Lesson video

Hello everyone.

Welcome back to another maths lesson with me, Mrs. Pochciol.

As always, I can't wait to learn lots of new things and hopefully have lots of fun.

So let's get started.

This lesson is called Calculate the Difference, and it comes from the unit, Calculating Within 20.

By the end of this lesson, you should be able to calculate the difference and find pairs that have the same difference.

Let's have a look at our keywords for this lesson.

Difference, same, subtraction.

Let's practise.

My turn.

Difference.

Your turn.

My turn.

Same.

Your turn.

My turn.

Subtraction, your turn.

Wonderful.

Now that we've said them, let's use them.

Let's have a look at our lesson outline.

So in the first part of our learning, we are going to be representing difference as subtraction, and in the second part of our learning, we are going to be exploring the same difference.

So let's get started with the first part, representing difference as subtraction.

In this lesson, Laura and Andeep are going to help us with our learning.

Hi guys.

Are you ready to get started? Are you ready to get started? Let's go.

Laura, hands out pencils, but she hasn't got enough for every child.

One.

One for you, one for you, one for you.

(gasps) How many more pencils does Laura need so that everybody has one? Hmm.

How could we work this out? Laura represents her problem using cubes to help her.

Altogether there are six children and we have four pencils.

Now we can see how many more pencils we need.

This will be the difference.

The difference between six and four is two.

Can you see? She's recorded that now.

We can see that there are two more cubes in one set than the other.

So the difference must be two.

Andeep thinks that he's spotted another way for Laura to solve this problem though.

He's going to show this problem as a bar model so that he can explain.

We have six children and four pencils.

Can you see his bar model? He's put six children as the whole and four pencils as a part.

We know that the whole subtract the known part will be equal to the unknown part, which in this case will be the difference.

If we subtract the known part from the whole, it should give us the difference between them.

Let's have a look then Andeep, 6 - 4 = 2.

So that is the difference between the pencils and the children.

Wow, Andeep.

That's really going to help us with our finding the difference learning, isn't it Laura? Let's have a practise of Andeep's problem.

What equation would help us to solve this problem? There are four red cars and nine blue cars.

How many more blue cars are there than red cars? So could you record this as an equation? Think about what we can use to help us.

Andeep starts you off with a clue.

The whole subtract the known part is equal to the unknown part.

Pause this video, record your equation and find the difference between the number of red cars and the number of blue cars and come on back to see how you get on.

Welcome back.

I hope Andeep's little clue there, helped you to record your equation.

Shall we see how he worked it out? We can see nine as our whole.

So if we subtract four from nine, it will give us the unknown parts.

So how are you gonna work that out then Andeep? 9 - 4.

We know that five and four combine to make nine.

So nine subtract four will be equal to five.

So that means that the difference between the number of red cars and the number of blue cars is five.

Well done Andeep and well done to you if you managed to find the difference was five.

Laura now hands out the books, but some of her books are missing.

How many fewer books than children are there? Laura now uses Andeep idea to help her to solve this one.

She creates a bar model, eight children and five books.

She knows that she has five books but she needs eight.

So the difference will be how many fewer books she has.

Hmm, let's think about this then.

The whole minus the known part will give us the unknown part, which in this case will be the difference.

So 8 - 5, which we know is equal to three will tell us that the difference between five and eight is three.

Three must be how many fewer books Laura has.

Andeep now comes along to check Laura's working.

If we add together five and three, it does equal to eight.

So he agrees that three must be the difference.

Over to you then, to have a go at this.

Can you create a bar model to represent this problem and write the equation to calculate the difference? Laura needs nine glue sticks.

She can only find six glue sticks.

How many more glue sticks does she need? So create a bar model to represent this problem.

Write an equation to then find how many more glue sticks Laura will need so that she has enough for all of the children.

Pause this video and come on back once you're ready to see how you get on.

Welcome back.

Let's see how Laura completed this task.

Laura knew that she had six glue sticks but she needed nine.

So her bar model was nine was the whole and six was how many glue sticks she has.

The difference will be how many more Laura needs to find.

We know that the whole subtract the known part will equal to the other part.

So 9 - 6.

Laura knows that 9 - 6 = 3.

So that shows her that she needs three more glue sticks because three is the difference between six and nine.

Well done to you if you found the same solution as Laura.

Andeep and Laura now explore some more subtraction problems. They wonder if they can use their knowledge of difference to help them.

Laura has four sweets and gives three of them to Andeep.

How many suites does she have left? There are seven children at the park.

Four of them are playing on the roundabout, the rest are playing on the swing.

How many children are playing on the swings? Do of these sound like a difference problem to you yet? There are six birds in the tree and two birds in the bird bath.

