Exploring problems involving addition and subtraction

Key Stage 1

Maths

Addition and subtraction within 10

This part whole model can be expressed as 7 - 3 = 4. Choose the other subtraction equation that can be written from this part whole model.

There are five elves standing up, and two elves sitting down. Altogether, there are seven elves. This can be written as an equation: 5 + 2 = 7. How else can this equation be written?

This part whole model can be expressed as 1 + 6 = 7. Choose the other addition equation that can be written from this part whole model.

﻿Hello, my name's Ms Robson. In this lesson, we are going to be exploring problems involving addition and subtraction. We're going to be doing one of my favourite activities ever. We're going to start by finding a missing number before completing a talk task together, before I ask you to do some independent questions. Then we're going to figure out together how to solve the triangle. And that is the really exciting activity that we get to do. And then it'll be turn for you to have an independent go at solving the triangle. For this lesson, you will need a pencil and 10 countable objects. I'm going to be using cubes but you can use whatever you have around. Pause the video here to collect the items that you need and when you're ready press play. We're going to start by warming our brains up and doing some number bonds practise. I can see lots of bar models on the screen. The first one, the one that is all purple would represent nine because the bar is as long as nine on the number line. But there's no orange bar. So nine plus zero equals nine. Have a go at talking your way through these different number bonds and describing the number of bonds that you can see represented by the bar models. Pause the video here to have a turn and when you're ready press play. Let's have a look at them together. Eight plus one equals nine. Here I can say this part of the bar is just one. Seven plus two equals nine, six plus three equals nine, five plus four equals nine, four plus five equals nine. Join the with full sentences if you can. Three plus six equals nine, two plus seven equals nine, eight plus one equals nine. And lucky last is zero plus nine equals nine. If you manage to talk your way through all of those fantastic work. We are going to start our problem solving today by looking at these three numbers. I can see the number three and the number six in circles and the number one in a square. All three of these numbers on the number line add up to 10. I'd like you to pause the video here and see if you can prove that statement using cubes. Let me repeat it for you. All three of the numbers on the line, add up to 10. Pause the video and see if you can prove that statement. I'm going to prove it to you using my cubes. So the first part, I'm going to start on the left hand side with three. So here are three cubes. The next part is one. Here is one cube. And the last part is six one, two, three, four, five, six, six cubes. So I have three and one, one more than three is four. And if I remember my number bonds to 10 correctly, four and six make 10. So I've added three and one to make four, and then added six more to make 10. Did you manage to get 10 cubes altogether as well? We've proven this statement. That means that this statement is true. All of the numbers in this line add up to make 10. It's like a whole model with three parts Isn't it? Instead of having two parts. So we've had to add all three numbers together, but the total, the whole was 10. This time we have another one to look at, but one of the numbers is missing. Again, using your cubes see if you can figure out what the missing part is. Pause the video here to have a go. I'm going to start by representing the parts that I do know. So I know that in one of the circles is one, here's one. And then the other circle is five one, two, three, four, five, here's five. So I have 10 things altogether. I have one and five, I'm going to stick them together Altogether now one more than five is six. So if one more than five or six, what's the other part that I need in my number bond to make 10? The other part is four and because I have 10 things, I know that because I've already got four leftover anyway. So if I have 10 things altogether and I've got one part as five, one part as one, add them together to make six. And then the remaining part, the missing part under the star must be four. Should we check and see? Four, fantastic. So one and five make six, six and four make 10. I'm breaking it up. It's taking me two steps to get there Isn't it? Because first I'm adding the two that I could see, then I'm thinking about what must be left in order for the total of the line to be 10. We're going to have a few more tries at this together now. So can you get your 10 things? Can you get one and pop it in one group and two I pop it in another group. So you should have two and one. what is one more than two? One more than two is three. What number bond do I know that has three in it to make ten. Three and? If I need to, I could count on. So I've got three, four, five, six, seven, eight, nine, 10. Three and seven make 10, but also hopefully, I have my number bonds to 10 up here or because I have 10 objects and I've taken three to add one and two