Lesson video

Hello, I'm Miss Miah and I'm so excited to be a part of your learning journey today.

I hope you enjoy this lesson as much as I do.

In this lesson, you are going to be explaining the relationship between adjacent multiples of 9.

Your key words are on the screen now and I'd like you to repeat them after me.

Adjacent, multiple, fantastic.

Let's find out what these words mean.

Adjacent means next to each other.

And the second definition is multiple and multiple is the result of multiplying a number by another whole number.

Now this lesson is all about the 9 times tables, but in particular we are going to be explaining the relationship between the adjacent multiples of 9.

We've got 2 lesson cycles here and our first lesson cycle is all to do with adjacent multiples of 9 and our second lesson cycle, we are going to be comparing the adjacent multiples.

I'm super excited.

And in this lesson we've got Andeep and Laura to help us with our mathematical thinking and they're going to be joining us on our journey.

Let's begin.

So Andeep writes multiples of 9 in order and looks at adjacent numbers, and you can see that he's presented this in a table.

So adjacent numbers, remember that it means numbers that are next to each other.

Have a look at the numbers there and look at the multiples.

What patterns do you notice? Well, adjacent multiples have a difference of 9.

What does that mean? Well, let's have a look at the column.

When moving down the column, the product increases by 9.

And when moving up the column, the product decreases by 9.

Over to you.

I'd like you to identify what the adjacent multiple is.

We're starting at 45 and ooh, we are adding 9.

You can pause the video here and click play when you're ready to rejoin us.

Well, how did you do? If you got 54, you are correct because 45 add add 9, gives us 54, so that means our adjacent multiple to 45 is 54.

Now, Andeep looks at the first eight multiples, the digits within the multiple swap after 45.

Ooh, have a look.

Now, Izzy says, "What do you mean?" Well, it goes 45, 54.

So the digits 4 and 5 swap.

The next multiple is 63, which is 36 with digits swapped.

I see.

And 72 has the same digits as 27.

So what will 9 groups of 9 be? Have a think.

So over to you.

I'd like you to have a think about that.

Use Andeep's pattern to say what 9 groups of 9 will be.

You could pause the video here.

Well, 9 groups of 9 is 81 because it has the digits of 2 groups, which is 18, but we've swapped the digits around.

That is such a cool pattern.

Let's move on.

Now, Andeep notices another pattern.

I can see a pattern with the tens and ones digits.

Ooh, I wonder if you can see something between the tens and ones digits too.

What do you mean? Well, let's look at these 3 multiples and the 3 multiples that are highlighted here are 18, 27 and 36.

As you go down the list, the tens digit increases by one.

The adjacent multiple has one more 10 each time.

There's a pattern in the ones digit too.

As you go down the list, the ones digit decreases by one.

The adjacent multiple has one fewer one each time, but this is not a perfect pattern.

The adjacent multiple of 9 to 90 is 99, which actually doesn't fit the pattern.

Ah, so we need to be careful.

What about after 99? Well, the next adjacent multiple is 108, which is 10 tens and 8 ones.

So the pattern resumes again.

It's a good pattern for most of the multiples.

Here's another pattern.

So the digit sum of the multiples of 9 here is 9.

Well for example, the digit sum of 18 equals 1, add 8, which is 9.

The digit sum of 45 and 54 is 4 plus 5, which is equal to 9 because the digits are the same.

Ah, okay, but I know that 11 times 9 is 99 and the digit sum is 18, not 9.

18 is a multiple of 9.

The digit sum of a multiple of 9 is always a multiple of 9.

Over to you.

I'd like you to use other patterns to say what 9 groups of 9 will be.

You could pause the video here and click play when you're ready to rejoin us.

So how did you do? Well, there were various answers.

You may have got that 9 groups of 9 is 81 because it has one more 10 and one fewer one than 72.

9 groups of 9 is 81 because it has a digit sum of 9.

Let's move on.

Adjacent multiples can be represented on a number line, and here we can see multiples of 9 going from zero up to 45.

Now you can add or subtract 9 to find the adjacent multiples.

So the adjacent multiples of 18 are 9 and 27.

Now it's 9 because we've subtracted 9 and the next multiple of 9 from 18 is 27 and that's because we've added 9.

27 and 9 are multiples of 9 because their digit sum is 9.

Their tens and ones digit also follow the pattern that we discussed previously.

Now the adjacent multiple of 72 is? how many ways can you justify your answer? You can pause the video here and click play when you're ready to rejoin us.

So how did you do? Well, one adjacent multiple of 72 is 81 and that's because we've added 9.

You may have also got 63, and that's because you may have subtracted 9.

Now you can record an adjacent multiple using a mixed operation equation.

Now if you're wondering what that is, a mixed operation equation usually includes different operations within the same equation.

So you might have something like multiplication and addition in the same equation.

So for example, we've got the multiple 18 here and we can see that adjacent multiples of 18, which are 9 and 27.

We can see that 18 can be represented as 2 times 9.

