What does the 30 represent? That's right.

The 30 represents the number of boys on the bus.

You can see it in a part-part-whole model.

And what does this represent? Oh yes.

That's the number of girls and that's represented by the 32 in my equation.

So my 62 and my two parts here, represent the total number of children on the bus.

So there are 62 children on the bus.

But then two girls got off the bus.

So what's changed? Well, the number of girls has decreased by two.

So how many children are left on the bus? Well there are now 30 girls on the bus and there are still 30 boys on the bus.

So there are 60 children on the bus because two girls got off the bus, so the total number of children decreased by two.

How did my equation change? My equation changed from having one addend of 32 to an addend of 30.

This addend stayed the same.

The number of boys did not change and my sum changed.

I decreased one addend by two, so I decreased my sum by two.

So when one addend is decreased by an amount and the other addend is kept the same, the sum decreases by the same amount.

We can talk about this change using a stem sentence.

I've subtracted two from one addend and kept the other addend the same, so I must subtract two from the sum.

All right, let's look at another example.

So this time there are 30 children in a class.

There are 16 boys and 14 girls, then a boy leaves.

So how many children are there in the class now? Okay, well the maths for this one is quite straightforward but I really want to unpick the equation on what's happening.

So what does the 16 in the equation represent? Yes, that's right, the number of boys.

And where can I see the number of girls? Yep, that's right, this 14 represents the number of girls.

So what does the 30 represent? Oh, the total number of children.

Okay, let's see what happens with our equation.

So one boy leaves so that addend has one subtracted from it.

And now there are 15 boys.

The number of girls stays the same, so there are still 14 girls.

So I subtracted one from one addend and I've kept the other addend the same, so I must also subtract one from the sum.

So now there are 29 children in the class.

Okay, we've got some linked equations here and in a moment, I'd like you to have a go at finding the sum that will complete each equation.

First of all though, there are a few extra questions, I'd like you to think about as you're doing your jottings.

How are these equations linked? What's the most efficient method of completing them? And also how would you choose to complete them? And also when you've spotted some links, what would be a good way of representing, the links between the equations? Okay, so pause the video here.

Have a go at solving the equations, think carefully about what changes and what stays the same and then come back.

Welcome back.

Let's have a little look at these equations and as we're doing so, let's think about using our stem sentence to talk about what changes and what stays the same.

So first of all, 96 add four is equal to 100.

Then we've got 86 add four is equal to 90.

76 add four is equal to 80.

And 66 add four which is equal to 70.

So, how are they linked? What's the same and what's different, as you look at these equations? What's changing, what's not changing? Well, I can see that this addend, the four, is the same in every equation.

And I can see that the tens digit is changing in the addend, the first addend.

And I can see that the tens digit is changing in the sum as well.

Why might that be? I can also see that the ones digit in the addend, is always the same and so is the ones digit in the sum.

Why might that be? Did you spot the number of one to 10? I'm sure you did.

Okay, we can have a closer look in a minute at the link between the first equation and the last equation.

Okay, so the change, between 96 add four is equal to 100 and 66 add four is equal to 100 is to subtract 30.

So 96 subtract 30 is 66.

Four hasn't changed and because I've subtracted 30 from one addend and I've kept the other addend the same, I must subtract 30 from the sum.

So again, I can use my number bonds knowledge to help me here.

100 subtract 30 is equal to 70.

Now I'm quite interested in this pattern that we've uncovered.

So I'd like you to think about this equation.

96 add four is equal to 100.

How else might that change? And how could you represent that? I'd like you to have a little investigate of that.

So you're going to stop in a moment.

You're going to record any jottings on a piece of paper and then we'll come back and we'll share what we all discovered together.

So one more time, 96 add four is equal to 100.

How can you change that equation? What relationships might you find? Welcome back.

What did you find out? How did you change your equations? You might've recorded your equations like me, or you might've done something different.

Maybe you're a bit more systematic.

What do you notice about how I changed my equations? I started off in this top section by changing the first addend.

First of all, I decreased the addend, like we were doing before.

And then I looked at increasing this addend.

And I noticed that each time I changed this addend, my sum changed by the same amount, as long as I kept plus four the same.

And I just made a little note here of what the change was.

And I noticed again that each time my ones digit was a zero.

So that's drawing up at number one to 10 again.

Then I looked at what might happen, if I changed the second addend.

I could only increase it.

Why might that be? Why I couldn't decrease it? And again, each time I increased my second addend by a multiple of 10 and I kept my first addend the same, my sum increased by the same amount.

How can you explain what's happening here? Maybe pause and have a think about it.

I would use this generalisation to explain what's happening.

When one addend is changed by an amount, so that could be an increase or a decrease, and the other addend is kept the same, the sum changes by the same amount.

So you can see here, where I decreased one amount, one addend by 60 and I kept the second addend the same, my sum decreased by 60.

And here, where I increased my addend by 100, kept the second addend the same, my sum increased by 100 too.

I wonder what you found out? Maybe, this might inspire you to have a little bit more of an investigation yourself.

If you want to investigate, pause now and then come back and join us in a moment.

Let's look at using our generalisation, with another problem.

Together, two children have saved £100.

Yameena has saved £57 and Tom has saved £43.

Yameena is given another £10.

How much do they have now? So, have a think about how the addend and the sum have changed.

Here's the original problem, shown as a bar model.

Can you pause the video now and have a go at drawing the change in this equation? There are several different ways of doing it.

You might choose to use a bar model or you might choose something different.

