Lesson video

Hi there, my name is Miss Darwish.

And for our maths lesson today, we are going to be calculating across from zero.

But before we get started with the lesson, if I can just ask you to ensure your sat somewhere quiet, peaceful, calm, somewhere where you can get some work done.

Okay, so for today's lesson we're going to be, first of all, looking at consecutive cuboid, like a dice.

And then we'll look at some consecutive numbers and then we're going to be spotting some patterns when it comes to adding and subtracting throughout consecutive numbers.

And then at the end of the session, there will be a quiz for you to go and complete.

So let's get started.

So for the session just before we start, if I could just ask you to grab yourself a pencil or pen and something to write on and then a ruler.

Okay, ready? So consecutive numbers.

This cuboid has been labelled with consecutive numbers.

We can see three of the sides can you see that? So it's basically, like a dice except when a dice we'd have the numbers 1, 2, 3, 4, 5, 6.

This one's a bit different.

All the numbers are consecutive, but we can only see three of the sides.

What do you think are the numbers that we can't see? What do you think, do you want to write something down? What could the other numbers be that we can't see? Okay, should we have a look together? So, we can see 8, 9 and 10.

And of course a cuboid has 6 faces.

So if we can see 8, 9 and 10 the other three numbers could be 11, 12, and 13 and that would have a total of 63.

What else can it be? Is it just one option? I think there's more than one possibility.

So we could have 5, 6, 7, 8, 9, 10.

So we've still got 8, 9 and 10 there but also we could have 5, 6 and 7 that works.

So one possibility could be 8, 9, 10, 11, 12, 13, where 8, 9 and 10 are at the start.

And then we have 11, 12, 13 and then another possibility is that 8, 9 and 10 are the last three numbers of the consecutive.

And then we've got 5, 6 and 7.

And that gives a total of 45.

Are there any more possibilities? Did you have something close or did you have the same? Can you think of something else or is that's it? Okay, let's have a look.

Of course that's not it.

What if 8, 9 and 10 were in the middle and we had 6, 7 and 11 would that still work? Yes cause we still have 8, 9 and 10, the three faces that we can see and then there's also 6, 7 and 11 could be another three faces that we can't see.

And that would have a total of 51.

Well done if you said that.

Another possibility, we could have again 8, 9 and 10 in the middle just one before 8 would be 7.

And then the two numbers after 10 would be 11 and 12.

And that would definitely, work as well.

Let's have a look at that cube again.

Remember six faces on a cube 8, 9, and 10 are the only digits we can see.

So, so far we've seen one possibility, two possibilities, three possibilities, four possibilities.

And each one, did you notice has a different total? Okay, let's have a look at some consecutive numbers now.

So I've got three consecutive numbers in front of me.

2, 3 and 4.

Tell me why are they consecutive numbers? So 2, 3, 4 have a difference of one each time.

2 and 3 have a difference of 1, 3 and 4 have a difference of 1.

Well done okay, now let's have a look at 2, 3 and 4 Now the digits 2, 3, and 4.

I'm going to call them digits for now instead of numbers can carry any sign okay.

It can be a positive 2 or a negative 2.

3 can be a positive 3 or it can be a negative 3.

And the number 4 can be a positive 4 or it can be a negative 4 well done.

Now I want you to have a bit of thinking time now, maybe get your notepad or your piece of paper and your pen or pencil out and see how many different answers you can make.

Okay, so if you were to select three cards, what could you do? What different answers can you make? It could be plus 2, minus 3, plus 4, plus 2, plus 3, plus 4, minus 2, minus 3, plus 4, have a bit of a playground and jot down some calculations.

I'll give you a few seconds write as many as you can, until I say, drop your pen, pen drop or pencil drop.

I'll have a go as well.

And 3, 2, 1 pencil drop.

Okay, what did you come up with? In the time I gave you I know I didn't give you long enough but just some different answers to have to go through all the possibilities.

What did you make? Okay, should we have a look together? So we could have the easy option maybe you did that one as well 2 add 3, add 4 is equal to 7.

So I just took positive integers 2 add 3 add 4 is equal to 7.

Well done if you said that.

Or we could have had positive 2, positive 3, but negative 4.

So 2 add 3 takeaway 4 is equal to 1.

2 add 3 is equal to 5 and 5 takeaway 4 is equal to 1.

Well done if you said that.

Okay, or we could have had 2 takeaway 3 takeaway 4.

So if we have a look at our number line, 2 takeaway 3 takeaway 4, we would start at 2 and we take 3 away first of all, so we start at 2 we take 3 away we land on minus 1, and then we take 4 away because we start at 2 takeaway 3 takeaway 4.

So put your finger at 2, takeaway 3 for me.

You are at minus 1 correct.

Takeaway 4 where are you? Minus 5 so, 2 takeaway 3 takeaway 4 is equal to minus 5.

So that's a different answer that we could've made.

