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I can use knowledge of doubling, halving and the 2 times table to solve problems.

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

Doubling is a multiplication where one of the factors is 2
When one of the factors is 2, the other factor is half of the product.
Doubles facts to 5 can help to double and halve 2-digit numbers.

Common misconception

Children may revert to inefficient strategies to solve problems e.g. counting on, using fingers.

Within the second learning cycle, children are encouraged to evaluate strategies used by others. The most efficient strategies should be discussed together throughout the first learning cycle to support with this.

Keywords

Double / doubling - To become twice as many / to multiply by two.
Half / halving - One of two equal parts of a whole / To divide into two equal parts.
Check - To evaluate working, ensuring our response provides an answer to the given problem.

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Hi there, how are you doing today? I hope you're having a really good day.

My name is Ms. Combe.

I'm really excited to be learning with you today in this math session, where we're thinking about doubling and halving.

Now, you may have thought recently about the two times table, and hopefully you're starting to recall and remember some of those two times tables facts, because they're going to be really helpful in your learning.

If you are ready to get going, let's get started.

By the end of the session's day, you'll be able to say that you can use knowledge of doubling, halving, and the two times table to solve problems. We have a few keywords in our learning today.

I'm going to say them and I'd like you to say them back to me.

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

My turn, doubling, your turn.

My turn, half, your turn.

My turn, halving, your turn.

My turn, compare, your turn, excellent work.

Now you may be familiar with some of these words.

Keep an eye out for them in our lesson today and see if you can use them in your explanations.

In our lesson today, we're going to be using our knowledge of doubling, halving, and the two times table to solve problems. And we have two cycles to our learning.

In the first cycle, we're going to be using doubling and halving knowledge, and in the second cycle, we're going to be comparing doubling and halving strategies.

If you are ready, let's get started with the first cycle.

In our lesson today, you'll be meeting Jun, Aisha, Alex, and Jacob.

But actually, today, they're going to be taking part in the Oak Class Escape room, which sounds super exciting.

So, they're going to be detectives today.

So we have Detective Aisha, detective Alex, detective Jun, and detective Jacob.

And of course, you can come along and be a detective too.

Now, you might not be familiar with an escape room, but an escape room sets lots of tricky challenges and puzzles for you to work out in order to escape.

So let's see what the escape room has in store for our intrepid detectives.

\"To enter the room a key, you must find.

A double, the three pieces lie behind.\" Ooh, what's a great riddle to start our escape room? Let me read that again, \"To enter the room a key you must find.

A double, the three pieces lie behind.\" Hmm, I wonder what we have to do here.

Well, Aisha says, \"I know that a double is always even so cannot be 15.\" Ah, so Aisha is looking for doubles.

She thinks that we need to find the doubles in these numbers to find the next clue.

She says it can't be 15, 15 is an odd number.

A double is always even.

I wonder if you can spot any numbers that could be doubles or could not be doubles.

Well, that's right Alex.

He says, \"If we're looking for doubles, then I know 24 is double 12.\" So let's see what happens if we move 24.

Ooh, I wonder what that is.

I wonder what we're going to find next.

Well, Aisha says 12 is an even number, so that must be a double.

Yes, double six is equal to 12.

So I wonder what happens if we move 12.

Ooh, well, to enter the room a key you must find.

Hmm, I think that shape so far looks quite familiar.

It says, \"A double, the three pieces lie behind,\" but we found two pieces.

We have two numbers left, nine and 22.

Which ones of those are doubles? Well, that's right Alex, nine is odd.

So the final one must be 22 because that is an even number.

Aha, we found all of the pieces to the key.

I wonder what's going to happen next.

\"The key you have found, so advance into the room and look around.\" Let's see if the key fits into the lock of the door.

Success, we've managed to get into the next room and take a look around.

I wonder what we're going to find next.

Aisha and Alex find the next puzzle.

\"Solve the problem and insert the correct number of balls.

If you are right, in front of you, your next challenge falls.\" And here's the problem.

\"There are 12 bread rolls in a pack.

How many bread rolls are there in two packs?\" Hmm, I wonder what we need to do to solve that problem.

And then it says, \"Insert the correct number of balls.\" Well, I can see that Aisha has a collection of balls in front of her, and a funnel to put them in.

That might be important as well.

