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I can explain the relationship between multiples of 2 and multiples of 4

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

Multiples of 4 are double the multiples of 2
Multiples of 2 are half the multiples of 4
Multiples of 4 are all multiples of 2 but not all multiples of 2 are multiples of 4

Common misconception

Pupils may generalise the rule and assume that when dividing by 4 is the last digit is even, then the number is divisible by 4

Show children the relationship between 2s and 4s using the multiplication chart. Make clear that identifying the last digit as even is the first step - the last 2 digits should be a multiple of 4. Encourage discussions to highlight the relationship.

Keywords

Multiple - A multiple is the result of multiplying a number by another whole number.
Doubling - Doubling is the act of becoming twice as many.
Halving - Halving means to divide into two equal parts.

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Hello, I'm Miss Mia and I'm so excited to be a part of your learning journey today.

I hope you enjoy this lesson as much as I do.

In this lesson, you'll be able to explain the relationship between the multiples of two and multiples of four.

Your key words are on the screen now, and I would like you to repeat them after me.

Multiple, doubling, halving.

Fantastic, let's move on.

A multiple is the result of multiplying a number by another whole number.

So for example, say if we were multiplying four by four.

So four times four is 16, 16 is a multiple of four.

Doubling is the act of becoming twice as many.

So say if I double two, I would end up with four.

Halving means to divide into two equal parts.

So this lesson is all about our two times tables and four times tables.

And we have two lesson cycles here.

Our first lesson cycle is all to do with identifying multiples of two and four.

And our second lesson cycle is to explain the relationship between the two and four times tables.

So let's start off with our first lesson cycle.

Let's go.

In this lesson you will meet Andeep and Izzy, and they're going to help us with our learning.

Let's begin by counting in multiples of two.

Are you ready? Let's go.

Zero, two, four, six, eight, 10, 12, 14, 16, 18, 20, 22, 24.

Fantastic, now we're going to do it again.

This time I'm going to have a turn and then it's going to be your turn.

Okay, and for that, I will let you have time to say the next multiple of two.

Are you ready? Let's begin.

Zero, four, eight, 12, 16, 20, 24.

Fantastic, let's move on.

Now we're going to be recapping counting on in multiples of four.

If you've forgotten, think about it like this.

So if we start at zero, we're going to be adding on four each time to find the multiples of four.

These are also numbers that are in our four times tables.

Are you ready, let's recap together.

Three, two, one, zero, four, eight, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48.

Now we're going to take turns.

We're going to start off at zero.

I'll go first then it's your turn.

Are you ready? Let's begin.

Zero, eight, 16, 24, 32, 40, 48.

Well done, let's move on.

So Andeep and Izzy are counting in multiples of two and four.

They record which multiples they count together at the same time.

So let's have a look.

So on the screen you can see a table.

We've got our twos on the top row and our fours on the bottom row.

So when they're clapping they'll notice what numbers they say at the same time.

So let's see what happens.

One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

What do you notice? Well, all of the numbers said by the fours group are also said by the twos group and we can see that here.

So for example, zero is said by both.

So that's why there's a tick.

And then if we have a look at four, again, we say that number in our twos and fours.

So four is a multiple of two and four, and then we skip five.

So that means five is not a multiple of two and four, then for six, well six is a multiple of two but not four.

And then if we have a look at eight, eight is a multiple of both.

Now, not all the numbers said by the twos group are also said by the fours group.

Can you have a look at our table and pick out one of those numbers? Well, you may have picked out two.

So two is not a multiple of four.

You may have picked out six, 10, 14, and 18.

So these are multiples of two, but they are not multiples of four.

And lastly, for every number said by the fours group, the twos group says two numbers.

Let's move on, over to you.

I'd like you to identify which numbers are multiples of two, four or both.

On the screen you can see the numbers 10, 26, 20, four and eight.

You could pause the video here and click play when you're ready to rejoin us.

So how did you do? These are the numbers that you should have got.

Now we've got multiples of two here, 10 and 26.

And then for both we've got four, eight, and 20.

I know that 10 and 26 are both multiples of two because if I count on from zero and counting twos, I will say 10 and 26.

So for example, if I started at eight, I know that four two times is eight, and then the next multiple is 10.

So 10 is a multiple, but 10 is not a multiple of four.

Because if I was to count on in multiples of four, I would not say 10 or 26.

For example, let's start off by counting on from eight.

So eight, 12.

I did not say 10, let's carry on.

12, 16, 20, 24, 28.

I did not say 26.

