Lesson video

Hello, my name's Mrs. Hopper, and I'm really looking forward to working with you in this lesson on representing the 5 times table and linking it to the 10 times table.

So are you ready to do some counting in fives and tens, and explore how the 5 and 10 times table are related to each other? Are you? Excellent.

Let's make a start.

So in this lesson, we're going to be using knowledge of the relationships between the 5 and 10 times tables to solve problems. So are you ready for some 5 and 10 times table practise? I hope you are.

Let's make a start.

We've got two keywords in our lesson today, double and half.

So I'm gonna take my turn to say them, and then it'll be your turn.

Are you ready? My turn, double.

Your turn.

My turn, half.

Your turn.

Well done.

I'm sure there are words you know, but they're going to be really useful when we are thinking about that relationship between the 5 and 10 times table today.

So listen out for them and make sure you use them when you're talking about your work as well.

There are two parts to our lesson today.

In the first part we're going to be working out some missing numbers, and in the second part we're going to be solving problems. And we've got Aisha and Laura helping us in our lesson today.

Aisha and Laura are looking closely at the multiples of 10 and 5.

Can you see they've recorded some in the table here.

So their first row says zero groups of 5 is zero groups of 5, has a product of zero, it's zero groups of 10 and it's zero groups of 10 as an expression.

So we're recording our times table knowledge as an expression.

We're thinking about how many groups of 5 there are and how many groups of 10 there are.

And then we are looking at the product, the answer to our multiplication.

So they've started to fill in the second row.

They've got two groups of 5, a product of 10, and one group of 10.

So they know that two groups of 5 is equal to 10, and one group of 10 is equal to 10 as well.

And they can record that with a multiplication expression, 2 multiplied by 5, two groups with 5 in each group, and 1 multiplied by 10, one group with 10 in the group.

They're going to complete the rest of the table now.

I wonder if you can think about what's going to go in those gaps.

So they've got four groups of 5, and they can represent that with 4 multiplied by 5.

And they know that four groups of 5 is equal to 20, the product.

What about groups of 10? How many groups of 10 will they need? That's right, they'll need two groups of 10.

Two multiplied by 10 is also equal to 20.

And we can see there that our factors in our multiplication represent two groups and 10 in each group.

What about the next row? This time we've got six groups of 5, three groups of 10, and our product is 30.

So we can represent that with the multiplication expression, 6 multiplied by 5, 6 because we've got six groups, and 5 'cause there's five in each group.

And 3 multiplied by 10, 3 because there are three groups of 10, and 10 because there's 10 in each group.

What do you notice? Well the number of groups of 5 after zero is always even.

So we've got two groups of 5, four groups of 5, and six groups of 5.

And the number of groups of 10 increases by one.

One group of 10, two groups of 10, three groups of 10.

And the product increases by 10 each time.

The product is a multiple of 5 and 10 'cause it's got that zero in the ones, 0, 10, 20, 30.

It increases by 10 each time, by one group of 10 and by two groups of 5.

Let's look at the number of groups of 5 and the number of groups of 10.

So we can see that we've got two groups of 5 and one group of 10.

The number of groups of 5 is double the number of groups of 10, two is double 1.

Or we could say the number of groups of 10 is half the number of groups of 5, 1 is half of 2.

And we can see that that's also true for four groups of 5 and two groups of 10, and six groups of 5 and three groups of 10.

Aisha adds another row.

Can the row be completed? So she's put in three groups of 5.

So the number of groups of 5 is three, and it's represented by 3 multiplied by 5.

Three groups multiplied by 5, five in each group.

The product is 15, three groups of 5 is equal to 15.

What about groups of 10? We can't represent it as groups of 10.

There are no whole groups of 10 which are equal to 15.

If we have the next group of 10, which would be 4, we'd have 40, wouldn't we? And we already know that one group of 10 is 10, two groups of 10 are 20, and three groups of 10 are 30.

The next multiple of 10 would be 40.

15 is not a multiple of 10.

Three is an odd number, isn't it? The other groups of 5 after zero were even, two, four, and six.

Three groups is an odd number of groups of 5.

If there's an odd number of groups of 5, there will not be a matching number of groups of 10.

Laura adds in another row.

Can you finish the row and explain how you know? Pause the video, have a go, and when you're ready for some feedback, press play.

How did you get on? This time we had four groups of 10 and the expression 4 multiplied by 10.

Four representing four groups, and 10 representing the 10 in each group.

And our product was 40, four groups of 10 is equal to 40.

What about the number of groups of 5? Ah, the number of groups of 5 is double the number of groups of 10, and double 4 is 8.

So to get a product of 40 in the 5 times table, we need eight groups of 5, 8 multiplied by 5, 8 representing the number of groups and the 5 representing the 5 in each group.

Eight groups of 5 is equal to 40.

Well done if you got that right.

Laura is exploring the relationship between multiples of 5 and 10.

She uses number shapes to show this relationship.

She's shown that 2 times 5 is equal to 1 times 10.

She says, "So for every two groups of 5, that's one group of 10." Two groups of 5 is equal to one group of 10.

Aisha needs help finding the missing factor.

She says, "If 2 times 5 is equal to 1 times 10, then 4 times 5 must be equal to something times 10." What advice would you give Aisha to solve the problem? Laura says, "We know that four groups of 5 is equal to 20." So something multiplied by 10 should also give us 20.

Two groups of 10 is equal to 20, so the missing factor is 2.

And you could imagine those four groups of 5 fitting together to make two groups of 10 using those number shapes.

And there they go.

Four groups of 5 is equal to two groups of 10, and there are the 10s.

Aisha needs help with finding the missing factor this time.

If 2 multiplied by 5 is equal to 1 multiplied by 10, then 8 multiplied by 5 must be equal to something multiplied by 10.

And you can see we've got eight lots of 5 on the screen there.

I wonder if you can help her find the missing factor.

Laura says 10 is double 5.

So that means we will need half the number of groups of 10.

That's four groups of 10, 4 times 5 is equal to 40.

So can you picture those groups of 5 coming together to make groups of 10, so we'll only need half the number of groups of 10? Let's have a look.

And we've moved the 5s into pairs and we've replaced them with 10s.

So 8 times 5 is equal to 4 times 10.

We need half the number of groups of 10 that we did groups of 5, because 5 is half of 10 or 10 is double 5.

Over to you to check your understanding.

Can you find the missing factor? If 2 times 5 is equal to 1 times 10, then 6 times 5 is equal to something times 10.

You might want to use some number shapes to help you, or maybe you can picture them in your mind.

Anyway, pause the video, have a go, and when you're ready for some feedback, press play.

How did you get on? Did you spot that if it was 6 times 5, then it was 3 times 10? 10 groups double 5 groups.

So that means we will need half the number of 10 groups, and we could imagine six groups of 5 and they would form together to make three groups of 10.

Six times 5 is equal to 3 times 10.

Time for you to do some practise.

You're going to use your knowledge of the relationship between the 5 and 10 times tables, and the fact that you know that 2 multiplied by 5 is equal to 1 multiplied by 10, and you're going to fill in the gaps in these equations.

Pause the video, have a go, and when you're ready for some feedback, press play.

How did you get on? So did you spot that where we had a number of groups of 5, if our equation was equal, then we had half the number of groups of 10? So 4 times 5 was equal to 2 times 10, 6 times 5 was equal to 3 times 10, 8 times 5 was equal to 4 times 10, 10 times 5 was equal to 5 times 10, 12 times 5 was equal to 6 times 10.

Now for the next, we can see that same relationship with our missing numbers in a different place.

So this time, 10 times something was equal to 5 times 10.

Well, 10 times 5 is equal to 5 times 10.

Something times 5 was equal to 4 times 10.

Well, if we've got four lots of 10, we must have double the number of groups of 5, so we must have eight groups of 5.

And then 6 times something was equal to 3 times 10.

Well, if we've got six groups of something and it's equal to three groups of 10, it must be six groups of 5.

I hope you were successful with those.

And on into the second part of our lesson, we're going to be solving problems. Aisha and Laura are comparing the number of sticker sheets that each teacher has.

Ms. Coe has three sheets of 10 stickers, and Ms. Miah has four sheets of 10 stickers.

So who's got the most stickers? Can we use our stem sentence? "Mm roots of mm is less than mm groups of mm." Well if we write Ms. Coe's stickers as an equation, we can say that she has three sheets of 10 stickers, so that's 3 times 10, and we know that 3 times 10 is equal to 30.

She has three sheets of stickers and each sheet has 10 stickers on it.

What about Ms. Miah? Well, she has four sheets of 10 stickers.

So the 4 represents the number of sheets, and the 10 represents the 10 stickers on each sheet.

And 4 times 10 is equal to 40.

And we can represent the groups of 10 using 10 sticks.

So three groups of 10 and four groups of 10.

Three groups of 10 is less than four groups of 10.

There's one fewer group of 10.

So three groups of 10 is less than four groups of 10.

So who have the most stickers? Look like it was Ms. Miah's this time, wasn't it? This time Ms. Miah has eight sheets of 10 stickers, and Ms. Coe has four sheets of five stickers.

Hmm.

So there's our eight sheets of 10 stickers, 8 multiplied by 10, and 4 times 5.

We've got four groups of five stickers this time.

That's equal to 20.

Eight times 10 was equal to 80.

So eight groups of 10 is greater than four groups of 5.

And Laura says, "I didn't need to know the product because Ms. Miah has more groups that are bigger." Eight sheets of 10 stickers.

Ms. Coe only had four sheets, and each sheet only had five stickers on it.

Ah, what about this one? "Mrs. Hopper," that's me, "has four sheets of five stickers." "Ms. Miah has two sheets of 10 stickers." Hmm, I wonder what we're going to find this time.

Let's represent them with our number shapes this time.

So, Mrs. Hopper, that's me, I've got four sheets of five stickers represented with four groups of 5.

So that's 20 altogether.

What about Ms. Miah? Ah, she's got two groups of 10, two sheets with 10 stickers.

The product for both is 20.

So we can say that four groups of 5 is equal to two groups of 10.

Ms. Miah and I have the same number of stickers.

Over to you to check your understanding.

So this time, Mrs. Hopper, that's me, has four sheets of five stickers, and Ms. Miah has three sheets of 10 stickers.

So which one is greater, and how do you know? Pause the video, have a go, and when you're ready for some feedback, press play.

So who had more stickers this time? Ah, four groups of 5 is less than three groups of 10.

That group size is smaller, isn't it? Four groups of 5 would give us 20 stickers, but three groups of 10 would give us 30 stickers.

Three groups of 10 would be the same as six groups of 5.

So this time, Ms. Miah had more stickers.

Ooh now, another problem.

Ms. Miah has the same number of stickers as Mrs. Hopper, but she has 10 stickers on each sheet.

How many sheets does she have? So I've got six sheets of five stickers.

How many has Ms. Miah got? We've got the same number of stickers.

Hmm.

So six sheets of five stickers.

Six groups of 5 will be equal to how many groups of 10? So there are six groups of 5 and that's equal to 30.

But how many groups of 10 is that? Aisha says, "We know that there are two groups of 5 for one group of 10." So if we put our 5s together, we should make three groups of 10.

We'll need half the number of groups of 10 and there you can see them.

So six groups of 5 is equal to three groups of 10.

So Ms. Miah must have three sheets of 10 stickers to have the same number of stickers as my six sheets of five stickers.

Time to check your understanding.

This time Ms. Miah has the same number of stickers as Ms Coe.

She has 10 stickers on each sheet.

How many sheets does she have? So Ms. Coe has eight sheets of five stickers.

Ms. Miah has some sheets of 10 stickers, but they've got the same number of stickers altogether.

Pause the video, work out how many sheets of stickers Ms. Mia has and when you're ready for some feedback, press play.

How did you get on? Ms. Miah's got four sheets of 10 stickers.

Eight groups of 5 is equal to four groups of 10.

You could imagine those eight groups of 5 putting together in pairs to make four groups of 10, half the number of groups of 10.

Aisha and Laura are now comparing how many stickers Ms. Miah has compared to Ms. Coe who has six sheets of five stickers.

So the middle column represents the six sheets of five stickers, and that would be "equal to." So, are Ms. Miah's stickers less than, equal to, or greater than Ms. Coe's stickers? Ms. Miah has three sheets of 10 stickers.

Aisha's put Ms. Miah's stickers into the less than column.

Is she correct? Can you explain your thinking? No, she's not correct, is she? Three sheets of 10 stickers is equal to six sheets of five stickers.

If we have twice as many sheets, we'd have half as many stickers on each sheet and that would be five.

So six times 5 is equal to 30, and three times 10 is equal to 30.

So the number of groups of 5 is double the number of groups of 10.

So they've got the same number of stickers.

Time for you to do some practise now.

Can you fill in the blanks using your knowledge of the relationship between the 5 and 10 times table? And you're going to fill in those gaps with less than, greater than, or equal to.

And then for question two, you're going to sort the sticker sheets by comparing the other sheets to eight sheets of five stickers, so that's our equal bit.

So in the middle, if the number of stickers is equal to eight sheets of five stickers, that's where it goes.

Otherwise we're going to decide if it's less than that or greater than that.

You might wanna start out by working out how many stickers there would be on eight sheets of five stickers.

Pause the video, have a go at your tasks, and when you're ready for some feedback, press play.

How did you get on? Let's look at question one.

So one group of 5 is less than one group of 10.

If there's only one group, if it's a group of 5, it's going to be smaller than a group of 10.

Two groups of 5, how do we compare that to one group of 10? Well, two groups of 5 is equal to one group of 10.

You could even use your hands to show that.

I've got two groups of 5 and that's equal to one group of 10.

What about three groups of 5 and three groups of 10? Well, again, we've got the same number of groups, haven't we? But we've got three groups of 5, which has got to be less than three groups of 10.

Four groups of 5 is equal to two groups of 10.

Again, we can think about those four groups of 5, two groups of 5 makes one group of 10.

So four groups of 5 must be equal to two groups of 10.

And finally, for E, 12 groups of 5, again, is equal to six groups of 10.

We've got half the number of groups of 10 or double the number of groups of 5.

And we can see here one group of 5 must be less than one group of 10, and four groups of 5 for D, is equal to two groups of 10.

And here are the sticker sheets all sorted.

So our eight sheets of five stickers was equal to 40 stickers.

And that's the same as four sheets of 10 stickers, isn't it? So now we know we're comparing eight sheets of five stickers and four sheets of 10 stickers, which give us our equal to column.

So three sheets of 10 stickers must be less than four sheets of 10, and three and four sheets of five stickers are both less than our eight sheets of five stickers.

And then greater than was five sheets of 10 stickers, nine sheets of 10 stickers, and nine sheets of five stickers.

So well done if you've got all those in the right places.

And we've come to the end of our lesson.

We've been using knowledge of the relationships between the 5 and 10 times tables to solve problems. We've learned that we can use our knowledge of that relationship between 5 and 10 times tables to solve problems. We know that multiples of 5 are half the value of multiples of 10, and that multiples of 10 are double the value of multiples of 5.

So if I've got six groups of 10, that's going to be worth twice as much as six groups of 5, and six groups of 5 will be half as much as six groups of 10.

Thank you for all your hard work and your mathematical thinking today.

I hope I get to work with you again soon.

Bye-bye.