Lesson video

Hello, everyone.

Welcome back to another math 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 two 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 two to solve problems. Let's have a look at our key words.

The first one is divisible.

My turn, divisible.

Your turn.

The next word is even.

My turn, even.

Your turn.

Fantastic.

Now that we've said them, let's use them.

Here is this lesson's outline.

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

And in the second part of our learning, we're going to be using those divisibility rules.

So let's get started with exploring numbers that are divisible by two.

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

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

"Jacob and Sofia are looking at their two times table chart.

What do you notice?" Sofia has noticed that there is a pattern in the two times table.

She notices that all the products either have a ones digit of a zero, a two, a four, a six or an eight.

You're correct, Sofia.

Yes, they do.

Look, zero, two, four, six, eight.

They're all even numbers.

But I agree with Jacob.

What about the two digit numbers? Are they still even numbers because they have two digits rather than just zero, two, four, six or eight? Sofia is explaining that in a two digit number, if the ones digit is an even number, zero, two, four, six or eight, then that number is still even.

So that means that all the products in the two times table are even.

Look, 10 has a ones digit of zero.

12 has a ones digit of two.

14 has a ones digit of four, all the way to 22.

Two is an even number and the ones digit in 22 is two.

So that means that they are all even.

Jacob and Sofia choose one of the equations to explore a little bit further.

Sofia has remembered from our two times table facts that we can also record related divisions.

So we know if six times two is equal to 12, the related division fact will be 12 divided by two is equal to six.

"We can say that 12 is divisible by two." "Divisible? What does that mean?" Sofia, can you explain to Jacob what divisible means? When a number can be divided into mm equal parts without any left over, we can say that it is divisible by that number.

So in this case, we can say that all the products of the two times table are divisible by two.

The products of the two times table can be divided into two equal parts without any left over.

Yes, Jacob, we know that they will be divisible by two because they will be the related division facts.

So let's have a look at these.

Eight times two is equal to 16.

So 16 divided by two is equal to eight.

We can say that 16 is divisible by two because it is a product of the two times table.

So eight times by two is equal to 16.

So 16 divided by two is equal to eight.

There's non left over when we divide by two.

So that means 16 is divisible by two.

Sofia and Jacob now develop this knowledge by sorting some numbers depending on whether they are divisible by two or not.

Let's have a look at their first number.

20.

Hmm.

What do you think? Do you think 20 is divisible by two? Jacob knows that 10 times by two is equal to 20.

So 20 divided by two will be equal to 10.

That means that 20 is a product of the two times table, so it is going to be divisible by two.

So we can pop it in there.

Well done, Jacob.

I love how you use your times table knowledge there to help you to decide whether 20 was divisible by two or not.

Sofia, it's your turn now.

12.

Hmm.

What do you think? Do you think 12 is divisible by two? Let's see what Sofia thinks.

Sofia knows that six times by two is equal to 12 because she knows her times table facts.

So 12 divided by two will be equal to six.

There won't be any left over.

So that means that 12 is divisible by two.

"12 is a product of the two times table, so yes, it is divisible by two." Oh, 15 then Jacob.

What do you think about this one? What do you think about this one? Hmm.

Jacob remembers that even numbers can be divided into two equal parts without any left over.

So they will be divisible by two.

But what about 15? 15 has a ones digit of five, which tells us that 15 is odd.

We know that odd numbers are not divisible by two.

They won't be a product of the two times table.

So that means that 15 is not divisible by two.

Well done, Jacob.

I love how you used our old learning there to help you to solve this new problem.

Over to you then.

Can you help Sofia and Jacob with this one? 18.

They're not sure if this is divisible by two.

Pause this video.

Have a think.

Is 18 divisible by two or not divisible by two? And make sure that you have an explanation to help Sofia and Jacob understand why.

Pause this video and come on back when you can give them some advice.

Welcome back.

Let's have a look then.

You might have said 18 has a ones digit of eight.

Eight is an even number, so that means that 18 is an even number.

And we know that even numbers are divisible by two, so yes, 18 is divisible by two.

Or you might have said two times nine is equal to 18, so 18 divided by two is equal to nine.

There's non left over.

So we can see that 18 is divisible by two because it is a product of the two times table.

