Which word best fills in the gap in this sentence: We can think of addition as _____________ a point on the number line.

Write a calculation that the number line is modelling

Calculate (-33) + 25

Calculate (-29) + 29

Find the value of a:

Modelling Addition

﻿Hello, my name is Mrs. Buckmann. Today I'll be teaching you about further addition. Okay, so make sure you have a pen and paper. Remember to pause the video when I asked you to, but also whenever you feel like you need more time and you can always rewind to hear something again if you need to Let's begin. Okay, so for your try this, I want you to continue the pattern in this grid by filling in the missing numbers. And then also describe what patterns you do notice, pause and have a go. Okay, so I've got the completed grid here. Feel free to pause it now and have a quick check. I'm going to talk through the patterns. Okay, so we continue with this top line here, what's it going down in good bores and the second row, Going down in threes, the next row, while and if you notice they are all even numbers, and they're multiples of two so it's going down in two times table are going left And this bottom row here is ones and then we have this zero grid. And then we've got here is now going down towards the right in ones, then going down in twos, then going down in threes, and then going down in fours. Do you notice any other patterns? not just a cross, good. Also vertical patterns. So, those were horizontal patterns. Also got vertical patterns. So where we've got going down in ones, twos, threes and fours and then going up in one, going up in twos, going up in threes and going up in fours. Why don't you spot those two and anything else you might have spotted maybe about square numbers like in the diagonal 1, 4, 9, 16. 1, 4, 9, 16 Nice.

Okay, so we're going to have a look at GeoGebra to explore this addition model, and GeoGebra, you can look for online you can Google GeoGebra edition, applets, you might come up with it and McMaster made this one. So we started at 2, and now we've translated -4 rather than translate +4, which was towards the right direction,

4 is going to be towards the left direction, in the opposite direction, four spaces and we end up at negative two. So what if I change that -4 to -3. So here we can see, we still started 2, we've translated -3, so only three spaces to the left and we end up at -1. I can also change my starting point so I start at like 1, then actually, I'm starting at 1, -3 and up at -2. Hmm What about if I start at less Can we start at 2 and have -2? What's happening there? So I start at 2, or -2 and end up at 0. So actually 2 is the additive inverse of -2, because 2 plus -2 equals to 0.

Okay, so what we just saw is we can use translations on a number line to model addition. So if we had 12 plus -10, we know it equals 2, because we can see that from the number lines we start at 12, we go -10 to the left and we end up at 2. So we could have a negative that no longer translates in the positive direction but translates in the negative direction which is the opposite, so we go left 10 spaces. So you can say as a point started at 12, was translated 10 spaces in the next direction and finished at 2. Pause the video and add this to your notes to help you. Okay, so I wanted you to have a go so I've got a number line there and I want you to write a calculation and then in words, you can write the description. And then the other two have the calculation, but not the answers yet. So you have to add in the answers, the number line and the description. Pause the video and have a go. So the first one, the calculation would be 25 plus -25 equals to 0. And the description would be, a point started at 25, which translated 25 spaces in the negative direction and finished at 0. Let's swap the 0 in. Okay, the next one, did you get a number line looking like this? So starting at 25, going -37 in there to the left and up at -12. So the answer was -12. And then the final one starting -23, translated 18 spaces in the negative direction to towards the left and finishes at -41. Do check your answers. Why you didn't forget those? Right? Okay, so here's your independent tasks. There are four questions here. Do have a good go at it all. And it might be easier to look it on the worksheet. So, pause the video, look at the worksheet then come back when you're done. Okay, so let's go through it. The first one, convert each sentences into an equation involving the sum of two numbers. So point starts at 3, translated 10 spaces left and finishes at -7. So it's 3 plus -10 equals -7. And here are the next two. So notice for B, 3 plus -3 equals 0. So 3 is the additive inverse of -3, I'll just write that word down. As that is one that I'm going to use and a lot in future as well so additive. Inverse And it is when the sum of the numbers equals to 0, and the two, so we start at 13, we add -6 and we get to 7. But the next one, we start at 4, we add -8, and we get to -4. And start at -80, We add -10, we get to -90. Now we're doing the following. You might improve on a picture for this I got 0,

5, -5, 2, and 2. So those last twos are a positive. So Phil thinks when you add two negatives together, you always get a positive Or negative plus negative is a positive. Hmm. Find a counter example to show he is incorrect. There are so many ones you could have come up with That's not always right. There's one way not correct. So -3 plus -7 equals to -7. Is it ever correct? Can you ever add a negative to negatives and get a positive number?

