Lesson video

Hello, my name's Mrs. Cornwell and I'm going to be helping you with your learning today.

I'm really looking forward to today's lesson.

I know you're going to work really hard and we'll do really well.

So let's get started.

Welcome to today's lesson, which is called, "Know that addition is commutative" And it comes from the unit, "Addition and subtraction facts within ten." So in our lesson today, we're going to look at the order of the addends within an addition equation, okay? And we're going to think about what happens when we change those.

And by the end of today's lesson, you should feel really confident with what we've learned and you should be able to use that to help you with some of your other work.

Okay, so let's get started.

So our keywords today are, "Addend." My turn, addend, your turn.

And, "Sum." My turn, sum, your turn.

And, "Commutative." My turn, commutative, your turn.

That's a long word, isn't it? And, "Altogether." My turn, altogether, your turn.

Well done, excellent.

So in the first part of our lesson today, we're going to write addends in any order when combining groups, and we're going to see what happens when we change the order.

In this lesson, you will meet Sam and you will also meet Jacob.

Okay, so Sam has some pens and Jacob has some pencils.

There they are, look.

They put them together on the table then describe the parts of the whole.

Sam says there are 3 pencils and 4 pens.

There are 7 objects altogether.

"I will represent this as 3 plus 4 is equal to 7." Jacob describes them in a different way.

He says, "There are 4 pens and 3 pencils.

There are 7 objects altogether." I will represent this as 4 plus 3 is equal to 7.

Who do you think is right? I wonder.

That's right, they are both right.

The whole group of 7 is still the same.

They just described the parts in a different order, didn't they? If we change the order of the addends, the sum remains the same, doesn't it? So those parts, it doesn't matter which part of the whole we described first, the whole amount still remains the same, doesn't it? So let's describe this picture.

There are mm and mm.

So we're going to describe the parts there, aren't we? And then we're going to describe the whole.

There are mm-mm altogether.

Let's have a look.

There are 2 forks and 3 knives.

There are 5 pieces of cutlery altogether.

We can represent this as 2 plus 3 is equal to 5.

2 plus 3 is equal to 5, there we are.

Can we describe the picture in a different way, do you think? That's right, you could describe the knives first.

You could say there are 3 knives and 2 forks.

There are 5 pieces of cutlery altogether, and we can represent this as 3 plus 2 is equal to 5.

3 plus 2 equal to 5.

So we can see the 2 equations to represent what we described there.

What did you notice about the amount in the whole group? If we describe the parts in a different order, the whole group does not change, does it? We could say that addition is commutative, okay? This means that the addends can be added in any order and the sum remains the same even when those addends, those parts are described in a different order.

Okay, so now it's time to check your understanding.

Describe the parts of this group in two ways, then write two equations to represent it, okay? There's a stem sentence there to help you, isn't there? There are mm and mm.

There are mm-mm altogether.

So pause the video now while you think about that.

Okay, and let's see how you got on.

How did you describe the group? There are 4 apples and 5 oranges.

So you could describe the apples first.

There are 9 pieces of fruit altogether, and the equation to represent that would be 4 plus 5 is equal to 9.

You could have also said there are 5 oranges and 4 apples, so you could have described the oranges first.

There are 9 pieces of fruit altogether, and the equation to represent that would be 5 plus 4 is equal to 9.

If we describe the parts in a different order, the whole group does not change, does it? Addition is commutative.

If we change the order of the addends, the sum remains the same.

Okay, so we can describe the whole first and then describe the parts, can't we? So there are 7 birds altogether in the whole group, okay? There are 2 birds are standing and 5 birds that are flying.

So those are the parts.

So 2 plus 5.

We can represent this as an equation, can't we? We could say 7 is equal to 2 plus 5.

Let's describe the parts in a different way.

So, we could look and describe the birds that are flying first instead, couldn't we? So there are 5 birds that are flying and 2 birds that are sitting.

7 is equal to 5 plus 2.

If we describe the parts in a different order, the whole group does not change.

If we change the order of the addends, the sum remains the same.

Okay, so now it's time to check your understanding of that.

Okay, so there are 8 cups altogether in the whole group.

You can see them there, can't you? Describe the parts of the group in two ways, then find two ways to complete the equation there, okay? So pause the video now while you try that.

Okay, so let's see how you describe the group then.

So you could have said there are 3 cups with juice and 5 cups without juice, okay? And that would've been 8 is equal to 3 plus 5, wouldn't it? Okay? You could have also said there are 5 cups without juice and 3 cups with juice.