Well Aisha says, \"If there are two packs, it is 12 times two, or double 12.\" I wonder if you know what double 12 is or if you have a strategy for finding double 12.

Aisha partitions 12 into 10 and two.

Double 10 is equal to 20 and double two is equal to four.

20 plus four is equal to 24.

So there are 24 rolls in two packs.

So she says, \"We need 24 balls.\" Remember we need to put them in.

Let's see what happens when she puts them in.

Here they go, I wonder if she's right.

Ooh, fantastic, what have we found? I wonder what's going to be in that bag.

\"Over to you, how many satsumas will be in two packs? How many balls need to be placed in the tube this time?\" Take a close look at the table.

If there are 12 bread rolls in one pack, there were 24 bread rolls in two packs.

There are 14 sat satsumas in one pack.

How many satsumas are there in two packs? Pause the video and have a go.

Welcome back, how did you get on? Well, Alex says that two packs of satsumas is 14 times two or double 14.

He partitions 14 in order to double it.

Double 10 is equal to 20 and double four is equal to eight.

If he adds them together, 20 plus eight is equal to 28.

So there are 28 satsumas in two packs.

We need 28 balls, let's see what happens.

Fantastic, we found another bag.

We did it, well done, let's see what's in those bags.

\"Match and complete the statements, and what you can see, will be a picture of where the next clue will be.\" Ooh, it looks like we're going to have to solve some puzzle of some kind.

So Alex empties the bag and finds these statements.

Aisha says, \"It looks like we have a mixture of doubling and halving facts to match.\" Take a little look at some of those statements.

Can you see the doubling and halving facts? Can you see any matches that you might need to make? Alex decides to sort them out first and he recognises that these ones are the start of a statement, and these are the end of the statement.

That's a really good strategy if we're having to match things up, sort them out into equal groups first.

So for example, we have, if double nine is equal to.

And then on the other side we have 20, then double 20 is equal to.

Hmm, I don't think they match, that doesn't sound right to me, but I like Alex's strategy of sorting them out first.

Let's take a look at that first one.

If double nine is equal to, what? What is double nine equal to? That's right Aisha, \"I know that double nine is equal to 18, so half of 18 is equal to nine.\" If double nine is equal to 18, then half of 18 is equal to nine.

We've matched that pair up, what about the next one? \"Double three is equal to six, so double 30 is equal to 60, half of 60 is equal to 30,\" sayS Alex.

So which one matches? That's right, if double 30 is equal to 60, then half of 60 is equal to 30.

What about the last one? If half of 16 is equal to, hmm.

Well Aisha knows that if double eight is equal to 16, half of 16 is equal to eight, so we can match those up.

If half of 16 is equal to eight, then double eight is equal to 16.

And let's just check those two final ones match up.

If half of 40 is equal to hmm.

Well, \"Half of four is equal to two,\" says Alex.

\"So half of 40 is equal to 20, and double 40 is equal to 20,\" so those two match up.

If half of 40 is equal to 20, then double 20 is equal to 40.

So they've matched all of them up, but oh, I don't know.

I can't see a picture, can you? Aha, we have to turn them over, let's see what we find.

\"The next clue is near the bookshelf,\" says Aisha.

Aisha and Alex Rush off to the bookshelf and they find the next clue.

You now understand the role of two as a factor.

So put the cars in the garage they match to.

Here are the cars and here are the garages.

So we can see that each garage has a multiplication problem on it, but they're missing a factor.

So for example, two multiplied by mm, is equal to 24.

And we can see that the cars all have numbers on them.

10, 9, 12, 50, and seven.

Hmm, I wonder how we're going to solve this problem.

Ah, that's right Alex, well remembered.

\"When two is a factor, the other factor is half of the product.

So half of 24 is equal to 12.\" If we look at the first equation, we can see that two is a factor.

So the missing factor is half of 24, which is 12.

So that car must go into that garage, good start, Alex.

What about the next one? \"The next one also has a missing factor,\" says Aisha.

\"Half of 14 is equal to seven.

So two multiplied by seven is equal to 14.\" I can see that the blue car matches that one, so we'll put that in the garage.

Ah, the next one though, the factors have changed position, but Alex has remembered that that doesn't matter.

That missing factor is still equal to half the value of the product.

