Lesson video

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 will be solving problems involving adjacent multiples of nine.

And your keyword is on the screen now, and that is adjacent multiple.

I'd like you to repeat it after me.

Adjacent multiple.

Fantastic.

Let's find out what this word means.

So an adjacent multiple is a multiple next to another.

It could be before or after.

So think about an adjacent multiple of nine.

So I know that a multiple of nine is 27.

The adjacent multiples of nine would be? Have a think.

18 and 35.

Those are the adjacent multiples of nine.

So this lesson is all about solving problems involving adjacent multiples of nine, and we've got two lesson cycles.

The first lesson cycle is to do with solving worded problems. The second lesson cycle is looking at larger multiples of nine.

And to join us on our journey, we've got Lucas and Jun today.

They're going to help us with our mathematical thinking.

Let's begin.

Multiples of nine can be shown on a number line, and here we can see that we've got a number line.

The top part goes from zero to 12 and we're counting on in ones, and we're going to use this to help us to chant the multiples off nine.

So are you ready? We're going to chant all the way up to 108.

Let's begin.

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

Well done if you managed to chant the multiples of nine in the correct order as well.

Have a look, what multiple is missing? Hmm, well, we can add nine to find the adjacent multiple.

It is one more group of nine.

So that means the missing multiple was 80.

What multiple is missing? Well, using information from the multiples, we can use this to figure it out.

So we can subtract nine to find the adjacent multiple, it is one fewer group of nine.

Or we could have added nine to 54, which been one more group of nine, giving us 63.

So all in all, there are two ways you can find the missing multiples, especially when it's presented on a number line like this.

You can look at either adjacent multiple that's next to that missing multiple and add or subtract a group of nine.

So let's practise this, over to you.

What multiple is missing? And I'd like you to explain how you know.

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

So how did you do and what method did you use? Well, if you were to look at 18, you could have added nine to find the adjacent multiple, and in this case, it's 18 add nine is equal to 27.

So 27 was the missing multiple.

Alternatively, you may have looked at the adjacent multiple 36 and if you subtracted nine, that is also correct.

Now Lucas makes a shape using nine sticks.

Oh, it looks like a ladder.

Now he makes four of these shapes, and for each one, he's used nine sticks.

He says that he's used 36 sticks.

There are four groups of nine sticks.

I can write this as four times nine is equal to 36.

Now Lucas makes another of the shapes.

How many sticks has he used now? I just need to find that adjacent multiple of nine to 36.

I just added a group of nine.

I now have four times nine add nine.

So that is known as a mixed operation because you've got multiplication and addition in the same equation.

The adjacent multiple is 45.

It was efficient to calculate.

So Lucas didn't sit there and count the individual sticks because that's not an efficient way to do it.

He's used his knowledge of the nine times tables and the adjacent multiples of the nine times tables to help him.

So here, we've got a stacked number line to see this relationship.

So first, we began with 36.

Because he's made another shape using the same amount of sticks, we're adding nine to 36 and that gives us 45.

So he's got five shapes altogether, which means he's used 45 sticks altogether.

Now Jun has some flowers and they each have nine petals.

So one flower, nine petals.

"I have six identical flowers." Now Jun gave one of his six flowers to Lucas.

How many petals does Jun have now? "Well, I had six flowers, each with nine petals.

So six times nine is equal to 54.

I gave a flower away.

I gave a group of nine petals away." So six times nine is equal to 54, but we can write this as a mixed operation.

So that is the same as saying six times nine, subtract nine, which means that actually he's left with five groups of nine or five times nine.

We can also show this using a stack number line.

So we started off with six groups of nine, which is 54.

We've subtracted one group of nine which leaves us with 45 petals altogether.

It's an adjacent multiple and we can see that on the stack number line as well.

Now adjacent multiples can be used when you don't know the times tables facts you need.

Fish fingers come in boxes of nine.

How many fish fingers are in seven boxes? Well, Jun says, "I know I need seven times nine for this problem, but I don't know it.

I could count in nines, but I think that will take a while." "I know eight times nine equals 72.