And the equation to represent that would be 8 is equal to, that's right, 5 plus 3.

If we describe the parts in a different order, the whole group does not change.

If we change the order of the addends, the sum remains the same.

We know we can describe the parts of a group in any order.

There are 2 chocolates and 4 lollies.

2 plus 4.

Or you could describe it the other way around.

You could say there are 4 lollies and 2 chocolates.

And there, you can see we just described them in a different order, and that would be 4 plus 2.

Jacob is saying, "I think I could represent this as an equation.

I know the equal sign shows that two sides of the equation are the same." So that means that each side has to be equal.

So we could say 2 plus 4 is equal to 4 plus 2.

So when describing this group, they both mean the same thing, don't they? Okay, so 2 plus 4 is equal to 4 plus 2.

Sam is saying, "This can't be an equation.

It has two numbers on each side." The equal sign in an equation shows that each side of the equation is equal.

The whole group can be partitioned into 2 chocolates and 4 lollies.

We can describe either of these parts first and the whole will still be the same.

There we go.

So we can see that that side of the equation represents the 2 chocolates plus the 4 lollies, and the other side of the equation represents the 4 lollies plus the 2 chocolates.

Jacob describes the parts of the whole group in two different ways.

Let's record the addends.

There are 4 chocolate cakes and 1 cherry cake.

So mm plus mm.

And there is 1 cherry cake and 4 chocolate cakes.

Mm plus mm.

So what are the addends? That's right, the 4 chocolate cakes and 1 cherry cake is 4 plus 1, and the 1 cherry cake and 4 chocolate cakes is 1 plus 4.

If the parts are described in a different order, the whole group does not change.

Now let's complete the equation to show that the parts of the group are the same even when they're described in a different order.

So 4 plus 1 is equal to, that's right, 1 plus 4, well done.

So now it's time to check your understanding again.

Write the missing addends to represent the parts that were described, then use them to complete the equation, okay? So there is 1 cup with a straw and 2 cups without a straw.

You write which expression would represent that mm plus mm.

And then there are 2 cups with straws and 1 cup without a straw and you'll write the expression mm plus mm.

So pause the video now while you write the expressions to represent and describe that group in 2 ways.

Okay, and let's see how you got on.

So there is 1 cup with a straw and 2 cups without straws.

So that's 1 plus 2, isn't it? And then there are 2 cups with straws and 1 cup without a straw would be 2 plus 1.

Okay, so now use those expressions to complete the equation, okay? 1 plus 2 is equal to, all right? So pause the video while you complete that.

Okay, and let's see how you got on.

1 plus 2 is equal to 2 plus 1, that's right.

Excellent if you did that.

so Sam puts 3 pounds in the big piggy bank and Jacob puts 2 pounds into the piggy bank.

You can see their money bags there ready to put their money into the piggy bank, can't you? They each write a different equation to show how much money they have altogether.

"In my equation, I represent my money first" Says Sam.

And Jacob says, "In my equation, I represent my money first." So I wonder what their equations will be.

What equation does Sam write, do you think? That's right, she writes 3 plus 2 is equal to 5.

What equation do you think Jacob writes? That's right, he writes 2 plus 3 is equal to 5.

Write an equation to show that when combined, the addends are equal even when they're described in a different order.

Okay, so that will be mm plus mm is equal to mm plus mm.

What do we think it will be? That's right, 3 plus 2 is equal to 2 plus 3.

Excellent.

Sam and Jacob save up even more money.

There's Sam, she's saying, "Now we have far more money." She has 30 pounds and Jacob has 20 pounds.

And Jacob is saying, "I wonder if the addends can be described in any order now." What do you think? 30 plus 20 is equal to 50, that's right.

And 20 plus 30 is equal to 50 as well, isn't it? 30 plus 20 is equal to 20 plus 30.

No matter how large or small the numbers, if we describe the parts in a different order, the whole does not change.

If we change the order at the addends, the sum remains the same.

Here's the task for the first part of the lesson today.

Use the pictures to complete the equations.

Remember to describe the spots to help you.

Okay, so for example, you can see that picture there we could describe it as there are 2 red spots and there is 1 yellow spot.

And then if we would write 2 plus 1 is equal to.

Then we can describe it the other way around.

There is 1 yellow spot and there are 2 red spots.

So 2 plus 1 is equal to 1 plus 2.

That's right.

Okay, so pause the video now while you complete those equations using the pictures that are there.

And here is the second part of the task.

