Lesson video

Hi, my name is Mr. Tazzyman and I'm looking forward to learning with you today.

This lesson is from the unit all about equivalents and compensation with addition.

It'll give you some extra hints and tips on how to face addition problems and solve them mentally rather than jumping straight to a written method.

Here's the outline for the lesson today then.

By the end, we want you to be able to say I can solve addition calculations mentally by using known facts in a range of contexts.

These are the key words that you might hear during the lesson.

I'm gonna say them and I want you to repeat them back to me.

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

Ready? My turn, whole.

Your turn.

My turn, part.

Your turn.

My turn, adjustment.

Your turn.

My turn, capacity.

Your turn.

These are the meanings of those keywords.

The whole is all the parts or everything, the total amount.

A part is a piece or section of the whole, and that bar over at the bottom there describes that relationship.

An adjustment is a change to a number using either a subtraction or addition.

This can be done to a part or a whole.

Capacity is the amount that something can hold.

This is often used in relation to liquid, but not always.

A little sneak preview there for you.

So this is the outline then.

First of all, we're gonna think about money for charity, and then we're gonna look at some statistical context.

We'll start with money for charity then.

And here are two people that you're gonna meet throughout, Jun and Alex.

They're gonna help because they'll be there for some of the different contexts, discussing them.

They'll be responding to prompts and they might even give us some of the answers.

But it won't be just them, there will also be some other friends along the way who are buying cakes.

Mm, cake, lovely.

Let's get started then.

At Oak Academy is charity week.

The children form pairs.

There's a prize for the pair who raise the most money for charity.

Jun and Alex form a pair.

"I'm gonna do a bake sale after school." "I'm gonna get people to sponsor me to dress up in a onesie for the day!" There it is.

He's dressed as a panda.

Fancy that.

Jun sets up his bake sale.

He sells large cakes donated from a local bakery, slices of cake and cupcakes.

You can see the prices underneath as well.

The large cake costs nine pounds 75.

A slice of cake costs three pounds 25 and a cupcake costs 75 pence.

"I'll buy a slice of cake and a cupcake please", says Sophia.

Okay, Sophia, let me just add up how much that will be.

"I need a pen and paper to write out the column method." "Wait, I don't think you do," says Alex.

"This can be done mentally.

Look closely at the numbers." What has Alex noticed? "I noticed that the pence are complements of one pound, so my known fact is that 25 pence and 75 pence are equal to one pound.

Then I can adjust one part." He adds three pounds to that first part to give the price of the slice.

"If one part is adjusted but the other part isn't, then I need to adjust the whole." So he adds three pounds to the whole.

"That's four pounds altogether, please Sophia." This time Sam orders a different combination.

"I'll buy a large cake and a slice of cake please." "A new combination of items. Best used columns here!" "Wait, you needn't.

Look closely.

Use a known fact." What known fact could Jun use? "I can use my previous calculation.

Three pounds 25 plus 75 pence is equal to four pounds.

Then I can adjust one part by nine pounds to give a new price.

If I adjust one part but keep other parts the same, then I need to adjust the whole.

That's 13 pounds altogether, please Sam." Jun has some other items to sell.

He's got lemon cake, three pounds 75, sponge cake, two pounds 55, and a little chocolate for 15 pence.

"I'll have a slice of lemon cake and a little chocolate please," says Izzy.

"I'm not going for columns.

I'll resist the temptation.

I'll look at the prices and find a known fact.

I know that 75 added to 15 is equal to 90, so I know that 75 pence and 15 pence is equal to 90 pence.

Now for some adjustment." He adds three pounds to the first part to give him the lemon slice.

So then he adds three pounds to the total, giving three pounds 90.

"Three pound 90 altogether please, Izzy!" Okay, it's your turn.

Mentally calculate the cost of Lucas's order using a known fact.

We've got the same prices of the last set of items that we had and Lucas says, "I'll have a slice of sponge and a little chocolate please." Okay, pause the video here and give that a go.

