Lesson video

Hi there.

Thank you for joining me.

My name is Miss Jeremy, and today's math lesson is focused on using and explaining addition strategies.

So get yourself sorted with a nice quiet space.

And once you're ready, click play to begin the lesson.

Let's begin with our lesson agenda.

So in our warmup today, we're going to be looking at number bonds to 100.

We'll then look at some addition strategies that you can use, and then we'll apply this knowledge to using some magic squares, or to completing some magic squares at the end of the lesson, before your independent task and quiz.

For today's lesson, you will need a pencil and some paper and a nice quiet space.

So feel free to pause the video at this point, find those resources, and then press play once you're ready to begin the lesson.

Let's begin with our warmup.

We're going to be looking at some number bonds to 100.

On the left hand side here in pink, you can see that we have got some two digit numbers, and on the right hand side, we've got some matching two digit numbers.

We need to match up the pink side to the blue side so that we have got our number bonds to 100.

So let's have a look at the first one together, and then I'd like you to look at the other three independently.

So 42 plus something is equal to 100.

Well, when I'm thinking about this, I need to consider my number bonds to 10 to help me out here.

And I know that 42 ends in a 2.

If I use my number bonds to 10, I know that 2 plus 8 is equal to 10.

So I'm looking for a number that has 8 at the end of it.

Now, it could either be 88 or 58.

But I know that in this case, because I've got my 40 at the beginning, it couldn't be 88 because 80 plus 40 goes over 100.

So in this case, it's going to have to be 58.

So 42 matches up to 58, and 42 plus 58 is equal to 100.

Now I'd like you to look at the next one.

What are we going to add to 55 to equal 100? You use your number bonds to 10 to help you out with this one.

I'm going to give you 5 seconds.

So in this case, you should have seen that you were looking for a number that had a 5 as its second digit as its digit in the ones column, and the only one that was on offer was 45.

So 55 plus 45 is equal to 100.

Looking at the next one here, we've got 89.

So, 89.

Using my number bonds to 10, I know that actually I would need to add a 1 to a 9 to equal 10.

The only number that has a 1 at the end of it is the number 11.

So therefore, 89 plus 11 is equal to 100.

And then finally the last one, I know that 12 plus something is equal to 100.

And in this case, the answer is 88, because 2 plus 8 is equal to 10.

And then we've got our 80 plus our 10, which is equal to 90.

Overall, 90 plus 10 is equal to 100.

So you can see how we can use our number bonds to 10 to help us with identifying our number bonds to 100.

So, moving on.

Today we're going to be looking at some different addition strategies.

And I want to pose a question first of all.

My question is this.

This person here is stating, "When we're adding numbers together, we should always use the column method." And he's provided an example there, 52 plus 31.

We should always use the column method whenever we're adding numbers together.

Do you agree with this statement or do you challenge it? What do you think about this statement? Spend a couple of seconds now identifying what you think.

So in my opinion, I think the column method is a great method to use.

However, I don't think it's always necessary.

The column method is ideal when you need to regroup different digits within your columns.

So for example, if you had the number 299 and you're adding 156, I can see I will need to regroup the digits in my ones column and in my tens column, because they go over and they create a double digit, and we can't get a double digit into our columns.

So I know that for regrouping purposes, column method is great for that, because it allows us to lay out and regroup really easily.

There are other addition strategies to use though, and I think some of them are more efficient than the column method, and actually quicker to use.

If you're in a shop and you're trying to count out money, if you're trying to add things together in your head, often you don't have a piece of paper and a pencil there to write out your column addition.

So, actually, often it's quite useful to use some of the other addition strategies instead of the column method.

And you can always use the column method to check.

We're going to be looking at some of those addition strategies today.

So let's start with the partitioning method.

Partitioning means to break apart into different parts.

And the partitioning method is a great method to use when you don't need to regroup.

This is one of the addition strategies that I often use if I'm adding together two or three numbers that don't require any regrouping.

Let me show you how the partitioning strategy works.

We've got the question, 52 plus 31.

What I'm going to do is partition each of those numbers into tens and ones.

So I'm partitioning 52 into 50 and into 2, and 31 is going to be partitioned into 30 and into 1.

Now, what I'm going to do is I'm going to add together my tens, and then I'm going to add together my ones, and then I'm going to put them all together.

So what I'm actually doing is 50 plus 30.

You don't need to write this out, but I'm just showing you what my thought pattern is.

And that is equal to 80.