Half of 20 is equal to 10.

I can see that the red car must go in that garage.

Two left.

I wonder if you could spot which car goes in which garage.

Well if we look at the next one, the missing factor is half of 18.

\"Half of 18 is nine,\" says Aisha.

So that means the orange car must go in that garage.

Now we only have one car left, but let's just check we've got that one in the right place.

The final one has a missing product, two times 25 or double 25 is 40 plus 10, which is equal to 50.

Double 25 is equal to 50.

So the green car must go in that garage.

Well, we've put all the cars in the garages.

I wonder if we've got them in the right places.

Let's see what happens.

We were absolutely right, but now we have to do one extra thing.

Enter the order of the numbers found to open the door and reveal a final challenge for you to explore.

So we need to enter the numbers of the cars in the right order into this keypad to see what happens.

Let's see, 12, 7, 10, 9, 50.

I wonder what's going to happen.

We've opened the safe and we've found another challenge to have a go at.

Ooh, this one looks tricky.

I wonder what you notice about the equations that you can see.

Well Alex has noticed that double the diamond is equal to 28, so each diamond shape will be half of 28.

And he can see that because the diamonds are worth the same amount.

So something plus something or double something is equal to 28.

I wonder if you can work out what half of 28 is.

Aisha partitioned in order to help her.

Half of 20 is equal to 10 and half of eight is equal to four.

10 plus four is equal to 14, which means the diamond must be worth 14.

She then takes a look at the stars.

She notices that a star plus a star or double the star is equal to the diamond.

We now know the diamond is 14, so that means the star is equal to half of 14.

Alex again, partitions 14 in order to find half, half of 10 is equal to five and half of four is equal to two.

Five plus two is equal to seven.

So that means the star is equal to seven.

Do you think they're right? Do you think they've solved their final challenge? I think those equations look right to me.

Success, they've got through.

You found the value of the symbols in the last task, now it's time to break free, they're nearly there.

The final thing we must ask is, can you piece together the final key? Hmm, let's take a look.

So we have some parts of keys and we have different numbers.

Well, we know that seven was the value of the star and we know that 14 was the value of the diamond.

So this looks like the right key.

Let's see if it's going to work.

They approach the door, I wonder if they can escape.

Let's see what happens when they put the key in the lock.

\"You solved the problems and release the keys.

Now you've escaped, you are the bee's knees.

Success, Alex and Aisha, you've successfully been brilliant detectives and escaped the escape room, well done.

\"Over to you, wait for the safe to open.

What is the value of the star and the diamond now?\" Let's see what happens when we open the safe.

What is the value of the star and the diamond now? Pause the video and have a go.

Welcome back.

Well, if we know that double 15 is the value of the diamond, we can think about 15 as double 10 and double five.

Double 10 is 20, double five is 10.

20 plus 10 is equal to 30, so the diamond has a value of 30.

What about the star? Well we know that double diamond or double 30 is the value of the star.

Alex says that double three is equal to six.

So double 30 is equal to 60, the value of the star is 60.

Hopefully you've been able to escape as well.

Time for your first practise task, and it's time for you to create your own escape room.

\"Create your own doubling and halving challenges for another group to complete.\" You could be inspired by some of the things that you've seen in the escape room that the children have just completed.

Pause the video here, have fun creating other tasks and I'll see you shortly for some feedback.

Welcome back, now, hopefully you checked your challenges to make sure that they worked before giving them to another group.

Remember, your challenges will have been different to ours, but this is what Alex and Aisha came up with for Jacob and Jen to complete.

Aisha remembered some of the challenges that they just completed and just changed some of the numbers or wording slightly.

So she used the problem.

\"I have 24 bread rolls, they come in packs of two.

How many packs must I have bought?\" So she just changed the wording slightly, and if you did that, that's absolutely fine as well.

So, \"Like this worded problem,\" says Alex, \"we changed it from doubling to find the number of rolls, to halving to find the number of packs.\" And they can't wait to see if Jun and Jacob can escape their escape room challenge.

I wonder how your friends got on.

I hope you really enjoyed that escape room.

Now let's move on to the second cycle of our learning where we're comparing doubling and halving strategies.

This time detective Jun and detective Jacob are going to have a go.

They put the key in the lock.

\"You thought you had escaped, you are mistaken.