3 plus -1? No, I don't think you can because when you're already negative and you're adding negative again further left, well, you're never going to get to a positive number. He is incorrect. Okay, it's for your explore, I want you to generate examples for this diagram. So in this diagram, we have a start point at b, with c being a translation in the negative direction and a being our finishing point. Can you find an example where a is less than zero, b is greater than zero and then you need to work out c. a is less than zero and b is less than zero. b and c have the same absolute value. a and c have the same absolute value. Have a little go, if you're struggling you can come back The video and I will give you some more support. Okay, so just remind you, remember that this a is less than this is less than zero. So it means that a is going to be negative here b is greater than. So you can think here a is negative b is also negative in this case, okay? And absolute value what does that mean? Good, it is the distance from zero, okay, so like negative five has an absolute value of five. Okay, so and what I would do is I would just think of a random number for a so let's say here it needs to be in the first one, a must be less than zero. So let's say a was -5, and then b needs to be greater than 0. So let b be like 8 And then think okay, then what does c need to be. So I'd actually draw this diagram So if I was doing that one, I draw the diagram. I'd draw my a as my a, what do I say? -5, and b, I think I said 8, and then think Okay, so what is c then? Do you know? Have a go. Okay, so for the first one, a is less than 0 and b is greater than 0. Now I did just do an example which had not necessarily the same one that I was thinking here. So let me just do that one again. So we had -5, a, 8 even what was it? What was c going to be? Good, -13. Another example a -1, b 1, so c equals -2. And there are lots of examples you could have come up with there so that well done, just check yours carefully. So B, a less than 0 and b less than 0 So if a is -2 a b is -1, then c will end up being -1 b and c had the same absolute value. So b and c must be the same distance away from zero. So, b would equal 1 and C equals -1 a is 0 what about if b equals 2 and c equals -2, then a would also equals 0, wouldn't it? I wonder if that's always the case. Well, if b and c have the same absolute value will a always equal zero? Hmm If there had to be different numbers, if b and c couldn't be the same numbers, which is normally if we have a variable, we give something a letter, we don't let it be the same, but sometimes it happens to be, but here if b and c were both -2, then actually a would be -4. So it's not always the case. That a will be 0 there, but often a and c have the same absolute values So if a is 2 and let's say c then is -2, b will be 4. There is just one example there's so many I cannot go through them all I wish I could see all your work, but I can't check it all. But if you would like to share your work, I would love to see it. Please ask your parent or carer to share work on Instagram, Facebook or Twitter. Any of the work from the from the week if you want to share it you go for anything you're proud of you think Oh, I'd love Mrs. Buckmann and I'd love people to see this, go for it tag @OakNational and #LearnwithOak. And I look forward to seeing you in another lesson. But before you go, you need to do the exit quiz. That really helps you cement your understanding by just practising it and recalling it without like any guidance from me. Okay, so do have a go and look at the feedback read the feedback carefully and make sure you understand it. Even come back to the video and look over bits if there's anything you're unsure of. I'll see you later. Bye.

Two numbers are additive inverses if their sum is _____.

Which sentence best describes the calculation: 3 +(-4) = -1?

What is the additive inverse of -4.2?

Joanna thinks the following calculation pair are additive inverses: 10 + (-50)  + (-18) and (-10) + 50 + 18. Is she correct?

Write the sum that the number line is modelling.

Further Addition

In this lesson, we will learn how to model addition of a negative number as a translation on the number line and explore what happens when two additive inverses are added together.

Maths

Y7 Maths

Key Stage 3

Year 7

Positive and negative numbers

Number

THEME

UNIT

Negative numbers in context

Order and absolute value

Subtracting positive numbers

Subtracting negative Numbers

Multiplication as scaling

Negative scale factors

Further multiplication

Division

Further division

Axioms and negative numbers

Which word best completes the gap: -14 and 14 are additive inverses as they sum to ____

Which calculation gives the smallest answer?

True or false: The absolute value of a number is always greater than the number itself.

Find the absolute value of the number 0.

Calculate (-2) + (-5)

Fill in the gap: In the diagram below the top arrow can be visualised as stretching -10 by a scale factor of_____.

Calculate the following product: 0.5 x (-12)

What is the temperature 10 degrees warmer than -30 degrees?

Lesson overview:Further Addition

Core Content

Positive and negative numbers: