Lesson video

Hello everyone and welcome to lesson seven in our series on addition and subtraction.

I'm Miss Steadman.

Now, before we get started today just pause the video and make sure you've got paper, something to write with and any notes or jottings from yesterday's learning.

Okay, are you ready to get started? We're going to start off by having a look at the practise activity.

Mrs. Sharon left you with yesterday.

So you were looking at balancing equations and making sure that your addends on one side of the equation will equal to your addends on the other side of the equation.

And you were doing that by making sure that if you had increased one addend you decrease the other addend to keep the sum the same.

So we are going to look at these four sets of equations and see if they are true or false.

See if what's on one side of the equal sign is equal to what's on the other side.

And we're going to do this by comparing addends.

So, first of all, we've got 101 add 99 is equal to a hundred add a hundred.

So let's see how these have changed.

101 has had one subtracted to make 100.

So if I subtracted one from one addend, I need to add one to the other addend to keep the sum the same.

Has that happened? Lets see, 99 has had one added to it to make 100.

So I subtracted one from one addend.

I've added one to the other addend.

So the sum is the same.

So this gets a tick because it's true.

Okay, easy peasy, right? Let's have a look at another one.

This time we've got 27 add 56 is equal to 28 add 57.

Okay, let's see how the addends have changed.

27 has had one added to it to make 28.

So if I've added one to one addend I should have subtracted one from the other addend.

So this should go 56 subtract one should be 55.

Well, that's not 55, that's 57.

Well, that can't be cool, can it? Well, we'll have a little look in a bit more detail in a moment about this one, but we know that this one can't be right because we've added one to both addends rather than adding one and subtracting one.

So this one gets a cross Ooh, big numbers.

This is why this method really is efficient because you could have checked this by doing a written method but it would have taken you a lot longer than using the method we're using now.

Again, I'm going to see what's happened to my addends on both sides of the equation.

I've got 248,000 and I've got 564,000 it's equal to, 148,000 add 464,000 Okay, same as before.

I'm going to see what's happened to my addends.

No need to be put off by these big numbers because I can see only one digits changed here.

I've gone from 248,000 to 148,000.

The only digit that's changed is the hundred thousands digit.

That's got one less.

So I subtracted 100,000.

Okay, I subtracted 100,000 from one addend.

So I need to add 100,000 to the other addend.

Let's see if that's what's happened.

564,000 has changed to 464,000.

What did I say? I said I needed to add 100,000.

Wow, well looking at 100,000 digit and I can see that we have subtracted 100,000.

So in this case, rather than subtracting 100,000 and adding 100,000 we've subtracted 100,000 twice.

So this is not balanced again.

We'll have another look at this in a bit more detail in a moment, but for now we know that this one is a cross, it's not correct, it's not equal.

Okay, decimals.

Like I said before you could use a written method to check this but it's not the most efficient.

Now I remember Miss Parnham was really helpful last week when she was talking about how we can view decimals.

She gave a great representation of dienes and I'm going to use that to help me.

So I could call this 0.

27.

But I'm actually going to call it 27 hundredths So I've got 27 hundredths and 56 hundredths is equal to 23 hundredths and 60 hundredths Let's see what's happened to my addends.

So 0.

27 or 27 Hundredths has had four hundredths subtracted to make 23 hundredths.

So I subtracted four hundredths from one addend I need to add four hundredths to the other addend.

Has that happened? Say 56 hundredths, add four hundredths is 60 hundredths.

That is what's happened.

So I've subtracted four hundredths I've added four hundredths and my sum is the same.

So this last one is true.

Let's have a closer look at those two incorrect problems. Okay 27 add 56 is equal to 28 add 57.

So I have looked at what happens what's happening on each side.

So here I can see my 27 has been increased by one to 28.

And what should have happened is my 56 should have decreased by one to 55.

That would have kept my sum the same that would have kept my balance equal.

However, I've increased my 56 by one to 57.

And you can see from my balance so that means that one side has increased by two more than the other side.

So it's not a nice level balance.

It's an unlevel balance.

Well, what I should have done is subtracted one.

Okay, let's have a look at the next example.

Okay, so with this example again, I've just noted down how each addend has been changed.

So I've worked from left to right, but there's no reason why you couldn't start on the right and work backwards to the left, as long as you're comparing the addend and seeing if they're equal or not.

And that's fine.

So in this case 248,000 has been decreased by 100,000.

It's had 100,000 subtracted from it to give us 148,000.

So that means if I have decreased one addend by 100,000 I need to increase the other addend by 100,000.

However, I can see that 564,000 has also had 100,000 subtracted from it.

So from my balance scales, I can see that one side has ended up with as being 200,000 less than the other side.

