Lesson video

Hi everybody.

Mrs. Popel here, and I'm here to help you with your maths learning today.

I can't wait to learn lots of new things with you and hopefully have lots of fun.

So let's get started.

Today's lesson is called add and subtract two from even numbers within 10 and it comes from the unit addition and subtraction facts within 10.

By the end of this lesson, you should be able to add and subtract two from even numbers within 10 confidently.

Here are today's keywords, odd, even, two more and two less.

Let's practise them before we start to use them within our learning.

My turn, odd.

Your turn.

My turn, even.

Your turn.

My turn, two more.

Your turn.

My turn two less.

Your turn.

Well done.

Now that we know how to say them, we can now use them.

Here is our lesson outline.

You can see that the first part of our lesson we will be adding two to even numbers within 10.

And in the second part of our learning we will be subtracting two from even numbers within 10.

Let's get started.

In today's lesson you will meet Sam and Jacob.

They're going to help us with our learning today.

Sam and Jacob are describing some towers that they have built using their cubes.

Sam has made a tower using eight cubes.

She has made it using groups of two.

Jacob has made a tower out of five cubes, but when he tries to make them out of groups of two, it has one cube on top.

Why can't Jacob make his tower like Sam's? Sam lets Jacob know that that's because five isn't an even number so you can't make another group of two.

So he'll always have one on top.

Sam and Jacob decide to create towers to represent each number on their number line to check if Sam is correct.

Can you spot any odd numbers on this number line? Remember, odd numbers cannot be made out of groups of two.

These are the odd numbers.

They all have one extra at the top.

So we can see one, three, five, seven and nine all have that extra one at the top.

They cannot be made outta groups of two.

So that means the numbers at the top must be are even numbers.

These are the numbers that can be made out of groups of two.

Two, four, six, eight, and 10.

When we put them back on our number line, can we see a pattern of odd and even numbers? Jacob thinks that he's noticed a pattern, he thinks that it goes odd, then even.

Let's have a look.

One is an odd number.

It's one cube on its own.

It cannot be made into a group of two.

Two is our first even number.

It can be made outta a group of two.

Three has the extra cube on top.

So, so far our pattern is odd, even, odd.

Is Jacob correct so far? Four is an even number.

What do we think about five? Five is an odd number.

It has the extra one on top.

Six is an even number.

Seven is an odd number.

What do we think eight is going to be? Even.

It is following our pattern.

So if it follows our pattern of odd then even, nine must be odd, and 10 must be even.

Well done.

There is an odd number between each of the even numbers, so I can see that three is the odd number between two and four.

And seven is the odd number between six and eight.

Let's practise this learning.

So what number is missing from this number line? Will it be an odd number, or an even number? And can you work out which number is missing? Jacob has decided that the missing number must be odd because it's between the two even numbers two and four.

So what number is missing? Well done Sam, three is missing.

That is the odd number between two and four.

We could count in our ones to check that this is also correct.

One, two, three, four.

Well done.

Okay, so let's practise counting in just the even numbers because that's really going to help us with our learning today.

Can you find the first even number on the number line? Two.

That's correct.

So two is going to be where we are going to start our counting.

Two, four, six, eight and 10.

Let's practise that one more time.

Two, four, six, eight and 10.

Well done.

Now when we're counting in our even numbers, we don't always have to start from the same number.

We can start our count from anywhere.

So let's start our count from four.

Can you find four on the number line? Four.

What is the next even number after four? Six, eight and 10.

Well done.

Jacob now uses his cubes to build a sequence of even numbers.

We can see that he's built his tower of two.

What would be the next tower he will build? He will build a tower of four.

Then he builds a tower of six, and then he builds a tower of eight, and finally he builds a tower of 10.

Did you notice anything when Jacob was building his towers? Jacob noticed that to create the even number sequence, his towers needed another group of two each time.

So to make his tower six, he added another group of two cubes to his tower of four.

To make his tower of 10, he added another group of two to his tower of eight.

Let's check that.

So what even number is missing from this sequence, and how do you know? Can you explain why that must be the missing number? Jacob decides to count in his even numbers to find the missing number.

Two, four, six, eight, 10.

He realises that four is the missing number from counting in his even numbers.

He also knows that four must be the missing number because when he added another group of two cubes to two it gave him four, just like he did in his sequence before.

Well done.

If you've got that correct too.

Sam is also practising counting in her even numbers and she's exploring this on a number line.

Two, four, six, eight, 10.

What pattern do you think she's noticed? Sam has noticed that on the number line, I have to add two more to get to the next even number.

Two, four, six, if she adds two more to six, what would be the next even number? Eight and 10.

Fantastic.

We have to add two more each time to get to the next even number.

Let's have a go at this.

So what number would be missing from this problem? Two more than eight.

I know that when I add two more to an even number it gives me the next even number.

So I'm going to jump two on my number line and land on the number 10.

10 is the next even number after eight, it is two more than eight.

Sam knew that nine couldn't possibly be the answer because two more than an even number is an even number and we know that nine is an odd number so that cannot be possible.