Use two different colours to colour some spots on each number frame, okay? You don't have to use red and yellow, you can use any two colours, can't you? Describe the parts coloured in two ways and represented as an equation.

So for example, you can see somebody has coloured 7 red spots there and 2 yellow spots.

So we'll describe that to help us.

There are 7 red spots and 2 yellow spots, okay? 7 plus 2 is equal to.

And then describe it the other way around.

There are 2 yellow spots and 7 red spots.

So 7 plus 2 is equal to 2 plus 7.

Okay, so you pause the video now while you complete that task.

Okay, and let's see how you got on.

So for the first part of our task here, for example, Sam's shown us what she did.

She's saying, "I noticed that the addends represented the red spots first, then the yellow spots." Okay, because she saw that the 2 represented the 2 red spots and the 4 represented the 4 yellow spots.

So then she had to describe them the other way around, didn't she? So 2 plus 4 is equal to.

She completed the equation by recording the yellow spots first this time, then the red spots.

So 2 plus 4 is equal to 4 plus 2.

Well done.

So the second part of our task then is here.

So Sam's saying, "I coloured 3 red spots and 4 yellow spots then described them in two ways." She recorded the addends which represented the parts in an equation to show they both represented the same parts.

Okay, so there are 3 red spots and 4 yellow spots.

So she wrote 3 plus 4 is equal to.

Then she said there are 4 yellow spots and 3 red spots.

So 3 plus 4 is equal to 4 plus 3.

I could also write 4 plus 3 is equal to 3 plus 4 so it didn't matter if you chose to describe the red spots first or the yellow spots first, did it? Okay, so well done with that, you've worked really hard.

So in the second part of our lesson today, we're going to write addends in any order when increasing an amount.

So use the pictures to tell the story and write an equation.

First there were 3 girls in the room, then 2 boys went into the room.

Now there are 5 children in the room.

We can represent this as 3 plus 2 is equal to 5.

Sam says if the children had arrived in a different order, the number at the end of the story would change.

Is she right? Let's see.

First there were 2 boys in the room, then 3 girls went in the room.

Now there are 5 children in the room.

If we describe the parts in a different order, the whole does not change.

So 2 plus 3 is equal to 5.

What do you notice about the equations to represent each story? That's right, if we change the order of the addends, the sum remains the same, doesn't it? So let's check your understanding of that now.

Jacob tells a story here and writes the equation 5 plus 1 is equal to 6,.

Write which equation would represent the story if the parts had been added in a different order.

Okay, so pause the video now while you try that.

And let's see how you got on, what did you think? So we had 5 plus 1 is equal to 6, okay? But you could have also said 1 plus 5 is equal to 6.

So if you'd started with 1 apple and added the 5 instead of starting with 5 and adding the 1, you would've still had the same amount at the end, wouldn't you? Use the picture to help you act out the story, then write the equation.

So we've got first there were mm bricks in the tower.

Then mm more bricks were added.

Now there are mm bricks in the tower.

So first there were 3 bricks in the tower.

Then 4 more bricks were added.

Now there are 7 bricks in the tower.

We can represent this as 3 plus 4 is equal to 7.

Sam wants to build the tower using the blue bricks first.

How will the equation change, I wonder? So first there were 4 bricks in the tower, then 3 more bricks were added.

Now there are 7 bricks in the tower.

We can represent this as 4 plus 3 is equal to 7.

What do you notice about the sum in each equation? That's right, if we describe the parts in a different order, the whole does not change.

The sum is still 7 in each case, isn't it? Addition is commutative.

If we change the order of the addends, the sum remains the same.

The children think of 2 possible ways the eggs could have been added.

So we can see that there are 3 eggs at the end of the story, can't we? 3 is the sum.

It represents the whole group.

Let's record the addends.

So we could say 3 is equal to mm plus mm, or 3 is equal to mm plus mm.

I wonder how we could complete those equations.

Sam says, "I think at first there was 1 egg in the box and 2 more eggs were put in the box." 3 is equal to 1 plus 2.

Jacob is saying, "I think at first there were 2 eggs in the box and then 1 more egg was put in the box." So 3 is equal to 2 plus 1.

If we change the order of the addends the sum remains the same.

So either of the children could have been right, couldn't they there? We don't know until we see, but they both could have been right.

And we can see 1 plus 2 is equal to 2 plus 1.

Addition is commutative.

So now it's time to check your understanding again.

Tell the story shown by the picture and complete the equation.

Okay, so we've got a first then now, and you have to complete the story, don't you? Okay, so pause the video now while you have a try at that.