How many more birds are there in the tree? Laura and Andeep discuss each problem.

We notice the word gives here, so that makes me think that we are taking away.

Andeep agrees that it can't be difference because we are not comparing two amounts.

So let's solve this one anyway.

Four subtract three is equal to one.

So Laura will have one sweet left.

Some good calculating there, Laura, but it wasn't difference.

Should we try the next one? There are seven children at the park.

Four of them are playing on the roundabout.

The rest are playing on the swings.

How many children are on the swings? Does this sound like a difference problem? You're right Andeep.

We do have two numbers here, but we are splitting the whole.

Laura agrees that we are not finding the difference, we are not comparing in this question.

Who's gonna solve this problem anyway? Come on then Andeep.

Seven is the whole.

We know that four of them are on the roundabout, so three must be on the swings.

There are three children playing on the swings.

I love the partitioning you did there.

Well done Andeep, but still no difference Problem.

Let's see the third problem.

There are six birds in the tree and two birds in the bath.

How many more birds are in the tree? Oh, this sounds a bit more promising.

Here, we know the numbers and we are comparing them.

So Andeep thinks that this is a difference problem? Yes.

Laura has spotted the key word, more.

We know that this can be used when we are comparing numbers, so this one might be a difference problem.

Let's have a look.

There are six birds in the tree and there are two birds in the bath.

Hmm? How many more birds are in the tree? This is definitely a difference problem.

So let's have a look.

Six subtract two will be equal to four.

So we can see that there are four more birds in the tree.

The difference between six and two is four.

Wow.

So that one was a difference problem.

We finally managed to practise finding the difference.

Let's complete our story.

There are four more birds in the tree.

When we calculate the difference, we know two numbers and we want to compare them.

So let's practise this learning.

Which of these problems would we need to find the difference? Remember, when we are calculating the difference, we know two numbers and we want to compare them.

Think about the keywords that might highlight a difference problem.

Pause this video.

Have a think, which of these problems would we need to find the difference? Come on back once you think you've found them.

Welcome back.

I hope you had fun exploring those word problems there.

Let's have a look then.

Which of these would we have to find the difference? We can see that A and C are both difference problems. I wonder what it was that showed you that they were difference problems. Well, I noticed that in A and C, we had a number for Laura and a number for Andeep.

We knew both of the numbers that we wanted to compare.

I also spotted some key words.

In A, I can see how many more goals.

That certainly means that we are comparing there.

And in C.

What was the key word I spotted in C? That's right.

Fewer.

We were comparing how many fewer pets one child had than the other child.

Well done if you spotted that both of these problems were asking us to compare the two numbers.

So now the next part of our check, can you solve these problems? Andeep scored eight goals and Laura scored seven goals.

How many more goals did Andeep score than Laura? Pause this video.

Have a think.

Can you work out how many more goals Andeep scored than Laura? Come on back once you think you know.

Welcome back.

Let's have a look then.

How many more goals did you score then Andeep? Andeep notices that the difference between consecutive numbers is one.

So he must have scored one more goal.

He uses an equation to check this.

Eight subtract seven is equal to one.

Well done Andeep.

Let's have a look at the next problem then.

Laura has two pets and Andeep has four pets.

How many fewer pets does Laura have? Pause this video.

Work out how many fewer pets Laura has and then come on back to see how Laura worked this one out.

Welcome back.

Come on then, Laura, how many fewer pets do you have? We know that Andeep has four pets and Laura has two pets.

So four subtract two will calculate the difference.

Four subtract two is equal to two, because half of four is two.

I love how you are using your half knowledge there, Laura.

Well done.

So we now know that Laura has two fewer pets than Andeep because the difference is two.

Well done for completing those checks.

Now let's move on to Task A.

Task A has three different parts.

The first part is to play a game to practise calculating the difference.

So you're going to spin a spinner that has the numbers 1 to 10.

You're going to record your first spin and your second spin.

Then you are going to calculate the difference between them.

So let's have a look.

Ooh, eight is my first spin, so let's record it on my table.

Three is my second spin.

So let's record it on the table.

I'm now going to write an equation to find the difference between them.

I know that we subtract to find the difference.

So eight subtract three is equal to five.

We can now complete our stem sentence.

Eight and three have a difference of five.

Once you've had a go at playing that game, feeling more confident about calculating the difference.

Let's move on to part two.

Part two is to represent these problems as a bar model and calculate the difference.

Part three is to create your own different story to represent this equation.

10 - 6 = 4.

, Remember, a difference Problem asks us to compare two sets of objects or measurements.

