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I can rearrange subtraction 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 subtrahend and difference are parts and the minuend is the whole.
Subtraction equations can start with the minuend or the difference.

Common misconception

Pupils may find it more challenging to use equations starting with the difference, or may make mistakes writing these.

Emphasise the need for balance in equations. Both sides of the equation must be equal. Equations can start with the minuend or the difference.

Keywords

Minuend - The minuend is the number being subtracted from.
Subtrahend - A subtrahend is a number subtracted from another.
Difference - The difference is the result after subtracting one number from another.

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

Here is our learning outcome.

I can rearrange subtraction equations, and here are our keywords, so three keywords today.

I'm going to say each keyword, can you repeat it back? So the first keyword is minuend.

The next keyword is subtrahend, and the next keyword is difference.

Let's take a look at what those words mean.

So the minuend is the number being subtracted from.

A subtrahend is a number subtracted from another, and the difference is the result after subtracting one number from another.

So in the subtraction calculation, the subtraction equation, 7 - 3 = 4, seven is the minuend, that's the number being subtracted from.

Three is the subtrahend, that's the number that's been subtracted, and four is the difference.

That's the result after the subtrahend is subtracted from the minuend.

So it sounds really complicated, but actually, it's quite simple.

And here is our lesson outline.

So the first part of the lesson is understanding minuend as a whole.

And the second part of the lesson is rearranging subtraction equations.

Let's get started.

In this lesson, you will meet Lucas and Izzy.

Lucas is using bar models to represent subtraction equations.

\"The whole in a subtraction equation is called the minuend,\" says Lucas.

So the bar model there shows a whole and two parts.

Says the minuend, the minuend is the whole.

\"The parts are called the subtrahend and the difference,\" says Izzy.

So the subtrahend is the part we are subtracting, and the difference is the other part.

\"The subtrahend and the difference can be swapped around,\" says Izzy.

So we can move those two parts around so we'll bear the difference and the subtrahend.

There's still two parts and they still make the whole.

Lucas represents the equation, 17 - 5 = 12.

There's a bar model with minuend, subtrahend and difference on it.

So the minuend is the whole, remember, and the subtrahend and the difference are both parts.

So in this equation, 17 - 5 = 12.

Where's the minuend? Where's the subtrahend and where is the difference? Well, the minuend is 17, the subtrahend is five, that's the number we're subtracting, and the difference is 12.

That's the result after we subtract the subtrahend from the minuend.

And let's look at a representation using 10s frames.

So we start with 17, we can subtract five, so subtract five, and the difference is 12.

Lucas uses a bar model to represent the equation, 17 - 5 = 12.

Here's our bar model.

So 17 is the minuend.

The 17 goes here on our bar model, that's the whole.

The subtrahend is five and the difference is 12.

So five goes here, that's a smaller part, that's the part we're subtracting, and here's 12.

That's how you would represent the equation, 17 - 5 = 12, as a bar model.

Lucas uses the bar model to represent a 50 - 40 = 10.

So the minuend is 50, so 50 is the whole, the subtrahend is 40 and the difference is 10.

So those are both parts with 40 being the bigger part.

So 40 is a larger part than 10.

So the minuend subtract the subtrahend equals the difference.

Use the bar model to represent 100 - 30 = 70.

So where would those three numbers be put on the bar model? Pause the video and see if you can complete that bar model using the equation, 100 - 30 = 70.

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

So the minuend is 100, so the minuend goes to the top, that is our whole.

The subtrahend is 30 and the difference is 70.

So there's two parts to our bar model underneath, smaller part is 30 and the larger part is 70.

And that's how you'll complete the bar model using the equation.

So 30 is a smaller part than 70.

So remember, the minuend subtract the subtrahend equals difference.

Lucas and Izzy explore the relationship between addition and subtraction.

So Lucas starts by using a bar model to represent 30 + 60 = 90.

There's our bar model.

Here's 30 and here's 60, they're the two parts, they're the two addends that add up to make the whole, add up to make the sum, the sum is 90.

So the whole is 90.

This is the sum.

The whole can also be the minuend.

So Izzy writes two subtraction calculations using the bar model.

So Lucas has used 30 and 60 equals 90 to complete the bar model.

Izzy is now going to think of two subtraction equations that could also describe the bar model.

So you could have 90 - 60 = 30.

We could also have 90 - 30 = 60.