So let's pop 18 into divisible by two.

Well done to you if you said that 18 was divisible by two, and were able to explain it to Jacob and Sofia.

Jacob and Sofia now check each other's knowledge by selecting a number of objects to say whether or not the group is divisible by two or not divisible by two.

Sofia's going to choose a number of objects and then Jacob is going to decide whether the group is divisible by two or not.

Okay, let's do this.

Are we ready? (gasps) Oh, Sofia has chosen a group of pens.

Let's have a look then, Jacob.

What are you thinking? We can see that there are 10 pens here.

Jacob knows that 10 is divisible by two because 10 is an even number.

Yes.

Look, 10 can be divided into two equal parts.

10 divided by two is equal to five, and Sofia has split the pens into two equal groups, look.

So we can say that this group of 10 pens is divisible by two.

Right Jacob, I think it's your turn now to collect some objects for Sofia.

Oh, what are you going to collect, Jacob? (gasps) Jacob collects a pile of books.

Here we can see that there are six books.

Sofia knows that six is divisible by two because it's an even number.

Yes, six can be divided into two equal parts.

Six divided by two is equal to three.

So it is divisible by two.

There's no books left over.

Look, we have a group of three and a group of three.

Well done Sofia, and well done to Jacob.

Sofia and Jacob have now got a group of objects for you.

Is this group of objects divisible by two? Yes or no? And can you explain how you know? Pause this video, have a look at the objects, decide whether you think it is divisible by two or not, and explain how you know.

Here is a stem sentence to help you to explain what you are thinking.

Mm is or is not divisible by two because.

Make sure you explain how you know because that's going to convince Jacob and Sofia whether you are correct or not.

So pause this video, have a look at the objects, decide whether it is divisible or not by two, and then explain how you know.

Come on back when you are ready to share your learning.

Welcome back.

Let's have a look then.

We can see that we have nine blocks.

Nine is or is not divisible by two.

Hmm.

What do you think, Sofia? What do you think, Jacob? Jacob thinks that nine is not divisible by two because we know that nine is an odd number, and odd numbers cannot be divided into two equal groups.

A beautiful explanation there, Jacob.

Thank you for sharing that.

Well done to you if you said that nine was not divisible by two, and if you had a reason similar to Jacob's.

But you might have also said that nine is not a product of the two times table, so it can't be divisible by two.

Well done for completing this check.

Let's have a look then at task A.

Task A is to create your own version of Jacob and Sofia's game.

You're going to turn over a number card and sort it into whether it's divisible by two or not divisible by two, making sure that you're explaining each time how you know.

Part two of task A is to play the second game that Sofia and Jacob invented.

You are going to choose a number of objects.

This has to be less than 24.

And ask your friend to say whether the number in that group is divisible by two or not.

Make sure you explain how you know that that number is divisible by two or not, and use Jacob's stem sentence to help you when you're explaining.

So pause this video, have a go at task A, part one and part two, and then come on back when you're ready to see how you've got on.

Welcome back.

Let's have a look then.

I hope you enjoyed playing those two games there.

Part one was to turn over a number card and say whether the number was divisible by two or not.

Remember, if a number is even or the product of the two times table, it is divisible by two.

So let's have a look then.

24 is in the two times table, so I know that it is divisible by two.

14 is an even number, so that must be divisible by two.

Seven.

Hmm.

Seven isn't in my two times table, and I know that seven is odd.

So seven is not divisible by two.

The same with 19.

19 has a ones digit of nine, which means that 19 is odd.

So that cannot be divisible by two.

22.

I know that 11 twos are equal to 22, so it is a product of the two times table and is divisible by two.

11.

I know that 11 is an odd number, so that is not divisible by two.

Two is divisible by two because it's the number itself.

So that's one group of two, isn't it? 21 is an odd number, so that's not divisible by two.

16 is divisible by two, that's eight times by two, isn't it? And three is an odd number, so it's not divisible by two.

Well done if you manage to sort those numbers into the correct boxes.

Let's have a look then at part two.

Part two was to select a number of objects less than 24, and ask your friend to say whether the number is divisible by two or not.

Jacob's group of objects was 22 objects.

Sofia explained that 22 is an even number and is a product of the two times table.

