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'll be able to explain the relationship between adjacent multiples of three.

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

Adjacent.

Multiple.

Let's find out what these words mean.

So adjacent means next to each other, and a multiple is the result of multiplying a number by another whole number.

Now, this lesson is all about the three times tables, and there are two lesson cycles here.

Your first lesson cycle is all to do with adjacent multiples of three, so multiples of three that are next to each other.

And your second lesson cycle is to then use this information to solve problems. Let's get started.

Now, in this lesson, you're going to meet Andeep and Izzy, who are going to help us with our mathematical thinking.

Hmm, Andeep writes multiples of three in order and looks at adjacent numbers, numbers that are next to each other.

Now, you can see a table there.

You can see zero, and then you've got zero.

Then you've got one, and the one has been multiplied by three to give you three.

Then you've got two multiplied by three, which gives you six.

Then you've got three multiplied by three, which gives you nine.

And lastly, you've got four multiplied by three, which gives you 12.

What patterns do you notice? Now, you may have said something like this, "Adjacent multiples have a difference of three." What does that mean? Well, when you move down the column, the product increases by three.

And we can see that there, because once we count on in three, we go from zero to three, so there's a difference of three.

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

So you go from 12 to nine.

And we've subtracted three.

Over to you.

There's a table there and there's a missing gap.

I'd like you to tell me what the adjacent multiple is, and I'd like you to explain how you know to your partner.

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

So, what did you get? If you got 18, that is correct.

And that's because 15 add three is 18, which means we've increased by three.

Back to you again.

What is the missing adjacent multiple? This time we're starting at 24.

And because we're going up the column, we're subtracting three.

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

So, what did you get? You should have got 21, and that's because 24 subtract three is 21.

So 21 was the missing adjacent.

And remember, I say adjacent multiple because that is the multiple it's next to.

So 24 is next to 21.

Now, we had a look at adjacent multiples in a table before, and we were looking at what would happen if we increased or decreased by three, so we were going up and down.

This time we're looking at finding the adjacent multiples on a number line.

So we're actually looking at what happens when we go left and right.

So here we've got a number line that goes from zero all the way up to 36 and it shows our multiples of three.

So we've got 15 there.

And if we add three, our adjacent multiple of 15 is 18.

And that's because 15 add three is 18.

Now, the adjacent multiple of 33, we've got a missing number there and we're subtracting three, is 30.

And that's because as we go towards the left of the number line, we are decreasing by three each time, and so we are subtracting three.

So the missing adjacent multiple is 30 in this case.

And that's because 33 subtract three is 30.

So over to you, the adjacent multiples of 21 are? And there's two missing gaps here.

Have a think, what happens when you increase by three and decrease by three? You can pause the video here.

So, how did you do? Well, you should have got 18 and 24.

And that's because when we increase 21 by three, in other words add three, we end up with 24.

And when we subtract three from 21, we end up with 18.

So the adjacent multiples of 21 are 18 and 24.

Adjacent multiples can be represented using mixed operations, and I'll show you what this is.

So here we're starting at three, and we've added three to get six.

Now, you can write this as two times three is equal to one times three add three? In other words, six is equal to one group of three add three.

Now, let's look at another example.

So we start at 33 and we've subtracted three, and this gives us 30.

So 10 times three is equal to 11 times three subtract three.

Which means 30 is equal to 11 groups of three subtract three.

Over to you.

I'd like you to identify the mixed operation here by filling in the gaps.

So you're going to complete the equation, gap equals 10 times three, subtract, gap.

So quick clue here, you're starting off at 30 and you're subtracting three.

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

So, how did you do? Well, you should have got 27 as the missing number, which means 27 is equal to 10 times three subtract three.

Over to you for your main task for this lesson cycle.

For question one, you are going to be finding the missing multiples.

So I'm going to read you out the number line and you're going to be finding what the missing multiples are on this number line.

So zero, gap, six, nine, gap, 15, 18, gap, 24, gap, 30, 33, gap.

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

So for 2A, you've got three, six, and then for six, you're going to find the mixed operation equation by filling in the gap.

So six is equal to one times three add gap.

Then you've got 15, 18.

18 is equal to gap times three add gap.

And lastly, 21, gap.

And then you've got something is equal to gap multiplied by something add three.