Remember, we can swap around the subtrahend and the difference.

Lucas uses the bar model to represent 40 + 15 = 55.

So 40 is one of the parts, 15 is the other part, that's the smaller part, and 55 is the sum, is the whole.

The whole is 55.

This is the sum.

The whole can also be the minuend.

Now, can you write two subtraction calculations starting with the minuend? So pause the video and see if you can work out those two subtraction equations that you could write using those same three numbers.

And welcome back.

How did you get on? Did you manage to write both equations? Let's have a look to see if you wrote them correctly.

So the first one you might have written is 55 - 40 = 15.

You should also have written 55 - 15 = 40, so both starting with a minuend subtracting one of the parts which leaves you with the other part.

Very well done if you've got both of those correct.

So let's move on to task A.

So the first part of task A, you're going to use bar models to represent each equation.

So it's that first equation, we've got 50 - 20 = 30.

How would you complete the bar model? Where would the 50 go on the bar model? Where would the 20 go? Where would the 30 go? And don't forget to think about those different parts and think about if one part is bigger than the other whereabouts it would go on the bar model.

So that's part one of task A.

Part two of task A is use bar models to represent each equation.

Then complete two subtraction equations for each bar model.

So for the first equation, we've got 55 + 5 = 60.

How would you complete the bar model using those three numbers? And then can you write two subtraction equations, both beginning with the minuend, who would also use those same three numbers? So pause the video and have a go at task A.

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

So the answers for part one of task A are there.

Okay, so the first equation, we've got is 50 - 20 = 30.

So 50 was the whole and 20 and 30 were the parts, and 20 is a smaller part than 30.

That's how you should have completed the bar model.

So you got the answers for the other bar models up there as well.

And then let's have a look at part two.

So use bar models to represent each equation and then complete two subtraction equations.

So that first equation, we've got 55 + 5 = 60.

So 60 was the whole and 55 and five are the parts, and 55 is a much larger part than five.

And then the two equations you should have written were 60 - 5 = 55 and 60 - 55 = 5.

So very, very well done if you got those correct.

And let's move on to the second part of the lesson.

So the second part of the lesson is rearranging subtraction equations.

Lucas and Izzy rearrange subtraction equations.

\"I know that 10 - 4 = 6,\" says Lucas, so it's 10 - 4 = 6.

\"The equals sign means the equation is balanced.

I can change the order,\" says Izzy.

So we've got 10 - 4 = 6 and they balance each other out.

So 10 - 4 is equal to six.

We can change the order around.

We can change it to 6 = 10 - 4.

They are still equal, they still balance each other.

So 6 = 10 - 4.

So we've actually got there the difference first, the difference equals the minuend subtract the subtrahend.

The bar model shows the equation 60 - 40 = 20.

So we've got the number 60 and 40 and 20 are the parts.

What other subtraction equations could Lucas write to describe that bar model? Or 20 could be the subtrahend and 40 could be the difference.

So we could have 60 - 20 = 40.

Yeah, Lucas is right.

60 - 20 = 40.

The minuend subtract the subtrahend equals a difference.

There's two different ways of writing a subtraction equation starting with the minuend.

Can Lucas write any more equations using those same three numbers? I can rearrange the equation.

I know that 40 is equal to 60 - 20.

So 60 - 20 = 40, we can swap that around and 40 is also equal to 60 - 20.

But Lucas could write the equation, 40 = 60 - 20.

The difference equals the minuend subtract the subtrahend.

Now, here's one to try on your own.

Find the missing equation.

We're still using the same three numbers, 60 and 40 and 20.

So the minuend subtract the subtrahend equals a difference.

We've got there our two subtraction equations both starting with the minuend.

But the difference can also equal the minuend subtract the subtrahend.

What other subtraction equation can you you find? How else could you rearrange those numbers to make a different equation? So pause the video and see if you can work out the missing subtraction equation.

And welcome back.

Did you manage to find that last equation? Let's have look to see if you were right.

So we've got the two starting with the minuend.

We've got one missing that starts with the difference.

We've got the difference being 40.

The difference can also be 20.

So the last equation you could have is 20 is equal to 60 - 40.

Very well done if you found that missing subtraction equation.

Lucas uses this bar model.

\"I'm going to write four subtraction equations,\" says Lucas.

So we've got 12 - 4 = 8, that could be one of our equations.

