Use the Language of Minuend, Subtrahend, and Difference

Key Stage 2

Maths

Extending calculation strategies and additive reasoning

﻿Hello, again, my name is Ms. Woodall, and I'm really looking forward to taking you through this lesson. For this lesson, you will need a pencil and paper. It may be helpful if you had some cubes of two different colours or some Lego or some oranges and apples for this lesson too. If you need to pause the video to go and get these items, please do that now. Do you remember the practise activity from last time? I asked you to complete this bus timetable. Each time, the journey from school to the bus station was going to take 15 minutes. Let's have a look at my answers. The bus left school at 8:45 AM, so arrived at the bus station at 9:00 AM. The journey time was given to us as 15 minutes. On the next question, we have the time the bus arrived at the bus station, so we needed to subtract 15 minutes. We knew the journey time was 15 minutes, therefore the bus left school at 9:15 AM. The next one was a little trickier. The bus left school at 10 past 10, so we had to add 15 minutes to get to 10:25 AM. Finally, I set the challenge for you to think of your own times with a difference of 15 minutes. Did you manage it? I thought about the end of the school day. So at 3:30, we would leave the school and arrive at the bus station at 3:45 or 1545 in 24 hour clock. The difference in the journey time always stayed the same as 15 minutes. Well done if you manage that practise activity. In this lesson, we are going to use some of the vocabulary of subtraction, which you have used before. We are going to use minuend, subtrahend, and difference. There are four apples and one orange. What is the difference between the number of apples and the number of oranges? Four subtract one is three. So the difference between the number of apples and the number of oranges is three. If we look at the number sentence, what is the minuend represented in this question? The minuend is the apples, the four apples. What is the subtrahend represented in this question? The subtrahend is the oranges, one orange. What is the difference represented in this question? The difference is three. Let's think back to some previous learning. This was the representation that you explored with Mr. Whitehead. How are we using this to find the difference? What is the minuend? Yes, the minuend is six. What is the subtrahend? The subtrahend is four. And what's the difference? Six subtract four is two, so the difference is two. Can you write a number sentence for this representation on your piece of paper? Excellent. Let's have a look together. The minuend was six, the subtrahend was four, and the difference was two. Six subtract four equals two. Well done. Let's go back and think about our apples and oranges. This time, instead of a picture of an apple or an orange, I'm going to use Multilink cubes on screen. If you have any cubes or Lego bricks of the same size, you could use them as a piece of concrete equipment to help you to see the maps. Let's have a look then. So we've got four subtract one equals three. So we have four red cubes, we have one blue cube. So the difference between red and blue cubes is three. The minuend was four, the subtrahend was one and the difference was three. Can you see that there are three fewer blue cubes than red cubes? There were three fewer oranges than there were apples. Well done. Let's have a look at another example. This time, I've got five red cubes and two blue cubes. What's the difference between the red and the blue cubes? Let's think about this as a minuend subtrahend difference equation. So we've got five as the minuend, two as the subtrahend, and therefore the difference is three. We can see that the difference hasn't changed. Last time, we had four red cubes and one blue cube, and the difference was three. This time, we've added one to minuend and one to the subtrahend, so we've got five minus two, but the difference is still three. Can you have a go now at writing the equation to match this picture. We've got six red cubes and three blue cubes. What's the difference? Have a go at drawing that on your piece of paper and write the equation. Well done. There are six red cubes and there are three blue cubes. So the difference is three. There are three fewer blue cubes than there are red cubes. There are three more red cubes than there are blue cubes. We can see the three and the difference shown by the arrow here. Well done. What about in this example now? There are seven red cubes and there are four blue cubes. What's the difference? I've written the equation seven subtract four equals three. Do you think you could tell me which is the minuend, which is the subtrahend, and which is the difference? Well done. The minuend is the seven red cubes, the subtrahend is the four blue cubes, and the difference is shown by the arrow, there's the three. There are three fewer blue cubes than there are red. There are three more red cubes than there are blue. Well done. Let's look at all these representations and calculations together now. Four subtract one is three. Five subtract two is three. Six subtract three is three. And finally seven subtract four is three. What's the same about all of these calculations? Yes, that's right, they all have a difference of three. And we can see there are three more red cubes on each representation. What's the difference then between all of these calculations, what's changing? That's right, the minuend and the subtrahend are changing by one each time. The minuend in the first example is four and that becomes five and then six and then seven. The subtrahend in the first example is one, and that becomes two and three and then four. Could we create a stem sentence for what we have discovered? Have a good on your piece of paper and pause the video now, see if you can come up with a sentence to what's happening. Did you come up with a sentence similar to mine? I've added something to both the minuend and the subtrahend, so the difference stays the same. What have we added each time? That's right, we've added one. Let's see if we can say the same stem sentence together. I've added one to both the minuend on the sentence, so the difference stays the same. Have a go repeating that now. Well done. Let's have a look at the representation with the equations and link all of this to our new stem sentences. So there are four red cubes and one blue cube. Four subtract one is three. The difference is three. Now, if I add one to the minuend and one to the subtrahend, five subtract two is three. The difference stays the same. If I add another one to the minuend and one to the subtrahend, six subtract three is three. The difference stays the same each time. And finally, another one to the minuend and one to the subtrahend. Can you write the equation? That's right, seven subtract four is still three. Well done. We know you know the answers to these easy calculations and we can do these straightaway because we understand maths so well. But we need to be able to see the math