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I can rearrange addition equations.

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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

Equations can be represented using part-part-whole or bar models.
The sum is the whole and the addends are parts.
Equations can be written starting with the addends or with the sum.

Common misconception

Pupils may struggle starting equations with the sum. They may think = means 'the answer is..'

Ensure that children understand that 'equals' means that the equation balances (i.e. both sides have the same value.) This could be achieved through using balance scales and attaching the idea of equals with balance.

Keywords

Addend - An addend is a number added to another.
Sum - The the total when numbers are added together.
Equation - An equation shows that one number or calculation is equal to another.

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Hello there, my name is Mr. Goldie and welcome to today's math lesson.

I'm sure you're going to enjoy it.

And here is our lesson outcome.

So our lesson outcome today is I can rearrange addition equations and here are our keywords.

So I'm going to sage keyword, can you repeat it back? So the first keyword is addend.

The next keyword is sum, and the next keyword is equation.

Excellent, let's look at what those keywords mean.

So an addend is a number added to another.

The sum is the total when numbers are added together and an equation shows that one number or calculation is equal to another.

And here we have an example of an equation 10, add six equals 16.

So the two addends are 10 and six and the sum is 16.

And here's our lesson outline.

So the first part of today's lesson is using bar model representations, and the second part of the lesson is rearranging addition calculations.

Let's get started.

In this lesson, you will meet Lucas and Izzy and they're going to be helping you today with your maths.

Lucas is using bar models to represent addition equations.

The bar model represents the whole and the parts in an equation.

Here we got the whole, and here's one part, and here's the other part.

The whole in an addition equation is called the sum there.

Here's the sum, so the sum is the whole, and each part in an addition equation is called an addend.

Here's one addend, and here's the other.

Lucas uses a bar model to represent six, add eight equals 14.

So the sum is the whole and the addends add together to make the sum.

So six and eight are both parts or addends says Lucas, there's six and eight, they're both addends.

And 14 is the sum says Izzy, so 14 will go here on the bar model, Lucas uses a bar model to represent eight add 17 equals 25.

So eight and 17 are both parts or addins says Lucas three can put eight here on the bar model and 17 will go there on the bar.

Model 25 is the sum, says Izzy.

So 25 will go here on the bar model and 17 is a larger part than eight.

So 17 looks bigger on the bar model than eight.

So an addend add an addend equals the sum.

Use the bar model to represent seven, add 23 equals 30.

So here's a bar model.

Can you use the bar model to represent seven, add 23 equals 30? And think very carefully about where you'd put those three numbers.

So if you've got a whiteboard or a piece of paper, draw the bar model on your piece of paper or your whiteboard and then have a go at trying to put those three numbers onto the bar model in the correct places.

So pause the video and have a go at completing that bar model.

And welcome back.

How did you get on? Did you manage to complete it correctly? Let's find out if you were right.

So here's Lucas.

And Lucas is saying 23 and seven are both parts or addends.

But then when do you put them on the bar model? Well, 23 would go here and seven will go here.

Now seven is a small part than 23, so it would go here.

So try really carefully when you are drawing bar models, if the numbers are different sizes to try and represent them as looking like they're different sizes on the bar model.

And Izzy says 30 is the sum.

The 30 will go here on the bar model.

So remember, addend add addend equals the sum.

Now some equations have more than two parts, more than two addends.

So Lucas represents the equation 10, add six, add six equals 22 on a bar model.

So this time there are three parts, three addends.

So 22 is the sum.

So 22 goes here on the bar model and 10, six and six are all addends and 10 is bigger than six.

So it looks like it's bigger on the bar model as well.

So 10 would go here on the bar model and six and six would go here.

So sometimes bar models can be split into more than two parts into three or four or five parts.

Add end, add addend add addend equals the sum.

Sometimes the sum appears first in an equation and you might have seen equations looking a bit like this before.

So how could Izzy represent 220 equals 120 add 100? So here's a bar model.

Izzy's going to complete that bar model using that equation.

So 220 is the sum.

So 220 is the whole.

So 220 will go here and it doesn't matter that it appears first in the equation.

120 and 100 are both parts or addends.

So 120 would be here on the bar model and 100 would appear here.

So the sum can equal an addend, add and addend.

All we've done is swapped that equation around.

So we've got the sum appearing first.

Lucas represents 49 equals 46, add three using a bar model.

46 is the sum in this equation says Lucas.

So Lucas draws out a bar model and puts 46 here on the bar model.