Well done if you said that.

Okay, let's look at another possibility.

This time I selected positive 2, negative 3, positive 4.

So if we start at the 2 put your finger on the 2, takeaway 3 we are at minus 1 and now we got to add 4.

We got to go back that way.

And we're at 3.

So 2 takeaway 3 add 4 is equal to 3.

So we started off at 2 we took 3 away, which landed us on minus 1 and then we added 4, which is equal to 3.

So different answer we could have got lots of different options.

Maybe you had some of the similar ones.

Okay, let's have a look at spotting some patterns now.

So I've got down a few calculations.

Do you want to read them out with me? So the first one, 1 add 2 takeaway 3 is equal to 0.

Let's read the second one out together.

2 add 3 takeaway 4 is equal to 1.

Let's read the next one out together.

3 add 4 takeaway 5 is equal to 2.

The next one 4 add 5 takeaway 6 is equal to 3.

And then last one, 1 add 2 takeaway 3 is equal to 0.

Okay, have a think can you see any patterns there? What can you spot? So what have you noticed with the answers? The answers are consecutive the first answer was 0, 1, 2, 3.

Okay, what about the actual questions, the calculations? Think is on the 4 on the right.

Don't worry about the extra one there.

I'll come back to that later.

Did you notice a similar pattern in the calculation as well as the answer? So the answers are consecutive and also the calculations are sort of consecutive we start off with 1, then we start off with 2, then 3, then 4, and then we add on 2 then we add on 3 then we add on 4 then we add on 5.

And then even when we take it away, the consecutive taken away, 3 taken away with 4 taken away 5 taken away 6.

So lots of different patterns there to spot.

Okay, what about them? 5 add 6 takeaway 7.

What is the answer to that calculation? Have a think and then write it down for me.

Okay, did you write something down? Did you get an answer? Did you see the pattern as well? 1, 2, 3, 4, 5 did you spot a pattern in the answer as well? So the answers we have 0, 1, 2, 3.

This time we've taken away 7 through 5 add 6.

Well done if you said 4 is what follows along from the pattern well done.

Okay, this time then, a number add a number, takeaway a number is equal to 5.

But the digits make sure they're consecutive.

Not the number because if it's positive and negative it won't be consecutive.

Make sure the digits are consecutive again.

Again, we're following the pattern.

What did you get? 6 add 7 takeaway 8 is equal to 5.

Well done if you said that.

Nice and easy right? It's always easy calculations and quick.

I love how calculation can sometimes be really quick when we can spot some patterns.

Okay, let's do a bit of a prediction but without calculating anything okay.

So give a guess, have a guess.

Jot these down.

Write the actual calculation and then the answer without actually calculate anything.

Guess what the answers might be here.

94 add 95 takeaway 96 is equal to.

So write that down for me.

And then 108 add 109 takeaway 110 is equal to.

Then write the answer for me.

Okay, I'm going to give you 6 more seconds.

So thought you using column or anything like that? Just predict what the answer might be.

Okay, ready? So let's have a look at these.

Now 1 add 2 takeaway 3 is equal to 0.

Do you notice how the answer is also consecutive? It's actually the first number.

So 0, 1, 2, 3.

And then the second one, 2 add 3 takeaway 4 is equal to 1.

It's the consecutive number before the first number in our calculation and 3 add 4 takeaway 5 is equal to 2.

2 comes before 3, 4 add 5 takeaway 6 is equal to 3.

3 comes before 4 and the same for the next two.

So 94 add 95 takeaway 96 is equal to.

What's one less than 94? 93 well done if you said that.

And then 108 add 109 takeaway 110 is equal to, 107, 1 less than 108.

So a lot of patterns to spot there, consecutive numbers and calculations.

Well done if you got those right.

Okay, well done.

Now it's time for you to pause the video right now and to complete your independent task, good luck.

Okay, welcome back.

How did you find that? Let's have a look.

So complete the calculations below what to do you notice? So 1 takeaway 2 add 3 is equal to 2.

2 takeaway 3 add 4 is equal to 3.

3 takeaway 4 add 5 is equal to 4.

What do you notice there? The answer is the same digit as that middle number in the calculation.

Did you notice that? So now when we do larger numbers, it will be easier to do 87 takeaway 88 add 89 is equal to 88.

We get that middle number 983 takeaway 984 add 985 is equal to 984 bottom, 1002 takeaway 1003 add 1004 is equal to 1003.

Hopefully, you spotted those and you didn't add 1002 and then takeaway 1003 on the number line and then I'd 1004.

Cause that would have taken a very long time.

So it's always good to spot patterns.

Okay, if you would like to share your work with us here at Oak National, then please do ask your parent or carer to share your work on Twitter, tagging @OakNational and to use the #LearnwithOak.

well done on all the brilliant successful learning that you have completed today.

Now it's time for you to go and complete the quiz.

Good luck.