Okay, and let's see how you got on.

So if you describe the story, it will be first there were 4 balls in the box, then 2 balls were added.

Now there are 6 balls in the box.

6 is equal to 4 plus 2.

For the second part of this check, you've got to imagine the balls have been added in a different order and write the equation that would represent this, okay? So the pictures, that's still there, but you've got to imagine those balls have been added the other way around, okay? And tell the story for that.

So, pause the video now while you tell the story and write the equation.

Okay, and let's see how you got on with that.

So first there were 2 balls in the box, so the 2 balls that were added would be at the beginning of the story this time.

Then 4 balls were added.

Now there are 6 balls in the box and the equation will be 6 is equal to, that's right, 2 plus 4.

Well done.

The whole group of 6 is still the same.

We just added the parts in a different order.

If we change the order of the addends, the sum remains the same.

Jacob has represented a story on the tens frame.

First there were 5 pencils in the pot, then 4 pencils were added.

5 plus 4.

We can tell a different first and now story using the same parts in a different order.

First, there were 4 pencils in the pot, then 5 pencils were added.

4 plus 5.

Let's write an equation to show that when we change the order of the addends they are still equal.

So we need our equal sign because whatever is on either side of the equal sign will be the same when they equal.

5 plus 4 is equal to, that's right, 4 plus 5.

And there's Jacob saying, "I know the equal sign shows that 2 sides are the same." So now it's time to check your understanding again.

Write the missing addends to represent the parts that were described.

Then use them to complete the equation.

Okay, so first there were 4 beads on my bracelet, then I added 3 more beads.

So you write the expression to represent that.

Then first there were 3 beads on my bracelet, then I added 4 more beads.

And then you write the expression to represent that.

So pause the video now while you try the first part of our check.

Okay, and let's see how you got on.

So first there were 4 beads on my bracelet, then I added 3 more, 4 plus 3.

First there were 3 beads on my bracelet, then I added 4 more, 3 plus 4.

That's right.

Now use them to complete the equation, okay? So 4 plus 3 is equal to mm plus mm.

Pause the video now while you complete that.

Okay, and let's see how you got on.

4 plus 3 is equal to, that's right, 3 plus 4.

Well done.

Sam and Jacob are playing with the model farm.

They put the pieces together to make a fence.

Okay, so there they are.

"My fence piece is 5 centimetres long" Says Sam.

"I will put my piece on first, then add Jacob's piece." "My fence piece is 4 centimetres long" Says Jacob.

"I will put my piece on first then add Sam's piece." They each write a different equation to show how long their fence is when the pieces are combined.

What equation does Sam write? That's right, she would write 5 plus 4 is equal to 9.

What equation does Jacob write? That's right, he'd write 4 plus 5 is equal to 9, wouldn't he? Write an equation to show that when combined the addends are equal, even when they're described in a different order? So we would write mm plus mm is equal to mm plus mm.

What do you think it will be? That's right, 5 plus 4 is equal to 4 plus 5.

So Jacob uses cubes on a bar model to represent the fence pieces in the farm.

It shows us how we can change the order of the addends and the sum remains the same.

So, we're representing Sam's fence first, aren't we? "First, my fence was 5 centimetres long.

Then I added a piece which was 4 centimetres." And that will be 5 plus 4.

Then we can do it the other way around, can't we? We can do Jacob's fence piece first.

"First my fence was 4 centimetres, then I added a piece that was 5 centimetres." 4 plus 5.

"5 centimetres plus 4 centimetres is the same as 4 centimetres plus 5 centimetres" Says Jacob.

5 plus 4 is equal to 4 plus 5.

"I noticed that the whole group remained the same." It's still representing the same whole group isn't it? But just the parts are described in a different order.

We can use what we know about the order of the addends to help us find missing numbers in equations.

So if we have a look here, we've got 4 plus 3 is equal to mm plus 4.

Each side of an equation must balance, okay? On 1 side of the equation there is 4 plus 3.

4 plus 3, we can see it on our bar model.

On the other side of the equation there is 4 and a missing addend.

We know the addends can be combined in any order.

The missing addend must be 3.

Okay, so Sam says the missing number in this equation is 8.

What mistake has been made? So 6 plus 2 is equal to mm plus 6.

She knew that 6 plus 2 was equal to 8, didn't she? So she thought the missing addend was 8, but she forgot that we already had 6 on both sides of the equation, didn't she? There is a 6 on each side of the equation so the amount added to 6 must also be the same.