So that means those are both multiples of two because they are even.

Let's move on.

How many groups of two are there? How many can you see? There are two groups of two.

Now how many groups of four are there? There is one group of four.

So there are two groups of two cherries and there is one group of four cherries.

How many groups of two are there? Have a look.

Let's count in multiples of two, ready? Two, four, six, eight, 10, 12, 14, 16.

So there are 16 cherries altogether, but there are one, two, three, four, five, six, seven, eight groups of two.

So that means eight times two equals 16.

We can also say this as two eight times is equal to 16.

Now how many groups of four are there? Let's have a look.

There's one group of four cherries, two groups of four cherries, three groups of four cherries and four groups of four cherries.

So that means there are four groups of four, which means there are 16 cherries altogether.

And we can also say four, four times.

So this can actually be shown as a bar model.

Let's have a look at how that's represented.

There we are.

So what do you notice? For every one group of four, there are two groups of two.

Two pairs of cherries is the same as one group of four cherries, over to you.

I'd like you to fill in the blanks.

You can see groups of cherries there.

10 pairs of cherries is the same as something groups of four.

Pause the video here and click play when you're ready to rejoin us.

So how did you do? 10 pairs of cherries is the same as five groups of four.

Back to you, now you've got a missing number equation there that I'd like you to fill in the blank for.

So two times 10 equals four times something.

You can pause the video here.

So how did you do? Well, two times 10 is equal to four times five and that's because two times 10 is 20.

And I can also see that there are 10 groups of two.

I can see that there are five groups of four which is the same as 20 as well.

So both sides are balanced for this equation.

Okay, onto your main task for this lesson cycle.

For this task, you are going to be sorting the numbers that you can see on the screen there, numbers that are neither multiples of two nor four should go outside of the circles.

So you've have to sort the numbers.

Zero, two, three, eight, 12, 14, 28, 29, 30 and 32.

You need to decide whether these are multiples of two, both, multiples of four or neither.

For question two, you're going to be completing the sentences.

So I'll read the sentences out to you.

If there are eight wheels, how many cars are there? So think about it like this.

If there's one car, we know that there are wheels.

Now if there are eight wheels, how many cars are there? Let's look at the next one, if there are eight wheels, there are something amount of bikes.

Think about how many wheels a bike has.

If there are 12 pairs of socks, there are something groups of four socks.

If there are 16 legs, there are something amount of cows.

If there are 16 legs, there are something amount of farmers.

If there are 14 pairs of shoes, there are something groups of four shoes.

You can pause the video here.

Off you go, good luck.

So how did you do? For question one you should have got this.

Now neither three or 29 are multiples of four and that is when counting on in multiples of two or four, three would not be said and 29 will also not be said.

Now if we look at multiples of two, we can see that we've got two, 14 and 30.

And then for multiples of four we can see that we haven't got anything.

But for both we've got zero, eight, 12, 28 and 32.

That is because multiples of four are also multiples of two.

Let's move on, now for question two, I'm going to read you out the answers and I'm also going to give you an explanation as to why you should have got that answer.

Let's look at question one.

We know that one car has four wheels, so that means two cars will have eight wheels altogether.

So if you've got two, well done.

Let's move on to the next question.

Now, if there are still eight wheels, but this time there are bikes, we know that a bike typically has two wheels.

So that means there must be four bikes because two four times is eight.

Let's move on to the next question.

If there are 12 pairs of socks, that means there are six groups of four socks.

And that's because if there are four socks in one group, we need three groups of four to make 12.

Now let's look at the question to the right at the top.

If there are 16 legs, there are something amount of cows.

Well, I know that a cow has four legs.

In order to get 16 legs altogether, we need to multiply four by four to get 16.

And then if we look down this time we're looking at farmers, a farmer would have two legs.

So that means with eight farmers there'll be 16 legs altogether because two legs eight times is 16 legs altogether.

If there are 14 pairs of shoes, there are seven groups of four shoes because seven four times is 28.

If you've got all of those correct, well done, good job.

Let's move on to our second lesson cycle.

Now for this lesson cycle, you are going to be explaining the relationship between the twos and fours.

Andeep and Izzy are comparing the twos and fours times tables.

What is the same, what is different? Now on the left hand side you can see the two times tables and on the right hand side you can see the four times tables.

Products in the four times tables are also in the two times tables.

Apart from multiplying by zero, multiples of four are double the multiples of two and apart from multiplying by zero, multiples of two are half the multiples of four.

Over to you.

