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 explain that the addends can be added in any order and it comes from the unit calculating within 20.

By the end of this lesson, you should be able to explain that the addends can be added in any order.

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

Addends, efficient, strategy.

Let's practise them.

My turn, addends.

Your turn.

My turn, efficient.

Your turn.

My turn, strategy.

Your turn.

Wonderful.

Now that we've practised our keywords, let's use them.

Let's have a look at these lessons outline.

The first part of our learning, we're going to be adding three addends by combining different pairs and in the second part of our learning, we're going to be adding three addends by changing their order.

So let's get started with the first part.

Adding three addends by combining different pairs.

Laura, Aisha and Andeep are back to help us with our learning today.

Are you ready guys? Let's get started.

Laura and Andeep are on snack duty today.

They lay out some fruit on each table for their classmates to choose from.

This table has two apples, four oranges and three bananas.

But how many pieces of fruit are there all together? Hmm.

I wonder how they could work that out.

Andeep has remembered that we can add together three addends.

There are two apples, four oranges and three bananas.

So we can record this as an expression.

We can record this as two plus four plus three.

Laura asks Andeep how he would work this out? Andeep knows that two and four combine to make six.

Look, so he's going to add those first.

Now he can add the third addend, which is three.

So his new expression will be six plus three, which he knows is equal to nine.

So two plus four plus three must be equal to nine.

Well done Andeep.

There are nine pieces of fruit altogether.

Laura loves how Andeep added two addends first, but she thinks that she will have added it slightly different.

Should we see what Laura would've done? Laura notices that four and three combine to make seven.

So she adds these two addends first.

She then adds the third addend, which is two seven plus two, which she knows combines to make nine.

She also finds that two plus four plus three is equal to nine.

There are nine pieces of fruit altogether.

Wow.

How interesting is that? Laura used a different method but she found the same sum.

I wonder why that is.

When we add three numbers, the sum will be the same, whichever two addends we add first.

Let's have a look at the children's strategies.

You might have chosen like Andeep to add the two and the four together first and then add the three which was equal to nine.

Or like Laura you might have chosen to add four and three together and then add that to two, which was also equal to nine.

Hmm.

Which way do you think you would've solved this problem? Let's have a practise of that then.

So how could this three addend addition have been calculated? Hmm.

Three plus one plus six and we can see that it is already equal to 10.

So we are just thinking about the strategy that you would've used to solve this because we've already got the sum.

Think about the strategy used by Laura and Andeep previously.

You may want to share your strategy with somebody else to see if they did it the same way as you.

So pause this video and come on back once you've thought about your strategy and we'll see how Laura and Andeep would've tackled this problem.

Welcome back.

I hope you've done lots of great thinking there.

Should we see how Laura and Andeep would've solved this problem? You might have chosen to first add together three and one and then add the six.

So three plus one is equal to four, then plus the six.

We can see a number pair there that makes it really easy for us to solve, which would equal to 10 or you might have chosen to add the one and the six because we know that one more than six is seven.

We then add that to three, the other addend, and again we can see a number pair to 10, 3 and 7 is equal to 10.

Which strategy did you choose to use? Laura now creates a new equation to show how she solved the problem.

She takes the three addends, three plus one plus six.

Hmm an equal sign and then she puts four plus six the other sides of the equals.

Hmm.

What does Laura's equation now show? Laura can now see that three plus one plus six is equal to four plus six.

Is that right? Yes, Andeep well done a good spot.

The equal sign means the same as and both of these expressions are equal to 10, so they must be equal.

3 plus 1 plus six is equal to 10, and 4 plus 6 is also equal to 10.

So we can say that these expressions are equal.

We could also show this by putting another equal sign.

Hmm.

Okay then Laura, show me what you are thinking.

I see.

Do you see what Laura's done there? She has shown that 3 plus 1 plus 6 is equal to 4 plus 6, which is equal to 10 because we know that all of those expressions are equal to 10.

Wow Laura, all of that information in one equation.

I'm very impressed.

Andeep, do you think you could have a go to show your strategy? Andeep decided to add six and one first.

So his equation is going to look slightly different.

We know that 3 plus 1 plus 6 and 3 plus 7 are equal to 10.

So this equation would look a little bit different to Laura's, let's have a look.

3 plus 1 plus 6 we know is equal to 3 plus 7 because they both equal to 10.

There is Andeep strategy in one equation.

Wow, I'm so impressed guys.

Well done.

Now over to you.

Aisha has a turn at creating her own equation to show her strategy for solving the problem.

1 plus 4 plus 5 is equal to 10.

Does this equation correctly show her method? Hmm.

1 plus 4 is equal to 5 plus 5 is equal to 10.

Aisha has explained that she combined 4 and 1 to make 5, and then 5 plus 5 is equal to 10.

But does her equation correctly show that? Pause this video and have a think about Laura's equation.

Is it correct? If it's not quite correct, what could we do to fix it? Come on back once you've got an answer.

Welcome back, I hope you had some good thinking time there.

Let's have a look then.

Is Aisha's equation correct? No, not quite.

What's wrong with it, Andeep? Her strategy is correct.