So let's have a look at this idea.

When we add two to an even number, it gives the next even number.

Sam decides to check this with an equation two plus two.

She uses her 10 frame, and her number line to check that she's correct.

She has two counters on her 10 frame.

She adds one more which is three, and she adds another one, which is four.

Sam realises that she doesn't need to count in her ones now because she knows that counting in twos is more efficient.

Two, four.

Two more than two would be equal to four.

So two plus two is equal to four.

Four is the next even number after two.

Let's have a look at this worded problem.

First, Jacob picked up six, then he picked up two more.

How many pencils does he have now? Let's write an equation to help us.

We know that Jacob had six pencils to start with.

He then picked up two more, so I know that we need to add two.

Jacob has noticed that he's adding two more to an even number so he knows that the answer must be the next even number.

So he had six to start with, what is the next even number after six? Eight.

Well done.

Six plus two must be equal to eight because eight is the next even number after six.

Let's have a go at this one.

How much money do Sam and Jacob have all together? I can see that Jacob has four pounds, and Sam has two pounds.

Write an equation to match this picture and complete the bar model to help us find how much money Jacob and Sam have altogether.

Sam has a go at solving this problem.

Sam can see that the first amount is four pounds.

Then we are adding two pounds, so that must be four plus two.

Four must be a part, and two must be a part.

So that's how she completed her bar model.

Next up, she has to find the whole.

So four plus two must be equal to six.

When we add four plus two the sum is six.

So six is the whole.

Sam and Jacob had six pounds all together.

Sam says that she can use the first equation to help her solve this second equation.

She knows that four plus two is equal to six.

So how will she work out what two plus four is equal to? Sam has noticed that they are the same addends but in a different order.

She has remembered that addition is commutative and that means that we can change the order of the add-ins but the sum will remain the same.

So four plus two is equal to six, so that means that two plus four must also be equal to six.

The children are now solving these equations using what they have learned to help them.

Jacob has noted that when one addend is even and we add two, we can think of this as the next even number.

Sam is also reminding us that we can swap the order of the addends, and the sum will still remain the same.

Zero plus two is equal to two, so two plus zero must be equal to two.

Four plus two.

I can see this as the next even number after four, which is six, so two plus four swapping those add-ins around must also be equal to six.

Six plus two.

Two more than six will be the next even number which is eight.

So two plus six must also be equal to eight.

Well done if you got those correct.

Over to you, task A is to find the missing numbers and complete the equations.

Remember that adding two to an even number in any order gives the next even number.

You can see that we've got some equations, some partial number lines with missing parts and some bar models with missing parts for you to apply your learning.

Have a go at these problems and come on back to see how you've got on.

Welcome back.

I hope you enjoyed solving those problems. Zero plus two.

I can see this as two more than zero.

This will be the first even number, which is, two.

Four plus two.

I can see this as the next even number after four, which is six.

Two plus two, I can see this as two more than two, which is four.

Now have a look at D.

I can see that the add-ins have been swapped around two plus eight, but I can also see this as two more than eight, which I know will be the next even number which is 10.

Well done if you got that one 'cause that was swapped around.

Let's have a look at these partial number lines.

I can see that this number line is starting with six, two more than six will be eight, so eight must be the missing part.

I can see that this partial number line is starting with four.

Four plus two will be the next even number, which is six.

Let's have a look at these bar models.

Two and six are my parts so I know if I add them together it will give me the whole.

Two plus six, or I can also see this as six plus two.

Two more than six will be the next even number which is eight.

Well done if you've got that one.

And finally I can see that six is the whole and two is a part, so I know that that missing part must be the even number before six because if we add two to an even number, it gives me the next even number.

So I know that the missing part must be four.

Because six is the even number after four.

Well done if you completed all of those questions.

Let's move on to the second part of our learning to subtract two from even numbers within 10.

Let's practise counting backwards in our even numbers because that's really going to help us with this part of our learning.

What is the largest even number on our number line? 10.

That's right.

We're going to start with 10 and we are going to count backwards in our even numbers.

10, eight, six, four and two.

Fantastic.

Let's do that one more time.

10, eight, six, four and two.

Well done.

Now remember, we don't have to start with 10 every single time we can count from anywhere on our number line.

So let's start with six.

Six.

Can you find six on our number line? Six, four, two.

Well done.

Jacob now decides to create his own backwards sequence of even numbers.

He builds a tower of 10.

He then builds a tower of eight.

He then builds a tower of six.

What tower will he build next? Four.

And finally he builds a tower of two.

Did you see what was happening there? As Jacob was building those different towers.

Jacob noticed that to create the backwards even number sequence, he had to remove a group of two from the tower each time.

So to create his tower of eight, he had to remove a group of two.

To create his tower of six, he had to remove another group of two, and so on until he reached his tower of two.

Sam explores why this might be.

She notices something as she's counting backwards on her number line.

It's the same jumps as when we added two, but the number is decreasing.

The number is getting smaller.

So that must mean that we have to subtract two to get to the previous even number.

We start with 10 and if we subtract two, we will be on eight.