So you could use this stem sentence to help you.

There are mm mm.

There are mm mm.

How many mm mm are there? Have a go at part one, part two and part three and come on back once you've had a chance to explore all three tasks.

Enjoy.

Welcome back.

I hope you enjoyed those three different tasks there.

Should we see how Laura got on with task one, playing the game.

Let's have a look then Laura.

Laura landed on two first and then five.

Ooh, how is she going to record that as an equation? When we subtract to find the difference, we write the larger number first.

Five subtract two.

We know that two less than five is equal to three.

So what's the stem sentence going to be then, Laura? We can explain this as two and five or five and two as either way, they still have a difference of three.

Oh, I see.

So we can record this as a stem sentence with two and five or five and two.

Which way you going to record then Laura? Two and five have a difference of three.

Well done, Laura, did you enjoy playing that game? Let's have a look at how she represented our first word problem then.

Laura has seven sweets and Andeep has three sweets.

We have to subtract three from seven because that will help us to find the difference.

Laura notices that seven subtract three is a near-double.

Double three is six, add one, is seven.

So the difference must be four.

So we can now see that Laura has four more sweets than Andeep because the difference between three and seven is four.

Well done if you spotted that.

And B, there are five children outside and seven children inside.

So how many fewer children are outside? Let's have a look then, Laura.

Let's represent it.

There are five children outside and seven children inside.

If we subtract five from seven, that will let us know the difference and that will be how many fewer.

We notice that five and seven are consecutive odd numbers.

We've done lots of work on that.

The difference between consecutive odd numbers is two.

So seven, subtract five must be equal to two.

So there are two fewer children outside than inside because the difference between five and seven is two.

Well done if you managed to complete both of those word problems. Now let's have a look at task three.

Task three.

Let's hear the children's stories, then.

Laura used the stem sentence to help her to create the story.

There are 10 oranges in a box.

There are six bananas in a box.

There are four more oranges than bananas in the box.

Well done.

Let's have a check.

I can see 10 oranges.

Yeah.

Six bananas, Yeah, and the difference is four.

Well done, Laura, that's a great story and it does represent 10 - 6 = 4.

Come on then, Andeep, what was your problem? Andeep created his story using the measures of his sunflower.

My sunflower is six centimetres tall.

Laura's sunflower is 10 centimetres tall.

My sunflower is four centimetres shorter than Laura's.

Wow.

Let's have a check then I can see the two lengths.

10 and 6.

Yep.

And the difference between them is four.

So that does represent 10 - 6.

Laura notices that Laura compared 10 and 6, whereas Andeep compared 6 and 10.

But we know that the difference is still four, no matter which way around we compare them.

Well done Laura.

A really good thing to notice there.

Well done to you for completing task A and learning cycle one.

Let's move on to the next part of our learning.

Exploring the same difference.

Andeep noticed something that interested him.

What do you think he noticed? Even though the numbers we were comparing in the first learning cycle were different, the difference was the same.

Well done, Andeep.

A good thing to notice there.

We can see, look in both bar models, the difference was three, but the wholes and the parts were different.

Laura and Andeep decide to explore the idea that different numbers can have the same difference using the number rods.

Laura chose the yellow and black rods.

She predicts that the difference will be the light green rod.

Come on then Laura, let's have a look.

(gasping) Ooh, the green rod is too long because the lengths are now not equal.

Andeep suggests that Laura tries a shorter rod.

Let's try the red rod.

That's one shorter than the green rod.

There we go.

They're equal now.

Well done Laura.

So what have you found? Laura found that the black and yellow rods have a length difference of the red rod.

What are you going to choose Andeep? Andeep chooses the green rod and the pink rod.

Let's have a look them.

(gasping) Wow, look at that.

Andeep also found two rods that have a length difference of red.

Do you think they could find any more? Andeep thinks that he can find more pairs with a length difference of the red rod.

Do you think we can help him? Over to you then for check one.

Can you find more pairs of rods that also have a length difference of the red rod? Remember that the bars must be equal for it to be the correct difference.

So using your own rods that you have or use the ones that we provided for you.

Can you find more pairs that have the same difference as the red rod? Come on back when you think you've found them all.

Welcome back.

I hope you enjoyed exploring there.

Let's see if you manage to find all of the pairs with the length difference of a red rod.

(gasping) You may have found these, the green rod and the white rod.

Let's check that this does actually have a difference of the red rod.

Yes, well done.

So green and white.

You may have found yellow and green.

Yes, they have a difference of red or pink and red.

Let's have a look.

Yes, that has a difference of the red rod.

We've noticed that the pink rod must be double the length of the red rod look, because there are two red rods, which is equal to one of the pink rods.