together. I've got seven left. So the missing number under that first star must be the number seven. It is. One and two make three, three and seven make 10. Do you see how I'm adding those three parts together? Starting first, While using the two circles that I can see and then figuring out what's under the star by using my number bonds to 10. Let's have a go at the next one together as well. One is a part and three is a part. What is one more than three? One more than three is four Fantastic. Four and what make 10? Four and six make 10. Let me add them together. So I had put it on a bit of an angle so I can remember where I've changed here. So I have one as a part three as a part, and the remaining part had to be six. So let's check and see if six is under the star. It is, fantastic. For the last one, I want you to get your objects, make one as a group, make five as a group. One more than five is six. Six and what do we need to add to six to make 10? Six and four make 10. So adding them together now I have 10 altogether. One was a part, five was a part, four was a part. Five and one makes six and six and four make 10. So we have to take two steps in these problems. And it's time now for your talk task. So I can see you have to where the middle number is missing. And then one where the end number is missing. You still do the same thing, you add the two numbers together that you can see. And do you figure out how many are left in your number bond to 10? Pause the video here to see if you can figure out what the numbers under the stars are and when you're ready, press play. Let's have a look at the second one first. So this one here in the middle one and seven, What's one more than seven? One more than seven is eight. So if eight is what's my two circles are added together under the square must be the rest of my number bonds 10. So eight and two make ten. Eight and two make 10. Let's try the next one. There's one and one and something. So one and one, double one is two. So if those two parts together are two then under the star must be the rest of the number bonds to 10. Two and eight make 10. Here's 10, two and eight make 10 or in this case one and one and eight make 10 There's eight. And lucky last we have six and one. Six, one more than six is seven. So I have one, two, three, four, five, six, seven. I have six and one as a part, I add them together to make seven and seven and what do I need to add to seven to make 10? Seven and three, seven and three make 10. So under the star must be the number seven. Oh, the number three. Oh, I was a bit confused there, sorry. Six and one make seven and three more makes 10. So we are now going to apply that skill of adding all three numbers together or finding one of the numbers and adding three to make 10 to this problem solving activity. On the screen I can see a triangle. Now it might look a bit tricky but really all we've done is taken the lines that we were working on before and put three of them together to make a triangle. So now we have one, two, three vertices and we have our sides, our edges that we're going to have to fill in the missing numbers on. So I know where all of the numbers in the vertices are but I'm going to work through each one as a line, and then check that all three of the sides work together. So we're going to start by looking at this one here. So there are three sides, we'll do this one first. One and two, one and two makes? So that's one more than two, one more than two is three. So how many more do I need to make 10? Three and? Three and seven make 10. Here's seven, so I had one as a part, two as a part, and then another mystery part. I added the one and the two together to make three. And I know that three and seven make 10. Let's check and see if that's the number seven, fantastic. I have the number one in this vertex and then number three in this vertex let's have a go. So I need three as a part and one as a part. Three and one make, so one more than three is four. Three and one make four. And the missing part then must be four and six. Four and six make 10. What I'd like to do is quickly show you a way that you can work these out by using subtraction instead. So if I put my star back and we pretend that we don't know what's under there. I have 10 altogether, I know the row must equal 10. So here is 10 altogether. And instead of adding the different parts together to figure out how many altogether. I'm going to take some away from the whole to figure out how many are left. So I'm going to take away one because I can see the parts of one is already there and I'm going to take away six. One, two, three, four, five, six. I take away six as well. Then I am left with the remaining part. How many can you see here? There are three. So let's check under the star and three. So one is a part, six is a part, three is a part. I can do this as an addition, by adding the two bits together that I know and thinking about my number bonds or I can do it as a subtraction where I start with 10. I know that the whole, the total of the row is 10 and I can take away the different parts. So we've just checked the side here but this time let's have a go at doing it as a subtraction to check to see if we're right. So we need 10 altogether. We know that the row is equal to 10 is 10. I'm going