Consolidation and application (Part 1)

Key Stage 1

Maths

Exploring calculation strategies

Will this equation require regrouping: 30 - 12 = ?

Will this equation require regrouping: 41 - 13 = ?

Will this equation require regrouping: 36 - 13 = ?

﻿Hello, I'm Mrs Crane and welcome to today's session. We're going to be carrying on with our new day, exploring calculation strategies. And today's objective will be to consolidate addition and subtraction requiring regrouping, by using the column method. Let's get started then. For this lesson, you will need a pencil and some paper. Please pause the video now to go and get those things, if you haven't got them already. So I start off today with a little riddle. Why do lions eat raw meat? Why do lions eat raw meat? Well, because they don't know how to cook. Let's go get started with our agenda for today. So we are going to be, as I said earlier, consolidating our knowledge and practising addition and subtraction equations, which require regrouping or using the column method. That sounds a lot. So today I've broken into two separate independent tasks. You'll start with a quiz to test your knowledge. Then we'll look at Star words for today. Then we're going to recap the column method for addition. You'll then do your independent tasks one, and we'll review the answers together. Then we'll recap the column method for subtraction, and you'll do your independent tasks two, and we'll review the answers together. And finally, there'll be a quiz to see what you've remembered. So we're going to do it in two separate parts today. Pause the video now to complete your starter quiz. Welcome back. So let's do today's Star Words. We'll use my turn, your turn to do the words today. So let's get started. Place value. Tens, ones, column, regroup, subtract, add, is equal to. Let's get started there. So as I said, we're going to be consolidating our learning today. And firstly, we're going to look at addition using the column method. So here's our example. Our question one. 54 plus 16 is equal to, Now you can see here, I've got my place value grid and I've got my Dienes on it. Don't mind about this for the moment, we'll look at that after. We've partitioned 54 into five tens. One, two, three, four, five and four ones. One, two, three, four, to show 54. We've then underneath it partition 16 into one ten, and one, two, three, four, five, six ones. Now, which column do I need to start with? Well done to those of you that said the ones column. We always start with our ones column. So let's add four ones and six ones. I know that four ones and six ones is going to give me 10 ones. I put my 10 ones here. What's gone wrong then? What has gone wrong here? Well done to those of you that said you can't put 10 ones in the ones column. So we need to do something called regrouping. We need to regroup 10 ones for one ten. Why have I put my one 10 and not here? Well done those of you that have said one 10 can't go in the ones in because it presents a 10 So we must put it over here so that we don't forget to add it. Now I can do my tens addition. So I've now got five ten's here, plus one, two tens. Five tens plus two tens is going to give me seven tens. Let's count them together and check. One, two, three, four, five, six, seven tens. Fantastic. So my answer is going to be 70. Because I know there's nothing here, so I must imagine there's a zero here as a place holder. Now what we're going to do is have a look at what this looks like, when we've written it down. So here we've got 54, again, partitioned into five tens and four ones, and 16 partitioned into one 10 and six ones. Again, we're going to start with our ones columns, because we know that was where we must start. So four plus six is equal to 10. This time have shown straight away in the correct column. I know that I've got one 10 here and zero ones here. That zero is that as a placeholder for me to remember that represents 10 and not just one. Then I can do five plus one is six, plus another one is seven. I know that seven actually represents seven tens, because they are my tens column. So my number is 70. Same as my number is here. They look similar. This is the Dienes and this is the numbers. Let's have a look at them. I'm wondering, for example, this time, my equation is 47 plus 35. I've got a question at the top of our corner here. It says, what is the same and what is different between Question 1 and Question 2. I want you to consider that question as we're going through the example and we'll come back to that at the end. So I know I must start with my ones. This time, I've got 47 partitioned into four tens and seven ones. And 35 partitioned into three tens and five ones. I'm going to add my seven ones and my five ones. So seven in here adds eight, nine, 10, 11, 12 ones. So I'm going to write 12 ones here. I've got 12 ones. I need to do something because I can't have 12 in my one's column. So I need to regroup 10 of those ones into one group of 10 and leave myself with two here, because I had 12. So my two placed here, my 10 is regrouped into the tens column. Now I can add my 10. I have four tens here. Five, six, seven, eight. I know that eight represents eight tens. Let's check them here. One, two, three, five, six, seven, eight. Then my answer is 82. Let's have a look then, at what that looks like when we write it down. So I've got 47 partitioned here into my tens and ones. And 35 partitioned here into my tens and ones. Going to start with my ones column. Seven plus five I know it is equal to 12. So I've