Lesson video

Hello everybody, and welcome to today's lesson.

I'm Mrs. Crane and in today's lesson, we're going to be applying and consolidating by looking at our knowledge of different related number facts and how we can derive them and create them and how we can choose the most appropriate and efficient addition and subtraction strategy.

In a moment, I'll go through any equipment that we need for today's lesson.

If you can, can you please turn off any notifications on your phone, tablet or whatever device you're using to access today's lesson on.

Then if you can try and find somewhere nice and quiet in your home so that you're not going to be distracted during today's lesson.

When you're ready, let's begin.

Okay then let's look through today's lesson agenda.

As I said, firstly we're going to be starting off by deriving different facts.

Then we're going to be looking at efficient addition strategies, then efficient subtraction strategies, and then your independent task is going to be a mix of all three of those things.

So you're going to do a part on deriving facts, part on addition strategies and a part on subtraction strategies.

I had to slow down, saying subtraction is quite tricky, so let's see what equipment you'll need for today.

You're just going to need a pencil and some paper.

So if you don't have those things already, please pause your video now to go and get them.

Welcome back and let's get started by deriving some facts.

So let's have a look at how we derive related facts.

So here you can see I've got two ones, add four ones is equal to six ones.

What other facts could I use from this equation? Well, I know that two and four are six, so therefore I know that four and two is six.

That's using the law of commute activity.

Now I know that my whole is six, so I know if I take away four of it, I'm left with two, or if I think back to my whole as six, it hid and it went back again, being mysterious, trying to catch us both out there.

Six this time taking away my two and I'm left with that's right.

I'm left with my four.

So, from that I could think, well, I know that two and four is six.

So I know that 200 add 400 is 600.

If I know that I know that 2020 plus 4,040, is going to give me 6,060.

All based on this fact here, helping me answer questions that are quite a lot trickier if I first looked at them, but I know my number facts.

So actually they're not as tricky as they might seem.

Now, if you're feeling confident and you think you could derive all of the related facts for this equation here, pause your video now.

If you're not feeling so confident, don't worry, we're going to go through them together.

So you can see here five ones, oh not five ones, you can't, let's count them together.

One, two, three, four, five, six.

You can clearly see six ones, so can I.

Add two ones, is equal to eight ones.

Now, let's see what other equations I could have.

So I could have my six plus my two is eight.

Or I could say two plus six is equal to eight.

Then I can use my inverse, use my whole, eight subtract six, there's two remaining, eight subtract two, there's six remaining.

Can you think of any other related facts we could use there? Let's have a look.

Well if I know that eight take away six is two, I know that 80 take away 60 is 20.

If I know that six plus two is eight.

I know that 600 plus 200 is 800.

So we can find lots of different facts out from just this simple equation here.

Now we're going to stop looking at those for a moment.

We'll come back onto that when it comes to our independent task.

What we're going to look at now is the most efficient addition strategy.

So we're thinking about adding.

Now, let's have a look at our equation, 3,564, and I want to add a 4,698.

We have five strategies to choose from.

We could choose to partition one number, we could choose to partition both numbers, we could choose to count on during, using a number line, we could choose to round and adjust, or we could use near doubles.

Let's have a look at those numbers really closely again.

Now for this equation, I would probably partition one or both of those numbers.

They're not that close to count on a number line.

Although this is close to a multiple of 100, it's not that close to multiple of 1,000 for round and adjust, and they're not close enough to each other to be able to do near doubles.

So I would probably choose one of these two here.

Let's have a look then.

So I'm just going to partition one of them.

I'm going to keep this number here.

And I've partitioned 4,698 into 4,000, 600, 90, 8.

Remembering that when we add each one, we use that new sum, that answer to add on our next part too.

If we don't, then we're going to get the wrong answer.

So 3,564 plus 4,000 takes us to 7,564.

Add 60 takes us to 8,164.

Add 90 takes us to 8,254.

Add eight takes us to 8,262.

A much more efficient method of working that out than doing lots and lots of jumps on a number line or attempting to double it when our number doesn't double.

There, I can put my answer in here.

This time, if you're feeling confident and you think you can find an efficient strategy that you would use for this equation, pause the video now to have a go.

If you're not feeling so confident at that, don't worry.

We're going to go through it together now.

So looking at my equation, I can see 6,438, and I'm adding 2,997 to it.

What I notice about this number here, 2,997.

Well, I notice it's close to a multiple of a thousand, so I'm going to choose the method round and adjust.