and understand the structure so that when we end up dealing with bigger numbers or more complicated calculations, we can still feel as confident. Now, how else could we represent these calculations? Think about the work you completed with Mr. Whitehead to help. That's right, a number line would be a good way. Let's have a look. We've got a number line zero to 10, and marked on that is seven and four. I wonder if you could write the calculation that is being shown by this number line. Pause the video and have a go. Well done. Seven subtract four equals three, that was what this number line was showing. Now, why don't you pause the video and see if you can draw a number line for all the other calculations, four subtract one is three, five subtract two is three, and six subtract three is three. Have a go now. Well done. Is this what your number lines look like? Seven subtract four was three, that was the example that we had on the previous slide. Did you draw six subtract three is three, five subtract two is three, and four subtract one is three? Well done if you did. Now in each of these calculations, let's think about what's happening with the minuend and the subtrahend. So the first calculation we had was seven subtract four is three. The next one we had was six subtract three is three. What happened to the minuend and the subtrahend just then? That's right, they were both reduced by one. Let's have a look at the next one. Five subtract two is three. Did you see the minuend changed by one and the subtrahend changed by one? What about this time? Four subtract one is three. Again, the minuend the subtrahend changed by the same and therefore the difference stayed the same. Well done. So our first stem sentence we had was I've added something to both the minuend and the subtrahend, so the difference stayed the same. We added one each time to the minuend subtrahend, so the difference stayed the same. In that last example, we subtracted one from both the minuend and the subtrahend, so the different stayed the same. I wonder if we could join these stem sentences to make a generalisation. Have a think now and pause the video. How could we join these stem sentences to create a generalisation. Well done. If the minuend and the subtrahend changed by the same amount, the difference stays the same, so it doesn't matter if we're adding one, as long as we do it to the minuend the subtrahend, the different stays the same. Or if we subtract one to the minuend and the subtrahend, the different stays the same. Can you repeat this generalisation with me? If the minuend and the subtrahend are changed by the same amount, the difference stays the same. Well done. Let's have a look at applying our understanding now to a problem. Sam and Ellie are playing a game. Sam had 83 points and Ellie had 94 points, that's 11 more than Sam. Sam and Ellie both scored another 27 points each. How many ballpoints does Ellie have compared to Sam now? Why don't you pause the video and have a go at working out this problem? Think about that generalisation that we just made together. If the minuend of the subtrahend are changed by the same amount, the difference stays the same. Have a go now. Well done. Let's have a look at how I solved the problem. Ellie had 94 points to start with and Sam had 83 points. That meant we had a difference of 11. Now, both of them scored 27 more. And because I know that if I change the minuend and the subtrahend by the same amount, the difference will stay the same. So therefore, I know that Ellie will still have 11 more points than Sam. If I wanted to work it out, Ellie had 121 point, Sam had 110 points, which has a difference of 11. Well done if you've got the answer too. Let's have a look at a missing number problem now. We've been given the fact at the top, 10 subtract seven has a difference of three. Let's use our stem sentence. If the minuend and the subtrahend changed by the same amount, the different stays the same, and see if we can work out these missing number problems. Why don't you pause the video and have a little go yourself now? Off you go. I'm going to look at the next one, 12 subtract nine equals something. I'm going to look at what we've done to the minuend and what we've done to the subtrahend to see if the difference will stay the same. The minuend was 10 and it's now 12, so it had an increase of two. The subtrahend was seven and now it's nine, so that's also had an increase of two. And therefore, if the minuend and the subtrahend are changed by the same amount, the difference stays the same, so I know that that missing number will be three. Let's look at the next one. The minuend again, has been increased by two. The subtrahend has also been increased by two. So therefore, we know that the difference will stay the same. The next one is a little bit different. The minuend has been increased by two, the subtrahend, we don't have, but we know that the difference has stayed the same. So therefore we know that the minuend and subtrahend both have to be increased by the same amount. So the minuend was increased by two, the subtrahend needs to be increased by two to give 13 so that the difference stays the same. The next one is similar. The minuend has been increased by two to give 18. So the subtrahend, we haven't got yet, and the difference has stayed the same as three. So we need to increase the subtrahend by the same amount as the minuend. So we'll increase that by two. 18 subtract 15 has a difference of three. The next one, we have a missing minuend, but we have the subtrahend, which has been increased from 15 to 17, but the difference has stayed the same as three. And using our generalisation, if the minuend and the subtrahend are changed by the same amount, then the different stays the same. Therefore, we need to increase the minuend by two. 20 subtract 17 equals three. And finally, the subtrahend has increased by two from 17 to 19, leaving a difference of three, so we need to increase the minuend by two. So 20 increased by two gives us 22. Now, we could just look at the first fact and the last fact, and we could have worked out that from seven to 19, we've increased that by 12, and therefore 10 increased by 12 gives us 22. So we didn't necessarily need all those other facts in order to help us work out. But well done If you've got there. It's your turn now. Demonstrate your understanding by filling in the missing numbers. Why not have a go at creating your own related to missing number calculation for someone else to fill in, maybe somebody at home. And if you're ready for a real challenge, answer the question on Felicity had red and blue marbles, and that will really impress us. Remember, if the minuend of the subtrahend are changed by the same amount, the difference stays the same. Well done for your learning today. Hope to see you again soon.

Use the Language of Minuend, Subtrahend, and Difference

Use the Language of Minuend, Subtrahend, and Difference

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UnitMaths / Extending calculation strategies and additive reasoning

Maths