Lesson video

Hello, my name's Miss Robson.

In this lesson, we are going to be looking at the relationship between addition and subtraction.

We're going to start by looking at some addition equations.

Then, we're going to look at the same problem, but look at the subtraction equations.

We're going to talk about related facts, and then it will be time for you to complete your independent task and the quiz.

For this lesson, you will need a pencil, some paper, a part whole model, or if you don't have one, you could draw one on a piece of paper, and some objects for counting.

It might help you to have two different colours.

Pause the video here to collect the resources that you need, and when you're ready, press play.

We're going to start today with some more number bond practise.

We've been doing this in some of our previous lessons, so hopefully you're quite familiar with your number bonds already.

Today, we're looking at number bonds to 8.

I can see that these part whole models have lots and lots of different parts missing.

So some of them have the whole missing, and some of them a have a part.

Your job is to figure out what part is missing.

So, if we look together at this one here, 6 and something make 8.

6, 7, 8.

6 and 2 make 8.

So, you need to write 2 in this empty box here.

Pause the video here to have a go at filling in all of the blanks, and when you're finished, press play.

Let's look at the answers together.

We'll go through and read them.

We'll read them across and down.

So, 0 plus 8 equals 8.

1 plus 7 equals 8.

2 plus 6 equals 8.

Can you join in? 3 plus 5 equals 8.

4 plus 4 equals 8.

5 plus 3 equals 8.

6 plus 2 equals 8.

7 plus 1 equals 8.

And, 0 plus 8 equals 8.

Fantastic.

First, we're going to talk about addition equations, before we look at the inverse of subtraction.

On the screen, I can see some fish.

How many goldfish are there? How many blue fish are there? Can you represent the parts using manipulatives? This is where it might be helpful for you to have some different colours.

Doesn't matter if they're not the same colours as the fish, but just two different colours.

Pause the video here to represent the fish using manipulatives.

So, I'm going to count 1, 2, 3, 4, and I'm using orange cubes to represent the goldfish.

So here I have four orange cubes to represent the goldfish, and I need three blue cubes to represent the blue fish.

So I have four as a part and three as a part.

I've also covered them on the screen.

So if you wanted to, if you have some fish in front of you, you could be covering them with cubes.

That's quite an accurate way to count.

So I've got four cubes to represent the four fish, and three cubes to represent the three blue fish.

So, 4 is a part.

3 is a part.

Let's put that into a part whole model.

4 is a part, 3 is a part.

So now that I've put those numbers into a part whole model, I'm going to have a go at filling in the two different addition equations that I can create from this part whole model.

I can start with the goldfish, and put the goldfish in my head, so, four in my head, and three on my fingers.

Or, I could move the parts around, and we've talked about this with addition before.

Because with addition, it doesn't matter which part you add first, you're still going to have the same whole, because you're adding the the parts together.

So if I add them this way, or if I add them this way, it doesn't matter.

I'm still going to have the same amount all together.

So I could also put the blue fish in my head, and put the goldfish on my fingers, so 3 in my head and 4 on my fingers.

I could do 4 plus 3, or I could do 3 plus 4.

Let's try both and see, just to check that the answers are the same.

So 4 in my head, 3 on my fingers.

Ready to join in? 4, 5, 6, 7.

Or, 3 in my head, and 4 on my fingers.

Ready to join in? 3, 4, 5, 6, 7.

Both times I ended up with a whole of 7.

1, 2, 3, 4, 5, 6, 7.

The whole is 7.

I've completed two different addition equations there, but they are both the same fish and the same story, just in a slightly different order.

So one of the stories, the first one, 4 plus 3, would be add the goldfish and the blue fish together.

The second story would have been the other way around, add the blue fish and the goldfish together.

In both cases, the answer is 7, because the parts are the same, and we're adding them together, just in different orders.

Let's have a look at the same problem, but considering it from a a subtraction equation point of view.

So, what subtraction equation could I write, to show how many blue fish there are? Pause the video here to think about how you could write a subtraction equation to show how many blue fish there are.

We know that all together, there are seven fish.

So let me start with the whole of 7.

And, I want to write a subtraction equation to show how many blue fish there are.

So I'm going to have to take away the goldfish.

So here are my 7, and I'm going to take away the 4 goldfish, 1, 2, 3, 4.

