Lesson video

Hello everyone.

Welcome back to another maths lesson with me, Mrs. Pochciol.

I can't wait for us to have lots of fun together and hopefully learn lots of new things.

So let's get started.

This lesson is called identify the patterns and relationships between the five and 10 times tables, and it comes from the unit doubling, halving, quantitative, and partitive division.

By the end of this lesson, you should be able to identify the patterns and relationships between the five and 10 times tables.

Let's have a look at this lesson's keywords.

Multiple, odd, even, double and half.

Let's have a go at practising them.

Are we ready? My turn.

Multiple.

Your turn.

My turn.

Odd.

Your turn.

My turn.

Even.

Your turn.

My turn.

Double.

Your turn.

And finally my turn.

Half.

Your turn.

Lots of words that you will have heard before there, so let's get using them.

Here is this lesson's outline.

In the first part of our learning, we're going to be looking at the products in the five and 10 times table and in the second part of our learning, we're going to be looking at the relationship between the products.

Are we ready to get started? Let's start looking at those products in the five and 10 times tables.

Jacob and Sofia here to help us with our learning today.

Are you ready guys? Let's get started.

Jacob is practising his skip counting to find out how many fingers there are in total.

He notices that each hand has five fingers, so that means he can skip count in multiples of five.

Are we ready? Shall we join in with Jacob? Five, 10, 15, 20, 25.

What's next? 30, 35, 40, 45, 50, 55, 60.

There are 60 fingers in total.

Beautiful counting there, Jacob.

Well done.

Jacob highlights all the multiples of five on his 100 square.

Let's have a look.

Five, 10, 15, 20, 25, 30.

I'm starting to notice a bit of a pattern here.

35, 40, 45, 50.

Are you noticing the same thing that I am? 55 and 60.

Hmm? I wonder if you notice the same thing that I did.

I noticed that all the multiples of five were in the five ones column and the tens column of my hundred square.

Look, can you see? There weren't any numbers in any other of the columns on my 100 square.

Hmm.

I wonder why that is.

We'll be coming back to this a little bit later on, but for now, let's have a look at what Sofia's up to.

Sofia is now skip counting to find the total number of fingers that she has in front of her.

What have you noticed Sofia? Sofia's noticed that she can count in multiples of 10.

This is going to follow the same pattern as when we count in ones because it's just one 10, two 10, three tens.

Come on then, Sofia.

Join in with Sofia if you think you can.

10, 20, 30, 40, 50, 60, seven tens, 70, eight tens, 80, nine tens, 90, 100.

Hmm.

What comes next? I know that 11 would come next if I'm counting in my ones, so I know that that is 110, 120.

Well done to you, Sofia.

Beautiful counting there.

Sofia now highlights all the multiples of 10 on her 100 square.

Let's have a look.

10, 20, 30, 40.

I'm noticing something again.

50 and 60.

All of Sofia's multiples of 10 are in the same column in our 100 square.

Look.

Ooh.

Sofia has noticed something else though.

What do you think she might've noticed? Think about what we've looked at so far in our lesson.

Hmm.

Let's have a look.

Sofia notices that both her and Jacob have highlighted some of the same numbers, so they have.

Look.

We can see that in both our multiples of five and our multiples of 10, the multiples of 10 are in both of them and they've both been highlighted on the 100 squares.

Look, we can see the multiples of 10 are also multiples of five.

Look.

Sofia and Jacob now decide to explore this a little bit further.

They're now going to look at the products of the five and 10 times tables.

Jacob knows that multiples of 10 have a ones digit of zero.

So let's look at those first.

We know that all of the multiples of 10 have a ones digit of zero, but what about in the five times table? Can you see any multiples of 10 in there? There we go.

Look, 10, 20, 30, they all have one digits of zero.

So what does that mean? We can see that the even multiples of five are also multiples of 10.

So all the multiples of 10 are multiples of five but not all multiples of five are multiples of 10.

That's because the odd multiples of five have a ones digit of five and we know that they cannot be multiples of 10 because multiples of 10 all have a ones digit of zero.

So it can't possibly be a multiple of 10.

Wow, I've never noticed that before.

So multiples of 10 can also be multiples of five.

Well done for spotting that Sofia and Jacob, but I just wonder why.

Why is that the case? How can a multiple of 10 also be a multiple of five? Jacob and Sofia decide to explore why this is the case.

Jacob remembers that two groups of five is equal to 10 so we can see that for every one group of 10 there will be two groups of five and we can see this really clearly with our hands.

So get your hands.

We have a group of 10 because I have 10 fingers but I can also split this and see this as two groups of five fingers.

Can we see one group of 10 or two groups of five? You can also see this the other way around.

You might see this as for two groups of five.

We can also see this as one group of 10, two groups of five and one group of 10.

Let's practise this a little bit further.

We know that even groups of five will result in a multiple of 10.

So here we're going to use some counters to help us to visualise this.

So if we see two times by five, we can see this as two groups of five, which we know is 10.

But remember, we can also see two groups as five as one group of 10.

So we know that two times five is equal to 10, but we could also see this as one times 10 is equal to 10.

Let's have a look at the next one.

Four times by five, we know that that's four groups of five.

What is four times by five then? We know that four times by five is 20.

So how many groups of 10 would also equal to 20? Let's have a look.

I can see that we've got four groups of five there.

Remember, two groups of five can be equal to a 10.

So here I could also see this as two groups of 10.

So two times by 10 is also equal to 20.

Are we starting to notice this pattern here? Let's have a look at the next one.

Six times by five.

I know that six times by five is equal to 30.

So how many groups of 10 would also be equal to 30? Two groups of five is equal to one 10.

So let's group them.

There we go.

So I can see that three tens will be equal to six fives.

Let's have a look.

Three times by 10 is equal to 30, and finally we have eight times five.

We know that eight times five is equal to 40, but how many tens would also be equal to 40? Two groups of five is equal to one 10.

So let's group them into groups of two.

I can see that four tens are also equal to 40.

Are we starting to notice this pattern now between the five and 10 times table? I think we might need a little bit of a practise.

So let's have a go at a check.

Two more equations here for you to have a go at.

You can see that on the left, I've shown you the five counters so you to remember just how we did before.

You can use those five counters to see how many groups of 10 will be equal to the same product.

So pause this video, have a go at finding those missing numbers in those equations and come on back when you're ready to see how you've got on.

Welcome back.

Let's have a look then at how we got on.

So in the first one, I can see that it's 10 times by five and I have ten five counters.

10 times by five is equal to 50, but how many tens is also equal to 50? Let's group them into twos because I know that two fives are equal to a 10.

So that will give us five tens.

Five times by 10 is also equal to 50.

Now, this next one I didn't give you the number.

So let's see how many counters we have.

One, two, three, four, five, six, seven, eight, nine, 10, 11, 12.

So that's 12 times by five, which I know is 60.

Now, let's group them again because two fives are equal to one 10.

So how many tens do I have? I have six tens there that are also equal to the same product.

So six times 10 is also equal to 60.

Well done if you manage to complete that check and well done if you're starting to notice this pattern without using your counters.

Let's continue practising this with task A.

Task A is to sort the numbers into multiples of five, multiples of five and 10 and not to multiples of five and 10.

Sofia is reminding us that even multiples of five are also multiples of 10.

So think about what you remember about each of the multiples to help you to sort the numbers.

Pause this video and come on back when you're ready to continue the learning.

Welcome back.

Let's have a look then.

How did you get on, Sofia? Let's start with the number 12.

Sofia has noticed that 12 has two ones, so that isn't a multiple of five or 10 because we know that multiples of five have a ones digit of five or zero and a multiple of 10 has a ones digit of zero.

Two isn't either of those, so that's not a multiple of five or 10.

The next one, a multiple of 10 is also a multiple of five.

So 20 is a multiple of five and 10.

Sofia noticed that if a number has five ones then that is a multiple of five but it can't be a multiple of five and 10 because it doesn't have a ones digit of zero.

So 35 must be a multiple of five.

48 is not a multiple of five or 10.

50 is five groups of 10 or 10 groups of five.

So we know that that must be a multiple of 10 and five.

Sofia used her times table knowledge there.

Well done, Sofia.

Five we know is a multiple of five.

10 is a multiple of five and 10 because it has that ones digit of zero.

70, the same, it has that one digit of zero so it's a multiple of five and 10.

15 has a ones digit of five, so what does that tell us? That tells us that it must be a multiple of five and two is not a multiple of five or 10.

Well done to you if you managed to complete task A and got all of them correct.

Let's continue with our learning.

In the second part of our learning, we're now going to use some of this knowledge and the relationships between the products to help us to solve some problems. Are we ready? Let's go.

When looking at the products again, Jacob notices something.

He notices something between these two equations here.

What do you think he might have noticed? Jacob has noticed that 10 is double five and two times 10 is double two times five, the products are double.

So the products in the 10 times table are double the products in the five times table.

Wow, look at that.

That's a great thing to notice.

Well done, Jacob.

Sofia also notices that we could look at this the other way around.

And that the products in the five times table are actually half of the products in the 10 times table.

So two times five is half of two times 10.

Yes, look.

20 and 10.

10 is half of 20.

Wow, what a great thing to notice, guys.

Should we have a little explore of this? We can use this knowledge to help us to find missing products.

So if Sofia knows that four times 10 is equal to 40, what would four times five be without any calculating at all? We know that four times five will be half of four times 10.

Half of 40 is equal to 20.

So four times five is equal to 20.

Did you see? No skip counting, no using her times table charts.

She just used the knowledge that she had.

Let's have a look at the other way around.

If we know that four times five is equal to 20, we can really efficiently also work out that four times 10 is equal to 40 because it will be double the product of the five times table.

Well done for spotting this, Sofia.

That knowledge can really help us to solve some problems more efficiently.

Let's have a practise of this.

So over to you, with do check.

Use this knowledge to find the missing products here.

Each time, explain how you knew that that was going to be the answer.

Think about what we know about five and 10 to help you.

Pause this video when you've managed to fill in the missing products and then come on back to see how you've got on.

Welcome back.

Let's have a look then.

Jacob knows that five is half of 10, so six times five will be equal to half of six times 10.

Six times 10 is equal to 60 and we know that half of 60 is equal to 30.

So six times five is equal to 30.

No skip counting in sight there, we just used the knowledge that we had.

Let's have a look here.

We know that 10 is double five, so eight times 10 will be equal to double eight times five.

Eight times five is equal to 40.

So double 40 is 80.

Eight times 10 is equal to 80.

Well done if you got those correct and well done if you managed to explain how you knew what the product was going to be.

Jacob and Sofia now play a game to practise this learning.

How many points did each of them score? Sofia threw five beanbags into the five-point bucket and Jacob threw five beanbags into the 10-point bucket.

They're now going to work out what each of their scores were.

Jacob knows that he scored five lots of 10, so that's five times by 10.

He uses his times table grid to help him here.

He knows that five times 10 is equal to 50.

So Jacob scored 50 points altogether.

How many points did you score Sofia? Sofia knows that she scored five lots of five, so that's five times by five.

Sofia and Jacob scored the same number of beanbags but Sofia's were worth five points, not 10 points.

Sofia remembers that five is half of 10, so because she got the same number as Jacob, she knows that her score will be half of Jacob's score.

Let's partition 50 to find out what half of 50 is.

We know that half of 40 is equal to 20 and half of 10 is equal to five.

So Sofia's score must be 25 because half of 50 is 25.

Did you see how Sofia used her knowledge there to work out what her score would be? She used Jacob's score to help her work out hers rather than having to use her times tables.

Well done Sofia and well done Jacob.

Sofia and Jacob decide to have another turn but they'd like your help now to work out what their scores are this time.

Over to you then.

Jacob and Sofia scored three beanbags, but Sofia scored three beanbags in the 10-point bucket while Jacob scored three beanbags in the five-point bucket.

Can you work out what each of their scores were? Make sure to show those equations and use that knowledge to help you to find the products.

Pause this video and come on back when you found out what each of their scores are.

Welcome back.

Let's start with Jacob then.

So Jacob scored three beanbags in the five-point bucket.

We can see this as three times five, which we know is equal to 15.

So Jacob scored 15 points.

Well done if you've got that one.

Sofia also threw three beanbags into her bucket, but each of her beanbags were worth 10 points, not five points.

So this is still three times by 10.

10 is double five.

So Sofia knows that her score will be double what Jacob scored.

Jacob scored 15 and we know that double 15 is equal to 30, so three times 10 is equal to 30.

Well done if you've got those equations and well done if you said that Jacob would score 15 points and Sofia would score 30 points.

Let's practise this a little more then with task B.

Task B is to use the patterns and relationships between the five and the 10 times tables.

So what you're going to do is you're going to turn over a number card.

You're going to work out what that number is times by five and then work out what that number is times by 10.

Remember to use this knowledge to help you.

A number times 10 is double that number times by five or a number times by five is half of that number times by 10.

So pause this video, have a play of our game and then come on back when you're ready to continue the learning.

Welcome back.

I hope you enjoyed playing that game and I hope our new knowledge of patterns and relationships between the five and 10 times table helped you to solve that really efficiently.

Are we ready? Let's see how Jacob and Sofia got on.

Six was their first number card, so they wrote six in that box.

We know that six times 10 is equal to 60, so six times five will be equal to half of 60, which is 30.

Well done Jacob and well done Sofia for that first turn.

Let's have a look at their next turn.

Nine.

We know that nine times five is equal to 45.

Sofia had to use her chart there to help her because she wasn't sure what nine times five was, but that's okay because she can now use this knowledge to help her to solve nine times by 10.

Nine times by 10 will be double 45 because 10 is double five.

Nine times by 10 is equal to 90, double 45.

Well done, Jacob.

Well done, Sofia, and well done to you for completing task B.

Unfortunately, that's the end of our learning today, so let's have a look at what we've covered.

All multiples of 10 are also multiples of five.

Multiples of 10 have a ones digit of zero.

Even multiples of five have a ones digit of zero.

Odd multiples of five have a ones digit of five.

So three times five is equal to 15.

We know that three times 10 will be double that value which is 30, and three times 10 is equal to 30.

We know that three times five will be half of that value which is 15.

So you can see that you can use the relationships between five and 10 to help you to solve problems that involve the five and 10 times table.

Well done for all of your hard work today.

Just look at how much we've learned.

I can't wait to see you all again soon.

Thanks for joining me today.

Goodbye.