If 1 is the whole and 0.8 is a part, what is the other part?

If 5 is the whole and 2.1 is a part, what is the other part?

If 10 is the whole and 7.3 is a part, what is the other part?

If 10 is the whole and 1.6 is a part, what is the other part?

If 10 is the whole and it is made of 3 parts.  What could the parts be?

Decimal Number Bonds

Key Stage 2

Maths

Decimals

I think of a number with one decimal place and round it to the nearest whole number.  The answer is 62.  What is the highest possible number I could have thought of?

I think of a number with one decimal place and round it to the nearest whole number.  The answer is 435.  What is the lowest possible number I could have thought of?

I think of a number with one decimal place and round it to the nearest whole number.  The answer is 9.  How many possible numbers could I have thought of?

﻿I was reminded recently that it's a good idea to drink two litres of water every day to keep healthy. These glasses hold around 250 millilitres of water, and I've had three of them so far. It's still a way to go but I have some more to the side ready in case I need it during this lesson. Maybe you could get some water handy before we start the lesson. And as well as that check you're in a quiet space, make sure that you've got all that you need. I'll show you in a moment some of the things that we'll be using, make sure you're free of distractions. Press pause if you need to while you get yourself organised with water, turning off tablets and televisions and just finding a really good quiet space so that you can focus on your learning with me for the next 20 minutes. Press pause, come back when you're ready to get started. In this lesson, we are finding number bonds for numbers with one decimal place. We will start off by thinking about some partitioning with a quick task. Before we look at one being the whole and what two parts could be added to make that whole. We'll repeat that process by thinking about five being the whole and 10 being the whole, and then what the two parts could be that would make those numbers. That will leave us ready for the independent task Things that you'll need, pen, pencil, ruler, a pad, some paper to work on to. Press pause, go and get yourself sorted, come back and we'll get started. Okay so a partitioning task to start our lesson. Let me show you what I mean. I'm asking you to partition each of the numbers on the left into any hundreds, tens, ones and tenths and to record the partitioning as an addition equation. This is what I mean, for 2.3, you would record that as two add 0.3. 2.3 is equal to two add 0.3, I've partitioned 2.3 into ones and tenths. Press pause, work through the other six numbers, partitioning them into any hundreds, tens, ones and tenths and recording correctly as an addition equation. Come back when you're ready to check. How did you get on? Hold up your pads, your paper for me, let me have a look. Really good start, fantastic. Let's take a look, mark your answers. So 47.6 partitioned into tens, ones and tenths. 7.8 is equal to seven add 0.8. 19.5 has three parts, 5.2 has two parts, some ones and some tenths, three parts here, tens, ones and tenths, and four parts, hundreds, tens, ones, and tenths. How did you get on? Good, lots of big smiles, we're ready to continue. Okay, if one is the whole and 0.3 is a part, what is the other part? How do you know? Take a moment to think about that, to look at the diagram. If you've got an idea of what the missing part is, then focus on the, "How do you know?" If you're not sure how to explain how you know, pay really close attention to the next few slides? So one is the whole, I can represent that with a counter. I know that I'm working with tenths, I know one part is three tenths. I know that the missing part and the known part, total one, they total 10 tenths. So that's how many more attempts are needed to make one whole? Seven tenths. One is the whole 0.3 is a part and 0.7 is a part. Still looking at those same numbers, we could think about it this way. So we could explain our thinking this way. The flat represents one. One part is three sticks, three tenths. I know that one flat is made up of 10 tenths. So I need seven more tenths to make the whole. The unknown part is seven tenths, 0.7. We could also think about it on a number line. Maybe visualising that number line. From zero to 0.3, that's one part, three tenths. I know that the whole needs to be one and therefore, seven more tenths, 0.7 is needed to complete the whole. The whole is one, the parts are 0.3 and 0.7. Can you say that sentence back to me, on three, one, two, three. Fantastic, and I heard some of you saying it slightly differently. Some of you said the whole is one, the parts are 0.3 and 0.7, but some of you said the parts are three tenths and seven tenths. Excellent, we know that they are equivalent. We could think about it like this, in a slightly more efficient way. So notice, I haven't changed the numbers yet. I'm showing you different ways of thinking about one being the whole and 0.3 being a part, and how we can explain and find out what the missing part is. So in this approach slightly smarter, we could be thinking, "Right, I know my number bonds to 10, "so if I think of 10 instead of one, "and I think of three instead of 0.3 "then the unknown part is seven in this case." And we can think 10 is equal to three plus seven and use that to explain the unknown part when the whole is one and when the known part is 0.3, we can make those connections. Here's another one then. So we've looked at four different ways of thinking about and explaining how we could find and say what the missing part is. So take a moment. Not only to tell me what the missing part is, what the unknown part is, but how you know and how you can convince me that you know. Press pause, come back when you're ready with some explanations. Are you ready? So fine, let's get the answer out of the way. What is the unknown part? 0.1, one tenth. Now, I wonder how you explained it. How you've thought about how you know that's the unknown part. Did you use the idea of the place value counters? One is the whole, we know one part is 0.9 or nine