And then I'm doing 2 plus 1, which is equal to 3.

And altogether that is equal to 83.

Now, I could have done that in my head.

I could have worked out that 50 plus 30 is 80, 2 plus 1 is 3, the answer is 83.

And that saves me having to write out a column method to solve this problem.

So partitioning is a great strategy to use if you don't need to regroup.

We've got another example on the screen here.

71 plus 14.

I'd like you to spend a little bit of time now identifying how you would use partitioning to solve this.

If you want to pause the video, you can pause it to complete this addition equation.

But if you think you can do it in your 10 seconds, then spend 10 seconds doing it now.

Okay.

Let's look at it together.

So, partitioning out these numbers, I can see that I'm partitioning the 71 into 70 and 1, and the 14 into 10 and 4.

And I'm going to add together my tens first of all.

I've got 70 plus 10, which is equal to 80, and then I've got 4 plus the 1, which is equal to 5.

So, adding those together, the answer is 85.

So here partitioning is a really useful strategy to use, particularly if no regrouping is required.

So always remember if you don't have to regroup and you've worked out you don't need to regroup, use your partitioning.

Let's move on and look at another example of an addition strategy that we can use instead of the column method.

So this addition strategy is called the rule or the law of commutativity.

Quite a tricky one to say.

The word is commutativity.

And what the role of commutativity says to us is that when we add or multiply together numbers, we don't need to worry about which order we put the numbers in, because the answer is the same.

Now, really importantly, this works just for our addition and our multiplication.

It doesn't work for subtraction and division.

What we say with this particular rule is that for an equation like 17 plus 41 plus 3, if I wanted to mix up the numbers in that particular equation and start, for example, with 3 instead, the answer would be exactly the same.

And that works for addition and also multiplication.

Now, it works really well for a question like the one on the screen.

Because if I were to try and complete this equation in the order that it arrives in, so, 17 and then adding that onto 41, I might struggle with that a little bit.

I mean, it's okay because there's no regrouping, but what I really want to do is I'd like to add 17 and 3 together first.

And the reason is that they are number bonds.

17 plus 3 gives me 20.

I know that.

I've got that number bond knowledge already.

And if I know those are 20, if I know 17 plus 3 gives me 20, then all I need to do, is in my head, add 20 to 41.

And I can do that really easily, because 20 is a nice round number.

It's an easy number for me to work with.

I can just add it onto my tens.

I can see straightaway the answer is 61.

So where might have been tempted in the past to use a column method to do 41 plus 17, and then maybe add on the 3 afterwards, if you swap around the numbers in the equation and work them so that they work for you, actually using this rule of commutativity, you can get to the answer really efficiently without needing to write anything down.

So have a look at this example and see what you think about this one.

32 plus 16 plus 18.

Have a think.

Which of those numbers should we swap around? Which ones would be best to work with first, using our number bond knowledge? And then have a look at what the answer might be.

I'm going to give you about 10 seconds to do that.

Okay, so I can see straightaway here, using my number bonds to 10, I'm remembering that 2 plus 8 gives me 10.

So actually, I'd like to add my 32 and my 18 together first.

Knowing that 8 plus 2 gives me 10, all I need to do then is I have my 30 and my 10, which gives me 40.

Plus my 8 and 2, which is 10.

That gives me 50.

So I know that I've got 50 plus 16.

And I can do that in my head really easily.

50 plus 16 is equal to 66.

So, super simple.

Didn't need to write anything down.

This is a question you might be tempted to use the column method for.

We don't need to.

Use those number bonds, look for those digits that go together, and swap them around based on the rule of commutativity.

So this is a really great rule to use if there are number bonds.

Looking at the next type of math strategy, addition strategy that we can use, it's called round and adjust.

Now, round and adjusted does exactly what it says on the tin.

If a number is close to another number, we can add a little bit onto it, round up to that number that's easier to use, and then adjust for it later on.

Let me show you an example.

I've got 49 plus 13.

Now, this would require, traditionally, me using a column method because I can see as regrouping in this in the ones column.

But instead of that, why don't I round and adjust? 49 is a tricky number to add to 13.

But 50 is a very easy number to add to 13.

So what if I were to just make this into 50 instead? I'm going to round it.

I need to add 1 to that 49 to make it 50.

So I need to remember that I've added 1, because I need to take that 1 away later.

But at the moment, that's 50.

So 50 plus 13.

Well, that gives me 63.