If all multiples of four are multiples of two, then all multiples of two must be multiples of four.

Do you agree with Andeep? I'd like you to justify your thinking to your partner.

If you're not sitting next to anyone, just jot your idea down on paper.

So what did you get? Andeep is incorrect.

Not all multiples of two are multiples of four.

For example, if we have a look at the number six, so two times three is six, six is not a multiple of four.

Andeep and Izzy continue to spot patterns.

Well if I know that two times 13 is 26, then I know four times 13 must be 52.

Do you agree? I'd like you to justify your thinking to your partner.

Well Andeep is correct because if we double a factor then the product also doubles, back to you.

If I know four times eight equals 32, then I know two times eight is 16.

Do you agree? I'd like you to justify your thinking to your partner.

You can pause the video here.

So how did you do? Well Andeep is correct because if we halve a factor, then the product also halves.

Andeep has arranged an array.

How many groups of two are there and how many groups of four are there? Have a think.

Well we can see that there are six groups of two.

So that's two, six times or six times two is 12.

So that means we have 12 altogether.

Now we can see that there are three groups of four.

So that's three times four, which is 12 over to you.

How many groups of four are there and how many groups of two are there? You can pause the video here and when you're ready to join us, click play so we can carry on.

So what did you get? So there are seven groups of four, seven groups of four is equal to 28 and there are 14 groups of two and that's also equal to 28.

Can you see a relationship there? Well we know that seven times four is 28.

Now if we look to our equation at the bottom, four has halved to two.

So that means the other factor does not double.

We will not get the same product.

So whilst the four has halve to two, the seven has doubled to 14, which means our product is 28.

Oh this time we've got pairs of cherries.

So how many groups of two can you see? So that's two.

One group of two, two groups of two.

Three groups of two, four groups of two, five groups of two, six groups of two.

Seven groups of two and eight groups of two.

So looking at our number line, we can see that eight groups of two is equal to 16 and we can represent this by writing eight times two is equal to 16 or two, eight times is also equal to 16.

Now how many groups of four are there? Well let's have a look.

So that's one group of four, two groups of four, three groups of four, four groups of four.

There are four groups of four.

Four groups of four can also be written as four times four, which is equal to 16.

What do you notice? Four times four is equal to 16.

So if you double four times two, that's also equal to 16.

Hang on a minute, that means I can use that fact in other situations as well now.

So we're going to explore that in a bit.

Eight times two is equal to 16, so half of eight times four is also equal to 16.

Over to you.

How many ways can you group 12? You can pause the video here and click play when you're ready to rejoin us.

Well we can have six times two which is equal to 12.

And then if we half a factor and double the other, we can have three times four, which is also equal to 12.

And lastly we can also have one group of 12.

So one times 12 is equal to 12.

Now Izzy is completing the question below.

You can see that you've got your twos on the left hand side but only the even numbers of your twos.

So you've got zero, two, four, six, eight, 10.

And then on the right hand side you are multiplying from the numbers in ascending sending order.

So it's going from zero all the way up to five.

Now Izzy started by following the instructions on the arrows.

Can you help her complete the table? Well let's have a look at what we've got.

We know that anything multiplied by zero is zero.

Then we know that two times two is equal to four.

That also means if we look at the right hand side now, one times four is also equal to four.

So two times two is equal to four.

One times four is equal to four, they're both equal.

Now we've got four times two is equal to two times four, that's eight.

Six times two is equal to three times four.

That is 12.

Eight times two is equal to four times four and that is 16.

And lastly, 10 times two is equal to five times four and that's 20.

What did you notice? An even number times two gives you a product in the four times tables, over to you.

An odd number multiplied by two gives a product in the four times tables.

I'd like you to justify your answer.

So is it A, for example, four times two is equal to eight.

So eight is a multiple of four or is it B? For example, five times two is equal to 10 and 10 is not a multiple of four.

You can pause the video here.

So what did you get? It's false and that's because, let's have a look at B.

Five times two is 10 and we know that 10 is not a multiple of four because when counting in multiples of four, we will not say 10.

Onto your main task for this lesson cycle.

So for question one, you're going to use the array to complete the questions.

How many groups of four are there and how many groups of two are there? And for question two, you are going to fill in the gaps using the images to help you.

And then you're going to fill in the gaps for the sentences that you see below.

So when you double a factor, the product, and when you have one factor, the product.

And for question three, you're also going to fill in the gaps using the bar models.

You can pause the video here and click play when you're ready to rejoin us.

So how did you do? So for question one, you should have used the array to complete the questions.