Let's have a look at another road you should have taken.\" Hmm, I wonder what they're going to discover.

Let's have a look at what Jun and Jacob did and evaluate their strategies to help them find the correct answer.

So Jun and Jacob are faced with the same problem that Alex and Aisha were.

I wonder what strategies they've used.

\"To enter the room, a key you must find.

A double, the three pieces lie behind.\" So the numbers are slightly different this time.

Jacob said that their strategy was to halve all of them to see if they were a double.

Hmm, do you think that's an efficient way to think about this problem? Well Alex actually reminded him that we know that doubles will always be even, so all even numbers can be halved.

So actually, this would've been a lot more efficient than calculating for each number.

All we have to do here is spot the even numbers.

We know that 15 and 13 are odd, so they just can't be doubles.

We can rule those out straight away, which means we don't have to know the answer for 18, 22, and 60.

We don't have to know what they're the double of.

We just need to know that they're even, and so therefore, they will be the doubles.

So we could have found the key slightly quicker there.

Good strategy.

Over to you, \"Which of these numbers are an example of a double of a whole number?\" Think about what we've just talked about, about odds and evens.

Pause the video here and have a go.

Welcome back, did you spot that 80, 16, 22, and 20 are all even numbers and therefore, they will be a double of a whole number? Jacob says, \"Well, I wasn't sure about 50 because it has an odd number of tens.\" What do you think? Do you think that's an example of a double of a whole number? Well that's right Alex, \"Multiples of 10 are even numbers.

So they could be the result of a double.\" So 50 works as well.

25 and nine are odd numbers, so they would not be included as an example of a double of a whole number.

Well done if you just spotted those even numbers.

Jun and Jacob move through the challenge.

\"Solve the problem and insert the correct number of balls.

If you are right, in front of you, your next challenge falls.\" So here's their challenge.

\"I have 24 bread rolls, they come in packs of two.

How many packs must I have bought?\" And here's what Jun did.

\"Double 24, so double 20 is equal to 40 and double four is equal to eight.\" 40 plus four is equal to 48.

But oh, I don't think we've got enough balls.

He doesn't think that he's got 48 balls to put in the machine.

Is he wrong then, what do you think? Has he answered the question correctly? Well, unfortunately Jun has not quite used the right strategy.

As Aisha says, \"We are not doubling here.

24 is our whole or product.\" We've got 24 bread rolls, and they come in pack of two.

So we need to think about how many groups of two are equal to 24, which means we need to half the product, we need to half 24.

What is half of 24? Well, we know half of 24 is 12 and we can do that by partitioning.

Half of 20 is equal to 10, half of four is equal to two.

So the number he was looking for is 12.

Let's see.

Absolutely right Jun, well done.

And he's found the next part of the puzzle.

\"Over to you, how many plates will be in one pack? How many balls need to be placed in the tube this time?\" Look carefully at the table, pause the video here.

Welcome back, how did you get on? Well, Jun knew that two packs or double something is equal to 70.

So one pack is half of 70.

I wonder what strategy you use to find half of 70.

Because it has an odd number of tens, we can partition it into 60 and 10.

Half of 60 is equal to 30 and half of 10 is equal to five.

So half of 70 is 30 plus five, which is 35.

There will be 35 plates in one pack.

So we need to put 35 balls into the machine, let's see.

Great job Jun, and hopefully, you managed to get the correct answer to find the next part of the puzzle.

Jun and Jacob move on to thinking about the cars in the garages.

You now understand the role of two as a factor.

So put the cars into the garage, they match to.

Here are the cars and here are the garages.

Remember, here we have two as one of the factors in all of the equations.

Jacob decided to skip count to work each answer out.

He's counted in multiples of two until he reached the product.

So for the first one he said 2, 4, 6, 8.

That's two, four times, which means four must go in that garage.

Now that is a fine strategy, but is it the most efficient strategy that he could use? Hmm, well Alex says that counting in twos is not the most efficient strategy, and that Jacob could use halving facts instead.

\"Oh yes,\" he says, \"the factor here will be half of 24.\" Remember, if one of the factors is two, then the missing factor is half the product.

The product is 24.

Jacob has partitioned 24 into 20 and four to find that half of 24 is 12.

So that car goes in that garage.

