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 use knowledge of divisibility rules when the divisor is 5 to solve problems, and it comes from the unit doubling, halving, quotative, and partitive division.

By the end of this lesson, you should be able to use your knowledge of divisibility rules when the divisor is 5 to solve problems. Here is our key word for today, divisible.

Let's practise.

My turn, divisible.

Your turn.

Fantastic.

Now we should be confident in what that means now.

Let's have a look then at our lesson outline.

In the first part of our learning, we're going to be exploring numbers that are divisible by 5.

And in the second part of our learning, we're going to be using those divisibility rules to solve some problems. Let's get started then with the first part, exploring numbers that are divisible by 5.

Jacob and Sofia are back to help us with our learning today.

Are you ready, guys? Let's get started.

Jacob and Sofia continue to explore some more divisibility rules.

Let's explore the 5 times table.

They have a look at their charts.

Sofia notices that all the products in the 5 times table have a ones digit of a 5 or a zero.

So they do 5, 10, 15, 20, 25, 30, they do.

Sofia also remembers that from our 5 times table facts, we can also record some related divisions.

We know that 4 times 5 is equal to 20, so 20 divided by 5 is equal to 4.

We can say that a number is divisible when it can be divided equally with none left over.

So here, we can see that 20 is divisible by 5, because 4 groups of 5 are equal to 20.

So 20 divided by 5 is equal to 4.

When a number can be divided into 5 equal parts without any left over, we can say that it is divisible by 5.

We can say that all the products in the 5 times table will be divisible by 5, because of those related division facts that we can create.

Of course, Jacob, well done.

7 times 5 is equal to 35.

So we can say that 35 is divisible by 5, because 35 divided by 5 will be equal to 7.

There'll be none left over.

That means that it has been shared equally between 5, or that it's put into groups of 5 with none left over.

35 is divisible by 5.

So let's have a look at our 5 times table chart to find some more numbers that are divisible by 5.

Sofia knows that 55 will be divisible by 5.

Jacob, is she correct? Yes.

11 times 5 is equal to 55, so we know that 55 divided by 5 will be equal to 11.

It will be shared equally or grouped equally with none left over, so it is divisible.

Well done, Sofia.

Over to you then.

Can you use our times table chart to find any other numbers that are divisible by 5? Jacob has a stem sentence to help you to generate your ideas.

I know that, mm, will be divisible by 5, because, mm, times 5 is equal to, mm, so, mm, divided by 5 is equal to, mm.

Explore the 5 times table chart, and use this stem sentence to find your own numbers that are divisible by 5, and come on back when you've had a chance to share a few with the people around you.

Welcome back.

Let's have a look then.

Sofia, what did you notice? Sofia knows that 40 will be divisible by 5, because 8 times 5 is equal to 40, so 40 divided by 5 will be equal to 8.

None left over.

Beautiful, well done.

I love how you use the stem sentence there, Sofia.

Jacob knew 40 was divisible by 5 straight away without even using his times table chart, because 40 has a ones digit of zero, and we know that all the products of the 5 times table have a ones digit of a zero or a 5.

Well done to Jacob and well done to Sofia.

I wish I could hear all of your great ideas.

I'm sure they were wonderful.

Let's move on then with our learning.

Jacob and Sofia now use their sorting game to help develop their knowledge around whether numbers are divisible by 5 or not.

Let's have a look at their first number.

50, hmm.

What do we think about 50? I'm pretty confident with this one.

Jacob knows that 50 is divisible by 10, because 5 times 10 is equal to 50.

Wait, if 5 times 10 is equal to 50, then 10 times 5 is also equal to 50.

So that means that 50 is also divisible by 5.

Well done, Jacob.

I love how you use your knowledge there of your 10 times table as well as your 5 times table to find that 50 was divisible by 5.

12 then Sofia, what do we think about the number 12? Is that divisible by 5 or not? We know that 12 isn't a product of the 5 times table.

It also doesn't have a ones digit of a 5 or a zero, so that means that it isn't divisible by 5.

Well done, Sofia.

15, oh, let's have a look at this one.