We can also have 12 - 8 = 4.

That can be our other equation.

So they're both starting with the minuend.

So the minuend subtract to subtrahend equals the difference.

We can swap around the equation, 12 - 4 = 8 to become 8 = 12 - 4.

We can swap around 12 - 8 = 4 to become four is equal to 12 - 8.

Izzy uses the equation 80 + 40 = 120.

I'm going to use a bar model to help me write four subtraction equations.

So Izzy has the three numbers, 80 and 40 and 120, and she's going to use a bar model to represent that equation.

So 120 is the whole and 80 and 40 are the parts.

So remember, the 120 can be the sum or the subtrahend, it's the whole.

So she could have 120 - 80 = 40.

She could also have 120 - 40 = 80.

We can swap around the subtrahend and the difference.

Izzy can also rearrange those equations as well.

So 40 is equal to 120 - 80 and 80 is equal to 120 - 40.

Lucas uses this bar model.

So we've got the numbers 150, 80 and 70.

\"I'm going to write a subtraction equation,\" says Lucas, using those three numbers, using that bar model to help him.

150 = 80 - 70.

Is Lucas correct? What do you think? Has he written down a correct equation? Pause the video and see if you can work out the answer.

And welcome back.

What do you think? Is Lucas correct? Let's find out.

No, he's not right.

Sorry, Lucas, but that's not right.

The difference between 80 and 70 is not 150.

And the calculation that Lucas has written is 150 is equal to 80 - 70.

80 - 70 = 10, 10 is equal to 80 - 70, not 150.

Lucas could have written down 80 = 150 - 70.

80 is the difference between 150 and 70.

Lucas could have instead written down 70 = 150 - 80.

So 70 is the difference between 150 and 80.

So be really careful when you're writing those equations, particularly the ones where you're starting with the difference, they get a little bit difficult.

And you may have spotted there the large number, the minuend, the whole, is actually in the middle of the equation, that's one to spot.

Lucas and Izzy score 70 points in a computer game.

Lucas scores 40 points and Izzy scores 30 points.

How could I represent this using the bar model? What's the whole or the two parts? For the whole is 70, that's the number of points they score altogether.

40 is the number of points that Lucas has scored and 30 is the number of points that Izzy has scored.

Izzy writes four subtraction equations using that bar model.

What would she write? Or she could have 70, the whole, subtract 30 equals 40.

70 points subtract Izzy's points ends up with Lucas's points.

We could have 40 is equal to 70 - 30, we just rearrange that subtraction equation.

We could also have 70 - 40 = 30, so we swapped around the difference and the subtrahend.

Could also have 30 is equal to 70 - 40, we've just rearranged the whole equation.

Here's one to try on your own.

So Lucas and Izzy scored 55 points in the computer game.

This time, Lucas scores 25 points and Izzy scores 30 points.

Represent this using a bar model then write four subtraction equations.

So have a go trying to draw out a bar model, think about where those numbers will go on the bar model.

And then can you write four subtraction equations to describe that bar model? So pause the video and have a go at that problem.

And welcome back.

How did you get on? Let's have a look, see if you've got it right.

So first of all, the bar model should look like this.

We've got 55 is the whole, 25 is the smaller part and 30 is the larger part.

And then let's try and write our four subtraction equations.

So he could have 55 - 25 = 30, we could have 30 is equal to 55 - 25.

We could also have 55 - 30 = 25.

And the last equation could be starting with the difference, so 25 = 55 - 30.

So we've got two subtraction equations starting with the minuend, starting with the whole, and we've got two subtraction equations starting with the difference.

Very well done if you found all four equations.

Izzy thinks of two numbers that have a sum of 130.

So Izzy's looking for two numbers that add up to make 130.

So the addends could be 90 and 40.

So 90 is larger than 40, so 90 would go here and 40 could go here.

So the whole can be the sum or the minuend in an equation.

So Izzy writes four subtraction equations using the bar model.

What would she write? Well, she could have 130 - 90 = 40, so the whole subtract one of the parts equals the other part.

She could have 130 - 40 = 90.

So she's just changed around the subtrahend and the difference, just reordered the calculation.

She could reorder the calculation, rearrange the calculation to start with the difference, so 40 = 130 - 90, or she could have 90 = 130 - 40.

Find another way of completing the bar model.