If we subtract two from eight, what number will we then be on? Six.

Well done.

And if we subtract two from six? Four and if we subtract two more, two, well done.

Let's check this learning.

So what even number is missing from this sequence and can you explain how you know? I can see zero, two, four, eight and 10.

Which number is missing? Sam notices that the missing number is the previous even number to eight.

She knows that two less than eight is six.

So six must be the missing number.

Well done if you got that correct.

Let's have a go at this one.

So what is the missing number? I can see that our starting number is eight and I want to know what is two less than eight.

We know that two less than eight will be the even number before eight, which is, six.

Well done if you got that.

Six is the even number before eight, so that must be the missing number.

Let's explore this a little further.

So subtracting two from any even number gives the even number before it.

Here is our equation, six subtract two.

You can see that I've got six counters on my 10 frame and my number line to help me.

Let's subtract two from six.

You can see that six minus two is equal to four.

Four is the even number before six.

Well done if you've got that.

Now let's use our knowledge to complete this bar model.

Sam has noticed that 10 is the whole and two is a part.

So 10 subtract two should give her the other part.

Is she correct? Yes.

So let's do this on our number line.

Let's start with 10 and we we're going to subtract two.

I know that that will leave me with eight.

Eight is the previous even number before 10.

Sam used a different method to help her.

She remembered that eight and two are a number pair to 10, so she knew that eight would be the missing part because eight and two are equal to 10.

So 10 subtract two must be equal to eight.

Well done Sam.

Jacob now has a go at solving some more equations on his own.

Which one has he got to correct? Eight subtract two is equal to six, six subtract two is equal to eight, and two subtract two is equal to two.

Which one of those is correct? That one is correct.

Well done.

Jacob knows that he got that one correct because six is the even number before eight.

B cannot be correct because eight is the even number after six, not before six, and you can see that we are subtracting.

So it's the even number before.

Because Jacob's been a superstar this week, he's earned six golden stars.

He earned two for being kind.

and the rest for his great work probably in his maths learning.

How many stars did he get for his great work? You could use this bar model and an equation to help you solve this.

I know that Jacob has earned six golden stars altogether.

We also know that two of them are for his kindness to other children.

So that must mean if we solve six subtract two, that should give us the amount of stars that he earned for his great work.

We know that two less than six or six subtract two will be the even number before six, which is four.

So we know that Jacob has earned four stars for his great work this week.

Six is our whole, two is our part, and four was our missing part.

Well done if you got that correct.

Now over to you with task B.

So task B is to find the missing numbers to complete these equations.

Again, we've got some equations, we've got some partial number lines with some missing parts and also some bar models with some missing parts.

Remember, when we subtract two from an even number, it gives the previous even number.

Remember that when you are solving these problems. Then part two, have a go at solving some word problems. You might want to use a 10 frame or a bar model like we did previously to help you solve these.

Have a try these problems and come on back when you're ready to see how you've done.

Welcome back.

I hope you had a great time solving all of those problems. Let's see how we've done.

10 subtract two.

We can see this as the even number before 10, which is equal to eight.

Four subtract two is equal to two.

Six subtract two is equal to four.

And eight subtract two is equal to six because six is the even number before eight.

Let's look at our partial number lines.

We can see that this number line starts with two.

If we have two, and we subtract two, what number will be at the other end of our number line? Zero.

Well done if you got that one.

That was a little bit tricky.

This next number line, we can see that 10 is the number that we are starting with.

We are subtracting two, which will be the even number before 10, which is eight.

Well done if you've got those correct.

Let's move on to the bar models.

So we can see that eight is our whole and two is our part.

We know that if we subtract two from eight, that will give us the missing part.

So eight subtract two, what is the even number before eight? Six, well done.

And in this next bar model we can see that six is our whole.

Again, we have two as a part.

So if we subtract two from the whole, we will find the missing part.

Six subtract two is equal to four.

So four must be the missing part.

Well done if you managed to have a go at all of those.

Let's have a look at the word problems now.

Jacob has four toy cars.

He puts two of them back in the box.

How many cars does he still have out to play with? Sam used her 10 frame.

First she put on four cars and she subtracted two of them.

This left her with two cars.

She could have also used her knowledge that subtracting two would give the even number before four.

And question B, Sam has eight apple and cherry flavoured sweets.

Two of them are apple flavoured.

How many sweets are cherry flavoured? So let's see how Jacob worked this one out.

Jacob knew that eight is the whole.

Two of the sweets were apple flavoured.

So Jacob changed the colour of two of his counters.

If we subtract the part from the whole, it will give us the missing part.

So eight subtract two.

Jacob noticed that he had six counters left, so that must mean that's how many cherry sweets there are.

Eight subtract two is equal to six.

Is he correct? Six is the even number before eight.

Well done if you got that correct.

Well done for completing this lesson and well done for completing all of the challenges today.

Let's summarise what we've learned.

Adding two to an even number gives the even number after.

Subtracting two from an even number gives the even number before.

When we count forwards in even numbers, we add two more each time, and when we count backwards in even numbers, we subtract two each time.