15's been a tricky one in our last few lessons.

Is it now divisible by 5 though? 15 has a ones digit of 5, which tells me that it's a product of the 5 times table.

So yes, it is divisible by 5.

3 times by 5 is equal to 15.

So 15 divided by 5 is equal to 3, none left over.

So yes, well done, Jacob.

It is divisible by 5.

Well done to you.

Now I think we should turn over one more card, but this time, do you think you could help Sofia and Jacob to explain whether 25 is divisible by 5 or not divisible by 5? Remember to explain why when you've decided, because that's really going to help Jacob also learn from what you know.

Pause this video, have an explore of the number 25, and then come on back when you've decided whether it's divisible by 5 or not.

Welcome back.

Let's have a look then.

25, what are we thinking? You might have said 25 has a ones digit of 5.

When a number has a ones digit of 5 or zero, we know that it is divisible by 5.

Or you might have said 5 times by 5 is equal to 25.

So 25 divided by 5 is equal to 5.

There will be none left over, so that means that 25 is divisible by 5, because it's a product of the 5 times table.

So let's pop 25 into the divisible by 5 column.

Well done to you if you said either of those explanations and decided that 25 was divisible by 5.

Let's continue to practise this learning then with task A.

Task A is to continue the sorting game that Jacob and Sofia have created, sorting each of those number cards into whether they are divisible by 5 or not divisible by 5.

Make sure you explain before you pop it into the column that you think it belongs to.

Pause this video, have a go at sorting the cards and explaining how you know, and then come on back when you are ready to find out how you've got on.

Welcome back.

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

Remember, if a number has a ones digit of a 5 or a zero, or if it's the product of the 5 times table, it is divisible by 5.

So let's have a look then.

25, we know straight away that that is divisible by 5.

It's a product of the 5 times table, 5 times 5.

42, I've never seen 42 in my 5 times table, so that is not divisible by 5.

35, we can see that it has a ones digit of 5, so that must be divisible by 5.

19 does not have a ones digit of 5 or zero, so that can't be divisible by 5.

20 is divisible by 5, it has the ones digit of zero.

11 is not divisible by 5, that is not in my 5 times table.

45 is in my 5 times table, that's a product of the 5 times table, so that is divisible by 5.

52 is not divisible by 5, it has a ones digit of 2, so that can't be divisible by 5.

30 has a ones digit of zero, so that must be divisible by 5.

And 4 is not even large enough to make one group of 5, so it can't be divisible by 5.

Well done for completing task A.

Let's have a look at the next part of our learning.

Now we're going to use those divisibility rules that we have just created.

Let's get started.

Jacob and Sofia solve some worded problems, and they record each problem as an equation.

Let's have a look at some worded problems then.

There are 15 biscuits.

If I put them into bags of 5, how many bags will I need? Jacob and Sofia recorded this problem as 15 divided by 5 is equal to 3, so that means that there will be 3 bags needed to bag up all 15 biscuits.

15 was our dividend, our whole.

We divided them or put them into bags of 5, and that meant that we needed 3 bags.

Well done.

Let's have a look at the next one.

If 20 conkers are shared equally between 5 children, how many conkers will they each get? 20 will be our dividend, that's the number of conkers.

We divide it by 5, because that's how many children there are.

And they will each get 4 conkers each.

Well done, Jacob and Sofia, a beautiful equation there.

And finally, a dress maker has a ribbon that is 30 centimetres long.

She needs 5 centimetre lengths.

How many 5 centimetre lengths can she make? So for this one, we know that 30 is our whole or our dividend.

We are cutting it into 5 centimetre lengths.

30 divided by 5 is equal to 6, so she will be able to make 6, 5 centimetre lengths.

Well done, guys.

Hmm, let's have a look at those equations then.

Do you notice anything about those equations? Maybe something specifically about the dividends? Hmm, Sofia, Jacob, do you notice anything? Sofia notices that all the dividends are products of the 5 times table.

So they are 15, 20, 30.

Jacob also remembers that when the dividends have a ones digit of a 5 or a zero, they can be divided equally by 5.