So 22 is divisible by two.

So that group of objects was divisible by two.

Sofia got 17 objects for Jacob.

17 is not divisible by two because 17 is an odd number, and it's not a product of the two times table.

Some beautiful explanations there, Sofia and Jacob, and well done to you for completing task A.

Let's move on to the second part of our learning.

Using the divisibility rules to solve problems. Let's get going.

Jacob and Sofia solved some worded problems. They record each problem as an equation.

There are 10 socks.

If I put them into pairs, how many pairs can I make? We can see this as 10 pairs of socks being put into pairs, which is dividing by two.

10 divided by two is equal to five.

So that means we will be able to make five pairs of socks.

The second one.

There are 14 children.

If they get into groups of two, how many groups will there be? Hmm.

What's our dividend here? We know that our dividend is going to be 14 because there's 14 children altogether.

They get into groups of two, so my divisor is two.

14 divided by two is equal to seven.

So that means that they will be able to make seven groups of children.

And finally, I go into a bakery and buy 12 loaves of bread.

I can fit two loaves in each bag.

So how many bags will we need? We know that 12 is our dividend, our whole, and we can fit two loaves in each bag.

So two, again, is our divisor.

12 divided by two is equal to six.

So there will be six bags needed to carry all of those loaves of bread.

Well done, Jacob and Sofia.

That was some great solving of those problems. Let's have a look at those equations a little bit closer.

Do we notice anything about the dividends in these problems? 10, 14 and 12.

Hmm.

Do you notice anything? Sofia, what do you think? Sofia has noticed that all the dividends are products of the two times table.

So they are.

10 is in the two times table, 14 is in the two times table, and 12 is in the two times table.

And Jacob remembers that when the dividends are even numbers, they can equally be divided by two.

Remember, if a dividend is even, it is divisible by two.

So let's have a look at this problem.

If we have 76 socks, can we make pairs? Hmm.

Sofia notices that this question involves pairs, and we know that pairs are groups of two.

So if 76 is divisible by two, then we will be able to make pairs.

But 76, that is a lot higher than our times table chart goes, isn't it, Jacob? So how are we going to work this one out? That's a good idea, Sofia.

Do we have any knowledge that we could use to help us to solve this problem that doesn't involve using our times table chart? Jacob remembers that if a number is even it can be divisible by two.

So let's have a look then.

76.

We know that if the ones digit is even in a two digit number, then that two digit number must be even.

So let's have a look at 76.

76 has a ones digit of six, which is an even number, so that means that 76 must be an even number.

If 76 is an even number, that means that it is divisible by two, and that we will be able to make equal pairs from them.

So yes, 76 socks will make pairs.

Wow, Sofia and Jacob, I love how you used what you knew there to help you to solve that problem when the number was larger than what was on your times table charts.

Do you think you could have a go at this and use your knowledge to solve this problem? Let's have a look.

What if there were 57 socks? Could we make pairs from 57 socks? Use the knowledge that Jacob and Sofia have just used to solve their problem to say whether 57 would be able to be made into pairs equally.

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

Welcome back.

Now, let's have a look then.

57 is a lot larger than all of those numbers on our two times table chart, isn't it? So we're going to use the knowledge that Jacob and Sofia used previously.

Sofia can see that in the number 57, 7 is the ones digit, which is an odd number.

So that means that 57 must be an odd number.

Odd numbers cannot be equally divided by two.

So that means that 57 socks would not be able to make pairs.

Well done to you if you said that 57 socks would not make equal pairs.

Let's continue with our learning.

All even numbers are in the two times table, so are divisible by two.

Jacob now creates his own problem for Sofia to solve.

We have 31 slices of bread.

Two slices are needed to make each sandwich.

Can 31 slices of bread make a whole number of sandwiches or will there be some bread left over? Hmm.

We can see that to make equal groups of two, the dividend must be divisible by two.

31 has an odd ones digit.

So 31 is not an even number and isn't divisible by two.

That means that 31 slices of bread will not make a whole number of sandwiches.

There will be some bread left over, which means it's not divisible by two.

Well done.

Wow, that was a great problem there, Jacob.

Sofia, I think you should now make one for Jacob.