That was much more efficient than skip counting in twos to 24, which may have taken a long time and he may have lost his place and had to again.

Remember in the next one, the two has changed position, but we can still find half of 26, which is equal to 13.

What about the next one? Well, Jacob says that that was much quicker and he knows that half of 30 is 15.

It's one of those facts that he's just started to learn and recall.

What about the last one then? Let's just check that last car fits in that garage.

Well Jacob says, \"half of four is equal to two, so this one must be 20.\" Oh, but there isn't a 20 car.

Can you see the mistake Jacob has made? That's right, Alex, \"Here you need the product, not the factor.

Look, the product is missing from the equation.\" So it's double 40, not half of 40.

\"Double four is equal to eight,\" says Jacob.

\"So double 40 is equal to 80,\" that car matches, perfect.

Over to you, \"Jun completes the doubling problem.

He knows that it cannot be correct.\" He has filled in 10 as the missing number, but hmm, he's not sure where he went wrong.

Can you help him, pause the video here? Welcome back, how did you get on? Well, he can see it now.

He partitioned 14 into one and four when it should have been 10 and four.

He said that double one is equal to two and double four is equal to eight.

When he should have said double 10 is equal to 20 instead.

14 can be partitioned into 10 and four.

So double 10 is equal to 20, double four is equal to eight.

20 plus eight is equal to 28.

So double 14 is equal to 28.

Well done if you spotted that and were able to give Jun some advice on how to fix it.

Time for your second practise task.

\"Explore each of the children's strategies to look for any mistakes, and compare the strategies they've used.

Has Jacob used the most efficient strategy to solve this problem? Here's the problem, \"There are 13 cards in a pack.

Lucas buys two packs, how many cards does Lucas have now?\" And this is the strategy that Jacob has used.

\"I know that two packs will be 13 plus 13, so I'll start at 13 and count on 13 more.

Lucas will now have 26 cards.

Are there any mistakes there? Is that the most efficient strategy? Can you find a more efficient way to solve the problem? For B, I'd like you to find the errors in Jun's calculations.

And for C, I'd like you to help Alex work out where he went wrong here.

He said double nine is equal to 20.

He said I will represent nine with nine counters to help him double nine, and he'll just count them twice.

Where could he have gone wrong? Good luck with those three tasks.

Pause the video here and come back when you're ready for some feedback.

Welcome back, how did you get on? Well for A, there was nothing wrong with Jacob's strategy.

Jacob could have started on 13 and encountered on 13 more, but it's not very efficient.

It would be more efficient to see this as doubling.

Double 13 using partitioning, would've been more efficient than counting on.

Double 10 is equal to 20, double three is equal to six.

20 plus six is equal to 26.

So it's the same answer, but the way we got to it was a little bit more efficient than counting on.

For B, I asked you to find the errors in Jun's calculations.

Half of eight is equal to 16.

Well, when we halve a number, it will not be more than the whole.

Half of eight cannot be 16, he doubled it by mistake.

Half of eight is actually equal to four.

Let's look at the next one.

Double seven is equal to 14.

That's fine, double seven is equal to 14.

Seven plus seven is equal to 14.

What's about the next one? Half of 22 is equal to 12.

Hmm, that's not quite right either.

Here he can see the tens have been halved.

Half of 20 is equal to 10, but he has not halved the ones.

Half of two is equal to one, not two.

So half of 22 is equal to 11.

What about the last one? Half of six is equal to three, yep, that's correct.

Even though we have six written in words and then the digit, that's absolutely fine.

For C, where did Alex go wrong? So he doubled nine and he got 20, and he laid out nine counters and counted them twice.

What happened? Well, he thinks he miscounted.

He knows that double nine is 18, not 20.

So counting can be an inefficient strategy and knowing your double facts makes it a lot more efficient to work out the answer.

And he knows that if you didn't know his double facts, partitioning to double rather than counting twice would still be a more efficient way.

We've come to the end of the lesson and I'm really pleased with how hard you've worked today.

I hope you've really enjoyed that Escape Room Challenge.

Let's summarise our learning.

Doubling is a multiplication where one of the factors is two, when one of the factors is two, the other factor is half of the product.

Doubles facts to five can help us double and half two digit numbers.

Thank you so much for all of your hard work today, and hope to see you in another math lesson soon.

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