tenths, so if the whole needs to be made of 10 tenths, the missing parts is 0.1, it's one 10th. Did you think about it in a different way? Raise your hand if you did. Okay, keep your hand up if you were using the idea of the flats and the sticks, yeah? Okay, so the flat is worth one 10 tenths, we know we have nine tenths, nine sticks, how many more sticks did we need? One stick, and of course mathematically, that stick is representing one 10th, 0.1. Did anyone think about it on a number line? Give me a wave, good. So we know that we've got nine tenths and we're trying to reach one, we need one more 10th, 0.1. Say the sentence with me please, on three. Let's do it together, one, two, three, the whole is one, the parts are 0.9 and 0.1. Did anyone think more smartly by making connections to number bonds to 10? Give me a thumbs up if you did. Okay, so instead of one you were thinking of the whole being 10, one of the parts being nine and the unknown part when we're thinking about number bonds to 10 being one. 10 is equal to one add nine, which helps us when we think about the whole being one and the known part being 0.9, to say that the unknown part is 0.1. Okay, another one for you, press pause. You've got those four different approaches for not only finding the unknown part but explaining and convincing me that it's correct. Press pause, come back when you're ready with your explanations. Ready? Okay, once again let's get the answer out of the way. What is the unknown part? Six tenths or 0.6, they're both equivalent as we know. How did you explain it? Give me a wave if you went for the place value counters or drawings of them. Hold your work up if you were using any drawings of the flats and the sticks. Give me a wave if you went for the number line and then give me a big nod if you were using connections to number bonds to 10. Okay, so I went for the number line. One is the whole, I know that four tenths, 0.4 is one part, it's the known part, so the unknown part is that space between 0.4 and one, six tenths. Anyone that made the connections to number bonds to 10 instead of 0.6, we're thinking about six. And instead of 0.4, we'd be thinking about four and then making that connection back. What do you notice that's different about this one? The whole is no longer one, it's five but we are still looking for an unknown part. Press pause, if you want to at this point, and have a go at finding the unknown part, then come back when you're ready to look at it together and think about how we can explain it, press pause. You're back and you're ready? Okay, let's take a look. So we are finding out the length of the space between 0.7 and five. We're working out the size of that space to fill in that unknown part. Now a tip for you, is to kind of use our rounding to the nearest whole number skills, it's to from 0.7 is to find out what the distance is from that to one, what the difference is between 0.7 and one, 0.3. And thinking of it this way, if one is made of 0.7 and another part is 0.3. Now 0.3 is not the unknown part from our whole that is five, but it is helping us to find out what it is. So we're now at one, what is the length of the space between one and five. Four. So now in two smaller parts, we have found out the length of the space between 0.7 and five, it's 0.3 and four. It's four and 0.3, four and three tenths, 4.3. Using that kind of thinking, can you have a go at this one? So focus on a number line and use my tip of first of all, finding out the length of the space between your known part and the nearest, sorry not the nearest, the next whole number. Press pause and have a go. Ready? How did we get on? Okay, so a number line, yours looks something like this? Hold it up, let me have a look. Good, so we want to know the length of the space between 2.3 and five. And my tip was to find first of all, the length to the next whole number. 2.3 plus 0.7 is equal to three, and once we're there, we're working from three to five, two. So what is the unknown part? Say it again, good, 2.7. Say the sentence with me, the whole is on three one, two, three, the whole is five, the parts are 2.3 and 2.7. Well done everyone. Here's another one. Oh, I wonder if this will be slightly quicker. I wonder if you've noticed anything too, like I have, that suggests this will be quicker than the previous two. Press pause, let's see if we are quicker, come back when you're ready. Ready? So was it quicker than the previous, why? Using my suggestion of working from the known part to the next whole number, or the next whole number is five, which is our whole. So in this case we've found the unknown part 0.9. Let's say the sentence together. If I read the words and you fill in the gaps, so just get ready to call out the numbers that are missing. The whole is, the parts are, and. Good, let's do that again. One, two, three, the whole is, the parts are and, well done. I think you're ready for a short task. Get ready to press pause. And if the whole is five, what could the parts be? So the parts are all here. I would like you to find from this selection, two parts that would make the whole five. If you're ready for a challenge, suggest your own parts that would make five, but keep it to there being two, two parts in total and for the whole of five. So press pause, come back when you're ready. Are you ready? How did you get on? How many different ways did you find to make five using the parts I've given you? Hold them up, let me see. Oh wow, you were busy. Look at all of those, well done everyone. Did you find these then? 1.8 and 3.2 and these two, 2.8 and 2.2. How about these two? You did, say the sentence for these two. The whole is five, the parts are 0.7 and 4.3. Oh, did you not say it that way round? Does it matter? So we can see the parts are 4.3 and 0.7, yes. The whole is still five, good. How about, did you get these two, 3.5 and 1.5? Good work. Finally, finally, sorry 2.6 and 2.4. Did anyone complete the challenge? If you did, hold up your paper so I can see the parts that you came up with, two parts that would make five that were not on the screen. Very good, some really good thinking there, really pushing your learning on, well done. Okay, let's