# Lesson video

In progress...

Hello, I'm Miss Mia 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'll be able to explain the relationship between adjacent multiples of six and on the screen now you can see the keywords.

I'd like you to repeat them after me.

Adjacent, multiple, let's find out what these keywords mean.

Adjacent means next to each other.

A multiple is the result of multiplying a number by another whole number.

This lesson is all about our six times tables and we've got two lesson cycles here.

Our first lesson cycle is all to do with adjacent multiples of six and then our second lesson cycle, we are going to be solving problems to do with this.

In this lesson you'll meet Andeep and Izzy.

Let's get cracking.

Andeep writes, multiples of six in order and looks at adjacent numbers.

Numbers that are next to each other.

So we've got a table here.

We can see that zero multiply by six is zero.

One multiplied by six is equal to six.

Two times six is 12, three times six is 18, and four times six is 24.

Are there any patterns that you notice? Well adjacent multiples have a difference of six.

What does that mean? When we move down the column, the product increases by six.

So here we can see that zero has increased by six to six.

Now when moving up the column, the product decreases by six.

So we can see that 24 has decreased by six and we get to 18.

So the adjacent multiple of 24 is 18.

Over to you.

The adjacent multiple is so on the screen you can see you've got the multiples 24, 30, 42, and 48.

So what did you get? If you got 36, you are correct.

And that's because our multiple that we were starting off with was 30 and then we added six, 30, add six is 36.

Back to you.

What is the missing adjacent multiple? This time we are going up the column, so there will be a difference of six and the multiple will get smaller.

So how did you do? You should have got 42 and that's because 48 was the multiple we were starting with and we subtracted six because we are going up the column.

So 48, subtract six is 42.

The adjacent multiple of 48 in this example is 42.

Now adjacent multiples can also be represented on a number line.

This time instead of going up and down a column, we're going left and right on a number line.

And on this number line we've got the multiples of six from zero all the way up to 30.

Now we can see that that adjacent multiples of six are zero and 12.

So if we go to the left of six, we're decreasing by six.

There's a difference of six and we end up with zero.

Now let's point to six again.

If we increase this multiple by a group of six, we end up with 12.

So the adjacent multiple of six is 12.

Over to you.

What did you get? Well, the adjacent multiple of 48 in this example is 54 and that's because we've had to add six to get the missing multiple.

We also know that the adjacent multiple 48 can be 42, if we subtract six.

Oh, this time, you are going to find two missing adjacent multiples of 60.

So what did you get? Well, to work out both adjacent multiples, we would've had to subtract six and add six.

So this is what you should have got, 60 subtract six is 54 and then 60 add six is 66.

Now did you know you can record an adjacent multiple using a mixed operation equation? So we're going to be looking at this example here.

Andeep says that he knows one group of six is six.

So we can represent this using an array.

So six is equal to one times six.

Now we know that 12 is one group of six, add six and we can see that's been represented on our array.

So as a mixed operation you would record this as 12 is equal to one times six, add six or two times six is equal to one times six, add six.

These are known as mixed operation equations.

Let's have a look at another example.

18 is equal to three times six.

So Andeep says that he knows three groups of six is 18.

18 subtract six gives you 12.

Now let's see what happens with the array.

12 is three groups of six subtract six.

So we need to subtract six.

So in other words, 12 is equal to three times six, subtract six.

We also know that 12 is made of two groups of six.

So two times six is equal to three times six, subtract six.

Now we've got a number line from zero all the way up to 72 and we are counting on in multiples of six here.

So you can see the multiples of six on this number line.

24, add six gives us the multiple 30.

You can write this as six times five is equal to six times four, add six or 30 equals four groups of six, add six.

Now let's have a look at another example.

So 66, subtract six is equal to 60 or we could record this as another mixed operation.

So 10 times six is equal to 11 times six.

Subtract six, 60 equals 11 groups of six subtract six.

So what you may have noticed here is that there are different ways of writing your mixed operation equations as long as both sides are equal to each other.

And how will we know that? Well the product will always be the same.

Back to you.

You're going to complete the mixed operation equation using the number line to help you.

So what did you get? Well, we're starting off at 48 and we're subtracting six.

That gives us 42.

So that means 42 is equal to six times eight, subtract eight or you could have had six times seven is equal to six times eight.

Subtract six.

Onto the main task for this lesson cycle.

For question one, you're going to find the missing multiples on this number line and I'm going to read out the numbers for you.

Zero six, gap 18, gap 30 36, gap 48, gap 60, gap 72.

For question two, you're going to find the missing adjacent multiples and complete the equations.

So for two A, you've got six 12 gap, and then you've got a mixed operation here.

18 is equal to two times six, add gap 18, 24 gap.

Then you've got 36 gap.

And I'll give you a hint here.

You are adding on six and then that is equal to a mixed operation with something that you add on another group of six too.

And lastly you've got 54, 48 gap.

And then you've got another mixed operation equation here.

But at the end you are subtracting six.

For two B, you're going to be writing your own.

So for example, 48, 54, I know that 54 is equal to six times eight, add six.

So how did you do? For question one, I'm going to read you through the answers on the number line.

So you should have got these multiples.

0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72.

And for question two, this is what you should have got.

So the adjacent multiples that were missing for the first question was 18 and 18 is equal to two times six, add six.

Then the missing multiple in the second question was 30.

So 16, 24, 30, 30 is equal to four times six, add six.