Does that help?" "My answer is the adjacent multiple because it is one fewer group." "Well, if eight groups of nine is 72, then seven groups of nine is nine less than 72." "There are 63 fish fingers in seven boxes.

Thanks, Lucas." Now fish fingers come in boxes of nine.

How many are needed for 81 fish fingers? "I need to know how many groups of nine are in 81, but I don't know.

I could count in nines, but I think that will take a while." So Lucas says, "I know 10 times nine equals 90.

So if there were 90 fish fingers, we'd need 10 boxes." "81 is nine less than 90, so it's the previous adjacent multiple." "So if 10 groups of nine is 90, then nine groups of nine is nine less than nine." Nine boxes are needed because nine times nine is equal to 81.

Thanks again, Lucas." Over to you.

Lucas needs to solve this worded problem.

What calculation does he need to do? There are 36 pizza slices.

If each pizza is nine slices, how many pizzas are there? You can pause the video here and click play when you're ready to rejoin us.

So what did you get? Well, the calculation that we needed was 36 because that's our dividend.

That's how many we have altogether and our divisor is nine because that's how many pizza slices there are.

Our quotient is what we are solving.

So what adjacent multiple fact could he use? Well, we know that five times nine is equal to 45.

So four times nine is equal to 36.

Over to you for the main task of this lesson cycle.

You are going to use adjacent multiples to solve each problem.

Show what you have done using an equation.

So for question A, Lucas is making nine-sided shapes with sticks.

He has already made 10 shapes from the sticks that he has.

If he adds another nine-sided shape, how many sticks will there be? B, there are nine flowers with nine petals each.

If Jun gives away one flower, how many petals will there be altogether? C, Lucas now has seven flowers with nine petals each.

He has given a flower.

How many petals does he have altogether? Question D, Lucas has filled six buckets with nine litres of water ready for a water fight.

Jun brings one more bucket of water with the same amount.

How many litres of water have they used altogether? E, pancakes are sold in packs of nine.

Jun buys seven.

He gives one pack to his friend and then buys another two more at a discounted price.

How many individual pancakes does Jun have altogether? You could pause the video here and click play when you're ready to rejoin us.

Off you go, good luck.

So how did you do? Well, let's look at question A.

Now Lucas is making nine-sided shapes with sticks.

He's already made 10, so that's a key point there.

If he adds one other nine-sided shape, how many sticks will there be? Well, we know that 10 is one of our factors.

We also know that nine is one of our factors.

10 is a factor because that's how many shapes he's already made and each shape has nine sides.

So that's our other factor.

Now he's made one more shape, so that means we're adding on one more group of nine, which means he's used 99 sticks altogether.

Now for question, our factors are nine and nine and that's because we've got nine flowers with nine petals each.

So you should have got nine times nine and we are subtracting a group of nine because Jun gave away one flower.

So altogether, he has 72 petals.

And lastly for question C, our factors are seven and nine.

So seven times nine gives us 63 and then we add on another group of nine because he is given another flower that has nine petals as well.

So 63 add nine is 72.

So 72 petals again altogether.

Now for question D, this is what you should have got.

So we know that our factors to begin with are six and nine because there are six buckets and each bucket is filled with nine litres of water.

Then we know that Jun brings one more bucket, which means we're adding on another group of nine.

So that means we've got 63 litres of water altogether.

And lastly for question E, we can see that pancakes are sold in packs of nine, so that's one of our factors.

Now Jun buys seven, but he gives away one at this point, which leaves us with six packs, then buys another two more.

So six add two packs is eight packs, so which means our new factor is eight.

So if nine's a factor and eight is a factor, we end up with 72 as our product.

This could have also been represented like this.

So seven times nine, subtract nine, is 54.

Two times nine equals 18, 54 add 18 equals 72.

So 72 pancakes altogether.

Well done if you manage to get all of those correct.

Now let's move on to our second lesson cycle and that's all to do with larger multiples of nine.

Let's go.

Now adjacent multiples can be used to find larger multiples.

How? Well, the biggest times table fact that Lucas knows is 12 times nine, which is equal to 108.

Are there bigger multiples? Jun says, "Yes.

All numbers that can be divided exactly by nine are multiples of nine.