shown my two because it's the two ones that represented in 12 there. And I've put my one because it is representing one 10, into my tens columns Now I can add four and three is equal to seven, plus one is eight to eight. So my answer again is 82. Same as is here. Now let's look back at our question. What is the same and what is different between Question 1 and question 2 The same, we both had to regroup. Both questions required us to regroup. What was different then, was that when we regrouped in question one we're left with nothing in our ones box here or here. When we regrouped in question two, we were left with something in our one's box in here. Why do you think that might be? Why do you think we were left with some numbers in Question 2 and not Question 1. For question one, the ones column, the two numbers in the ones column. Were now in the bonds of 10. So they gave us an answer which was in our ones column, they gave us 10 exactly. Whilst here seven and five are now our number bonds of 10. They're number bonds that create a number that's greater than 10. They create number 12. You can see here and here. So I know when a number falls in our ones column, have bond to total greater than 10, we're going have a number left in our ones column. Now it's time for independent tasks, Part 1. You've got some equations I'd like you to answer here. I'd like you to use either drawing out Dienes, expanded method or trying the column method to solve these equations. I'd like you to have a think. Do you notice any patterns in the numbers? And can you explain them? And we've got a little question here. Tom thinks all of the equations require regrouping. Is Tom correct or not? Explain why. Pause the video in a moment. Remember just the Part 1. We'll look Part 2 together in a moment. Part 1. We'll go through the answers together as well. Pause the video now to complete your task. Welcome back. Let's have a look at Part 1, answers. We'll go through the answers first, and then we'll look at these two questions. 37 plus 23 is equal to 60. 35 plus 25 is equal to 60. 34 plus 26 is equal to 60. 67 I know where 30 came from. 53 plus 37 is equal to 90. 52 plus 28 is equal to 80, and 51 plus 19 is equal to 70. But then let's look at the patterns that we can notice in these numbers. So I have a look at this column first. I can see that my answer is the same in each box. As my is the same, I'm looking at my tens and my ones. My tens, and my ones are the same. My tens sorry about the same. My ones aren't the same. Seven and three that always makes 10. Five and five that always makes 10. Four and six that was makes 10. So the different number bonds to 10 that are in my ones column here. But the numbers in my tens column, in both all the three equations are obviously the same. Let's have a look then at this column here. 90, 80, 70. I notice that my answers are decreasing in tens. So let's have a look more closely at what's happening in my numbers. Five, five, five the tens column stays the same here. Three, two, one, Oh! I've noticed that my tens are decreasing in ones. And if I look at my number bonds three and seven, that makes 10. Two and eight that makes 10. One and nine that makes 10. So that all numbers bond to 10 So my tens column is decreasing in groups of 10 each time. So let's have a look at this question. Tom thinks all of the equations require regrouping. Is Tom correct or not? And Why? Let's look at the answers. Did they all require regrouping? Yes they did. So Tom is correct. They do. Let's explain why then. I know that all of those ones columns when I looked at them, made number bonds to 10. So I know that when my one's column makes a number bond to 10, I will need to regroup. Because I will have 10 ones. So I'll need to regroup my 10 ones for one 10. Right then well done for working really hard on that one. What we're going to do now is have a look at Part 2. So We're going to be consolidating our learning. This time we're going to be looking at subtraction, Using the column method. You can see our equation is 30 subtract 14. I've got 30 represented here with my three tens. I want to take away 14 from it. I now have to start with my ones column. So to do that, I need to do some regrouping straight away. I need to regroup two, three-- Sorry again. It'll be three tens for two tens and 10 ones. So here are my time ones, and here are my two tens here. So my numbers still represent 30, just shown in a different way. Now I can take away four of my ones, from my 10 ones. If I take four of those away, I'm going to be left with six. Imagine I've taken those away and I'm left with just those here. The six are going to move down to here. So I've got six ones remaining. I now need to take away one 10 from my two tens. Just going to leave me with one 10. Then my answer is going to be 14. One 10, 14, 16, sorry I've got six one's here, not four ones I'm getting confused with how many I'm taking away. I've taken away four to leave me with six. So I've got 16 here. Now we're going to have a look at what that looks like when we've written it down as numbers. Again, I've got 30 here three tens and zero ones. And 14 here, one 10, four ones. Straight away when I look at this, I know I cannot subtract four from zero. So again, I need to do my regrouping. This time I'm going to regroup three tens, to two tens and 10 ones. 10 ones subtract four ones is going to give me six ones remaining. Because I know 10 subtract four is equal to six. Two subtract one is equal to one. I know that represents one 10. So my number is 