Is Lucas correct, what do you think? Has he started completing the bar model correctly? Pause the video, what do you think? Welcome back, what do you think? Was Lucas correct? Has he started completing that bar model correctly? Well here's Izzy and Izzy says sorry, but that's not right.

49 is the sum and 46 and three are both addends.

So 49 is the whole on the bar model.

So if we were completing the bar model correctly, 49 would go here.

It's the whole, it's the sum.

46 is one of the parts and three is one of the parts and that's how the bar model should have been completed.

And let's move on to task A.

So represent each equation using a bar model.

So there are four bar models here.

All you've got to do is complete the bar models by using the equation.

So the first one is five, add nine equals 14.

Where would the 14 go on the bar model? Where would the nine and where would the five go? And don't forget to think carefully about the sizes of the numbers and think about where you would put them on the bar model.

That's part one of task A.

Part two of task A, represent each equation using the bar model.

The sum might be in a different place to look very, very carefully or there might be three parts.

Three addends.

Okay, so again, think carefully about how you would represent each equation using a bar model.

So pause the video and have a go at task A and think very, very carefully about where you are going to put the numbers on those bar models.

Good luck.

and welcome back and let's see how you got on.

So here are the answers for the first part of task A.

So the first equation was five, add nine equals 14.

So you can see there the 14 is represented as the whole, it's the sum on the bar model.

And nine is a larger addend larger part than five.

So nine has got to be represented in the bigger part of the bar model.

And let's look at part two of task A.

So the very, very first one, we've got 26 equal six out 20.

So 26 is the sum.

Remember a sum can appear first in an addition equation.

So 26 is the whole and 20 and six of the parts.

On the one underneath we've got 10 add 10 add eight equals 28.

So are three parts to that one and eight is the smallest part.

So we've got 10 and 10 and eight and the whole, the sum is 28.

So very, very well done if you represented those equations correctly using those bar models, excellent work.

And let's move on to the second part of the lesson, which is rearranging addition calculations.

Izzy looks at this bar model now we've got a bar model with 16 as the sum and nine and seven as the addends.

What equations does the bar model represent? Izzy writes two equations, so nine add seven equals 16.

Nine and seven are the addends, the parts, they add up to make the sum.

Izzy could also write seven, add nine equals 16 so she can swap around the order of the addends, seven add nine also equals 16.

Lucas says the addends can be written in any order.

It doesn't make any difference.

They still add up to make the same sum.

Are there other equations represented by the bar model? What do you think? Can you think of any more? Izzy thinks hard about other equations that she could write.

So she's already got nine, seven equals 16 and seven nine equals 16.

I know I could write the sum of the start of the equation says Izzy, clever girl Izzy.

So Izzy could write 16 equals nine and seven so she can swap around the sum and the addends, but the sum at the start of the equation, she could also write 16 equals seven, add nine.

Remember you can swap around those addends as well.

These equations are still correct, says Lucas.

The sum is equal to the addends.

So we've got there four different equations you can write just by using that one bar model.

Izzy looks at this bar model.

I can write four different addition equations using this bar model says Izzy.

So Izzy writes two equations starting with an addend so she could write 20, add 50 equals 70.

She could swap the addends around the other way.

50 add 20 equals 70.

Izzy writes two equations starting with the sum.

So this time she puts the sum first.

So Izzy can write 70 equals 20 add 50, Izzy can also write 70 equals 50 add 20.

So there are four different addition equations we can write just using that one bar model.

Write four different equations using this bar model.

So the bar model, we've got 160 and 40.

Start two equations with an addend, start two equations with the sum.

So pause the video, see if you can have a go at writing four different addition equations using this bar model.

And welcome back, did you manage to write four different equations? Did you start two of them with addends? Did you start two of them with a sum? Let's look to see whether you've got them right.

So you should have written 60, add 40 equals 100.

You should also have written 40, add 60 equals 100 and it doesn't matter which order they appear in.

You should also have started two equations with the sum.

So you should have written 100 equals 60, add 40.

And you should also have written 100 equals 40, add 60.

And don't worry if you've got them in a different order, as long as you've got those four equations, you have got the right answer.

Excellent work, Izzy uses the equation 40, add 50 equals 90.

I'm going to represent the equation using a bar model says Izzy, says equal 90 as the whole as the sum and 40 and 50 as the part.

And again she's remembered the 40 is a smaller part than 50.

So when she's represented those two numbers on the bar model, she's made 50 the bigger part.

Izzy then writes three more addition equations.

So she's got 40 at 50 equals 90 already.

She's going to write three more addition equations.

So she's going to write 50 add 40 equals 90.