Now that I've rounded, I need to adjust for that rounding.

So I need to remember I added on 1.

So now I need to take away 1.

And my answer is 62.

That's rounding and adjusting.

You look at a number that is close to a much easier number.

You round to that number by adding or subtracting, and then whatever you did before, you have to do the opposite to adjust for it later on.

Let's look at another example.

61 plus 23.

Which number would you like to around and adjust? And what is the answer to this question? Spend 5 seconds working this one out.

Okay, let's see whether we can round and adjust.

So I can see that 61 plus 23, I could use partitioning for this actually fairly easily, but I can also use rounding and adjusting, because I know that 61 is very close to 60.

I have to minus 1 to get to get there.

And so I can do 60 plus 23 in my head really easily.

I know that's going to be 83.

But because I subtracted 1 earlier on, I need to adjust for it.

I need to add 1 on now.

So my answer is actually 84.

I rounded and then I adjusted afterwards.

And you can see that rounding and adjusting is really useful to avoid the need for regrouping.

So if you don't want to regroup, like in our first example, round and adjust and make it easier, use easier numbers for you.

Always remember that whatever you did at the beginning, though, you have to go back and adjust for it at the end.

That's really important.

So we've looked at three methods.

We've looked at partitioning, where we break the numbers apart into tens and ones.

Then we've looked at commutativity, where you can mix up the order of the numbers in the equation.

And then we've looked at rounding and adjusting, where you can round to an easier number, add the numbers together, and then adjust for it afterwards.

There are three equations on your screen that I'd like you to complete using each of those strategies.

So for A, use partitioning, for B, use commutativity, and for C, use round and adjust.

Spend a couple of minutes doing that now.

Pause the video to complete the task and then resume it once you're finished.

Okay, let's have a look at the answers.

So, mark your own work as you go.

You should have got 87 for the first one, 83 for B, and 56 for C.

And you can see here that there's absolutely no need to use the column method for any of these equations.

We have three really good addition strategies, some of which you can do in your head without even writing a single thing down on a piece of paper.

For the next part of the lesson, we're going to be looking at applying our three new addition strategies, partitioning, commutativity, rounding and adjusting, to a concept called the magic square.

And this is what you can see on the screen now.

The magic square is set out in a way that it is a 4 by 4 grid.

For each row, column, and diagonal on this grid, the total sum of the numbers in those boxes is 34.

So to give you an example, if I were to add up all of the numbers in this column here, it would give me 34.

If I were to add up all of the numbers in this row here, it would give me 34.

And if I were to add up all of the numbers in this diagonal, just here, as you guessed, it would give me 34.

Our challenge is to work out which numbers we should place in these boxes.

And we're going to be using our addition strategies to help us out with that today.

So let's look at some examples.

As you can see on the screen, there are three circles that are highlighted in pink.

Those are the first three examples of parts of this magic square that we can fill in using addition strategies.

And we're going to have a practise of that right now.

So let's begin by looking at the number that is on the bottom left of our screen.

I'm going to call that a, and this one up here is b.

So what we're going to do is see whether we can work out what a is, based on the information that we have, that that entire row should equal 34.

The first thing I'm going to need to do is identify what these three numbers are when added together.

And I'm going to use some of my addition strategies to help me with that.

Once I've worked out what those three numbers are altogether, I'm then going to need to subtract that from 34 to work out what that missing part is.

So, these are my calculations.

I'm going to write a so I know I'm focusing on circle a.

I need to add 13, plus 8 plus 1.

And the first thing I'm going to do is use my rule of commutativity.

Because I could work in order here.

I could start with 13 here, add on 8, add on 1.

But actually, I think I'd like to add 8 plus 1 first, because I can do that in my head.

I know that's 9, and that's really easy for me to do so.

So the only thing that's left for me to do is 13 plus 9.

Now, if I wanted to, I could use a column method for this.

I could use my fingers to count on.

This does require regrouping for the column method.

So actually what I'd rather do is use the round and adjust strategy, because I can see that 9 is very close to 10.

What if I were to add on 1 and make this into 10, and then add 13 to it? I would get 23.

Then what if I were to adjust it by minusing 1? Because I added on 1 to round it first, I need to undo that.

I'm going to minus 1.

And I know that the answer is 22.

So I know that all three of those numbers together is equal to 22.

Remember, I'm not done yet, because I need to take it away from 34.

So I'm going to do 34 minus 22.

And I can do this using partitioning again.