to take away the first part, which is one, so take away one. And I'm also going to take away three. One, two, three, because I know that is my other part. So the third part must be one, two, three, four, five, six. I know that one and three make four and four and six make 10. And I also know that 10 take away one is nine and take away three more is six. So there's the number six. I can work them out using my addition or my subtraction. Whichever one you find easiest or you might like to do both to check your answer afterwards. We've got one more let's do it together. So there's the number two and the number three. Let's start by doing our addition. So two and three, put three in your head and two on your fingers ready? Two, sorry, three, five. So altogether we've got five so far five and what make 10? Five and five make 10. Let's try the subtraction version. So I think the number there might be five but I'm going to try subtraction too Here are my 10 things, One, two, three, four, five, six, seven, eight, nine, 10. I'm going to take away two, that's the first part I know two and I'm going to take away three and I should be left with one, two, three, four, five. So I know that two and three and five make 10 Let's check and see it's the number five. So it's time for you to have a go at the independent task. You have two triangles to investigate and all of them are missing. They all have their vertices but they are missing the other numbers. The numbers in the squares, you can use addition or subtraction or both to work out the missing numbers. It's time now for you to pause the video and complete your task. When you're finished press play I'm going to work through the independent task answers. And I'm going to do the first triangle as an addition triangle, practising my addition skills and the second one as a takeaway. So you can join in if you'd like to or you can check your answers to see if we have the same numbers. So let's start with this side here. One and two, so I'm starting with addition two, three. One and two makes three. And I know that three and seven makes 10. So let's check. There you go. So two and one and seven makes 10. Then I'm going to do the other side, this one over here, five and one, one more than five is six. So those two numbers together would be six. And I know that six and four make 10. So one and five and four, one and five and four make 10. So the missing number must be four. And then the one that bottom, the lucky last edge of my triangle, five and two, five, six, seven. So there are seven there already. So the missing number has to be the missing parts of tens are seven and three. Seven and three make 10, fantastic. Let's do the next one as a subtraction. So triangle number two, I need my 10 things for my subtraction. I could count back in my head but I like to have my things to check just in case. So I've got 10 things. I'm going to start with the first row over here. And I know that I need to take away one 'cause that's one of the parts I know and two, and I'm left with one, two, three, four, five, six, seven. So 10 take away one, take away two is equal to seven. Let's check. There you go. Then I'm going to do the next side, this one over here. I'm going to start with 10 again. So let me reassemble my stick and I'm going to take away one, one is a part and I'm going to take away four. One, two, three, four. So I've taken away four and I've taken away one and I'm left with one, two, three, four, five. Five, I can check that by using my addition 'cause I quite like my addition. So five and sorry four and one make five and then five and five make 10, fantastic. And then let's check the last one. So putting my keys back together again, I've got 10. In fact, this time I'm going to try and count in my head 'cause I'm going to put those down. So I'm starting with 10 and I'm going to count back four first. So 10, nine, eight, seven, six. So now I'm at six, I'm going to take away the two six, five, four. So if I've done 10 take away, four is six and six takeaway two is four. Let's have a look and see the missing number was four. If you've managed to solve these triangles, you need to give yourself a really big double pat on the back because they are tricky, but there are lots and lots of fun. If you've enjoyed this task, you could rub out all of the numbers from all of the vertices and squares that are sat on the edge of the triangle. And you could try and come up with your own numbers or see if the rows equal up to a different number instead of 10. Maybe try and make them all make nine. I wonder if you could do that. Thank you so much for joining me today. I hope you've had as much fun as I have. That is one of my favourite activities to do. If you'd like to keep trying or if you'd like to come up with your own triangle, you can share your work with us. If you'd like to, please ask your parent carer to share your work on Instagram, Facebook, or Twitter by tagging @OakNational and using the #LearnwithOak. We'd love to see what you been getting up to. Thanks again for joining me. See you next time.

Exploring problems involving addition and subtraction

Exploring problems involving addition and subtraction

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UnitMaths / Addition and subtraction within 10

Maths