7 take away 4 is equal to 3.

Let's have a look at a part whole model.

So that time, I had 7 all together, and I took away how many goldfish there were to find out how many blue fish were left.

But, I could also have 7 all together, and take away the blue fish, so take away 3 to find out how many goldfish there were.

So, I could have done 7 take away 3, or 7 take away 4.

7 take away 3 is equal to 4, and 7 take away 4 is equal to 3.

In both of those equations, I've used all of the numbers from the part whole model.

So I have a whole of 7 in both, and I have the part of 3 and 4, and 3 and 4.

But, depending on which one I take away from the whole, gives me the other part.

So, 7 take away 3 is equal to 4, but 7 take away 4 is equal to 3.

I've used all of the numbers from the part whole model.

This is the same problem, but looking at it from a subtraction point of view.

So, instead of seeing that there are this many of one colour and this many of another and adding them together, instead what I have done is looked at how many there are all together, taking away one colour to find the other, or taking away this colour to find that much.

The Talk Task is going to be, to look at the part whole models on the screen and talk about the related addition and subtraction facts that you can find out from those part whole models.

I'm going to start by showing you this part whole model over here.

7 is the whole.

3 is a part, and 4 is a part.

For all of these part whole models, we know all of the parts and the wholes.

So it's not going to be about finding the answer.

We have no missing information to fill in, but what we are trying to do is make sure that we are adding parts together to make a whole, taking parts away from the whole to find out what the other part is, and checking to make sure that the maths make sense.

It's not about finding the answer.

It's about proving the different equations.

So proving that this plus this is equal to 7, and that this plus this is equal to 7.

And proving that taking one part away will leave you with the other part.

Okay? So, for the first one, I'm starting with 7 as the whole.

Here is the whole, 7.

And I have used my two different colours to support my addition equation here.

I have 3 plus 4 is equal to 7.

And the other way around, I have 4 plus 3 is equal to 7.

So let me check those on my number line.

3, and I'm going to jump on 4.

1, 2, 3, 4 is equal to 7.

Fantastic.

And 4 plus 3, so counting on 3, 1, 2, 3, is equal to 7.

I found both of the addition equations for that part whole model.

So I could write them down.

3 plus 4 equals 7.

4 plus 3 equals 7.

Then, I'm going to do the subtraction equations.

So I've got my whole, I'm going to stick it together.

7 take away 3 leaves me with 4.

That's correct.

And 7 take away 4 leaves me with 3.

That's correct.

7 take away 3, I have 4 left.

7 take away 4, there are 3 left.

Let's check on the number line.

So for these, I'm starting with the whole and taking away a part.

7 take away 3, 1, 2, 3, is equal to 4.

And, 7 take away 4 is equal to 3.

So 7, 1, 2, 3, 4, is equal to 3.

7 take away 4 is equal to 3.

So, I found the two subtraction equations, as well.

7 take away 3 is equal to 4, and 7 take away 4 is equal to 3.

For the remaining one, two, three part whole models, I'd like you to have a go at using some different coloured objects to represent the different parts and finding two addition equations and two subtraction equations.

Pause the video here to have a go at the Talk Task, and when you're ready, press play.

We're going to go through one of the equations together.

We're going to look at this one here.

So, I'm going to make 5 as a part and 2 as a part.

So, 2 plus 5 two equals 7.

5 plus 2 equals 7.

7 take away 2 equals 5, and 7 take away 5 equals 2.

Hopefully, you managed to find all four of those equations.

Let's quickly check and prove again by using our number line.

So, I'm going to start with the addition equations, starting at 2 and counting on 5.

1, 2, 3, 4, 5, equals 7.

2 plus 5 equals 7.

And 5 and 2 more, 1, 2.

5 and 2 more is 7.

Then starting at 7, to find my subtraction equations, 7 take away 2, 1, 2, is equal to 5.

So that is 7 take away 2 equals 5.

And then, 7 take away 5, 1, 2, 3, 4, 5.

7 take away 5 is equal to 2.

Hopefully, you managed to find all four of those equations too.

We're going to look again at this big picture, and we're going to remember one of the stories that we've told before, the story about the dwarves wearing hats and the dwarves not wearing hats.

I can see that there are five dwarves wearing hats, and there are two dwarves not wearing hats.

Let me pop those parts into my part whole model.