So the way that she combined four and one to make five and then added five and five, but the expression on either side of the equal sign are not equal in her equation.

Remember, both sides of our equal sign must be equal, otherwise the equal sign is not correct.

So let's have a look.

We can see that one plus four is equal to five, whereas 5 plus 5 is equal to 10.

So these are not equal.

Andeep, what does Aisha need to do to make her equation correct? She needs to put the three addends before.

I see.

1 plus 4 plus 5 is equal to 10 and she combined 4 and 1 to make 5 plus 5, which is equal to 10, now it's correct.

Aisha needed to add plus five to the first expression to make them equal.

Well done Aisha for a good strategy and thank you to Andeep for helping Aisha.

Did you notice that too? Let's have a look at task A to practise this new learning.

Match the expressions to create an accurate equation.

So you can see that the cards underneath, we have some three addend expressions, we have some two addend expressions and we have some sums. Can you match up the three addend expression with a two addend expression that equals the correct sum? Remember all sides of the equals must be equal, so make sure to do a quick double check to check that they are equal before you move on to the next one.

Pause this video, have a go at task A and come on back when you're ready to see how you've got on.

Welcome back, I hope you had fun playing my matching game.

Shall we see how we got on? Hmm, let's see.

Three plus five plus one.

Can I see a two addend edition that's had two of my addends combined? Hmm, let me see.

Three and five.

Can I see? I can see an eight.

Eight plus one, three and five combine to make eight and we add the third addend, which is one.

And we know that eight plus one is equal to nine, so I need a nine on the other side of that equals to show the sum.

Three plus five plus one is equal to eight plus one, which is equal to nine.

Well done if you've got that first one.

Let's have a look at this next one then.

Three plus two plus four.

Hmm.

I can see a four addend, but that is six plus four and we know that three and two do not combine to make six, so it can't be that one.

So somebody must have combined the second pair, which is six, I can see it three plus six.

Can you see? The three addends stayed the same? We've combined the two and the four so we know that they both equal nine.

Three plus two plus four is equal to three plus six, which is equal to nine, next one then.

Five plus two plus three or I've seen that one straight away because I know that five and two combine to make seven and then we add three, number pair to 10.

Nice and easy.

We know that that equals 10.

Five plus two plus three is equal to seven plus three, which is equal to 10.

And finally, these are our last three cards, but let's double check that they are correct.

Six plus two plus two.

I know that double two is four, so 6 plus 4, which is equal to 10.

Well done if you've got all of those correct.

Are we ready to move on to the second part of our learning? We're going to now be adding three addends by changing their order.

Hmm so we were combining different pairs, but now we're changing their order.

Let's get going.

Laura and Andeep hand out the fruit again.

This table has three apples, four oranges, and two bananas.

They record the expression again.

Three plus four plus two.

How many pieces of fruit are there all together? Hmm.

How's Laura gonna solve this one? Oh, there are nine pieces of fruit altogether.

That was really fast, Laura, how did you work it out that quickly? Laura knew that three and two combine to make five and five plus four is equal to nine.

Wow, that was really fast, Laura, but hang on a minute Andeeps right, can we just swap the numbers around like that? Yes.

Oh I remember because addition is commutative.

We can swap the addends around in an addition to make it easier for us to add them.

Laura knew that three and two pair to make five.

So she swapped the addends so that they were next to each other.

Hmm.

I like that idea.

Well done Laura.

So then you only had to add four.

The final addend.

It's a really good strategy isn't it, Andeep? Because addition is commutative, we can add them in any order and the sum will remain the same.

So remember, when you've got a three addend edition, you can swap them around to make it easier for you.

Andeep now wonders how he would've solved this problem.

How would you swap the addends to make it easier for you, Andeep? He doesn't think that he'd swap them around because he knows that three and four is equal to seven and two more is equal to nine.

Both the children use different strategies, but they both found that the sum was nine.

Well done guys, really good thinking there.

Laura and Andeep now represent their ideas as part-part-whole models.

What's the same and what's different? Hmm.

You might like to have a think about that.

Hmm.

Let's have a look, we've got the same whole so we can see that both of the holes are nine and we've got the same parts, three, four, and two.

But wait, they're in a different order.

Can we see? Andeep has three, four, and two and Laura's part-part-whole model has three, two, and four.

They're in a different order.

They now represent their ideas on a number line to check that they are correct.

Andeep started with three and added four, then two more and he found that the sum was nine.

Can we see those steps on his number line? He started on three, added four and then added two, which was nine.

Whereas Laura's strategy was a little different.

She also started on three, but she added two, which gave her five and then added four and she still ended up arriving at nine.

But both strategies got them to the same sum even though they added them in a different order.

This shows that when we change the order of the addends, the sum will still remain the same.

Both of these equations are equal to nine.

So we can say that the expressions are equal.

Hmm, hmm.

Can you explain that for me, Andeep? First, let's remove the sum from our equations and leave us with the expressions.

Just like we did in our first learning cycle, we can now show that these expressions are the same with an equal sign.

There we go, we can now see that three plus four plus two is equal to three plus two plus four because we know that they both sum to nine.

So we know that both expressions are equal.

So let's have a practise at this.