16, because that can be seen as my number here. Just written differently. Part 2. Then the question two. Again, I want us to consider what is the same and what is different between Question 1 and Question 2, okay? We'll go back to the answer at the end. So here I've got 32 subtract 18. I've got 32 shown here with my three tens and my two ones. I would like to take away 18 from it. I know I start with my ones. I need to take away eight ones from two ones. I can't do that without regrouping. So I'm going to regroup three tens again, to become two tens and 10 ones. Those two are going to remain here because it was 32. So this number has still represents 32. Now I'm able to take eight ones away from my 12 ones. As you've two ones here, and 10 ones here that makes 12 ones in total. That is going to leave me with four ones. So I'm left with four ones by taking away one, two, three, four, five, six, seven, eight, nine. I'm left with just those four ones that have come down here. Now I can subtract my tens. I'll start with one 10 for my remaining two tens, to just leave me with one 10. Then my answer would be 14. Let's have a look then what that looks like with our numbers when they're written. 32, say three tens and two ones and 18 one, 10 and eight ones. Now I know I have to start with my ones column. Two and I'd like to take away eight from my two. I can't do that without regrouping, just like we did here. We're going to regroup three tens to become two tens and 10 ones. This time I'm doing it with written numbers rather than with Dienes 12 subtract eight is equal to four. So I'm going to put my four in here. Two subtract one is equal to one. Now I know that one, isn't one, is one ten because it's my tens column. Then my answer is 14. Exactly the same as my answer here. Now let's go back to this original question. What is the same and what is different between Question 1 and Question 2. When I was subtracting in question one, I was subtracting from a multiple of 10. This was a zero here. There was no number or no one's Diene in my ones blocks here. So I still need to do regrouping. But when I was subtracting from a multiple of 10, I didn't need to remember my ones, because there weren't any ones. For this pair, this time eight is still greater than two. so I still need to do regrouping. But I need to remember that my two is still here. Just like it's here. And when I subtract I don't subtract just from that 10, I subtract from that 12 in here. Well done to those of you that noticed that straight away. I think we're already done. For Part 2 of your independent task today You've got some more equations here. Again, I'd like you to use either drawing out Dienes, expanded methods, or trying to column method to solve these equations. I'd like to have a look, See if you notice any patterns in the numbers, and can you explain them? And again, Tom thinks all of these equations are going to require a grouping. Is Tom correct or not? And I'd like to have a go at explaining why. Please pause the video now and complete your task. Welcome back. Let's have a look at the answers. So 37 subtract 24 is equal to 13, 37 subtract 25 is equal to 12, and 37 subtract 26 is equal to 11. Next column. 53 subtract 38 is equal to 15, 53 subtract 28 is equal to 25, and 53 subtract 18 is equal to 35. Do you notice any patterns in the numbers, and can you explain them? Start with this column here then. I've got 13, 12 and 11 as my answers. The answer decreasing in ones each time. So let's have a look at our equations. 37 stays the same each time by look down the column. 24, 25, 26. Oh! My number is increasing each time. So as my number in my equation increases by one, the number of my answer decreases one. Let's have a look then at this column here, 15, 25, 35. As opposed to the pattern, my answer increasing in steps of 10 each time. So let's have a look then at the numbers in our equation. 53, 53. 53 stays the same each time. So have a look 38, 28, 18. Oh! Are they just my ones stay the same as an eight each time. But the 30, 20, 10. The tens are decreasing in steps of 10 each time, as the answer is increasing in steps of 10 each time. Now Tom thought all of these equations required regrouping. Was he correct or not? Let's have a look. I know that when my number in my ones column that I'm taking away from is greater than, the number that's in the original, this part of my equation. Then I have to regroup. Seven I want to take four away from it. Excuse me three. I didn't need to regroup to do that equation. How about do I need to regroup to do this equation? Can I take five away from seven? Yes I can and it gives me two. Can I take six away from seven here? Yes I can. And it gives me one. Can I take eight away from three without regrouping? No, I can't. Because this number in the ones column is greater than this number in the ones column. So some of my equations required regrouping, but not all of my equations required regrouping. When you look here you've got eight and three, eight and three. This column required regrouping, this column didn't require regrouping because the number was greater that was taking away from than I had remaining. Perhaps regroup here. Well done working so hard today. Please pause the video now to complete the final quiz and answer the last few questions. And I'll see you again saying thank you and goodbye.

Consolidation and application (Part 1)

Consolidation and application (Part 1)

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UnitMaths / Exploring calculation strategies

Maths