﻿Hello, Mr. Whitehead here, and I am ready to teach your next maths lesson. You're going to need a few things. Your practise activity from last lesson, a pen or pencil, and some paper, and yourselves. Press pause, go and grab what you need, and come back when you're ready. Welcome back. So, here is the practise activity that you were set at the end of last lesson. Can you hold yours up, if you had to go at it? And I want to have a little look and see who was rushing for some solutions, and who was slowing down and thinking about the maths, and showing me the maths through your jottings, through your notes, through any diagrams. Okay, let's have a look at each part of the problem, and I want to show you how I've solved them, and give you the chance to compare to your own solutions. Okay, so the first part. Were your eyes drawn to the parts in red? 35 there and the 33 there. Now of course, those numbers are 35,000 and 33,000. I wonder if the red parts caught your attention and you were able to connect them back to a fact, or a little bit of mental working out. That stem sentence at the bottom, as you find ones? Ah, join in, if you can. If I know that 35 ones add 33 ones is equal to 68 ones, then I know that 35,000 add 33,000 is equal to 68,000. So, we've moved there from a known fact, or maybe a little bit of mental working, to calculate. But we've moved from that to a related fact. In the part whole diagram, for the fact, parts of 35 and 33, the whole would be 68. In the related facts, what changes are going to happen to the parts and the whole? The parts would become, got to help. Good, and the whole would become? Well done. So now, the stem sentence has changed for a generalisation. We were using this last lesson. So, looking closely this time at the missing sum that we're working out, that two in the number 235,000, the two represents? 200,000. Using the sentence, if one addend is changed by an amount, 200,000, the other addend is kept the same. Yeah, 33,000. The sum changes by the same amount, 268,000. Hold up for me any jottings, or working out, or diagrams that you used as part of showing me how you solved this part of the problem. Have a look at mine. Compare the two. Have we all shown the increase of 200,000 to the addend, and then to the sum, with one addend being kept the same? Okay, next parts. That five in 535,000. The first five has caught my attention. Tell me what it's worth. 500,000. If I compare that to the addend 35,000, I can see there has been an increase. An increase of? 500,000. The next addend has stayed the same, so the sum, 68,000, needs to increase, as well. Increase by? Good, by 500,000, and it's going to increase to? 568,000. Again, hold up your jottings and diagrams, and then compare to mine. Have we all shown an increase to one of the addends? Kept one the same, and increased the sum by the same amounts. Now, perhaps you noticed the increase from the addend 235,000. What is the increase from that addend to 535,000? 300,000. Then looking at the some 268,000, maybe you've increased that by 300,000 to find the missing sum. Either approach will work, as long as you apply the same increase to both the addend and the sum. This is how I showed my thinking. So, in a similar way, but this time, increasing by 300,000. When I compare the two, increasing from 35,000, and increasing from 235,000, I don't think either is more efficient than the other. The difference is simply where I notice the increase. And as long as, like I said, as long as we've applied that increased correctly to the sum, we'll reach the same solution. Before we look at the challenge, I just want to say that, of course, written addition works, as well. And some of you may have used formal methods to find the missing sums. It's really important for a depth of understanding, a really clear understanding of addition, really important that we can look at our equations, look at our problems, and decide will it be more efficient to use a mental approach? I can use a mental approach because, or it's more efficient to use a written method. When you can make those choices and give your explanations, it's a good sign of how deep your understanding is. Challenge. You were asked to write a similar problem, but this time, using 40,000 add 60,000. This is mine. Hold yours up so I can see what yours looks like. If you'd like to have a go at mine, press pause, and then play again when you're ready for the learning in this lesson. Okay, a quick, quick habit to recheck. Some words we're going to use today related to addition. The vocabulary of addition. Addends and sum. You can have two or more addends in an equation. In this equation, there are two of them. The result of adding, combining, totaling the addends is the sum. Looking at the second equation, some things have changed, some things have remained the same. Can you call out for me the word addend or sum for the numbers that I say in the second equation? Number one is an addend. Call out for me number three, addend or sum? And how about four? Good, sum, addend, addend. We're also going to use the words known and unknown. Right now, all of the addends and sums are known, but now, this addend is unknown, and this sum is unknown. In this lesson, look carefully at the equations, and whether or not there is a known addend or a known sum, or an unknown addend or unknown sum. Here are two equations from last lesson, and here are two equations from this lesson. Take a moment. You can press pause and ask yourself, what's the same about the two sets of equations, and what's different? Press pause now. Ready? Looking at the two sets of equations, what's the same? Did you notice all equations are addition equations? Did you notice that in each equation, there is