Sofia now challenges Jacob with her problem.

There are 1,004 shoes at the shoe factory.

Goodness me, that's a large number, Sofia.

Have they made enough shoes to make pairs? Hmm.

Jacob, I'm not sure about this one.

What are we going to do? Jacob notices that number is so big so he can't solve that problem.

Sofia suggests that Jacob just needs to think about what he knows because he can solve this problem.

Jacob can say that 1,004 has a ones digit of four, which is even.

So that must mean that 1,004 is an even number.

If 1,004 is an even number, that means that it is divisible by two.

So we know that yes, they have made enough shoes to make pairs.

Wow, Jacob, I'm so impressed.

Yes, he applied what he knew to an unknown number.

I am so, so impressed with you using your previous knowledge to help you to solve this problem that you thought you couldn't solve, Jacob.

Well done to you.

Right then, over to you.

Taking inspiration from Sofia and Jacob, create your own is it divisible by two problem for your friend to solve.

Think about what you might share between two groups or put into groups of two or pairs that will help you to create your problem.

You can also use this stem sentence to help you if you need a little bit of a starting point.

There were, mm, mm.

If they were put into two groups, groups of two or pairs, would this make a whole number? So pause this video, have a go at creating your own problems for your friends to solve, and then come on back when you're ready to continue the lesson.

Welcome back.

Let's have a look then.

Come on then, Sofia and Jacob.

They decided to create another one because they enjoyed it so much.

Let's listen to what they said.

You might have said there were 73 slippers.

If they were put into pairs, would this make whole pairs? Oh, I like that.

I love wearing my slippers.

Come on then Jacob, will that make whole pairs? 73 has an odd ones digit, so it's not even.

That means that they wouldn't be able to put all the slippers into a pair.

What was your next problem then, Jacob? "There were 64 children.

If they were put into two groups, would there be an equal number in each group?" Oh, I like that question.

Come on then, Sofia.

64 has an even ones digit, so that means it is even.

There would be an equal number of children in each group if they were divided into two groups.

Well done to Jacob and Sofia, and well done to you for creating your own.

I wish I could hear them.

I bet they are fantastic.

Let's continue this lesson then with task B.

Task B is to turn over a card and sort it into whether it's divisible by two or not divisible by two.

But you'll notice that this time, our numbers are all larger than your two times table charts.

So you're going to have to use what you know to sort them into the different columns.

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

So just like we were just doing with our own creations, have a look at each of the problems and put a tick if you think it is divisible by two and put a cross if you think that it's not divisible by two.

Once you've had a go at task B, part one and part two, come on back to then continue the lesson.

Welcome back.

Let's have a look then at task B, part one.

Remember, if a number is even, it is divisible by two.

So straight away, I can see 43 is not divisible by two because that's an odd number.

70 is even, 68 is even.

So they are both divisible by two.

99 is not divisible by two.

It has a ones digit of nine, which means that 99 is odd.

The same with 37.

37 is odd so it is not divisible by two.

52 has a ones digit of two, so that means it's even and divisible by two.

28.

Oh, that's just after my two times table chart, but I know that because it's even, it would be in the two times table.

So that means it is divisible by two.

83 has that odd ones digit.

80 is divisible by two, that's an even number.

And 91 is not divisible by two.

Well done if you manage to complete that task and pop all of the cards into the right columns.

Let's have a look then at part two.

Part two.

Can 56 socks be put into pairs? Yes, because 56 is an even number, so it is divisible by two and will make pairs.

If there are 79 children, can they be put equally into groups of two? Hmm, 79.

No, 79 is an odd number, which is not divisible by two, so not all the children can make a group of two.

And finally, can 85 cows be split equally between two fields? Hmm, let's have a look.

85.

No, 85 is an odd number, which is not divisible by two.

So that means that the cows won't be able to be split equally between the two fields.

Well done for completing part two and completing task B.

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

All numbers in the two times table are even.

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

If a number is even, it is in the two times table and it is divisible by two.

If a number is odd, it is not divisible by two because it cannot make a whole number when divided by two.

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

I'm hoping that you've loved exploring those divisibility rules of two.

Make sure to come back and join me again to have a look at some other divisibility rules.

See you all soon.

Goodbye.