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

So for example, we've got two adjacent multiples here, 36 and 33.

33 is equal to 12 times three subtract three.

You can pause the video here, off you go, good luck.

So, how did you do? So for this question, we're going to look at question two in more detail.

But for question one, I'm going to read out the number line and you can mark them as I go along.

And you can count along with me as well in threes.

Ready, we're going to start at zero.

Zero, three, six, nine, 12, 15, 18, 21, 24, 27, 30, 33, 36.

If you found all the missing multiples, well done, good job.

For question two, you were meant to find the missing adjacent multiples first and then complete the equations.

So for 2A, you should have got six is equal to one times three add three.

You should have got 18 is equal to five times three add three.

And for the last question, you should have got 21, 24.

24 is equal to seven times three add three.

Now, you could have wrote your own adjacent multiples equations.

You've got two examples here, so 33 to 36.

That is equal to 11 times three add three.

And then 27 to 24, which is equal to nine times three subtract three.

Let's move on to the second lesson cycle, solving problems. So everything that we've learned, you're now going to use.

Hmm, Andeep filled out the three times tables facts using his knowledge of the twos, fives, 10s, which is something we should all know.

And the four and eight times tables.

So we can see the tables here.

We've got zero, three, six, that's already been filled out.

Then we've got 12, which is four times three.

Then if we look at our middle column, we've got five times three, which is 15, because we know our five times tables.

We know eight times three is 24, because we should know our eight times tables.

And lastly, 10 times three, which is 30.

That means Andeep only needs to calculate six more facts to complete the three times tables.

That's fantastic.

And that's because we are using the power of what we know already.

You can use an array to represent finding the missing facts, and you can see an array on the screen there.

So we've also got three times tables on the right hand side, and this time we've got our facts from three times three all the way up to seven times three.

Andeep says, "If I know five times three is equal to 15," then he also knows that six times three is five times three add on another group of three.

And he says that he can show this using an array by adding on one more group of three.

And there we have it.

So six groups of three is 18, and that is also equal to six times three.

So we can see that we've added on another group of three to figure out what six times three is.

So something is equal to five times three add three, and we now know that is 18.

Now, we can use this fact, six times three, which is equal to 18, to find out what seven times three is.

Hmm, so that means something is equal to three times six or six times three add on another group of three.

Let's show this using an array.

So we have six groups of three here.

We need to add on one more group of three to calculate seven times three.

Which means we're actually just adding three onto 18, which gives us 21.

Over to you.

I'd like you to draw an array to calculate what nine times three is.

Andeep says that he knows eight times three is 24, and I'd like you to use this tip to help you.

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

So, how did you do? If I was to start off with this, I would've drawn eight groups of three, and then I would've added on an extra group of three.

So in other words, if you know that eight times three is 24, all you're doing is adding on three to 24 to get 27, or you could've also used your fact of 10 times three, which is 30, and then subtracted three to get 27, so taking away a group of three.

Hmm, okay, let's move on.

Now, Izzy says that if she knows 12 times three is 36, then she also knows that 13 times three is 39.

Is Izzy right? I'd like you to prove it.

Now, you may have got something like this.

Izzy is correct because she has added three more to 36 to find the adjacent multiple.

Now, that's key there, adding on three more to find the adjacent multiple.

And we're going to show this using an array.

So we've got 12 times three, which looks like this, and that's equal to 36.

And then we've added on one more group of three, which gives us 13 groups of three.

So that means 36 add three is 39, so 39 is the multiple.

So that means 13 times three is 39.

Over to you.

Izzy says that if she knows 13 times three is 39, then she also knows that 14 times three is equal to 42.

Do you agree? I'd like you to explain how you know to your partner.

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

So, how did you do? Well, Izzy is correct, and we can see that because it's been represented on a number line.

So on our number line we've got our multiples of three.

Now, we know that 13 times three or 13 groups of three is 39.

Now, if we add another group of three, we find our next adjacent multiple, which is 42.

So if you said that you do agree, you are correct, well done.

Now, did you know you can compare adjacent multiples using knowledge of groups? Let's have a look.

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

"How?" "I can show you using an array." Here's one group of three, there's two groups of three.

So that means one times three is less than two times three, or two times three is greater than one times three.

Now, we've got four groups of three.