Wow.

A good spot there, Andeep.

Let's have a look then.

Green and brown.

Yes, that has a length difference of the red rod.

Ooh, black and blue.

Let's have a look.

Yes, well done.

Black and blue.

Or you might have found orange and brown.

Ooh, let's have a look.

That looks a little bit close for me.

Let's look.

Oh it is, it does have a length difference of red rod.

Well done.

Well done to you if you managed to find some of these and a super well done if you managed to find them all.

Let's move on with our learning.

Just like the number rods, we can have different pairs of numbers that have the same difference.

Here Andeep has represented one and four using cubes.

He can see that they have a difference of three.

If he adds another cube to each tower, he can see that the difference will still be three, but the numbers will be different.

So let's add another cube to each tower.

So now we've got two and five.

(gasps) The difference is still three.

We can say that two and five have a difference of three.

Hmm.

Andeep adds another cube to each tower.

He now has three and six.

What do we think the difference is going to be now? The difference is still three.

Three and six have a difference of three also.

When we add or subtract the same amount to or from each tower, the difference will remain the same.

We can represent difference as subtraction.

So let's write an equation to represent the differences here.

We can see that our difference is three, but what subtraction will we have done to find the difference? The difference between one and four is three.

So we can say that 3 = 1 - 4.

<v ->Hmm.

Wait, does that work?</v> Hmm? Remember, the larger number has to be written first because subtraction isn't commutative.

Although we can compare them in either way.

When we are subtracting that larger number must go first.

So our equation would be 3 = 4 - 1.

Let's have a look at this next one.

What do we think the equation could be to represent the difference here? Hmm, I can see that we have a tower of two and a tower of five.

So five subtract two will be equal to three.

The difference between five and two is three.

And the third one, let's have a look.

We know that the difference is three, but what calculation have we done to find the difference? We can see that we have six subtract three.

I think there might be more towers that can be made with a difference of three.

Do you? Over to your next check then.

Can you find any more pairs of numbers, up to 10, so no numbers bigger than 10, that also have a difference of three? And can you show these as an equation? Andeep's written an example for you.

Remember, that when we record difference as a subtraction, the larger number must be written first.

Pause this video.

Have an explore.

See if you can find any more numbers with a difference of three.

Come on back when you think you've found them.

Welcome back.

Let's have a look then at what you might have found.

Andeep followed the pattern of adding more cubes onto each tower so that he could find more pairs.

So let's have a look then, Andeep, what's the first one that you found? Seven subtract four.

Yes.

Seven and four do have a difference of three.

Well done to you.

Another cube to each tower then.

What do we find now? 8 - 5 = 3.

Eight and five have a difference of three.

Oh, could we do one more, do you think, Andeep? And finally, 9 - 6 = 3.

Well done if you managed to find all of those equations that have a difference of three.

Let's move on then to Task B.

Task B, you're going to spin the spinner and this number is going to be your difference.

Your job is to find as many pairs of numbers within 10, remember no numbers bigger than 10, that have this difference, and show these as equations.

Andeep's going to show you an example first.

(gasping) Six.

He lands on six.

So we know that six has to be the difference that he can find.

We know that 6 and 4 are a number pair to 10.

So 10 subtract 4 will be equal to six.

10 and 4 have a difference of 6.

Hmm.

I wonder if you can find any more with a difference of six.

Pause this video.

Have a play of Andeep's game.

See if you can find lots of same difference pairs and come on back to see how Andeep gets on with finding the rest of his difference of six problem.

Welcome back.

Right.

Let's have a look then.

Andeep, did you find any more pairs that have a difference of six? Oh, we know that nine and three will also have a difference of six.

He can work backwards from nine to make sure that he doesn't miss a pair.

8 - 2, will also have a difference of six.

Seven and one also have a difference of six.

Well done Andeep.

Ooh, Andeep has noticed that each time he's subtracting one from each number just like he did with the towers.

Look, 10, 4, 9, 3, 8, 2, 7 and 1.

Wow.

It's a good strategy to use there.

Laura thinks that Andeep's missed one though.

What could it be? Of course, six and zero have a difference of six too.

He forgot to include zero.

Well done to you if you managed to find lots of different pairs of numbers that had the same difference.

Let's have a look at what we've learned in today's lesson.

When comparing numbers, we can look at the difference between them.

The difference between two numbers has a value.

The difference can be shown as a bar model.

Difference can be calculated as subtraction and different pairs of numbers can still have the same difference.

Thank you so much for joining me today and well done for all of your hard work.

I'm hoping that you are starting to feel a lot more confident with calculating difference.

Goodbye.