So that's why we were able to equally divide in each of those problems. 15 divided by 5 is equal to 3, none left over.

20 divided by 5 was equal to 4, none left over.

And 30 divided by 5 was equal to 6, there were none left over.

Because all of the dividends were divisible by 5.

Remember, if the dividend has a ones digit of a 5 or a zero, that means that it is divisible by 5.

Jacob and Sofia now apply their learning to another worded problem.

The children sit in 5 teams to play a game at a party.

If there are 65 children at the party, will the 5 teams be equal? Hmm, let's have a look at this problem.

For the teams to be equal, the total number of children has to be divisible by 5.

You're quite right there, Sofia.

So let's have a look then.

65.

Oh, 65.

Jacob is struggling to find the answer to that, because it's not on his times table chart.

How are we going to work this one out then? Sofia reminds Jacob that he can use what he knows to say whether a number is divisible by 5 or not, he doesn't need his times table chart all of the time.

We know that numbers with a ones digit of a 5 or a zero are divisible by 5.

So Jacob thinks that 65 will be divisible by 5, because it has a ones digit of 5.

Do you agree with Jacob? What do we think? Yes, 65 can be split equally into 5 teams, so the party will be able to go ahead with all of the children involved.

How lovely is that.

And well done to Jacob.

Even though you were worried you wouldn't be able to solve this problem, you thought about what you knew, and you were able to solve it, well done to you.

Let's have a look at another one.

How are they going to solve this problem? Stickers come in sheets of 5.

How many stickers could I have all together? Circle the correct answers.

Hmm, let's have a think about this problem.

Jacob's not sure how this problem is going to link to his divisible to 5 knowledge that we've been using with our learning.

What do you think Sofia? Sofia notices that the stickers come in sheets of 5, so that means our whole or the number of stickers that we have altogether must be a number that is divisible by 5.

So that's how it links to our divisible by 5 knowledge, Jacob.

So we know that a number is divisible by 5 if it's a product of the 5 times table.

So what do you think then Jacob? Can you see any products of the 5 times table in there? There we go.

5 and 40.

That is 1 times by 5 and 8 times by 5.

So that means that those two answers are divisible by 5, and they could be the amount of stickers that we have altogether.

Hmm, do you agree with Jacob and Sofia's final answer? Sofia can't see any more products of the 5 times table that are on her chart, so she doesn't think there's any more possible answers.

Do you agree with that? Hmm, Jacob, what do you think? Remember, our chart only goes up to 12 times by 5, but there could be more products that aren't on our chart.

That's a good idea there, Jacob.

So let's explore the other answers.

We know that all numbers that have a ones digit of a zero or a 5 are divisible by 5, so that means that we could also have had 105 stickers, 75 stickers, and 90 stickers, because they all have ones digits of zero or 5.

The only possible answer that it couldn't be was 52, and why is that? That's because 52 has a ones digit of 2, so it can't be divisible by 5.

I wouldn't be able to have that many stickers with only sheets of 5.

Well done, Sofia, and well done to Jacob, and well done to you if you spotted those extra answers there.

The children now explore this problem.

There are 90 conkers.

How many children can share this number of conkers? Hmm, Sofia thinks that they can only be shared equally between 10 children.

While Jacob thinks that they can be shared equally, either between 10 children or 5 children.

What do you think? Who do you agree with? Do you agree with Sofia or do you agree with Jacob? Do you agree with both of them? Or do you agree with neither of them? Hmm, let's have a look.

I think we need them to explain their thinking, don't we? Sofia suggests that 90 is the product of the 10 times table, because 9 times by 10 is equal to 90, so that means it must be divisible by 10.

I love how you used your prior learning there, Sofia.

Jacob agrees, but 90 has a ones digit of zero, which tells us that it's also divisible by 5.

Wait, so that's why you suggested that it could be divisible by 10 and 5, Jacob.

Well done.

Oh, that's a good point, Sofia, so hang on then.

Numbers can be divisible by more than one number, because 90 is divisible by 10, but it's also divisible by 5.

Yes, that's because, remember the products in the 10 times table are also products in the 5 times table, so you will notice that some of the numbers that are divisible by 5 will also be divisible by 10.