Now this is really important.

We are looking at the number 18.

So 18 is 2 groups of 9.

27 is 3 groups of 9 or one more group of 9 than 18.

So how can we represent this? Ah, we can do this using a mixed operation equation and I'll show you how.

So we know that 27 is 3 groups of 9 or one more group of 9 than 18.

So we can write this as 2 times 9, add 9.

Let's look at another example.

So this time we've got 36.

We've added 9 to get 45 as our adjacent multiple of 9.

You can write this as 5 times 9 is equal to 4 times 9, add 9.

So 45 is equal to 4 groups of 9, add 9.

And another example here would be we've got 99 and we subtracted 9 to get 90.

So that means 10 groups of 9 or 10 times 9 is equal to 11 times 9, subtract 9.

Or in other words 90 is equal to 11 groups of 9, subtract 9.

Over to you.

You are going to be completing the equation.

Something is equal to 8 times 9, subtract something.

Now you've got a bit of help on the screen there.

You can pause the video here and click play when you're ready to rejoin us.

So how did you do? If you got 63 is equal to 8 times 9, subtract 9, you are correct.

You may have also got, instead of 63, you may have written 7 times 9 is equal to 8 times 9, subtract 9, which is also correct.

Onto your main task for this lesson cycle.

So for question one, Andeep says that adjacent multiple of 9 to 45 is 53.

Andeep is incorrect.

Explain why in more than one way.

Question 2, you are going to be finding the missing adjacent multiples and you're going to be completing the equations that you see on the screen.

So 2A, 9, 18, blank.

27 is equal to 2 times 9, add blank.

45, 54, blank.

Something is equal to something multiplied by 9, add something.

90, blank, 108, Something is equal to something multiplied by something, add 9.

And lastly 54, 45, blank.

Something is equal to something multiplied by something, subtract 9.

And for question 2B, you're going to write your own.

For example, I've got the sequence 63, 54.

So 63 is equal to 6 times 9, add 9.

You can pause the video here.

Off we go.

Good luck.

And click play when you're ready to rejoin us.

So how did you do? For question one, Andeep is incorrect.

Now you might have said that the digit sum of 53 is 8 and not 9 or a multiple of 9, so it cannot be correct.

Something else that you may have said is that one less than 5 is 4.

So the adjacent multiple of 45 should have a ones digit of 4 and not 5.

45 add 9 gives the next adjacent multiple of 9, which is 54 and not 53.

For question 2, this is what you should have got.

So the sequences, let's start off with that.

We're counting on in 9.

So 9, 18, your next adjacent multiple was 27.

Again, we're counting on in nines for the next 2 examples as well.

And I know this because the numbers are getting bigger.

So 45, 54, 63.

90, 99, 108.

And for the last sequence, the numbers are getting smaller, so that means I'm subtracting 9.

So you should have got 54, 45, 36.

Now for your mixed operation equations, for the first example, we are adding 9 because 2 times 9 is 18.

We need to add another group of 9 to get 27.

For the next example, 63 is equal to 6 times 9, which is 54.

And then we're going to add on another group of 9 to get 63.

The following example, you should have got 99 is equal to 10 times 9, add 9.

And lastly 36 is equal to 5 times 9, which is 45, and then you're subtracting a group of 9.

Now for question B, some of the examples that you may have written were 99 to 90.

So what I've done there is I've subtracted 9.

I also know that that is equal to 11 groups of 9, subtract a group of 9.

And then you may have written 18 to 27.

So you know that 18 is equal to 3 times 9 and then subtract a group of 9 to get 18.

If you manage to get all of those questions correct, well done.

I'm super proud of you.

Let's move on to our second lesson cycle.

And this lesson cycle is all about comparing our adjacent multiples.

Andeep filled out the 9 times table facts using knowledge of the times tables he already knows.

Oh, that's quite a big, Andeep only needs to calculate 5 more facts to complete the 9 times table.

Andeep wants to find 6 groups of 9.

So Andeep knows that 5 times 9 is equal to 45 and 6 times 9 is the adjacent multiple.

He can write this as 5 times 9, add 9, which will then give him the answer.

He can add 9 to 45 by adding 10 and adjusting by 1.

So that's the same as saying 45, add 10 which is 55, and then subtracting 1 which is equal to 54.

6 groups of 9 is 54.

I can add another multiple.

So he did all of this by using his times tables fact that he already knew to be able to work that out.

That's quite efficient.

Now you can compare adjacent multiples using knowledge of groups.

So on one side we've got 9, and then on the other side we've got 2 groups of 9, or in other words 2 times 9 Andeep says that he knows 2 times 9 is greater than 9 straight away.

How? 9 is just one group of 9.

So it is less than 2 groups.

So we can see that without calculating, Andeep has been able to reason why 9 is less than 2 groups of 9.

So the inequality sign that we would place there is this which shows that 9 is less than 2 times 9.

Now Laura says that she could do this one.

54 is the adjacent multiple to 5 times 9.

