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 10 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 10 to solve problems. Let's have a look at our keywords: divisible.

My turn, divisible; your turn.

Fantastic, let's get using it then.

Here is today's lesson outline.

In the first part of our learning, we're going to be exploring numbers that are divisible by 10, and in the second part of our learning we're going to be using those divisibility rules to solve some problems. Are we ready to start exploring? Let's explore some numbers that are divisible by 10.

In this lesson, Jacob and Sofia are going to help us with our learning.

Hi guys, are you ready to get started? Let's get going.

Jacob and Sofia decide to explore more divisibility rules.

Are there equal groups of 10 in 34? Hmm, how are we going to work this one out then, Sofia and Jacob? We know that 34 will not have equal groups of 10 because 34 is not divisible by 10.

Let's use the counters to explain what we're thinking.

Here, you can see we have 34 counters.

We can make three equal groups of 10, but here, we only have four counters.

Those four counters can't make another group of 10, so that means that 34 cannot be made from equal groups of 10.

Are there equal groups of 10 in 40? Hmm, let's get those counters out again.

Here are 40 counters.

We can make four equal groups of 10 and there will be none leftover.

So that means that there are equal groups of 10 in 40 and 40 is divisible by 10.

Jacob and Sofia wonder how the 10 times tables can help them.

What do we notice here? Hmm, let's have a look at those products of the 10 times table.

We know that there is a pattern in the 10 times table.

Every product has a ones digit of zero; 10, 20, 30, 40, look, they all have a ones digit of zero.

Yes, that's why 40 was divisible by 10 then, because that's in our 10 times table look and it has a ones digit of zero.

And 34 is not a product of the 10 times table and doesn't have a ones digit of zero.

So that wasn't divisible by 10.

But what about the three-digit numbers? Let's have a little look at those.

They may be three-digit numbers, but these products still have a ones digit of zero.

Look, they just have the hundreds digit now as well, but the ones are all still zeros.

Look, 100 had a zero, 110 has a ones digit of zero, and 120 has a ones digit of zero.

So that means that even if it is a three-digit number, if the ones digit is a zero, it means that it's a product of the 10 times table.

Fantastic! What a great thing to notice there guys.

Well done.

Remember, from our 10 times table fact, we can also record related division facts.

We know that two times 10 is equal to 20.

So that means that 20 divided by 10 will be equal to two.

We know that a number is divisible when it can be divided equally with none leftover.

So we can say here that 20 is divisible by 10, because it divides with none leftover.

Look, 20 divided by 10 is equal to two.

It's an equal group.

When a number can be divided into 10 equal parts without any leftover, we can say that it is divisible by 10.

So we can say that all the products of the 10 times table will be divisible by 10, because if four times by 10 is equal to 40, then 40 divided by 10 will be equal to four.

There's none leftover, so that means it is divisible by 10.

Yes, all the related division facts will show that they are all divisible by 10.

40 is divisible by 10 because four times 10 is equal to 40.

So 40 divided by 10 is equal to four.

Sofia and Jacob now develop this knowledge by using their sorting game.

They're going to sort the numbers depending on whether they are divisible by 10 or not.

Let's have a look at the first number.

30, hmm, what do you think about that then, Jacob? Jacob knows that three times by 10 is equal to 30, so that means 30 divided by 10 will be equal to three.

So 30 is a product of the 10 times table.

That means that it is divisible by 10.

Well done, Jacob.

I love how you used your knowledge there.

Have you got one for Sofia now? 90, what are you thinking about 90 then, Sofia? Sofia knows that nine times by 10 is equal to 90, so 90 divided by 10 will be equal to nine.

There will be none leftover, so that means it is divisible by 10.

90 is a product of the 10 times table.

So yes, it is divisible by 10.

Well done.

15, hmm, what are we thinking with this one? We know that products of the 10 times table that are divisible by 10 or have a ones digit of zero.