So again, it's not an equal equation.

Okay, lets now look at the next part of practise activities.

Okay, the last practise activity was to explain the information in this diagram and to show it as an equation, perhaps as a bar model you might've chosen to represent it in a different way and to use the stem sentence, to explain what's happening.

So I'm sure you notice the same thing as I did first of all, which is that this represents a balanced equation as shown on the balance scales.

So we know that this pair of addends on the left is equal to this pair of addends on the right.

They're going to have the same sum.

I decided to start with the addends on the right because I could see I had all the information I needed.

You might have chosen to start with the addends on the left and that's fine too.

And I decided I would use a bar model to help me first of all.

So I put the information I had on the right into a bar module at the top.

So you can see that as my 0.

75 kilogrammes, that's my 0.

5 kilogrammes.

And then I thought about how that changed to get to the addends on the right.

So, first of all, I was trying to think about how to deal with these decimal numbers.

And then I remembered Miss Parnham again.

And I decided that rather than calling this 0.

75 and this 0.

725 kilogrammes I would think of them in terms of thousandths.

So this is 725 thousandths, and this is 750 thousandths.

And that helped me to work out really quickly that the change between these two addends is that this one had had 25 thousandths subtracted or 0.

025.

And I've shown that change here on my bar model.

0.

75 subtract 0.

025 is 0.

725.

And then I knew that because I had subtracted 0.

025 from one addend, I would need to add it to the other addend.

So here I had 0.

5 shown here in my bar model, and I knew I needed to add 0.

025 which I just drew one on the side there.

And that gave me 0.

525, or in terms of thousandths 525 thousandths.

To check that what I'd done worked I also wrote out an equation.

I said that 0.

75 add 0.

5 was equal to 0.

725 add 0.

525.

And I just showed the change here.

I showed adding 0.

025 and I showed subtracting 0.

025.

So let's just double check.

I can use the stem sentence to explain that.

I have added 0.

025 to one addend.

So I need to subtract 0.

025 from the other addend to keep the sum the same.

Your presentation might be slightly different to mine but hopefully you found the same missing number that I did.

The next part of our math planning.

We are going to look at the math story involving journeys to school.

As we go through the story think about what's different and what stays the same.

Sorry, Diego walked for three minutes to get to his friend's house.

Then he walked for another six minutes to get to school.

What does this part represent? Yes, that's right.

That's the six minutes it takes Diego to get to school.

And where can you see how long it takes him to get to his friend's house? Yes, that's right, the three in the equation and the three here in the part whole model.

All together it takes Diego nine minutes to do his journey.

Dana walks for 23 minutes to get to her friend's house.

And then another six minutes to get to school.

What does this represent? That's right.

This represents Dana's journey to a friend's house.

And this six represents her journey to school.

What represents Dana's total journey time? That's right.

Both parts here altogether, Dana's journey takes 29 minutes.

What's the same, and what's different with these calculations? Wow, I can see that this addend is three, this addend is six and this sum is nine.

This addend is 23, this addend is six and this sum is 29.

So what's the same and what's different.

Well, the same is that this six has stayed the same.

What's different is well we still have three ones in this addend and this addend but we've added two more 10s.

Therefore the sum has two more 10s.

So our sum has changed slightly different from yesterday's learning today our sum will be changing.

Where can you see the extra 10s? You can see it in the sum in the second equation.

You can see it in the first addend on the second equation and you can see it in the part, whole model here, well done.

Okay, let's have a look at this different calculation from a known fact.

So I'm sure you all know four add three is equal to seven.

Pay careful attention and see what changes and what stays the same.

Okay, can you tell me what's happened? What's the same and what's different? Yes, that's right.

We're still adding three so this addend is unchanged but the first addend has increased by 10.

So the sum has also increased by 10.

What things can happen next? Let's have a look.

Okay, so now instead of four add three is equal to seven, we've got 24 add three is equal to 27.

So what's the same, that's right, we're still adding three.

You can see it here on the number line.

And here in the addend.

What's changed from four, add three is equal to seven.

That's right, we've added two more 10s.

So now we have 24 add three.

And because we've added two 10s to this addend, we've had to add two 10s to our sum.

So our sum is now 27.

What do you think is going to happen next? Do you think you can carry on the sequence and fill in what happens? Can you explain what's happening each time? Pause the video now and have a go.

What did you notice happening? We carried on to 94 add three is equal to 97.

How high did you go? What did you notice happening? What was the same and what was different? While each time you should have been adding three as you can see on the number line but you would have noticed that as one addend increases, say from four to 14 or 24 or 94, or all the numbers in between that you were looking at the sum increases by the same amount.

So from four, add three is equal to seven.