900 is a multiple of nine because it is 100 groups of nine." "I can add a group of nine to find another multiple.

108 add nine is 117." "117 is 13 groups of nine.

13 times nine is equal to 117." Jun says, "I know 20 times nine is equal to 180 because two times nine is 18 and one factor is 10 times the size." "The adjacent multiple is 20 times nine, add nine.

That's 189, which is 21 groups." "Exactly.

You can add or subtract nine to find adjacent multiples of nine." Over to you.

Lucas and Jun are calculating 51 times nine.

Who is correct? Now Lucas says, "I know 50 times nine is equal to 450, so I just need to add another group of 50." Jun says, "I know 50 times nine is 450, so I just need to add another group of nine." You could pause the video here and click play when you're ready to rejoin us.

So what did you get? Well, Jun is correct and that's because we're adding another group of nine.

Lucas is incorrect because he's added another group of 50.

Now adjacent multiples can be used to find larger multiples.

"Jun, I know that 18 times nine equals 162.

Bet you don't know a better fact." "Well actually, if 18 times nine equals 162, then 17 times nine equals 153 and 19 times nine equals 171." "What? How did you know that?" What did you think? How did Jun figure that out? Well, Jun explains how he knows.

"We start with 18 times nine equals 162, which is 18 groups of nine.

19 times nine is 19 groups of nine.

I have shown 18 groups of nine and we know this is 162.

If I show 19 groups of nine, this is one more group of nine.

162 add nine is equal to 171.

So 19 times nine is equal to 171." So 19 times nine equals 18 times nine, add nine.

Now in this example, Jun's shown 18 groups of nine and we know this is 162.

If I show 17 groups of nine, this is one fewer group of nine.

17 times nine is equal to 18 times nine, subtract nine.

162 subtract nine equals 153.

So 17 times nine equals 153.

Over to you.

Lucas knows that 14 times nine equals 126.

Use his fact to tell your friend two other facts.

You could pause the video here.

So how did you do? Well, 15 times nine is equal to 14 times nine, add another group of nine.

So that means 15 times nine is equal to 135.

So that's the next multiple of nine.

And 13 times nine is equal to 14 times nine, subtract nine.

So 13 times nine is equal to 117, which is the previous multiple of 126.

Onto the main task for this lesson cycle.

So for question one, you're going to solve the equations below using your knowledge of adjacent multiples of nine.

So 20 times nine is equal to 180, so 21 times nine must be equal to? If 30 times nine is equal to 270, so 29 times nine is equal to? 60 times nine is equal to 540, so 61 times nine is equal to? And lastly, 70 times nine is equal to 630, so 69 times nine is equal to? And for question two, if 27 times nine is 243, you are going to write two adjacent multiples of nine.

Explain or show how you know.

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

So how did you do? Well, for the first question, you should have got 189 and that's because we're adding one more group of nine to 180.

For the second question, you should have got 261 as your product because we're subtracting a group of nine.

We've gone from 30 groups of nine to 29 groups of nine, so we need to subtract one group of nine.

For the third question, you should have got 549 as your product because we've gone from 60 groups of nine to 61 groups of nine, which is adding on one more group of nine.

And lastly, you should have got 621 as your product because we are going from 70 groups of nine to 69 groups of nine, which means we're subtracting one group of nine.

Did you remember when you needed to add a group and when you had to subtract? And for question two, you might have said 28 times nine is equal to 252 because 28 times nine is equal to 27 groups of nine, add nine, or 243 add nine.

You may have also said 26 times nine is equal to 234 because 26 groups of nine is equal to 27 groups of nine subtract nine or 243 subtract nine.

Well done if you managed to get those questions correct.

I'm very proud of you.

We've made it to the end of this lesson, now let's summarise our learning.

So in today's lesson, you solved problems involving adjacent multiples of nine.

Now you should understand that adjacent multiples of nine can be found by adding or subtracting a group of nine.

You should also understand that you can now use facts, you know to find facts we don't know using adjacent multiples.

And lastly, larger multiples of nine can be found using adjacent multiples.

That was an epic lesson.

I hope you learned a lot and I look forward to seeing you in the next one.

Bye.