Welcome back.

Jun starts by saying, "I know that 55 plus 15 is equal to 70, so I know that 55 pence and 15 pence is equal to 70 pence.

Now for some adjustment." And he adjusts the 55 pence by adding two pounds to it to give him the price of the sponge.

So therefore he has to adjust the whole by two pounds as well.

"Two pounds 70 altogether please Lucas." Did you get two pound 70? I hope so.

Okay, let's move on.

Alex gets lots of people sponsoring him for the day.

He adds up the sponsorship money, which is equal to 28 pounds and 42 pence.

As a final gesture, Jun shakes out a few coins from his piggy bank to add to the total.

Can you see the coins there? What is Alex's total now? Alex adds up the total of the coins.

What is the total value? Have a look at those coins there.

Can you work out how many pence there are? "That's 58 p altogether.

Thanks, Jun." "So now you need to add that to your total." "I'll write it down as an equation." 28 pounds 42 pence plus 58 pence is equal to? "I've spotted something." What has Alex spotted? 42 pence and 58 pence are complements to one pound.

"That's my known fact, which I can adjust from." So he's added 28 pounds onto the 42 pence as an adjustment, which means he needs to do the same for the whole and he's got 29 pounds altogether, just for wearing a panda onesie.

That's pretty good going.

"29 pound altogether.

Great, worth it." The money raised by four pairs during charity week is shown in the table below.

Jun and Alex want to calculate the totals.

"We'll need a written method here." "But look at the numbers.

I think I'll use my head." What does Alex mean? Alex calculates the totals in his head using adjustment.

"This one I can do mentally by counting on." What do you think? 30 plus 29 pounds is equal to 59 pounds.

"This one I can do mentally as well." What do you think? "One part is three pounds less.

I can adjust." 30 plus 29 pounds is equal to 59 pounds.

If we adjust the second part by three pounds, we have to adjust the whole by subtracting three pounds as well and we end up with 56 pounds.

Look at this one.

Alex says, "I can use adjustment once more." What do you think? 30 plus 26 pounds is equal to 56 pounds.

He says, "I'll use the last equation as a known fact." It's been adjusted by adding 76 pence to one of the parts, so the hole also has to have an adjustment of adding 76 pence, so it's 56 pounds and 76 pence.

And the last one, what can you see there? He says, "Again, I can use adjustment." What do you think? "Here's what I know from last time." 30 pounds, 76 plus 26 pounds is equal to 56 pounds 76 pence.

He's adjusted the second part by adding 14 pence so that it matches the second part in the new equation, which means he also has to add 14 pence onto the whole giving 56 pounds 90 pence.

No columns in sight.

Well done, Alex.

Okay, let's check your understanding.

Which of the following money additions could be completed mentally using adjustment? Pause the video and have a think.

Welcome back.

These two were selected and Jun explains, "The expression shown in C would need regrouping and bridging.

This might be more efficiently solved with a written method." Alex and Jun are the winners of charity week.

They will find out their prizes in assembly later.

"Not only did I win, I also learned something.

I don't always have to rush to columns By looking closely at the numbers, I can save time by adding in my head.

Known facts and adjustment are so useful." Here's the first task then.

The number one is asking how many combinations of two items can you find? Mentally, calculate the cost for each combination using a known fact and adjustment.

You've got lemon cake at two pounds 65, cherry slice at one pound 35 and a minty cupcake at 35 pence.

For number two, it says below is a table showing the total of four pairs raising money for charity.

Using known facts and adjustment, mentally calculate their totals and complete the table.

Don't forget to use the previous calculation as a known fact in the next.

That will really help you out.

Pause a video here and have a go at those two questions.

Good luck.

Welcome back.

Let's look at number one first.

There are three combinations, lemon and minty cupcake.

Here's the jottings for that.

You should have ended up with a total of three pounds.

Lemon and cherry slice.

That one had a total of four pounds.