one unknown part? Maybe an addend, maybe a sum, and two parts that are known. Differences. Last lesson, we were finding unknown sums. This lesson, the sums are known, but an addend is unknown. That key difference is all part of the learning in this lesson. We're moving on from finding unknown sums, to finding unknown addends. Here's a problem to get us started. Can you read it aloud with me? On Monday, the house point total for two houses was 83. Hufflepuff had 36 house points, and Slytherin had 47 house points. On Tuesday, the total increased by two points. Hufflepuff's points stayed the same. What happened to Slytherin's points? I wonder in school, when you're faced with problems like this, if your teachers encourage you to use a drawing to help you see the maths. A drawing I like to use, a diagram I like to use to help me see the maths in a problem, is a bar model. I'm going to read the problem again, and start to draw my bar model to help me see the maths that I might need to do. On Monday, the house point total for two houses is 83. Hufflepuff had 36 house points, and Slytherin had 47 house points. On Tuesday, the total increased by two points. Hufflepuff's points, 36, stayed the same. What happened to Slytherin's points? The total has increased by two points. Hufflepuff's stayed the same. What happened to Slytherin's? Now that I've drawn my bar model, I can start to see the maths that I need to do. I need to calculate. The whole was 83, so the sum of the two parts was 83. 36 add 47, equals 83. Then there was an increase. I know that one of the addends stayed the same, and one of the addends changed. The total, the sum changed, as well. Here's a sentence that maybe you can start to read with me. The sum has increased by two. One addend has stayed the same. So, the other addend must increase by two. Slytherin's points increased by two. Why don't you press pause and have a go at representing that same maths in a part whole diagram? Press pause now, and then we'll take a look together. Ready? So, the parts were 36 and 47, and the whole was 83. The number of points increased, Slytherin's increased, and the total increased, both by two. So, I can show that in those sections of the part whole diagram. The sum increased 85, and Slytherin's increased to 49. Here's another problem. There is a difference between this problem and the last one. So, if you'd like to, also try and work out what that difference is. Read the problem aloud with me. On Tuesday, the house point total for two houses was 85. Hufflepuff had 36 house points, and Slytherin had 49 house points. On Wednesday, the total decreased by three points. Slytherin's points stayed the same. What happened to Hufflepuff's points? If you want to, press pause now, have a go at drawing a bar model. When you're ready, press play, and compare it with my bar model. Are you ready? Let's have a look at the problem again and start to draw the bar model. On Tuesday, the house point total for two houses was 85. The total was 85. Hufflepuff had 36 house points, and Slytherin had 49 house points. Wednesday, the total decreased by three points. Slytherin's points stayed the same, so 49 stays the same. The total decreases. What happen to Hufflepuff's? How can I show it? Ah, I can show a decrease on my bar model by removing part of it. Now that I've got my bar model drawn with a part showing an amount to remove, to decrease, I can start to see the maths that I need to do. So, the total was, the sum was 85, where 36 add 49 at the addends. Now, I know that the sum, the total, is going to decrease by three. So, the new sum, the new total number of house points will be 82. I know that one of the addends stayed the same, so the sum has decreased by three. One addend has stayed the same, so the other addend must decrease by three. What happened to Hufflepuff's house points? They decreased by three. They now have the 33 points. Once again, press pause and fill in the parts of the part whole diagram. Show me the parts as they were, and the whole as it was, and try to show me the changes that happen to the whole, to the sum, and to one of the addends. Press pause, and then play again when you're ready to compare. Are you ready? Okay, so parts and the whole. The parts were 36 and 49. The whole was 85. The sum, the whole, decreased by three, one addend. One of the parts stayed the same. So, decrease the other addend by three. I can show those two changes, and the new sum, the new whole, and the new addend, the new parts, which matches our equation here. So, we've been using two sentences so far, with some gaps. Two stem sentences to talk about the changes that have been happening to the sum, and one of the addends. Now, I wonder if you want to press pause and have a go at writing down a generalisation. A sentence that doesn't have any of the gaps. A sentence that we can use whether there is an increase or a decrease. Press pause, and have a go if you'd like to, then play again when you're ready. Okay, so here's a sentence that I've written. I'd like to have a go at reading it with you. On three, can we read it together? One, two, three. If the sum is changed by an amount, and one addend is kept the same, the other addend changes by the same amount, and that change can be an increase or a decrease. Let's use this sentence with our next problem. Here's our third problem. Does anyone notice the difference between the first two problems? But in the first problem, one addend and the sum increased. In the second problem, one addend and the sum decreased. See if you can spot the difference with this problem, as well. Let's have a read together. Later in the term, the house point total for the two houses is 364. Hufflepuff had 125 points, and Slytherin had 239 