Video: Contexts where the Minuend is Kept the Same, and the Subtrahend Increases

﻿Hi year five and six. My name is Mrs. Grinds, and I'm here to teach your maths lesson today. You'll need your practise activity from your last lesson, a pen or pencil and some paper, press pause go and find what you need and then we can begin the lesson. In the last session you were left with this practise slide. How did you get on with it? Let's look at number one first of all. Here we had to fill in the missing symbols. Do I need to work out all of the calculations in order to do this? No, you're right I don't need to, I can use what I know. The more we subtract, the less we're left with. The less we subtract, the more we are left with. Let's have a look at the first set of calculations, well actually before we do that, what did you notice about the calculations? That's right, the ones on the left-hand side are all the same 87 subtract 33. What do you notice about the ones on the right-hand side? That's right, the subtrahend is increasing by 10 each time. We had the generalisation in the last session, the more we subtract, the less we're left with and the less we subtract, the more we are left with. Let's say it together. The more we subtract, the less we're left with, the less we subtract, the more we are left with. If I look at the first set of calculations, I can see that the subtrahend is 10 more in the calculation on the left than in the calculation on the right. I know that the more we subtract, the less we're left with therefore 87 subtract 33 is less than 87 subtract 23, as I'm subtracting more from the subtrahend in the calculation on the left. So the less I'm left with. So I would insert the less than symbol. Let me just get it to come up. There we go. 87 subtract 33 is less than 87 subtract 23. Okay, let's look at the next set of calculations. Ah, this time I can see that the calculations are the same either side the minuend is the same in both calculations, 87 and the subtrahend is the same in both calculations 33. So of course the difference in both calculations will also be the same. So I'm going to insert the equal symbol. 87 subtract 33 is equal to 87 subtract 33. Okay, let's look at the final one. On the final set of calculations I can see that this time the subtrahend is 10 more on the calculation on the right. And I know the more we subtract the less we're left with. So I know that this calculation would be less than 87 subtract 33 as the subtrahend is more. So this time I'm going to insert the greater than symbol. 87 subtract 33 is greater than 87 subtract 43. How did you get on with those ones? Did you do okay? Excellent, well done. Okay let's look at number two. What have we to do this time? Ah, this time you've got to be the teacher and spot the mistake. Is 143 subtract 55 less than 143 subtract 35? Yes, that's right. I know this is correct because the minuends are the same and the calculations 143, but in the calculation on the left, 143 subtract 55 you're subtracting more. And I know that the more we subtract, the less we are left with. So that one's correct. I can add a tick there. Okay let's look at the one underneath. The next question says 20.3 subtract 0.7 is less than 20.3 subtract one. I know this is incorrect and a mistake as both calculations have the same minuend 20.3, but 0.7 is less than one. And the less we subtract, the more we're left with. So this should be 20.3 subtract 0.7 is greater than 20.3 subtract one. So this is actually incorrect. This is the mistake. Did you manage to spot that mistake there? Okay, let's look at the challenge. What's the same and what is the different in this one? Look carefully. Yep, that's right. Both the minuends are the same, 7/8 and we're looking at the fractions and the subtrahend I can see that they both have a numerator one, but one has a denominator of two and one has a denominator of four. I know that the bigger the denominator, the smaller, the fraction, therefore half is bigger than one quarter. The more we subtract the less we're left with so 7/8 subtract 1/2 is less than 7/8 subtract 1/4. So I'm going to insert my symbol there, less than to make that correct. I hope you found those okay. Okay, today, we're going to apply what we have learned in the previous lesson. Do you remember what it was? Of course you do, you've just been saying it lots and lots. The more we subtract the less we're left with, the less we subtracts, the more we're left with. Let's look at this problem here. Harvey's buying groceries, the bill is 98 pounds, but he thinks he has a voucher for 20 pounds off. So he'll only have to pay 78 pounds, 98 pounds subtract 20 pounds equals 78 pounds. But Harvey's voucher is actually worth 30 pounds. Is he going to pay more or less for his groceries? What do you think? Let's put it on a number line to help us work this out. So, first of all, I've got my minuend here 98, because the bill to start with is 98 pounds. He thinks he's got a voucher for 20 pounds so my subtrahend 20 is here. Let's work out what the difference would be. So he thinks he's going to have to pay 78 pounds. That would be the difference. So 98 subtract 20 would be 78 but actually his voucher is worth 30 pounds. So we're going to do 98 subtract 30. Although actually, I don't even need to do that calculation I can use what I've already got here. So I know my minuend is the same. It's still 98 pounds is the total of the bill. But this time the voucher is 30 pounds. So I know the difference is going to be 68 pounds. Now I knew that really quickly without having to do the calculation, because think about what is the same and what is different between these calculations? What do you notice? Have a closer look. That's right, the minuends are the same they're both 98, since 98 pounds is the total of the bill. But our subtrahend here is 20, 20 pounds voucher. And the subtrahend here is 30 because it was a 30 pound voucher. There's a 10 pound difference between the vouchers. I've kept the minuend the same and I add mm to the subtrahend, so I must subtract mm from the difference. So how much, how much have we added to the subtrahend? So if I've got 20 pound voucher, but then it's actually a 30 pound voucher we've added 10 pounds, haven't we? To the subtrahend. So let's put that into our sentence stem. I've kept the minuend the same, and I did 10 to the subtrahend so I must subtract 10 from the difference. So I know that he's actually going to be paying 68 pounds. So is he paying more or less with a 30 pound voucher? Yup, you're right. He's actually going to be paying less, isn't he? If he's now paying 68 pounds. If we put it onto a bar model, I can see I've still got my minuend of 98 pounds at the top here 'cause that's the total he has to pay. He thought he had a 20 pound voucher. So that's my subtrahend. And he thought he was going to have to pay 78 pounds. But in actual fact, we know he had a 30 pound voucher. So we're adding 10 to our subtrahend, which means we subtract 10 from our difference, which you can see here in my jottings. So in actual fact, 98 subtract 30 equals 68. Okay, let's have a look at another one now. So this time we've got Molly, Molly was walking from home to school. She needed to walk 1,400 metres to get there. She walked 625 metres. How far is she from the school? Then she walked a further 100 metres. How far is she from the school now? So again, we can use that sentence stem to help us with this. I've kept the minuend the same and I add mm to the subtrahend so I must subtract mm from the difference. Just have a think about what you'd put in there. Okay, let's put this one on a number line to help us. So we've got Molly. We know the total distance she's walking is 1,400 metres. She's walked 625 metres already. So 1,400 is our minuend so that's how much she's going to walk in total. And 625 is our subtrahend. Let's see what our difference would be. So we know the difference is 775 metres. So she's still got 775 metres to go. But if she walks a further 100 metres, let's have a look on the number line, our minuend stays the same, she's still walking 1,400 metres in total but now we're subtracting 725 metres. So we can see that we've added a hundred metres to our 625. So if we think about our sentence stem, I've kept the minuend the same and added 100 to the subtrahend so I must subtract 100 from the difference. So we know she's got 675 metres left to get to school. Okay. Here's a practise question for you now. Quite similar to the one we've just done together. Molly was walking from school to home now, she needed to walk 1,400 metres to get there. She walked 850 metres. How far is she from her home? Then she walked up the other 100 metres. How far is she from home now? My challenge to you is, can you represent your solution in a variety of ways? So think about how we've represented it in today's session, we've used bar models, we've used number lines or you might have a more creative way of representing it, fill in the sentence then too, to represent the calculation. Have fun.

Lesson summary: Contexts where the Minuend is Kept the Same, and the Subtrahend Increases

In today's lesson, we will apply what was learnt in the previous lesson to contexts where the minuend is kept the same, and the subtrahend increases. Different methods demonstrated will include number lines, bar models and jottings.

Maths

Y6 Maths

Key Stage 2

Year 6

Contexts where the Minuend is Kept the Same, and the Subtrahend Increases

Extending calculation strategies and additive reasoning

Number

THEME

UNIT

Adjusting addends

Same sum' with larger numbers

Same sum' with decimals

Balancing equations using the 'same sum' strategy

Balancing equations using compensation

Balancing equations: Does the order of addends matter?

Increasing an addend

Decreasing an addend

Solve calculations mentally by relating them to known facts

Find an unknown addend

Introduction to same difference

Same difference in context

Use the Language of Minuend, Subtrahend, and Difference

Transform calculations using the same difference

Practice: Transforming Calculations to Make Them Easier to Solve Mentally

Transform a subtraction calculation to make the written algorithm easier to apply

Practice: 'Same Difference' in Different Contexts

Balancing equations to find unknown values

Explore how the difference changes when only the Minuend is changed

Apply the generalisation about how the minuend and difference change to solve problems

Explore how the generalisation can be used as a mental calculation strategy using Known facts

Thinking flexibly

Comparing Strategies

The more we subtract, the less we are left with. The less we subtract...

Contexts where the minuend is kept the same, and the Subtrahend decreases

Further practice to reason about how the change in the subtrahend changes the difference

Explore problems in which the new difference must be found

Balance Equations Where the Compensation Property of Same Sum Cannot Efficiently be Applied

Balance Equations Where the Compensation Property of Same Difference Cannot Efficiently be Applied

Contexts where the Minuend is Kept the Same, and the Subtrahend Increases

Video

Lesson summary: Contexts where the Minuend is Kept the Same, and the Subtrahend Increases

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