That's the other equation starting with the addends.

And then she's got to write two equations starting with the sum.

So 90 equals 40 add 50 and 90 also equals 50 add 40.

Lucas uses the equation 20 add 15 equals 35.

I'm going to represent the equation using a bar model says Lucas, put 35 as the whole as the sum here, 20 goes here and 15 goes here.

And again, Lucas was also remembered 20 is a bigger part than 15.

So 20's got to look like it's bigger on the bar model.

He then writes two more addition equations.

So he is written 35 equals 20, add 15 and he's also written 35 equals 15, add 20.

Both those equations start with a sum.

Which equation has Lucas missed? Can you work out which one is missing? Pause the video and see if you can work out what it is.

And welcome back.

Did you manage to work out the answer? Well you probably spotted that he's written the two that start with a sum, but he's only got one equation that starts with the addends.

So the equation right to the top is 20 outta 15 equals 35.

So the missing equation was 15, add 20 equals 35.

Very well done if you spotted Lucas's missing equation, there are 170 children in a school, 83 are girls and 87 are boys.

And numbers again a little bit bigger now.

We don't need to worry about adding them together 'cause we've already got the answer, we've already got the sum.

But how could Izzy represent this using a bar model? So how would Izzy complete a bar model using that problem? Where's the whole, where's the sum and where are the parts? Here's a bar model.

So when 170 is the whole, that is the sum and 83 and 87 are the parts.

83 add 87 equals 170.

Izzy writes four addition equations.

So she writes 83, add 87 equals 170.

She writes 87, add 83 equals 170.

She writes 170 equals 83 add 87.

So she swapped it around.

So she starts with a sum and then she's got one more to write, doesn't she? So 170 equals 87 add 83.

So she's put those addends in a different order.

Now here's a problem for you to try on your own.

So in Izzy's class there are 17 girls and 15 boys, there are 32 children altogether.

Represent this using a bar model and then write four addition equations.

So draw a bar model and then represent that problem using the bar model.

So you've got the numbers there, 17, 15 and 32.

Which of those is the sum? Which of those are the addends? And then once you've done that, once you've completed the bar model, write four addition equations, pause the video and have a go at solving that problem.

And welcome back, how did you get on? Did you manage to complete the bar model? Did you manage to write for addition equations? Let's see whether you are right.

So let's start off by completing that bar model.

So 32 is the sum, is the whole.

So 32 will go here and here's 17 and 15 is the parts and 17 slightly bigger than 15.

And then we can write our addition equations.

Let's start off with the two parts making the whole, so 17, add 15 equals 32 and 15 add 17 equals 32.

So we just swap those, addends around.

We could also start with a sum 32 equals 17, add 15 and 32 equals 15, add 17.

Very well done if you manage to complete that problem.

If you manage to complete the bar model correctly and you managed to write the four addition equations too.

Excellent work, Izzy looks at this bar model, both addends are missing.

There's a sum but no addends.

The addends could be 100 and 150 says Izzy, there could be lots of different things, couldn't they? But Izzy says they could be 100 and 150.

Izzy writes four addition calculations using these addends.

So 100 add 150 equals 250, 150 add 100 equals 250.

So we've got two addition equations starting with the addends.

Izzy could also write two addition equations starting with a sum.

So 250 equals 100, add 150 and 250 equals 150 add 100.

Look at this bar model, both addends are missing.

What could the addends be? Write four addition equations using these addends.

So think about two addends, two numbers that add up to make half sum 140.

And then can you write four addition equations using those addends.

And there are lots and lots of different possible answers.

So don't worry if you come up to a different answer to the one that Izzy comes up with in a minute.

So pause the video and have a go at solving that problem.

And welcome back, let's see how you got on.

So Izzy says the two addends could be 40 and 100.

You might have used 40 and 100.

40 could go here.

It's a smaller part, 100 would go here.

It doesn't matter if you come up with two different numbers, it really doesn't matter at all.

So Izzy's come up with quite a simple answer.

You may have come up with something slightly more difficult.

And then the four addition equations that we could write using those addends could be 40 add 100 equals 140, 100 add 40 equals 140 140 equals 40 add 100, add 140 equals 100 add 40.

So two equations starting with the addends and two equations starting with the sum.

And very well done if you managed to come up with four addition equations using the sum of 140, excellent work.

And let's move on to our task.

So task B, this is part one of task B.

So write four addition equations to describe each bar model.

So we've got there, the first bar model has got the sum 20 and the parts five and 15.

So can you complete four addition equations to describe that bar model? And the second bar model got the sum 130 and the 90 and 40.