points. Four points were deducted from Hufflepuff, and so the total decreased by four points. What happened to Slytherin's points? Once again, press pause. Have a go at drawing a bar model, and then come back and compare it to the one that I've drawn. Ready? So, later in the term the house point total for the two houses was 364. Hufflepuff had 125 points. Slytherin, 239 points. Four points were deducted from Hufflepuff's, and Hufflepuff were 125, and four were deducted, were removed, were taken away. I can represent the four there that I need to remove. What happened to Slytherin's? So, I can start to see the maths. The original equation had a sum of 364 and two addends of 125 and 239. If the sum is changed by an amount, and one addend is kept the same, the other addend changes by the same amount. But this time, I know that the total decreased by four. I know that Hufflepuffs points also decreased by four. So, this time I know the two changes that were made, so what happens to Slytherin's points? If the sum has changed, the other addend changes. One addend is kept the same. Slytherin's points remained at 239. Press pause, have a go at filling in the parts and the whole on the part whole diagram to represent the maths from the problem we've just looked at. Ready? So, to start with, the whole, 364, with two parts, 125 and 239. Now, we know that there is a change to the sum, to the total, to the whole, and to one of the parts, and they both decreased by four. We can represent that in the diagram, and the new part and the new whole, which matches our equation with a sum of 360, a new addend of 121, and one addend that doesn't change, 239. Okay, here's a problem for you to try on your own. I've taken the words away this time, and it's just the equations. Look closely. Are you looking for an unknown addend or an unknown sum? What's changing? What's staying the same? Use the sentence to help you. Press pause, have a go, and then come back and compare. Ready? So, we can see there is an unknown addend. I can see one addend has stayed the same. I can see the sum has increased by one. So, I need to increase the addend, 0.78, by the same amount to find the missing addend. Here's another one for you to have a go at. Agree or disagree, and why? Really important to explain why. Oh, so, still some addition, but now with an inequality symbol. I know sometimes the greater and less than symbols, we find a little bit tricky to remember which is which. Here is an image that I would like you to keep in your mind when you're thinking about the greater, less than, equal to symbols. With this image in your mind, I hope you can always remember one is less than three. So, the first symbol is the less than symbol. Two is equal to two, and three is greater than one. So, with that visual in your mind, we have a look at our problem, and can see it's the greater than symbol that's there. So, do we agree or disagree that the first part, the left-hand side, is greater than the right-hand side? Press pause, have a go, and think about how you would explain whether you agree or disagree. Are you ready? Some of you might still need a little bit more time, so I'm going to give you one more piece of support with some colour. Now, looking at the left-hand side in red and the right in blue, and just reordering slightly, so the red is on top and the blue is beneath. This might help you to explain a little bit more clearly, or to spot whether or not you agree or disagree. Press pause again, and come back, and we'll have another look. Right, have you sorted out those explanations? Do we agree or disagree? Give me a wave if you agree. Give me a wave if you disagree. Anyone unsure? Let's have a look together then. Now that I've arranged the two parts to the inequality in this order, it's easier for me to look and see what's the same and what's different? And I can see that two addends are the same. 20.35, 20.55. I can see one addend has changed from 20.45 to 20.35. There's a decrease of 0.1, of 1/10. Now that I know that there is a decrease from red to blue, I know that the red side is greater than the blue side. So, I agree with the inequality. Then I've got some some jottings there to help prove and explain why I agree. Right, that brings us to the end of this lesson. The practise activity is here on the next page. Press pause, copy down the information or take a picture. Your teacher will review the activity with you at the start of the next lesson. Just before you go, there has been a lot of learning today, and a lot of representations. For the Harry Potter house point problem, as we were using bar models, part whole diagrams, and equations. There's no need to use all three representations when solving problems. For the activity today, pick and choose the representation that will best help you see the maths and explain your thinking. If you want to represent it in more than one way, go ahead, but one way may well be enough. I've really enjoyed the lesson today, and hope you have, as well. Hope to see you again soon. Remember to press pause on the next page to get the practise activity copied down, or a photo taken. See you again soon.

In this lesson, we will be finding an unknown addend when the sum is changed.

In this lesson, we will be finding an unknown addend when the sum is changed. Resources provided by NCETM (CC BY-NC-SA: https://creativecommons.org/licenses/by-nc-sa/4.0)

Maths

Y6 Maths

Key Stage 2

Year 6

Find an unknown addend

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

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 Increases

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

Lesson overview:Find an unknown addend

Core Content

Extending calculation strategies and additive reasoning: