Lesson video

Hello, I'm Ms. 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'll be able to explain the relationship between adjacent multiples of 3.

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 3 times tables and there are two lesson cycles here.

Your first lesson cycle has all to do with adjacent multiples of 3, so multiples of 3 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 are going to meet Andeep and Izzy who are going to help us with our mathematical thinking.

Hmm, Andeep writes multiples of 3 in order and looks at adjacent numbers, numbers that are next to each other.

Now, you can see a table there.

You can see 0, and then you've got 0.

Then you've got 1, and the 1 has been multiplied by 3 to give you 3.

Then you've got 2 multiplied by 3, which gives you 6.

Then you've got 3 multiplied by 3, which gives you 9.

And lastly, you've got 4 multiplied by 3, which gives you 12.

What patterns do you notice? Now, you may have said something like this.

Adjacent multiples have a difference of 3.

What does that mean? Well, when you move down the column, the product increases by 3 and we can see that there because once we count on in 3, we go from 0 to 3.

So, there's a difference of 3.

And when moving up the column, the product decreases by 3.

So, you go from 12 to 9 and we've subtracted 3.

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 + 3 is 18, which means we've increased by 3.

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 3.

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 - 3 is 21.

So, 21 was the missing adjacent multiple.

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 3.

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 0 all the way up to 36 and it shows our multiples of 3.

So, we've got 15 there and if we add 3, our adjacent multiple of 15 is 18.

And that's because 15 + 3 is 18.

Now, the adjacent multiple of 33, we've got a missing number there and we're subtracting 3, is 30.

And that's because as we go towards the left of the number line, we are decreasing by 3 each time.

And so we are subtracting 3.

So, the missing adjacent multiple is 30 in this case, and that's because 33 - 3 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 3 and decrease by 3? 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 3, in other words add 3, we end up with 24.

And when we subtract 3 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 3 and we've added 3 to get 6.

Now you can write this as 2 x 3 = 1 x 3 + 3.

In other words, 6 is equal to 1 group of 3 add 3.

Now, let's look at another example.

So, we start at 33 and we've subtracted 3 and this gives us 30.

So, 10 x 3 = 11 x 3 - 3, which means 30 is equal to 11 groups of 3 subtract 3.

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 = 10 x 3 - gap.

So, quick clue here, you're starting off at 30 and you're subtracting 3.

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 = 10 x 3 - 3.

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

Question 1, you're 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, 0, gap, 6, 9, gap, 15, 18, gap, 24, gap, 30, 33, gap.

For question 2, you're going to find the missing adjacent multiples and complete the equations.

So, for 2A, you've got 3, 6, and then for 6 you're going to find the mixed operation equation by filling in the gap.

So, 6 = 1 x 3 + gap.

Then, you've got 15, 18.

18 = gap x 3 + gap.

And lastly, 21, gap.

And then you've got something = gap x by something + 3.

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

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

33 = 12 x 3 - 3.

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 2 in more detail, but for question 1, 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 3s.

Ready? We're going to start at 0.

0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36.

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

For question 2, you were meant to find the missing adjacent multiples first and then complete the equations.

So, for 2A, you should have got 6 = 1 x 3 + 3.

You should have got 18 = 5 x 3 + 3.

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

24 = 7 x 3 + 3.

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 x 3 + 3, and then 27 to 24, which is equal to 9 x 3 - 3.

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

Hmm, Andeep filled out the 3 times tables facts using his knowledge of the 2s, 5s, 10s, which is something we should all know, and the 4 and 8 times tables.

So, we can see the tables here.

We've got 0, 3, 6 that's already been filled out.

Then we've got 12, which is 4 x 3.

Then if we look at our middle column, we've got 5 x 3, which is 15, because we know our 5 times tables.

We know 8 x 3 is 24 because we should know our 8 times tables.

And lastly, 10 x 3, which is 30.

That means Andeep only needs to calculate six more facts to complete the 3 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 3 times tables on the right-hand side and this time we've got our facts from 3 x 3 all the way up to 7 x 3.

So, Andeep says if I know 5 x 3 = 15, then he also knows that 6 x 3 is 5 x 3 add on another group of 3.

And he says that he can show this using an array by adding on one more group of 3.

And there we have it.

So, six groups of 3 is 18, and that is also equal to 6 x 3.

So, we can see that we've added on another group of 3 to figure out what 6 x 3 is.

So, something is equal to 5 x 3 + 3, and we now know that is 18.

Now, we can use this fact, 6 x 3, which is equal to 18, to find out what 7 x 3 is.

Hmm, so that means something is equal to 3 x 6, or 6 x 3, add on another group of 3.

Let's show this using an array.

So, we have six groups of 3 here.

We need to add on one more group of 3 to calculate 7 x 3, which means we're actually just adding 3 onto 18, which gives us 21.

Over to you.

I'd like you to draw an array to calculate what 9 x 3 is.

Andeep says that he knows 8 x 3 = 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 3 and then I would've added on an extra group of 3.

So, in other words, if you know that 8 x 3 = 24, all you're doing is adding on 3 to 24 to get 27, or you could have also used your fact of 10 x 3, which is 30, and then subtracted 3 to get 27.

So, taking away a group of 3.

Hmm.

Okay, let's move on.