The missing multiple for the third question was 36, 42 and 42 is equal to six times six add six.

And the last missing multiple was 42 again.

And this time you could have had 42 is equal to six times eight minus six.

Now when it comes to writing your own, make sure that both equations on each side of the equal sign are balanced and that it equals the same.

So for example, we've got two adjacent multiples here, 48 and 54.

54 is equal to six times eight, which is 48.

Added another group of six that gives you 54 as well.

Now we're onto the second lesson cycle for this lesson and this time we're going to be solving problems. Let's go.

Andeep has filled out the six times table using knowledge of the times tables he already knows.

Wow, he's filled out quite a lot.

Have a look.

Now Andeep only needs to calculate five more facts to complete the six times tables.

That is the power of knowing and using facts.

Now you can use an array to represent finding the missing facts.

In other words, can use an array to help you find out the missing facts from a fact that you already know.

So we know that five times six is 30.

If we know that five times six is 30, then we also know that six times six must be five times six, add on another group of six.

Andeep says that he can show this using an array by adding one more group of six.

So six groups of six is equal to 36.

36 is six times six.

So here we need to add on one more group of six.

So 30 add six gives us our missing product and that is the same as five groups of six add six.

Now using this information we can then calculate what seven times six is.

Now that he knows six times six is 36, then he also knows that seven times six is six times six, add on another group of six.

He can clearly show this by adding one more group of six to our array.

Let's have a look.

So, once we add another group of six, seven groups of six is 42.

So 42 is equal to seven times six, which is also equal to six times six, add another group of six, over to you.

Draw an array to calculate what six times nine is, Andeep has given you a hint here.

He knows that six times eight is 48.

So how did you do? Well you should have got 54 and that's because we just needed to add on another group of six to six times eight to get 54.

And we know that six times eight is 48.

So what we needed to do was add six to get 54 as our final product.

Now Izzy says that if she knows 12 times six is 72, then she also knows that 13 times six is 78 is Izzy right? Prove it, well here is an array to show 12 times six which is 72.

Izzy is correct because she has added six more to 78 to find the adjacent multiple by adding on six more to 72, she gets 78 and that can also be represented as 13 times six.

Over to you.

If Izzy knows that 13 times six is 78, she says that she then also knows 14 times six is 84.

Do you agree? I'd like you to explain to your partner, you can pause the video here and click play when you're ready to rejoin us.

So how did your discussion go? Well Izzy, is correct and we can see that that's been demonstrated on our number line.

She has added six more to 78 to find the next adjacent multiple of six.

So 78 add six should give you 84 Which is the correct array for six times nine? I'd like you to justify your thinking to your partner.

So how did you do? A is correct because you need to add one more group of six to find the adjacent multiple.

Now you can compare adjacent multiples using knowledge of groups.

Andeep says that he knows two times six is greater than one times six.

How? Well can show this to you by using an array.

And we can see there's one group of six and there's two groups of six.

And immediately we can see that one group of six, so one times six is less than two times six.

Now we've got four times six and two times six which is greater.

We can visually see here that there are more groups of six in four times six.

So four times six is greater than two times six Over to you, which is greater, six times four or five times six.

I'd like you to justify how you know to your partner.

So how did you do? Well, six times five or five times six is greater than six times four because it has one more group of six.

And if I was calculating this, I would've swapped my factors around and instead of seeing it as five times six, I would've seen it as six times five, which tells me that six times five is greater because there's one more group of six in six times five.

And in this example we've got three times six, add six and three times six.

Now you're probably wondering, hang on, that's a mixed operation.

Can we compare this? Yes we can because three times six add another group of six is equal to 24 and three times six is equal to 18.

So that means three times six add six is greater than three times six, which is greater, seven times six or seven times six, add six, justify how you know to your partner.

You can pause the video here.

So how did you do? Well, seven times six, add six is greater than seven times six because it has one more group of six.

For question one, you are going to use what you know to build up the table facts.

Some of the facts have been filled in for you.

And for question two, you are going to fill in the missing symbols.

So you're either going to use less than, greater than or equal to.

You can pause the video here.

Off you go.

Good luck.

So how did you do? I'm going to go through the tables and I'd like you to mark your work as I go through the multiples.

So zero, six and 12 are already there, so we're going to carry on from 12.

You can chart along with me.

We're gonna start at 12, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72.

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

Let's move on to the next question.

For question two, this is what you should have got and we're going to look at the right hand side in more detail.

Don't worry, you can pause the video at the end of my explanations for these equations to mark the rest.

Let's look at two times six is something than three times six add six.

Well we know that three times six add six has to be greater than two times six because there's more groups of six in three times six, add six.

Now the second one, three times six, add six is greater than three times six because there's one extra group of six in three times six add six.

Six times six is actually equal to five times six, add six.

And this is because when we add one more group of six to five times six, it's the same as six times six.

Now six times eight is equal to seven times six add six.

And that's because once you've added that extra group of six, it becomes eight groups of six.

And lastly, nine times six is equal to 10 times six, subtract six because when we subtract a group of six from 10 times six, you end up with nine times six.

You can pause the video here to mark the rest of your work.

Brilliant.

I hope you've marked your work.

Let's move on.

We're now going to summarise your learning.

In today's lesson, you are able to explain the relationship between adjacent multiples of six.

You should now understand that adjacent multiples of six have a difference of six.

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

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

I hope you enjoyed this lesson.

I sure did, and I hope to see you in the next one.