I can do 30 minus 20, which is equal to 10.

4 minus 2, which is equal to 2.

My answer is 12.

So there I go.

I'm going to put 12 in that box there.

And I can check it.

I can add that together, those numbers together, in my head if I wanted to make sure they equal 34.

So I could maybe do my number bonds.

And by adding 12 plus 8, knowing that equals 20.

20 plus 13 is 33, plus the 1 is 34.

I know I'm spot on correct with that strategy.

So let's move on to b, and let's have a look how we're going to work out the answer to b.

So now I'm going to put b at the top, because I'm working all my calculations for b.

I need to add together those first three numbers.

So I'm going to do 11 plus 6 plus 13.

So, looking at that series of numbers, I think what I'm going to do is use the partitioning method initially to help me out here, because I'm going to add 11 plus 6 first.

And I can see straightaway, using partitioning, I've got my one 10 and then I've got to add my 1 and my 6.

That gives me 7.

So altogether, this is equivalent to 17.

And then I need to add on my 13.

And straightaway, I can see my number bonds to 10 here.

I can help myself out here, because 7 plus 3 is equal to 10.

So if I've got 10 there, and then I'm adding a 10 and a 10 there, that's equal to 20.

So I'm doing 20 plus 10.

So altogether, that's equivalent to 30.

So I know that those numbers are equal to 30.

And remembering that actually I need to get to 34 for the whole entire column.

Don't even need to write anything down.

I know the difference between 30 and 34 is 4.

So this first top number up here must be 4.

So that was even quicker than the first one.

You can see I used partitioning to initially add together two of the numbers, and then I spotted my number bonds there that helped me with answering the very final parts before I found the difference between the two.

So it's your turn to have a go.

We worked out 12 and 4 together.

You can see them written in green there.

I'd like you to use partitioning, commutativity, or rounding and adjusting to work out what c and d, we'll call these c and d, will be.

Remembering for c, you're looking at the row that goes along here and remembering that the row should equal 34 altogether.

And for d, remembering that you're looking at the diagonal that goes all the way across here.

And the diagonal should also equal 34.

Pause the video now to complete the task and resume it once you're finished.

Okay, how did you get on? Let's have a look at what the answers are.

So for c, let's focus on that first.

Well, I decided for c, I was going to use a round and adjust approach here.

So I had 9 plus 4 plus 7.

And actually, I think 9 is very close to 10.

So I'm going to add on 1 to that.

And 10 plus 4 is equal to 14.

So 14 then plus 7 is equal to 21.

I can use my knowledge of my 7 times table to help me there.

But then I've got to minus the 1 afterwards.

And so that's equal to 20.

So, those were equal to 20 altogether.

I needed to get to 34, and I know that the difference is 14.

So you should have got 14 for that top number there.

Then looking at the diagonal, then looking at d, the circle d, well, straightaway, I can see that I can use, I've got to do my 7 plus 11 plus 1.

I'd like to do 11 plus 1 first of all.

So that gives me 12.

12 plus 7.

I can use my partitioning to do that, because I know that 2 plus 7 is equal to 9.

So my answer there is 19.

I need to get to 34.

So if I wanted to get to 34, I could either use the column method to subtract, or I could count onwards.

So I can start at 19 and see how long it takes to get to 34.

And you should have seen that it should be 15.

So d should be filled in by the number 15.

So now that we've had a practise of using the magic squares, it's time for your independent task.

On the screen, you can see two magic squares.

But this time, the sum of each column, row, and diagonal is not 34.

It's 70.

I'd like you to use the same strategies we've been learning today.

So your partitioning, commutativity, and rounding and adjusting to work out what the missing parts of those squares are.

Remember, you're going to have to do some parts before others.

So for example, for the first square, you are going to find that you'll need to fill in things like this one first, because you've got three in a row, first of all.

Once you've done that, you can probably fill in this one.

And then after that, you can fill in some of the others as you go.

So do have a look at what you are able to fill in first, and then next you will have to complete the squares in a certain order.

Once you've finished, do come back and join us, because we'll go through the answers together.

Pause the video now to complete your task and resume it once you're finished.

So, as you can see on the screen here, we've got all of the answers.

Feel free to pause the video now to mark your learning to check how you got on today.

Thank you for joining me today, and well done for all your hard work.

If you'd like to, please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Thank you so much for joining me again today for another math lesson.

It's been great to have you.

Do join me again soon.

Bye-bye.