15 has a ones digit of five, which tells us that it's not divisible by 10 because it's not a product of the 10 times table.

So that means that 15 is not divisible by 10.

Well done, Jacob.

Let's have a look at one more, but this time, can you help Jacob and Sofia to work out whether this number is divisible by 10? What advice would you give them? Decide whether you think 60 is divisible by 10 or not divisible by 10 and explain how you know.

Pause this video and come on back when you're ready to see how you've got on.

Welcome back.

Let's have a look then.

60, you might have said 60 has a ones digit of zero.

Numbers with a ones digit of zero are divisible by 10.

So that means that 60 is divisible by 10.

Or, you might have said six times 10 is equal to 60, so 60 divided by 10 will be equal to six.

There will be none leftover, so that means it is divisible by 10.

We also know that 60 is divisible by 10 because it's a product of the 10 times table.

So let's pop 60 into the divisible by 10 column.

Well done if you said either of those.

Jacob and Sofia decide to create a divisibility rule for 10.

Sofia has noticed that all the numbers that are divisible by 10 and are products of the 10 times table all have a ones digit of zero.

So that means they found the divisibility rule for 10.

A number is divisible by 10 if it has a ones digit of zero.

It's as simple as that! Right, let's use this rule in our first task.

Task A is to turn over a number card and sort the card into whether it is divisible by 10 or not divisible by 10.

Remember to use Jacob and Sofia's divisibility rule to help you.

That should help you to solve this problem really efficiently.

Pause this video and come on back when you've sorted all the numbers to see how you've got on.

Welcome back.

Let's have a look then.

We know that if a number has a ones digit of zero or is the product of the 10 times table, it is divisible by 10.

I can see straight away 40 and 50 are both divisible by 10 because they both have ones digits of zero and they are products in the 10 times table.

17 and 42 do not have ones digits of zero, so they cannot be divisible by 10.

70 is divisible by 10.

68 is not divisible by 10.

That's not a product of my 10 times table.

10 is one group of 10, so that is divisible by 10.

85 has a ones digit of five, so that means it's not divisible by 10.

80 is a product of the 10 times table, so that is divisible by 10, and six is not divisible by 10.

Well done if you've got all of the numbers in the correct columns, and well done for completing Task A.

Let's now move on to the second part of our learning using these divisibility rules to help us to solve some problems. Let's get started.

Jacob and Sofia solved some worded problems and they recorded each problem as an equation.

So let's have a look at them.

There are 30 eggs.

If I put them into boxes of 10, how many boxes can we make? They recorded this equation as 30 divided by 10 is equal to three.

So that means that they will need three boxes to put all of the eggs into boxes of 10.

30 is our dividend, 10 is our divisor, and three is the number of boxes, the quotient.

If 40 cakes are shared equally between 10 plates, how many cakes will there be on each plate? What's the equation going to be here? We can see that 40 is going to be our dividend because that's the number of cakes.

We're sharing them between 10 plates.

So that means that our divisor is 10.

40 divided by 10 is equal to four, so that means there will be four cakes on each plate.

And finally, if a dressmaker cuts a 60 centimetre piece of ribbon into 10 centimetre pieces, how many pieces will she have? We can see this as 60 divided by 10 is equal to six.

So that means that there will be six pieces of 10 centimetre ribbon from the 60 centimetre piece.

Wow! Well done, Jacob and Sofia.

You did a great job of representing those problems with those divisions there.

Do you notice something though, about those equations? Sofia has noticed that all the dividends are products of the 10 times table; 30, 40, 60.

And Jacob also remembered that when the dividends have a ones digit of zero, they can equally be divided by 10.

So in each of those problems, look, we can see that they were equally divided by groups of 10 or into groups of 10 because they are divisible by 10.

Remember, if the dividend has a ones digit of zero, it is divisible by 10.

Let's use this knowledge to have a look at another problem.

Jacob and Sofia now apply their learning to this problem.