Well done, Jacob, and well done, Sofia.

I love how you are making all of these connections between your learning.

I'm very impressed.

Let's put this knowledge into practise then.

Over to you then for the next check.

Sofia tries to solve this one by herself.

Is she correct? Bread rolls come in packs of 5.

How many bread rolls could I have altogether? Circle the correct answers.

Sofia knows that numbers with a ones digit of 5 are divisible by 5.

So she circles those answers.

Is she correct? Pause this video, and have a look at Sofia's answers.

Is she correct? If you think she's not correct, what advice could you give her to help her make her answer correct? Pause this video, and then come on back when you've got some advice for Sofia.

Welcome back.

Let's have a look then.

Jacob, what advice have you got for Sofia? Jacob suggests that the products of the 5 times table have a ones digit of 5 or zero, so she's missed one possible answer.

Hmm, which answer has she missed? 60 has a ones digit of zero, so that could also be the number of bread rolls altogether.

60 is also divisible by 5 along with the other answers.

So 60 was the one that she missed.

Did you notice this? Well done, if you did.

Here's another one then.

Which of these numbers can be shared equally between both 5 and 10? Hmm, let's use that knowledge that we had previously.

Pause this video, explore the numbers, which of them can be shared equally between both 5 and 10.

Pause this video, and come on back when you've got an answer.

Welcome back.

Let's have a look then.

We know that for a number to be divisible by 5, we know it has to have a ones digit of zero or 5.

For a number to be divisible by 10, it has to have a ones digit of zero.

A number with a ones digit of zero is then going to be divisible by both 5 and 10.

So 100 and 80 can be shared equally between 5 and 10, because they both have a ones digit of zero.

Well done if you remembered this information, and were able to circle 100 and 80.

Let's get on then with task B.

Task B returns back to our sorting grid.

What I would like you to do is to sort the numbers, whether they are divisible by 5 or not divisible by 5, explaining each time why you are putting that number into that column.

Part two is then to decide whether each of these problems are divisible by 5 or not divisible by 5.

So read each of the problems and pop a check if you think it is divisible by 5 or a cross if you think that it isn't.

Again, remember to explain why you are putting that answer into that box.

Pause this video, have a go at part one and part two, and then come on back to complete the learning.

Welcome back.

Let's have a look then at part one.

Remember, if a number has a ones digit of 5 or zero, it is divisible by 5.

So let's quickly fly through these, are we ready? We should be really confident with this now.

75, yes, divisible by 5.

65, yes, divisible by 5.

68, not divisible.

99, not divisible.

77, not divisible.

90, I can see that zero, yes.

70, yes, I can see the zero.

It is divisible by 5.

62, nope.

80, yes.

91, not divisible by 5.

Well done if you are able to sort those cards into the correct columns, and well done if you were able to do it as speedy as I did there.

Let's have a look then at part two.

Part two was to look at each of the problems and decide whether they were divisible by 5 or not divisible by 5.

Can 63 cakes be put equally onto 5 plates? No, they can't, because 63 doesn't have a ones digit of 5 or zero.

That means that it's not divisible by 5, so 63 cakes will not divide equally onto the 5 plates.

Let's have a look at the next one.

If there are 90 children, can they be put equally into groups of 5? Yes, 90 has a ones digit of zero, which means it is divisible by 5.

So 90 children can be put equally into groups of 5.

And finally, can 85 sheep be split equally between 5 pens? Yes, 85 has a ones digit of 5, which means it is divisible by 5, so the sheep can be split equally between 5 pens.

Well done for completing part two and task B.

That unfortunately is the end of our learning today, but let's have a look at what we've covered.

All numbers in the 5 times table have a ones digit of zero or 5.

All numbers in the 5 times table are divisible by 5.

Thank you so much for joining me again today.

I'm super impressed that all of your hard work, and I'm hoping you are feeling so much more confident with these divisibility rules, as confident as I am at saying divisibility.

Thank you so much for all of your hard work as always, and I can't wait to see you all again soon.

Goodbye.