So, 2 is a part and 5 is a part.

The whole is 7.

All together, there are seven dwarves.

I'm going to try and write some related facts about these dwarves.

I might need your help for this.

So, 2 plus what is equal to 7? 2 plus 5 is equal to 7.

If I have 7 all together, 2 and 5 is equal to 7.

I need to add both parts together.

So, then 5 plus what is equal to 7? 5 plus 2 is equal to 7.

Using my other part, 5, 6, 7.

2, 3, 4, 5, 6, 7.

Either way that I add them together, I end up with 7.

There's my second equation.

So, 2 plus 5 is equal to 7, and 5 plus 2 is equal to 7.

Now, I'm going to think about my subtraction equations.

I'm going to start with my whole.

Here, I have 7 all together, and I'm going to take away 5.

7 take away 5 is equal to 2, my other part.

7 take away 5 is equal to 2.

So, my last equation will be 7 take away 2.

7 take away 2 is equal to? Is equal to? 5.

7 take away 2 is equal to 5.

There, I have written the four related facts.

So, related means they're all part of the same problem solving question.

I have the same part whole model for all of those equations.

7 is the whole.

5 is a part.

2 is a part.

But I have shown you that 2 and 5 makes 7, and that 5 and 2 make 7.

I've also shown that 7 take away 5 is equal to 2, and 7 take away 2 is equal to 5.

I've used the same parts, but in lots of different ways to write different equations.

That is what your independent task is today.

Here, we have the dwarves.

Now, they've been broken up into parts.

This one is the same as the one that we've just looked at.

So, it is your job to look at the picture and fill in the missing parts.

You need to complete the related addition and subtraction equations.

So they have the equation written for you with just one missing part.

This is the same story.

This one is about the elves, sorry, the dwarves that are not wearing hats and the dwarves that are wearing hats.

We're going to start by filling in the part whole model.

There are five elves.

I don't know why I keep calling them elves.

There are five dwarves wearing hats, and there are two dwarves not wearing hats.

All together, there are seven dwarves.

So, you can get your cubes to help you.

Using two different colours will help to have the two different parts.

So, I've got five blue cubes and two orange cubes.

The first equation is 5 plus 2 is equal to 7.

5 plus 2 is equal to the whole of 7.

And the second equation is 2 plus 5 is equal to 7, the whole again.

2 plus 5 is equal to 7, just like 5 plus 2 is equal to 7.

The next equation is a take away equation.

7 take away 5.

So, take away the part that is 5.

I am left with 2.

7 take away 5 is equal to 2.

So the last equation is 7 take away 2.

7 take away 2 is equal to 5.

The important part here to remember is not to get too carried away with just trying to put the numbers in the right place.

We don't want to just go through the rhythm and add in the number that we think is missing.

Using the cubes and actually taking things away or adding them together will help you to understand whether the equation is correct or not.

You can't just rely on the fact that one of the numbers is missing so you need to put that number in.

You first need to make it and check to make sure that, that equation makes sense.

Then, you can write the number in.

And afterwards you could check to see if all of the numbers from the part whole model have been used in your equations.

It's time now for you to complete your independent task.

You're going to be trying to write the related facts about the part whole models and the pictures that you can see.

Pause the video here to complete the task, and when you're finished, press play.

Let's go through the independent task questions quickly together and look at the answers.

So, here we have the parts of 1 and 6.

One elf is wearing glasses and six elves are not wearing glasses.

So, 1 is a part and 6 is a part.

One elf wearing glasses, and six not.

1 plus 6 is equal to the whole of 7.

1 plus 6 equals 7.

And, six elves not wearing glasses plus one elf, yes, wearing glasses.

6 plus 1 is equal to 7.

6 and one more is 7.

Then we look at the whole, and we try our take away equations.

All together, there are seven elves and one is wearing glasses.

How many are not wearing glasses? Six.

7 take away 1 is equal to 6.

Seven elves all together, and six are not wearing glasses.

7 take away 6 is equal to 1.

7 take away 6 is equal to 1.

Well done for all of your hard work in this lesson.

I hope that you've enjoyed yourself as much as I have.

I really, really enjoyed exploring related facts with you.

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

We'd love to see the work that you've been getting up to.

Don't forget to go and complete the quiz.

Thanks again for joining me, and see you next time.