54 is one more group of 9 because it is 6 times 9.

54 is greater than 5 times 9, which means 5 times 9 is less than 54.

Now 27 is 3 groups of 9, so 3 times 9, add 9 has to be greater.

That has one more group of 9 and is the adjacent multiple of 27.

So straight away, she knows that 27 is less than 3 times 9, add 9, which means 3 times 9, ad 9 is greater than 27.

Over to you.

Which is greater? Is it A, 72 or B, 7 times 9? I'd like you to reason and justify how you know to your partner.

You can pause the video here.

So how did you do? Well, 7 times 9 is less than 72 because it has one fewer group of 9.

72 is 8 groups of 9.

Let's move on.

You can complete inequality problems in different ways.

What could go in the gap? We've got a mixed operation here.

So 5 times 9, add 9 is greater than? What do you think you could put in there? Well, what would be the adjacent multiple that is less than this? Hmm, 5 times 9, add 9 is greater than what could that be? Well, 45.

45 is the adjacent multiple because it is 5 groups of 9.

45 is equal to 6 times 9, subtract 9.

4 times 9, add 9 has to be less than 5 times 9, add 9.

So you could have also had 4 times 9 add 9.

On to your main task for this lesson cycle.

So for question 1, using what you know, I'd like you to build up the table facts.

And for question 2, you're going to fill in the missing symbols using the inequality sign you see on the screen.

And for question 3, you're going to complete the gap to make this inequality correct.

Can you find different ways using, now this is key, adjacent multiples? Okay, so the mixed operation you have on the screen is 7 multiply by 9, subtract 9, which is less than? Have a think.

You can pause the video here and click play when you're ready to rejoin us.

Well this is what you should have got for question 1, I'm going to chant the 9 times tables.

I'd like you to chant it along with me because remember, the more practise we get the better we will get at knowing our 9 times tables.

Are you ready? Let's begin.

Zero, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, and 108.

Well done If you've got all of those correct.

Now, if you managed to use your table facts to help you, even better.

And we're going to look at how you could have done this.

So if you know that 5 times 9 is 45, all you had to do was add on another group of 9 to calculate what 6 times 9 was, which is 54.

So 45 add 9 would've given you 54.

Now if you already knew that 10 times 9 was 90, well again you could have added another group of 9 to figure out what 11 times 9 was, which is 99.

Let's move on.

For question 2, we're going to go through the answers.

Now, I've got 2 times 9 and then I've got 27.

Now I know that 27 is greater than 2 times 9 because 2 times 9 is equal to 18, whereas 27 is 3 groups of 9.

Then we've got 5 times 9 and 45.

I know that 45 is equal to 5 groups of 9, which means 5 times 9 is equal to 45.

For the next question, I know that 54 is equivalent to 6 times 9.

And I know that 6 groups of 9 is less than 7 groups of 9, so that means 7 groups of 9 is greater.

Now let's look at one group of 9 compared to 18.

Well, 18 is 2 groups of 9, which means 18 is greater.

I know that 99 is made of 11 groups of 9, which means 12 groups of 9 is greater.

Now 2 groups of 9 is equal to 3 groups of 9, subtract 9, because once you've subtracted 9 you end up with 2 groups of 9.

Let's have a look at 3 groups of 9, add 9.

That's equivalent to 4 groups of 9, which is 36, and 36 is less than 45.

Now 5 groups of 9 subtract 9 leaves me with 4 groups of 9, which means 6 groups of 9 is greater.

81 is equal to 7 groups of 9, well 7 groups of 9, add 9 is 8 groups of 9, which is 72.

So I know that 8 groups of 9, add 9 is equal to 9 groups of 9, which is 81, so we should have got equal to.

And lastly, I know that 10 times 9 at another group of 9 is the same as 11 times 9, so we should have got equal to as well.

If you managed to reason and justify your answers for all of these questions, well done.

I'm super proud of you because you are now showing that you can compare adjacent multiples.

Now for question 3, well we've got 7 times 9, subtract 9, which is basically 6 groups of 9.

And we know that 6 groups of 9 is equal to 54.

So anything greater or a multiple that is greater than 54, would've satisfied this equation.

So you may have tried 63 or 7 times 9, or 7 times 9, add 9.

6 times 9, add 9.

You may have also put 8 times 9, any multiple or mixed operation within the 9 times tables that was greater than 54 would've been correct.

Well done.

We've made it to the end of this lesson.

I'm super proud of you.

We're now going to summarise our learning.

So in this lesson you explain the relationship between the adjacent multiples of 9.

We now understand that adjacent multiples of 9 have a difference of 9.

You should also understand that if you add 9 to a multiple of 9, you get the next multiple of 9.

And if you subtract from a multiple of 9, you get the previous multiple of 9.

You should now be able to compare adjacent multiples of 9 by thinking about the number of equal groups.

I'm super proud of you.

I hope you really enjoyed this lesson and I look forward to seeing you in the next one.

Bye.