So here we've got four groups of three, which is four times three, and two groups of three, which is two times three.

Four times three is greater than two times three, and two times three is less than four times three.

And we can see that visually here because we've got more groups of three in four times three.

Now, you can also compare mixed operation expressions.

So here we've got three times three add three, which is equal to 12.

And in this example we've got two times three, which is six, add three, which is nine.

Hmm, which is greater? It's very easy to see this because we've represented this using an array.

Well, we know that three times three add three is greater than two times three add three.

And that's because when we calculate what that mixed operation represents, we know that that's 12.

We know that 12 is greater than nine.

Which is greater, six times three or seven times three? I'd like you to justify how you know to your partner.

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

So, how did you do? Seven times three is greater than six times three, and that's because it has one more group of three.

Onto your main task for this lesson cycle.

So for question one, you're going to use what you know to build up the facts.

So for example, you've got here zero, three, and six, which are already filled in.

So using what you know about two times three, how can you calculate what three times three is? Think about how many groups of something you're going to add to six to calculate the next multiple.

Now, for question two, Andeep knows that 20 times three is 60.

And I'd like you to use this to solve what 21 times three is and what 19 times three is.

For question two, you're going to fill in the missing symbols using your inequality sign.

Now, remember, if something is greater than, you're going to use the greater than sign, and if something is less than, you're going to use the less than sign.

And if both equations are equal, then you're going to use the equal sign.

You can pause the video here.

Off you go, good luck, and click play when you're ready to rejoin us.

So, how did you do? Let's look at question one.

For each of these adjacent multiples, you should have added three.

And for some of them, you may have even subtracted three.

So let's go through it.

We knew that two times three is six.

Now, by adding three to six we ended up with nine.

And then we could have done the same again.

So adding three to nine, we would've got 12.

Or we could have subtracted three from 15 because we know that five times three is 15.

So if we subtracted a group of three from 15, we also would've got 12.

Now, six times three is 18 because 15 add three or a group of three gives us 18.

And then to figure out what seven times three was, we would've added three again to 18 to give us 21.

We would've repeated this, so we would've added another three to 21 to get 24, and that would've given us our product for eight times three.

And again, we could have either added another group of three to 24, or subtracted a group of three from 30 to get 27, which is what nine times three is.

Now, when we get to 11 times three, what you should have done was add three to 30 to get 33.

And to calculate what 12 times three is, you should have added three to 33 to get 36.

Now, let's look at question two in detail as well.

So if we know that 20 times three is 60, 21 times three would be 63 because we just needed to add on one more group of three.

19 times three would've been 20 times three subtract a group of three.

And that's because we know that 19 groups of three is one less group of three than 20 groups of three.

So that means 60 subtract three would've given us 57.

If you got all of those questions correct, well done, I'm very proud of you.

Let's move on to question two.

So this is what you should have got.

So for the first question, three times three is greater than two times three.

Five times three is equal to three times five because the product is the same, it's 15, and it doesn't matter which order the factors are in.

Six times three is less than three times seven because there is one more group of three in three times seven.

Now, eight times three is less than nine times three, similarly because there is one more group of three in nine times three One times three is greater than zero times three because we know that anything multiplied by zero gives us zero, and one times three means that there's one group of three more than zero times three.

Now, let's have a look at the next question.

There's a mixed operation equation here.

So we've got two times three is less than three times three add three.

And that's because we know two times three is six, three times three is nine, and we've added on another group of three, which is 12.

So we know that 12 is greater than six.

Now, this question, three times three add three.

So that's three times three, which is nine, and you're adding on another group of three, which gives us 12.

12 is greater than three times three because three times three is nine.

And we didn't add on any other groups of three there.

For the next question, six times three is equal to five times three add three because five times three add on another group of three is basically six times three.

So they are equal, and you get the same product, which is 18.

For this question, we know that seven times three add three would be greater than seven times three because we've added on another group of three.

And for the last question, we know that 10 times three subtract three is equal to nine times three.

If you got all of those questions correct, well done.

Good job, we've made it to the end of the lesson, and now we're going to summarise our learning.

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

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

And if you add three to a multiple three, you get the next multiple of three.

You also understand that if you subtract three from a multiple of three, you get the previous multiple of three.

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

Bye.