Which of the year groups can be put into teams of 10? So we can see that we've got Year One, Year Two, and Year Three and the number of children that are in each year group.

Jacob wants to challenge himself to do this without using his times table chart.

Do you think he could do it? I think we can do this.

Come on then, Sofia.

What knowledge can we use so that we don't have to use our times table charts? Jacob knows that numbers with a ones digit of zero are divisible by 10.

So can you see any groups of children there that could be divisible by 10? We can see that Year One and Year Three both have numbers that have a ones digit of zero; 50 and 40.

So that means that Year One and Year Three can be put into teams of 10 equally.

Year Two would not be able to be put into groups of 10 equally because they have a ones digit of five, which is not divisible by 10.

So that means that when they're put into their teams of 10, there will be children left over that won't be able to make another group of 10.

Jacob and Sofia now have a look at another year group table.

Can you help them to see which of the year groups would equally be put into groups of 10? Use your knowledge to explain how you know they will or will not be able to be put into teams of 10.

Pause this video and come on back when you've had a chance to have a look and have a think.

Welcome back.

Let's have a look then.

We can say 30 has a ones digit of zero, which means 30 will be divisible by 10.

So that means that Year Four can be put into teams of 10.

Year Five and Year Six have 69 and 76 children.

So that means they don't have a ones digit of zero.

That means that they won't be divisible by 10.

So when they're put into teams of 10, there will be children left over.

Well done if you said that Year Four was the only year group there that could be put into teams of 10.

Let's carry on with our learning.

Jacob now wants to know if the whole school could be put into teams of 10.

He can see that in the whole school there are 300 children.

300 has zero tens and zero ones.

So that means that 300 is divisible by 10.

Is Jacob correct? Hmm, let's have a think.

If 300 has zero tens and zero ones, that means that 300 will be divisible by 10.

Hmm, that doesn't sound quite right to me.

300 is divisible by 10, but it doesn't matter about the tens digit.

If the number has a ones digit of zero, then the number is divisible by 10.

So it doesn't matter about the tens, Jacob.

It's only the ones that tell us whether the number can be divided by 10 or not.

That's a good thing to notice there.

So it doesn't matter about the hundreds or the tens number, it's just the ones we need to look for.

Keep this in mind when you have a go at Task B.

Task B is to decide whether each of these problems are divisible by 10 or not divisible by 10.

So have a read of each of those problems and if you think it is divisible by 10, you put a little tick in the box.

And if it's not divisible by 10, you pop a cross in the box.

Remember, for each problem make sure you explain how you know whether it is divisible by 10 or not divisible by 10.

Pause this video, have an explore, and then come on back when you're ready to see how you've got on.

Welcome back.

I hope you enjoyed exploring those problems there.

Let's have a look then.

Jacob has 80 stickers.

Can he share these between his 10 friends equally? Hmm, let's have a look.

80, yes! 80 is a product of the 10 times table, so that means it is divisible by 10 and can be shared equally.

So his 10 friends will be able to share those stickers and there won't be any leftover.

Next one then.

If there are 49 children, can they be put into teams of 10? Hmm, 49, no.

49 has a ones digit of nine, which means 49 will not be divisible by 10.

So all the children cannot be put into teams of 10.

And finally, can 160 cookies be split equally between 10 packets? Hmm, I remember that it's only the ones that are important when we're thinking about being divisible by 10.

I can see that 160 has a ones digit of zero, so that means it is divisible by 10.

The cookies will be able to be split equally between the 10 packets with none leftover.

Well done for completing Task B and completing our lesson.

I hope you're feeling a lot more confident now with the divisibility rules of 10.

Let's have a look at what we've covered today.

All the numbers in the 10 times table have a ones digit of zero.

All numbers in the 10 times table are divisible by 10.

Thank you so much for all of your hard work today.

Again, I hope you're feeling so much more confident at noticing when numbers are divisible by 10 or not.

I can't wait to see you all again soon for some more learning.

Goodbye!.