Pause now and have a go.

How did you choose to represent the change in the equation? I choose to show it using a bar model because I think it makes the change easy to see.

There are other ways of showing the change too, of course.

So, let's see how my model shows the change in this equation.

Where can you see the extra 10? That's right, you can see it in this part, where it's been added to the 57.

What stays the same? I've decided to keep the 43 the same.

What else has changed? Yep, the total length of the bar has changed because the total amount of money they have has increased.

Let's see what this looks like in an equation.

I've added 10 to one addend and I've kept the other addend the same.

So I must add 10 to the sum.

So 57 add 10 is 67 and then 67 add 43 is 110.

When one addend is changed by an amount and the other addend is kept the same, the sum changes by the same amount.

What was the change in this case? Yes, that's right.

It was to add 10.

Was there another method you thought of using? I suppose you, you're right.

I could have done 67 add 43 and recalculated the whole thing but I don't think that would have been, the most efficient way of solving the problem.

Ali has saved £21 and Sumaya has saved £37.

Altogether, they've saved £58.

Sumaya spent six pounds.

How much money do they have now? Think carefully about our stem sentence.

When one addend is changed by an amount and the other addend is kept the same, the sum changes by the same amount.

So, Sumaya has spent six pounds.

How have the addend and the sum changed? Is that an increase or a decrease? Oh, it's a decrease because she spent six pounds.

So I've subtracted six from one addend and I've kept the other addend the same.

So I must subtract six from the sum.

So, still got 21 for my first addend but my second addend has decreased by six to 31.

So my sum is going to decrease by six, to 52.

Then again, I could have recalculated.

I could have done 21 add 31 to find 52 but I think it was more efficient to know that my change was to subtract six, so all I needed to do because I knew the value of the change, was subtract six from my sum to get 52.

All right.

We're going to have a look at using this method now, with some larger numbers, which is when it can be really, really useful.

There are 36,168 football fans, waiting for a football match to start.

There are 21,152 fans for one team and there are 15,016 football fans for the other team.

2,200 more fans arrive.

How many football fans are there now? Well, how have the addend and just sum changed? More fans come, so that's 2,200 more.

So the sum and one of the addends are going to increase by 2,200.

Does it matter that I don't know which side they join? Well, no.

I can add 2,200 to either addend, as long as I also add it to the sum.

How would you choose to solve this problem? Would you prefer to do a written method? I could solve it that way but it's not the most efficient strategy.

Which addend would you add on the 2,200 to? I've decided to add it to this one.

Do I need to work out what the new value of this addend is? No.

I know what the value of the change is.

I know it's add 2,200, so I just need to make sure that I add it on to the sum and that will answer the question.

So, let's have a look at what that looks like in the equation.

I know that there are 2,200 more fans.

So there's an increase of 2,200.

So I need to add 2,200 to 36,168.

Oh, that's easy.

I can see, that that means I just need to increase my hundreds by two.

So that will give me 300 in that number.

And I need to increase my thousands by two.

So that will mean that the a thousands digit is an eight.

Oh, okay, well I can see my answer then.

It's 38,368.

Well, that was really quick, wasn't it? Really straightforward.

Sometimes the amounts we calculate with, could be decimals or larger numbers.

It doesn't mean we need to use written methods.

Sometimes mental methods could be much quicker.

The maths is easy in this case because we can see what's happening.

I'd like you to pause the video now and see if you can have a go at jotting down, what our equation would look like, if we'd added these 2,200 fans to the other addend.

You might like to draw a part-part-whole model to help you.

Pause the video now and have a go.

Okay, let's look at a decimal example now.

This is the last example, before you do some practise activities.

The combined mass of two cats is 10 kilogrammes.

The mass of one cat is 4.

6 kilogrammes and the mass of the other cat is 5.

4 kilogrammes.

Where can we see the mass of the cats? That's right.

This is one cat's mass.

This is another cat's mass.

And what does this represent? Oh yes, that's the total mass of the cats.

One of the cats gained 0.

8 kilogrammes.

What is the combined mass of the cats now? Well, how have the addend and sum changed? We've added 0.

8, haven't we? We don't know which cat has gained the weight, so we can add 0.

8 to either addend.

Do I need to calculate the new value of the addend? No, like with the previous example, as long as I know what the value of the change is, I only need to alter the sum.

So I just need to do 10 add 0.

8.

So even though these are decimal numbers, the maths we have to do is quite straightforward.

I just need to jot down, what 10 add 0.

8 is.

Let's have a look at what that looks like in our equation.

So 4.

6 add 0.

8, add 5.

4 is equal to 10 add 0.

8.

I could have added it to the other addend and that's, this is what this would have looked like.

4.

6 add 5.

4 add 0.

8, is equal to 10 add 0.

8.

As you can see, whichever addend I chose to add it to, I would have still got the same sum.

The only maths I needed to do, was add that increase of 0.

8 to my sum.

So as you can see, this is a very efficient method.

I didn't need to do any writing down, apart from possibly jotting down, add 0.

8.

Okay, it's your turn to have a go now.

So the first two questions, you need to work out the change in the combined mass.

And then the third one is a bit of a challenge, see if you can create your own problem.

Remember that when you change one addend and you keep the other addend the same, the sum is going to change by the same amount, whether that's an increase or a decrease.

Your teacher tomorrow, will go through these practise questions with you.

Well done for all your hard work today.

I've really enjoyed learning about addition and subtraction with you.

Goodbye for now, take care.