I'll explain why now.

I'm going to round 2,997 to 3000 by adding on three, then I can add it.

It gives me 9,438.

I can do that real quickly.

I have to adjust.

Remember it's round and adjust.

We can't just round and not adjust.

I'm adjusting by subtracting three because I've added on three too many.

So take away three from this number here, is going to give me 9,435.

I can put in my answer here.

Now we're going to have a look at the most efficient subtraction strategies, thinking about how do we take away? So we have got here 4,835, and I'm taking away 1,213.

I've already decided I'm going to do partitioning here.

I'm definitely not going to count on a number line.

I will be counting a lot of jumps and I can't really very easily round and adjust.

So I'm going to either choose to partition one or both numbers.

Now I'm partitioning one number because I find that most straightforward.

You might find it more straightforward to partition both numbers, up to you.

I'm going to keep my whole here.

So I'm going to keep 4,835, and I'm going to partition 1,213 into 1,210 and three.

I need to take away that 1000 gives me 3,835.

Then I take away my 200, 3,635.

Then I take away my 10, 3,625.

And then my three, 3,622.

So I can put in my answer, 3,622.

If you're feeling really confident, pause the video now to decide which strategy you're going to use.

Then I'd like you to have a go at working it out.

So looking at those two numbers, I can see they're quite close together.

So my strategy shall be to count on, using a number line.

It's going to be efficient because they're not far away from each other.

So I'm going to start.

You don't have to do it using a number line.

You could just do it mentally in your head if you want to.

It's up to you.

So off I'll put in my number, 2,990 from here.

I'm going to make one jump of nine to take me to 3000 and a jump of two to take me to 3002, recombine these two numbers here, nine plus two is equal to 11.

So my answer? Yeah, that's right.

I got carried away.

I was so speedy.

I skipped past the page.

That's right.

My answer's 11.

It takes not a lot of time if we're using that strategy, that's the most efficient one.

So as I said, today's independent task is going to be deriving facts and finding efficient strategies.

There's going to be kind of three main parts to it.

So your first part is look at these two part, three part whole models.

Can you write the related facts for each part whole model and what derive facts can you write? Part two is, there are three additional equations here.

Can you look at the following initial equations, decide which is the most efficient method and calculate your answer.

And then similarly, but for subtraction, have a look at these three subtraction methods, not methods, sorry, these aren't methods, there are clearly equations.

Decide which is the most efficient method though, or strategy, whichever word you'd like to use, then calculate your answer.

Remember to pause the video now to complete your task, but do not forget to resume it once you're finished so we can go through the answers together.

Okay, welcome back.

Let's have a look then at deriving the related facts and what our answers were.

So here I could say, I know that two plus five is equal to seven, and I know that five plus two is equal to seven.

I know that seven subtract five is equal to two and seven subtract two is equal to five.

Here, I could say that two plus one is equal to three, or I could say that one plus two is equal to three.

I could say three subtract one is equal to two, or I could say that three subtract two is equal to one.

And here I can say five plus four is equal to nine.

Or I could say four plus five is equal to nine.

I could say nine subtract five is equal to four, or you can say nine subtract four is equal to five.

Part two then, the efficient addition strategies.

So I'm going to go through the strategy and the answer.

So I would have used partitioning for this equation.

And my answer was 5,877.

This equation here, the numbers are quite close together, so I would have used near doubles.

And my answer would be 3,989.

For this equation here, my numbers are again really close together.

So again, I would've used near doubles and my answer would've been 5,217.

Last but not least, we're going to look at those efficient subtraction strategies.

So which method would I have used? I would probably use partitioning, either one or both numbers, depending on which I felt more confident with.

My answer was 2,604.

Next here, oh, looking at those numbers they're not far apart.

So that's right I would use counting on and maybe a number line to support myself with that calculation.

My answer would have been 23 and here, oh, I'm noticing this number is quite close to a multiple of 1000, so I would use round and adjust.

And my answer would be 2,566.

Fantastic work today.

Don't forget if you'd like to, please ask your parent or carer to share your work from today on Twitter, by tagging @OakNational and using the hashtag LearnwithOak.

Absolutely fantastic.

We've looked at lots of different strategies and you've had to jump between thinking about derived facts, addition, and subtraction.

So super work today.

I've been really, really impressed.

Don't forget to go and complete that quiz and show off all of that fantastic knowledge that you've learnt in today's lesson.

And hopefully I'll see you again for some more math soon.

Thank you and goodbye.