Cherry slice and cupcake.

That was a total of one pound 70.

Here's number two then.

We'll start with the first row, 25 and 40 pounds.

That's equal to 65 pounds.

For the next row we had 25 and 40 pounds as equal to 65 pounds as our known fact.

Jun used commutative here.

He swapped the parts, so he ended up with 40 plus 25 pounds.

Then he adjusted the first part by subtracting 50 pence, which of course meant that he had to adjust the whole by subtracting 50 pence as well, giving 64 pounds 50.

For the next one, he started with the known fact from the previous row, adjusted it by subtracting 20 pounds from the first part.

So he also adjusted the whole by subtracting 20 pounds to give 44 pounds 50.

Lastly, he started with the known fact from the previous row, adjusted it by adding 32 pence to the second part.

Consequently, the whole also needed to have an adjustment of 32 pence added, giving 44 pounds 82.

Okay, let's move on to the second part, statistical contexts.

In assembly, Jun and Alex discovered that their prize is tickets to a stadium concert that a mental health charity has organised.

"I want to go to one where there are lots of people," says Jun.

"I agree.

Let's look at the capacities." "Isn't capacity the amount of liquid a container can hold?" "It can be used in other contexts.

The number of people a stadium can contain is one." They look at a bar chart of stadium choices.

There it is, you can see we've got location at the stadium at the bottom, Leeds, Cardiff, Ipswich, London and Bognor.

And then on the Y axis we can see we've got capacity and that means the number of people and it's in 10 thousands.

"Let's look at each bar and write down its value." "Great idea.

We can place a ruler horizontally from the top of each bar to the axis to help." Really good tip, that.

35,000 in Leeds, 39,000 in Cardiff, 12,000 in Ipswich, 60,000 in London and 5,000 in Bognor.

Jun practises using known facts for addition.

"I wonder what the combined capacity of London and Cardiff is? I'll use a known fact to begin with.

40 plus 60 equals 100.

Now I will change the unit used from ones to 10 thousands.

40,000 plus 60,000 is equal to 100,000.

Time for some adjustment." So he subtracts 1000 from the first part so that he's now got a part that represents Cardiff.

That also means he has to subtract 1000 from the whole, which gives 99,000.

Alex also practises.

"I wonder what the combined capacity of London and Leeds is.

I use a known fact to begin with." 39,000 plus 60,000 is equal to 99,000.

He got that from Jun's workings.

"I'll adjust one part.

Instead of Cardiff's capacity, it's Leeds, reduction of 4,000.

London remains the same, so I need to adjust the total." 95,000.

Okay, your turn.

Use a known fact to solve Alex's question.

What's the combined capacity of Leeds and Cardiff? Have a go at that.

Pause the video and I'll be back in a moment.

Welcome back.

Here's a known fact that you might have used, 35,000 plus 40,000 is equal to 75,000.

You might have got that from thinking about 35 added to 40.

Then if you adjust the second part by reducing it by 1000, you end up with 39,000, which is Cardiff's capacity.

Therefore, you have to make sure that you subtract 1000 from the whole as well, giving you 74,000.

Jun and Alex go to the concert and have a fabulous time.

Later they look at the number of people who attended each concert in a table.

You've got location and attendance.

At Leeds, there were 34,300, Cardiff, 28,079, at Ipswich, 14,079, at London, 60,000, in Bognor, 921.

"Let's add some of these together.

Challenge me!" "Okay, I'll ask you a question then.

What was the combined attendance of the lowest two attendances?" What do you think? "I can see the two lowest attendance figures are Ipswich and Bognor.

I'll add them together." So he starts with 14,079 plus 921.

"Aren't you gonna use columns," says Jun.

"I don't need to.

Look at the numbers.

I spot something." What has Alex seen? "There is a compliment to 1000 here.

I know that 79 and 921 combined are equal to 1000.

That gives me a known fact to work from.