So we've still got the whole as being 130, what could the addends be? So can you think of two numbers that add up to make 130? And then can you write four subtraction equations? So four equations to describe the bar model that you have completed? So pause the video and have a go at that problem.

And again, welcome back.

How did you get on? Did you manage to complete that problem? Let's have a look.

Now, there's lots and lots of different answers to this one.

So don't worry if you came up with different numbers to the ones that Izzy has used.

So Izzy says, \"You might have used 20 and 110.\" So 20 is a smaller part, 110 is the larger part.

And now, Izzy's gonna come up with four subtraction equations.

So two starting with the minuend starting with the whole, so 130 - 20 = 110, and 130 - 110 = 20, and two starting with a difference.

So 20 = 130 - 110 and 110 = 130 - 20.

So very well done if you manage to come up with four different subtraction equations to describe your bar model.

And let's move on to task B.

So for the first part of task B, you're going to write four subtraction equations for each bar model.

So the numbers are given to you, you've got to work out what the four subtraction equations would be.

So, for example, you've got there 25 and 10 and 15.

So 25 is the whole and 10 and 15 are the parts.

So you've got to have two equations starting with the minuend, starting with the whole, and two equations starting with the difference.

That's part one of task B.

Part two of task B, complete the bar model using the addition equation and then write four subtraction equations shown by the bar model.

So the equation is 55 + 25 = 80.

Where would those numbers go on the bar model? Which one's the whole, which ones are the parts? And then can you write four subtraction equations using those same three numbers? That's part two of task B.

Part three of task B, Izzy organises a cake sale, she brings 45 cakes and sells 41 of them.

Represent this using a bar model then write four matching subtraction equations.

Okay, so that's part three of task B.

And then part four of task B, there's a lot of work to do in task B, isn't there? So find two numbers to complete each bar model and then write four subtraction equations shown by the bar model.

So this is one where there could be lots and lots of possible answers, but you've gotta come up with two numbers that equal 230.

And you've also gotta come up with two numbers that add together to make 340.

And then using the numbers you come up with, can you write four subtraction equations? So pause the video and have a go at task B.

And welcome back.

Let's see how you got on.

Let's look at those answers for task B.

So write four subtraction equations for each bar model.

So our first bar model, we've got 25 and 10 and 15.

So we've got underneath the four subtraction equations you should have come up with.

And don't worry if you put 'em in a slightly different order, that's not important.

Okay, the important thing is you've got the same four subtraction equations, okay? So that's part one of task B.

Here's part two of task B.

So complete the bar model using the addition equation.

So you should have put 80 as the whole and 55 and 25 as the parts, and hopefully, you even got 55 as the larger part.

And underneath are the four subtraction equations that you should have written.

So two starting with the whole and two starting with the difference.

So very well done if you've got that part correct.

Here's part three, so it's our word problem problem.

So Izzy organises a cake sale.

She brings 45 cakes, so that's the whole, and sells 41 of them.

So 41 was one of the parts and the other part was four.

And underneath are the four subtraction equations that you should have written using those three numbers.

And lastly, here are some possible solutions for part four of task B.

And again, you may have used completely different numbers to these, but you've got to make sure the two numbers add up to make the sum.

And then you've got to make sure you use the same three numbers in each subtraction equation.

So very well done if you got onto part four of task B 'cause there was quite a lot to do, and very well done if you came up with those four subtraction equations to describe each of those bar models.

And excellent work today.

And hopefully, you're feeling much more confident about rearranging subtraction equations.

And let's move on to our lesson summary.

So our lesson summary is the subtrahend and difference are parts and the minuend is the whole.

Subtraction equations can start with the minuend or the difference.

So we can have the whole, the minuend, subtract the subtrahend equals a difference and the difference equals the minuend subtract the subtrahend.