We go to 94 add three is equal to 97.

We can use this stem sentence to talk about what's happened.

So in this example, I've added 10 to one addend and I've kept the other addends the same.

So I must add 10 to the sum.

Can you pause the video and go back to your previous calculations and practise using the stem sentence to explain what's happened each time.

Did you have a good practise? We're now going to use the stem sentence with the calculation below.

We can to do it all together, but before we can do that you need to just make sure you're sure of how the addends have changed and how they've stayed the same.

So quickly pause the video, make sure you know how the addends have changed and then come back.

Okay, are you ready? So you can either repeat it after me, or you can join in with me.

So I can see that this addend has increased by 20 to 24, that's if this addend stay the same.

Let's go, I've added 20 to one addend and I've kept the other addend the same.

So I must add 20 to the sum.

So seven add 20 is 27.

Well then everybody let's have a look at a different example.

43 add 29 is equal to 72.

But what would happen if I increased one addend by 10? What will happen to the sum? Well, lets have a think, I'm adding 10.

So my ones digit isn't going to change but my 10s digit is going to change by one 10.

That's right.

So how am I going to change 72? Well, my ones digit, isn't going to change but my 10s digit is going to change by one 10 to an eight.

So my new equation is 43 add 39 is equal to 82.

Where can you see the change in the second equation? That's right.

You can see that the 10s digit has changed by one in one addend and in this sum.

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

So I must add 10 to the sum.

Okay, let's practise with another one.

Which addend has changed this time? So I've started with 43 add 12 is equal to 55.

And now I've got 53 add 12 is equal to 65.

Pause and have a go using the stem sentence to explain what's changed.

What did you think? Wow, let's compare our addends.

I can see that this addend 43 has changed to 53.

The ones digit still the same.

Can you see where that is changed though? Yes, that's right.

The 10s digit has changed.

I can see that my four 10s have increased to five 10s, so that's an increase of one 10.

My 12 has stayed the same and my sum I've still got a ones digit of five, but my 10s digit has changed from five to six.

So that's also an increase of one 10.

Okay, repeat the stem sentence after me.

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

So I must add 10 to the sum.

We can represent the change using the bar model.

So we're looking at the same equation.

43 add 12 is equal to 55 and the increase to 53 add 12 is equal to 65.

So my first bar model shows my two addends 43 and 12, and they show my sum 55.

Where else can you see 55? That's right, both bars combined.

If I change 43 to 53, I've added one 10.

So my sum is going to increase from 55 to 65.

This addend isn't going to change.

Pause, and have a go at drawing the bar model yourself, and then come back and see if your new bar model looks like mine.

Does yours look like mine? You might've joined it the other way round or you might have labelled it slightly differently.

Where can you see the change in my new bar model? And where can you stay, what stayed the same? Yes, that's right.

You can see that the 12 has stayed the same.

This addend hasn't changed.

And you can see that because the bar is the same size and the labelling is the same.

And the change you can see in two places, you can see that I've added 10 here, since this bar has got longer, because it's now representing 43 add 10, and you can see that the overall bar model has gotten longer too to 65.

Okay, we're going through stem sentence altogether.

So get ready.

Okay, I've added two one addend and kept the other addend the same.

So I must add to the sum.

And what do you know about this part of our stem sentence and this part of our stem sentence? Yes, that's right.

They always going to have the same value.

So if you've added nine to one addend and kept the other addend the same, you'll add nine to the sum.

If you've added a thousand to one addend and kept the other addend the same, you'll add a thousand to the sum and so on.

If you want to have a bit more of a practise with the stem sentence then you can replace these values with values of your own.

Okay, time for you guys to have a go now.

So for your practise activity today, we're going to start off by using a known fact.

So our known fact is 27 add 22 is equal to 49.

I'd like you to use this fact to help yourself the below calculations.

So think about how the addends have changed and what this means you need to do to the sum.

Then we have a bit of a reasoning problem for you.

Sam had 43 apples in one basket and 35 oranges in another.

Therefore he had 78 pieces of fruit altogether.

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

Sally gave him some more apples.

So now he has 63 apples.

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

Have a really good to think about how the addends have changed, which addends stayed the same and what that means for the sum.

Make sure you calculate efficiently.

And for your final challenge today, I'd like you to see if you can make up your own question, similar to the one on the previous slide about the fruit basket.

You might want to rewind and have a look at that.

Okay, remember that one addend will need to stay the same and one addend will change and that will change the sum.

Okay, so come back again tomorrow and we'll go through those practise questions.

Well done for your hard work today, I've really enjoyed learning about addition and subtraction with you.

And I'm looking forward to speaking to you again tomorrow.

Goodbye for now.