Now, Izzy says that if she knows 12 x 3 = 36, then she also knows that 13 x 3 = 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 3 more to 36 to find the adjacent multiple.

Now, that's key there.

Adding on 3 more to find the adjacent multiple.

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

So, we've got 12 x 3 which looks like this, and that's equal to 36.

And then we've added on one more group of 3, which gives us 13 groups of 3.

So that means 36 + 3 = 39.

So 39 is the multiple.

So that means 13 x 3 = 39.

Over to you.

Izzy says that if she knows 13 x 3 = 39, then she also knows that 14 x 3 = 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 3.

Now, we know that 13 x 3, or 13 groups of 3, is 39.

Now, if we add another group of 3, 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 2 x 3 is greater than 1 x 3.

How? I can show you using an array.

Here's 1 group of 3, there's 2 groups of 3.

So, that means 1 x 3 is less than 2 x 3 or 2 x 3 is greater than 1 x 3.

Now we've got 4 groups of 3.

So, here we've got 4 groups of 3, which is 4 x 3, and 2 groups of 3, which is 2 x 3.

4 x 3 is greater than 2 x 3.

And 2 x 3 is less than 4 x 3.

And we can see that visually here because we've got more groups of 3 in 4 x 3.

Now, you can also compare mixed operation expressions.

So, here we've got 3 x 3 + 3 which is equal to 12.

And in this example we've got 2 x 3, which is 6, add 3, which is 9.

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

Well, we know that 3 x 3 + 3 is greater than 2 x 3 + 3.

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

We know that 12 is greater then 9.

Which is greater? 6 x 3 or 7 x 3? 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? 7 x 3 is greater than 6 x 3 and that's because it has one more group of 3.

Onto your main task for this lesson cycle.

So, for question 1, you are going to use what you know to build up the facts.

So, for example, you've got here 0, 3, and 6 which are already filled in.

So, using what you know about 2 x 3, how can you calculate what 3 x 3 is? Think about how many groups of something you are going to add to 6 to calculate the next multiple.

Now, for question 2, Andeep knows that 20 x 3 is 60, and I'd like you to use this to solve what 21 x 3 is and what 19 x 3 is.

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 >.

And if something is less than, you're going to use the <.

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

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 1.

For each of these adjacent multiples, you should have added 3.

And for some of them you may have even subtracted 3.

So, let's go through it.

We knew that 2 x 3 is 6.

Now, by adding 3 to 6, we ended up with 9.

And then we could have done the same again.

So, adding 3 to 9, we would've got 12.

Or we could have subtracted 3 from 15 because we know that 5 x 3 is 15.

So, if we subtracted a group of 3 from 15, we also would've got 12.

Now, 6 x 3 is 18, because 15 + 3, or a group of 3, gives us 18.

And then to figure out what 7 x 3 was, we would've added 3 again to 18 to give us 21.

We would've repeated this, so we would've added another 3 to 21, to get 24, and that would've given us our product for 8 x 3.

And again, we could have either added another group of 3 to 24 or subtracted a group of 3 from 30 to get 27, which is what 9 x 3 is.

Now, when we get to 11 x 3, what you should have done was add 3 to 30 to get 33.

And to calculate what 12 x 3 is, you should have added 3 to 33 to get 36.

Now, let's look at question 2 in detail as well.

So, if we know that 20 x 3 is 60, 21 times 3 would be 63 because we just needed to add on one more group of 3.

19 x 3 would've been 20 x 3 subtract a group of 3, and that's because we know that 19 groups of 3 is 1 less group of 3 than 20 groups of 3.

So, that means 60 - 3 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 2.

So, this is what you should have got.

So for the first question, 3 x 3 is greater than 2 x 3.

5 x 3 is equal to 3 x 5 because the product is the same, it's 15, and it doesn't matter which order the factors are in.

6 x 3 is less than 3 x 7 because there is one more group of 3 in 3 x 7.

Now, 8 x 3 is less than 9 x 3, similarly because there is one more group of 3 in 9 x 3.

1 x 3 is greater than 0 x 3 because we know that anything multiplied by 0 gives us 0 and 1 x 3 means that there's one group of 3 more than 0 x 3.

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

There's a mixed operation equation here.

So, we've got 2 x 3 is less than 3 x 3 + 3, and that's because we know 2 x 3 is 6, 3 x 3 is 9, and we've added on another group of 3, which is 12.

So, we know that 12 is greater than 6.

Now, this question, 3 x 3 + 3, so that's 3 x 3, which is 9, and you're adding on another group of 3, which gives us 12.

12 is greater than 3 x 3 because 3 x 3 is 9, and we didn't add on any other groups of 3 there.

For the next question, 6 x 3 is equal to 5 x 3 + 3, because 5 x 3 add on another group of 3 is basically 6 x 3.

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

For this question, we know that 7 x 3 + 3 would be greater than 7 x 3 because we've added on another group of 3.

And for the last question, we know that 10 x 3 - 3 is equal to 9 x 3.

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 summarize our learning.

So, in this lesson, you explained the relationship between adjacent multiples of 3.

You should now understand that adjacent multiples of 3 have a difference of 3, and if you add 3 to a multiple 3, you get the next multiple of 3.

You also understand that if you subtract 3 from a multiple of 3, you get the previous multiple of 3.

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

Bye!.