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", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1705683711%2Fj9cc7y2dncu4daxluu0n.png&w=750&q=75", "imageKey": "9e8a516e-a887-dbe2-d6ab-ac15810c53a5/question/77a6a6a12d7a05ebadcea0d361280836.png" }, "questionType": "Multiple choice", "correct": [ { "text": "30 and 30" }, { "text": "25 and 35" }, { "text": "10 and 50" } ], "choices": [ { "text": "30 and 30" }, { "text": "25 and 35" }, { "text": "20 and 45" }, { "text": "10 and 50" } ], "id": "e6ece1ad-afc2-2948-539a-56dd8b4556b7", "lessonId": "e5044c99-acf9-5c1d-666a-2f7d4457175e" }, { "type": "Question", "question": { "text": "Which equations are equal to 50? " }, "questionType": "Multiple choice", "correct": [ { "text": "25 + 25 =" }, { "text": "100 − 50 =" } ], "choices": [ { "text": "70 − 10 =" }, { "text": "25 + 25 =" }, { "text": "100 − 50 =" }, { "text": "20 + 20 + 20 =" } ], "id": "c749ad33-1105-c599-16ce-aec45bd8f966", "lessonId": "e5044c99-acf9-5c1d-666a-2f7d4457175e" } ], "lessonId": "e5044c99-acf9-5c1d-666a-2f7d4457175e", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 3", "topic": null, "unit": "Understand additive relationships and apply them to rearrange equations", "lessonCount": "10", "age": [ 7, 8 ], "gradeId": "age_7_8", "gradeStage": "Key Stage 2", "lesson": "Use the additive relationship to rearrange subtraction equations" } }, { "id": "a1041a8a-cbaa-0045-e087-03d91da95b18", "type": "Resource", "resourceType": "Quiz", "title": "Use the additive relationship to rearrange subtraction equations", "quizType": "Exit quiz", "items": [ { "type": "Question", "question": { "text": "Which number is the minuend in this equation: 55 − 20 = 35" }, "questionType": "Multiple choice", "correct": [ { "text": "55" } ], "choices": [ { "text": "55" }, { "text": "35" }, { "text": "20" } ], "id": "78bf5ba4-17cb-81b5-cdd5-78263294362c", "lessonId": "e5044c99-acf9-5c1d-666a-2f7d4457175e" }, { "type": "Question", "question": { "text": "What is the difference between 11 and 9? " }, "questionType": "Short answer", "correct": [ { "text": "2" }, { "text": "two" } ], "id": "828d1dac-2a7e-77c3-15d7-76ed80221e93", "lessonId": "e5044c99-acf9-5c1d-666a-2f7d4457175e" }, { "type": "Question", "question": { "text": "Which equations are represented by the bar model? ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1705683707%2Fr11ziv9rggdwuxgqkru4.png&w=750&q=75", "imageKey": "a1041a8a-cbaa-0045-e087-03d91da95b18/question/acb826bb2c43fcbb736f9b2cdf77f1c1.png" }, "questionType": "Multiple choice", "correct": [ { "text": "44 − 20 = 24" }, { "text": "20 = 44 − 24" } ], "choices": [ { "text": "44 − 20 = 24" }, { "text": "24 − 44 = 20" }, { "text": "20 = 44 − 24" }, { "text": "44 = 24 − 20" } ], "id": "72e1e229-2aad-d00f-ceef-59a6a0bfe365", "lessonId": "e5044c99-acf9-5c1d-666a-2f7d4457175e" }, { "type": "Question", "question": { "text": "Look at the bar model. What part is missing? ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1705683708%2Fwfbhrovhjwiqj0wqyxhf.png&w=750&q=75", "imageKey": "a1041a8a-cbaa-0045-e087-03d91da95b18/question/640db166a7c17577db36baf770f5394e.png" }, "questionType": "Short answer", "correct": [ { "text": "5" }, { "text": "five" } ], "id": "7b60606b-3cea-f2ee-49cd-a2b4b7638da8", "lessonId": "e5044c99-acf9-5c1d-666a-2f7d4457175e" }, { "type": "Question", "question": { "text": "Izzy writes subtraction equations represented by the bar model. Which equation is NOT correct? ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1705683709%2Fwm3mpda2njt1x9kdow8h.png&w=750&q=75", "imageKey": "a1041a8a-cbaa-0045-e087-03d91da95b18/question/a12ab0fea36a5143d1a5455a461c61aa.png" }, "questionType": "Multiple choice", "correct": [ { "text": "32 − 28 = 60" } ], "choices": [ { "text": "60 − 32 = 28" }, { "text": "32 = 60 − 28" }, { "text": "28 = 60 − 32" }, { "text": "32 − 28 = 60" } ], "id": "a54957c6-04f4-5221-d684-eed0cba6eb3a", "lessonId": "e5044c99-acf9-5c1d-666a-2f7d4457175e" }, { "type": "Question", "question": { "text": "Match up the addition and subtraction equations. 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