And again, can you write four addition equations to describe it? Let's move on to part two of task B.

So complete each bar model using the equation and then write three more addition equations for each bar model.

That very, very first one we've got seven, add nine equals 16.

So complete the bar model.

So work out where those numbers would go on the bar model.

And then can you write three different edition equations? And this is part three of task B.

So on a minibeast hunt, Izzy counts 23 beetles and Lucas count 17 beetles.

Altogether they count 40 beetles.

Now can you represent this using a bar model? And then write four addition equations to describe that bar model.

That's part three of task B and then part four of task B.

So find two addends to complete each bar model and then write four addition equations.

So the first one has got a sum, 50.

So can you complete that bar model? What two numbers have a sum of 50? And then can you write four addition equations using those numbers? And the second one is 270, so slightly bigger number.

And again, can you complete the bar model and then write four addition equations.

So pause the video and have a go at task B.

And welcome back.

And let's look at how you got on with task B.

Here are the answers for part one of task B.

So write four addition equations.

Let's have a look at this second one, which is slightly harder.

So 130 was the whole and 90 and 40 were the parts.

So you should have come up with these four addition equations.

90 add 40 equals 130, 40 add 90 equals 130, 130 equals 90 add 40 and 130 equals 40 add 90.

And it doesn't matter if your addition equations are in a different order, as long as you've got those four addition equations.

Excellent work.

Here the answers for part two of task B.

So complete each bar model used in the equation.

So again, let's look at the slightly more difficult one.

So 50 equals 15, add 35.

So 50 was the whole and the parts were 15, the smaller part and 35 the larger part.

And you've already got the equation 50 equals 15, add 35.

So the three different addition equations you should have written were 15 add 35 equals 50, 35 add 15 equals 50 and 50 equals 35 add 15.

Very well done if you completed part two of task B.

And here are the answers for part three of task B.

So you should have completed the bar model by putting 40 as the whole and 23 and 17 as the parts.

And then you should have written those four addition equations.

And finally, let's look at part four of task B.

So here are some possible solutions.

There are lots and lots of different ways of making those sums. Lots and lots of different ways of making 150 and lots of ways of making 270 to make 270.

You may have used the numbers 145 and 125 and you should have written four different addition equations using those numbers.

So two, starting with the addends and two starting with the sum.

Very well done for working so hard on task B and excellent work if you got on to part three or part four of task B because there was quite a lot to do there.

So excellent work in today's lesson and hopefully you're feeling much more confident about using bar models and writing addition equations in different ways.

Excellent work today, very, very well done indeed.

Let's move on to our lesson summary.

So addition equations can start with the addends or the sum.

So addends are parts and the sum is the whole.

So you can write addend, add addend equals a sum, or you can write some equals, an addend, add and addend.

So bar models are very useful for representing this and they can really help you work out what those addition calculations are.

And sometimes there are more than two addends.

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", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1705683706%2Fw2o4mbjrj3nnoukocoyp.png&w=750&q=75", "imageKey": "01204473-cbaa-d622-e97e-152692025034/question/a4c49a6157a17194e6d1767b5ae88bf0.png" }, "questionType": "Multiple choice", "correct": [ { "text": "40 + 30 = 70" }, { "text": "70 = 30 + 40" }, { "text": "70 = 30 + 40" } ], "choices": [ { "text": "40 + 30 = 70" }, { "text": "70 = 30 + 40" }, { "text": "30 + 70 = 110" }, { "text": "70 = 30 + 40" } ], "id": "7eb4ad43-1cf2-15af-2af4-90e5080130f4", "lessonId": "bb62b4ec-87e5-b5ba-3288-c1db0eb6d8ea" }, { "type": "Question", "question": { "text": "Look at the bar model. What is the missing sum? 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", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1705683707%2Fws1cstwgyzonjdp51uzn.png&w=750&q=75", "imageKey": "01204473-cbaa-d622-e97e-152692025034/question/2862a1dc74249d7510dcf454a27b4785.png" }, "questionType": "Multiple choice", "correct": [ { "text": "11 and 13" }, { "text": "12 and 12" } ], "choices": [ { "text": "9 and 14" }, { "text": "11 and 13" }, { "text": "12 and 12" }, { "text": "15 and 10" } ], "id": "071563b6-809f-0978-e3dd-47b94074018b", "lessonId": "bb62b4ec-87e5-b5ba-3288-c1db0eb6d8ea" }, { "type": "Question", "question": { "text": "Which pairs of addends could complete the bar model? 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