Now to adjust the part and then the whole." So he's made an adjustment to one part and the whole of adding 14,000.

That gives 15,000.

They continue to analyse the table.

This time, Alex challenges Jun.

"I've a challenge for you.

List three combined totals we could add in our heads." "So which ones do we not need written methods for?" "Exactly! Look for complements on known facts you can work from." Jun writes a list with a justification and sum onto a sticky note.

"We've already done Ipswich and Bognor combined." Ipswich and Bognor compliment to 1000 and then he's written the equation at the bottom.

"I think that we could do Leeds and London.

I could use a known fact from before.

We calculated the combined capacity of these places.

35,000 plus 60,000 is equal to 95,000.

The Leeds attendance was 700 less." So he's made the adjustment of 700 less for the Leeds part.

"London was completely full.

Now to adjust the total." He subtracts 700 from that and he gets 94,300.

He writes this onto a sticky note.

Leeds and London, previous known fact, and then he writes the equation underneath.

He's collecting some sticky notes here.

"I also think London and Bognor is simple.

This is just adding on from 60,000.

It might not even need adjustment." 60,000 plus 921 equals 60,921.

Jun used understanding of place value really well there.

London and Bognor, simple addition using place value and he's written the equation there.

Okay, it is time for the second task.

For number one, we've got another bar chart and it says the bar chart shows some other stadium capacities in new locations around the world.

Use the information to help calculate the answers mentally.

We've got a similar bar graph then, capacity as the Y axis, and then we've got location of stadium as the X axis.

We've got Rome with 19,000, Berlin with 40,000, Paris with 37,000, Athens with 33,000 and Sophia with 3000.

For A, you need to say what's the combined capacity of Rome and Berlin.

For B, it's what's the combined capacity of Rome and Athens, and for C, it's what's the combined capacity of Athens and Paris.

Number two says the table shows attendance numbers in each of the stadiums. Write a list of at least three additions that you think could easily be completed mentally.

Include justification and a completed equation just like Jun did.

And Jun said, "Here's one of my examples to help remind you.

Leeds and London, previous known fact," and then he's written the equation.

Okay, pause the video here and have a go at those.

I'll be back in a little while with some feedback.

Good luck.

Welcome back.

Let's look at number one to begin with and A was what's the combined capacity of Rome and Berlin? You ready to mark? Let's do it.

Here are the jottings then that you might have used if you were using adjustment.

Starting with a known factor, 20,000 plus 40,000 is equal to 60,000, you might have adjusted the first part by subtracting 1000 and therefore also adjusted the whole by subtracting 1000, giving you a total of 59,000.

Let's look at B then, the combined capacity of Rome and Athens.

Here are the jottings.

You might have started with a known fact of 20,000 plus 33,000 is equal to 53,000 and made an adjustment of subtracting 1000 from the first part and then of course from the whole giving you 52,000.

And finally for number one, the combined capacity of Athens and Paris.

You might have started with 3000 plus 37,000 is equal to 40,000 and then made an adjustment of adding 30,000 to the first part and of course then to the whole giving you 70,000 altogether.

Here's number two.

Alex says these were his.

He's got Paris and Sophia complements to 1000, 35,157 plus 843 is equal to 36,000.

He's also put Rome and Berlin previous known fact, 18,400 plus 40,000 is equal to 58,400.

Then he's put Athens and Sophia, simple addition, using place value, 31,000 plus 843 is equal to 31,843.

Okay, we've reached the end of the lesson and here's a summary of the things that we've learned about.

When looking at addition calculations, it is easy to go straight to using a written method.

However, there are more efficient methods available with closer inspection of the parts of the calculation.

Sometimes adjustment can easily be used if there are complements within the parts, or if a quick mental addition can produce a useful known fact to work from.

This is true in a range of context, including money and statistical data.

My name is Mr. Tazzyman and I've enjoyed learning with you today.

I hope you have as well and I really hope I'll be able to see you again in a math lesson in the future.

Bye for now.