Which of these equations are correct? So which of these are equal on both sides? Pause this video, have a think, select the ones which are correct and then come on back to see how you get on.

Welcome back, I hope you had lots of fun exploring there.

Let's have a look then.

Laura has found that both A and B have expressions which have the same addends, but they're just in different orders, so we know that they must be equal.

So the first one we can see one plus five plus four, and in the second part the expression says five plus one plus four.

They are the same.

addends but in a different order.

And we know that we can change the order, but the sum will remain the same.

And in the second one, again six plus two plus one or one plus six plus two, the same addends just a different order.

We know that the sum will remain the same.

Let's have a look at C.

In C we can see that the addends are different on each side.

So we are not sure if they're going to equal the same sum, so we're gonna have to work it out to see if they are equal.

Two plus three plus three is equal to eight.

Hmm.

So let's have a look.

Is two plus three plus two also equal to eight? No, that's equal to seven.

So these expressions are not equal.

So that equation is incorrect because remember that equal sign mean that it's the same on both sides, whereas one side has eight, the other side has seven.

Hmm.

Well done if you spotted that.

After handing out all the fruit, Andeep and Laura now put their leftover fruit back in the box.

First, there were five apples in the box.

Then Laura added two more bananas.

Then Andeep put one more orange in.

There are now eight pieces of fruit in the box.

Hmm.

I love the equation underneath.

Can you see five plus two plus one is equal to eight? That represents this story.

Hmm.

Laura thinks that she can now change the order of the equation because it's an addition, so we know it's commutative.

Andeep doesn't think we can because the story is in this order.

Hmm.

What do you think? Do you think we could change the order? Laura thinks that she can retell this story in a different way but still get the same results at the end.

Let's have a listen then, Laura.

First, there were five apples in the box.

Then Andeep added one more orange.

Ooh, so she swapped that round.

Then Laura put two more bananas in.

So we can see that first Laura put the bananas in, in the last story, but she swapped that around.

Do we think it's still going to give us the same sum? Yes now, there are eight pieces of fruit in the box so we can see how the equation has changed, but what else has changed? We can still change the addends, but the story also has to change with it.

Can you see that we added one but we had to swap around the order that the fruit was added to the basket.

Laura and Andeep now represent their stories as part-part-whole models.

We can see again that we have the same parts in the same whole, but the parts are in a different order.

Five, one and two is equal to eight or five two and one is equal to eight.

When we are telling a first, then, then, now story, we have to remember it will change the order of our stories if we change the order of the addends.

Let's practise this learning with task B.

Task B part one is to change the order of these addends to find the sum in different ways.

Which way do you think makes the calculation the easiest? You might want to discuss this with your friends around you because what we find easy might be different to what our friends find easiest.

Remember, two plus one plus four is one of the six ways that we can write this equation.

Part two is to represent your equations on a number line just like Laura and Andeep did during this learning cycle.

And then compare different ways that you arrived at the same sum.

Pause this video, have a go at task B, part one and part two and come on back when you finish to see how you've got on.

Welcome back, I hope you had lots of fun there exploring all the different ways that you can add these three addends together.

Shall we have a look? So remember two plus one plus four is one of the six ways, but we are gonna look for the other five.

So Laura, which way did you add these three addends first? Two plus four plus one, we know that two plus four is equal to six and one more than six is seven.

So the seven is the sum.

Even when we change the order of the addend, the sum will remain the same.

So the sum will be seven for all of these equations.

Well done Laura.

I didn't even think about that.

So we don't even have to do any calculating for the rest of these because we know the sum will be seven.

All we're doing is swapping the order of the addends.

The sum isn't going to change.

So let's have a look at the other four ways that you may have recorded this.

Four plus one plus two.

Four plus two plus one.

One plus two plus four.

And finally, one plus four plus two.

I hope you managed to find all those different ways that you could have added them together, but which one did you find the easiest? Was it the same as Laura? Two plus four plus one.

Let's have a look at part two then.

Now we're going to represent each of the equations on a number line to have a look at the different ways that we could arrive at the same sum.

Two plus one plus four.

We start on two, add one, add four, and you can see that we've arrived at seven.

Let's have a look at the next one.

Two plus four plus one.

So again, we're starting on two, but this time we're adding four and then adding one, which again we've arrived at seven.

Four plus one plus two.

This time we're going to start on four 'cause that's our first addend.

We're going to add one and then we're going to add two.

Are we still going to arrive at seven? Yes, of course we are.

Well done.

Four plus two plus one.

So again, we're starting on four, but this time we're adding two and then adding one.

Again, we arrived at seven.

One plus two plus four.

So this time, what number are we starting on? We're starting on one.

We are gonna add two and add four and we arrive at seven.

And finally one plus four plus two.

Again, we are starting on one, we're adding four and we're adding two more, which we arrive at seven.

Well done if you manage to represent all of those equations on the number lines.

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

When we add three numbers, the sum will be the same whichever pair of addends we add first.

The order of the addends can change and the sum will remain the same.

Well done for all of your hard work today.

I hope you've seen how easy it can be to add three addends together.

I can't wait to see you again soon to continue our learning.

Bye.