And there we can see the 6 on each side of the equation, balancing, and then we can see one side has 2, so the other side has to have, oh, I wonder.

Addition is commutative, the addends can be combined in any order.

So we can see 6 plus 2 is the same as 2 plus 6, isn't it? "The missing addend is 2." Well done.

Okay, so now it's time to check your understanding again.

Find the missing number to complete the equation, okay? And then explain how you know you are right.

So we've got 3 plus 3 is equal to mm plus 3, okay? And we've got a picture there to help you and a bar model.

So pause the video now while you try that.

Okay, and let's see how you got on then.

So, 3 plus 3 is equal to 3 plus 3.

We can swap it round.

, can't we? Change the order of the addends.

There is a 3 on each side of the equation so the amount added to 3 must also be the same.

So it must have been 3 plus 3 is equal to 3 plus 3.

Addition is commutative, the addends can be combined in any order, can't they? So well done if you got that.

Jacob has written some equations, but he has made some mistakes.

He wants to find his mistakes, so let's help him.

Sort the equations to show if they're correct and explain how you know.

So 2 plus 4 is equal to 2 plus 4.

Do we think that's correct or not? That's right.

We can see, can't we? Both sides of the equation are exactly the same, they must be equal.

Okay, let's try this.

2 plus 1 is equal to 1 plus 2.

What do we think about that? That's right, that's also correct, isn't it? Each side of the equation has the same addends but in a different order, so we know each side is equal.

Okay, let's look at this one.

4 plus 5 is equal to 4 plus 4.

What do we think about that? That's right, the addends on each side of the equation aren't equal this time.

There is a 4 on each side of the equation so the amount added to 4 must also be the same.

5 is greater than 4, so 4 plus 5 must be greater than 4 plus 4.

Okay, and then what about this one? 3 plus 5 is equal to 8 plus 3.

What do we think about that? That's right, that's also incorrect.

There is a 3 on each side of the equation, isn't there? So the amount added to 3 must also be the same.

I think Jacob's made the same mistake that Sam made earlier there, hasn't he? He's seen 3 plus 5 and he's thought that's equal to 8, but he's forgotten that we've already got 3 on that side of the equation.

So well done if you spotted that.

And he's saying, "I understand now.

If we change the order of the addends, they will still be equal." Okay, so here's the task for the second part of today's lesson, okay? Fill in the missing numbers to make the equations correct.

So have a look and you've got to make each side of the equation equal.

So the first example there, we've got 2 plus 3 is equal to mm plus 3, okay? So have a think about that and how you could make those correct, okay? And then use a tick or cross to show whether the following equations are correct.

And when you've done that, explain how you know and how you could make the two sides equal.

Okay, so pause the video now while you try that.

Let's see how you got on.

So first of all, fill in the missing numbers to make the equations correct.

2 plus 3 is equal to, that's right, 2 plus 3, exactly the same addends in the same order.

Okay, and then 4 plus 3 is equal to 3 plus 4.

This time the same addends but in a different order.

Then 5 plus 3 is equal to, that's right, 3 plus 5 and 6 plus 3 is equal to 3 plus 6.

So well done if you did that.

And then the second part here, let's have a look and see what we think.

So 4 plus 1 is equal to 1 plus 4.

What do we think? That's right, that's correct, isn't it? Each side of the equation had the same addends but in a different order.

Okay, what about the next one then? 4 plus 2 is equal to 6 plus 4.

That's right, that's incorrect, isn't it? There is a 4 on each side of the equation so the amount added to 4 must also be the same.

Okay, and let's think about the third one then.

So 4 plus 3 is equal to 4 plus 4.

That's right, that's incorrect, isn't it? Because there's a 4 on each side of the equation so the amount added to 4 must also be the same.

And we know 4 plus 4 will be greater than 4 plus 3 because we've added 1 more, haven't we? Okay, and then let's look at this last one.

So we've got 4 plus 5 as equal to 6 plus 4.

That's right, that's not correct, is it? Okay, because there's a 4 on each side of the equation so the amount added to 4 must also be the same.

Well done if you spotted that.

So you've worked really hard in today's lesson, haven't you? And you've found out lots about changing the order of the addends and you'll be able to use that to help you in your work, won't you? So well done.

So let's think about what we've learned today.

When we change the order of the addends, the sum remains the same.

We say addition is commutative because the addends can be combined in any order and we can write an equation to show that when the order of the addends is changed, they remain equal.

So you've worked really hard in today's lesson, haven't you? And I've really enjoyed it, so well done.