take this a step further. How have I taken it a step further on this page? The whole is now 10, the part, the known part is 0.3, what is the other part, the unknown part. How do you know? Press pause, come back when you're ready. Ready? How did you approach it? I've used a number line and I'm using that tip from earlier. I'm working from the known part to the next whole number. One, three tenths and seven tenths is equal to 10 tenths or one. And from one to 10, I know that the length of that space is nine. So the unknown part 9.7. Let's say the sentence. The whole is 10, the parts are 0.7 and, Oh, have I made a mistake? I have the parts are 0.3 and 9.7, good work. Here's another one. Use that tip, work from the known parts to the next whole number and from there to 10, come back when you're ready, press pause. Ready? Here's your number line. 4.7 is the known part, so the next whole number is five which is three tenths away. Then from five to 10, the length of that space is five. So the unknown part 5.3. Final one, before we get started with the independent task. Press pause, come back. Ready? If 10 is the whole and 7.1 is a part, what is the other part? Number line, 7.1 is the known part, so my suggestion has been, yes, how far away is the next whole number? It's nine tenths away, and the next whole number is eight. From eight to 10, two, is two away. So the unknown part is, two and nine tenths 2.9. Say the sentence, I'm listening to you. Say the sentence this time, on three one, two, three. Well done, really good. We are definitely ready for our independent task. I've got six part whole diagrams for you. The wholes are either five or 10. I've given you one of the parts, I'd like to know what the unknown parts are. If you are ready for a challenge, number one, you could suggest your own parts that would make five or 10, or what if five or 10 was made up of three parts, what could those parts be? So some options there for you if you are ready to continue challenging yourself independently. Press pause, go and complete the activity, then come back and I'll show you the solutions. How did you get on? Give me a wave, if you completed all six. Give me a thumbs up if you tried the challenge. Brilliant, can you hold up your work, I'd really like to have a close look. Bring it to the camera a little bit closer. Oh, too close, too close. Oh, that's better. Good work. Okay, get your pen and pencil ready to mark your solutions. Here they are, the unknown parts to be added to the known parts to make either five or 10. Okay, let's see how do we get on. Give me big smiles, medium-sized smiles, I do not expect to see any sad faces because even if there was some that were incorrect, if you are able to now look at it or maybe go back and watch parts of this lesson again, then you can still take your learning forward if you're learning from those mistakes. So I hope any medium, medium smiles increase by the end, after you've given yourself a chance to go back and check again. Right, the challenge from that activity was thinking about three parts. What if the whole was 10 and it was made of three parts and not two. So here's a little task for us to finish with. 10 is the whole, one of the parts is 7.9, what could the other parts be? If they have one decimal place? Okay, press pause if you'd like to, have a little go, come back when you're ready to share. If not, just stay with me and we can look at it together. Okay, let's have a look. So I'm finding the space, the length between 7.9 and 10. I'm going to use that strategy of what's the space, the distance between the known parts and the near next, not the nearest, the next. Although it is also the nearest, but the next whole number, one tenth away 0.1. And from eight to 10, the length is two. Okay, so 2.1, that would be fine if we were looking for one other part, 7.9 and 2.1 is equal to 10, but we now need to split 2.1 into two, into two parts. So what could the parts be if 2.1 were the whole. If you stayed with me and now want to press pause and go and try this part independently, please do. Otherwise, let's carry on. So 2.1 is the whole. Okay, so that could be made of 0.1 and two. Two, and one 10th, is 2.1, but the question does say they have one decimal place. 0.1 has one decimal place, but 2.0, we would ordinarily write as two, so there's not really a decimal place there. So I'm going to remove that, instead I'm going to start with 2.1 is equal to 0.2 and 1.9, those two decimals both have one place. Okay, so it could be that. The parts could be 7.9, 0.2 and 1.9, but there could be more. There could be other ways of splitting 2.1 into two parts. For example, or ah, the unit sing a bit of a pattern. If the pattern has caught your eye and you would like to continue that pattern to help you find all of the possibilities, press pause now and keep on following that pattern, describe that pattern. Use it to help you find the missing parts. If you'd like to keep going with me, please do. I continued that pattern on paper, and I continued until I reached 0.9 and 1.2. After that, the two parts were switching places. So after 0.9 and 1.2, the next one that I would have used would be 1.9 and 0.2 and then 1.8 and 0.3. So I thought I'm going to stop there and say, I found all the possibilities but of course I could switch those parts around as well. So wholes divided into two parts or three parts with a bit of investigation there to help us with this task. If you would like to share your work with Oak National, please ask your parents or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak. Right, I am well and truly out of water. What a challenging lesson? I really, really enjoyed that working through from wholes of one to five to 10, including some investigation work there at the end. I'm really proud of you once again and looking forward to seeing anything that your parents or carers share on Twitter. Ready for the next lesson, I look forward to seeing you there. If you have any more learning lined up for today as always, enjoy it and see you again soon in maths, bye.

Decimal Number Bonds

Decimal Number Bonds

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UnitMaths / Decimals

Maths