Now you should have got that there were nine groups of four which was equal to 36.

And then you should have got 18 groups of two or two times 18, which also would've given you 36.

And the relationship between this is that when you halve a factor and double the other.

So in this case, if you halved four to two and if you doubled nine to 18, you would've still got the same product.

For question two, this is what you should have got.

So for the first row of cherries, so there are six groups of two cherries, which is 12, and there are three groups of four cherries, which is 12.

For the second row of cherries you should have got 10 groups of two cherries, which is 20, and then five groups of four cherries, which is also 20.

And lastly, for your third row of cherries, you should have got 12 groups of two cherries, which is 24 and six groups of four cherries, which is also 24.

So when you double a factor, the product doubles and when you halve one factor, the product halves.

And for question three, you would've been filling in the gaps using the bar model to help you.

So if six groups of two is 12, that means three groups of four is 12.

Because if you have six to three and then you double two to four, you end up with 12.

And then for question two, you should have got eight groups of two, which is 16, which means four groups of four is 16.

And lastly, you should have got 12 groups of two, which is 24.

So that means six groups of four is also 24.

Well done if you've got all of those questions correct, I'm super proud of you.

We've made it to the end of the lesson, fantastic work.

I'm now going to summarise your learning and these are all the achievements you should be proud of.

So for this lesson, we explained the relationship between multiples of two and multiples of four.

You should now understand that multiples of four are double the multiples of two and that multiples of two are half the multiples of four.

You also understand that multiples of four are all multiples of two, but not all multiples of two are multiples of four.

I really enjoyed that lesson and I hope you enjoyed it too.

I look forward to seeing you in the next lesson.

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How can we use the adjacent multiples in this example?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1706170040%2Finyuvjz8d16nlw68bmln.png&w=640&q=75", "imageKey": "8f1171cd-c210-c378-ee15-153ba353c30b/question/a4d2d0e0bf6654be26d2b7683e2585d5.png" }, "questionType": "Multiple choice", "correct": [ { "text": "48 - 4" }, { "text": "40 + 4" } ], "choices": [ { "text": "48 - 4" }, { "text": "40 + 4" }, { "text": "Count along the number line up to the missing number" } ], "id": "e5f6878c-fa1f-e3b1-e732-dcea97490d1f", "lessonId": "506c22e7-9401-55c3-6393-8e370804ab59" }, { "type": "Question", "question": { "text": "Izzy knows that 13 × 4 = 52. She used the known fact of 12 × 3 = 48 and ______ 4." }, "questionType": "Multiple choice", "correct": [ { "text": "added" } ], "choices": [ { "text": "added" }, { "text": "subtracted" } ], "id": "ecf7523c-211b-42f8-3eb1-f2e60c805060", "lessonId": "506c22e7-9401-55c3-6393-8e370804ab59" }, { "type": "Question", "question": { "text": "Using your knowledge of groups, order the calculations starting with the smallest multiple." }, "questionType": "Ordering", "elements": [ { "order": { "text": "1" }, "item": { "text": "4 × 4" } }, { "order": { "text": "2" }, "item": { "text": "5 × 4" } }, { "order": { "text": "3" }, "item": { "text": "4 × 8" } }, { "order": { "text": "4" }, "item": { "text": "10 × 4" } } ], "id": "c4c31a74-db86-d829-bce6-1dde5ebb4518", "lessonId": "506c22e7-9401-55c3-6393-8e370804ab59" } ], "lessonId": "506c22e7-9401-55c3-6393-8e370804ab59", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 3", "topic": null, "unit": "2, 4 and 8 times tables: using times tables to solve problems", "lessonCount": "15", "age": [ 7, 8 ], "gradeId": "age_7_8", "gradeStage": "Key Stage 2", "lesson": "Explain the relationship between multiples of 2 and multiples of 4" } }, { "id": "675097c2-b952-9c76-cdcd-9b345c9168a1", "type": "Resource", "resourceType": "Quiz", "title": "Explain the relationship between multiples of 2 and multiples of 4", "quizType": "Exit quiz", "items": [ { "type": "Question", "question": { "text": "Which numbers are multiples of 2 and multiples of 4?" }, "questionType": "Multiple choice", "correct": [ { "text": "12" }, { "text": "16" }, { "text": "20" } ], "choices": [ { "text": "12" }, { "text": "14" }, { "text": "16" }, { "text": "20" }, { "text": "22" } ], "id": "37dbda1b-34c9-61a6-0b68-2737fe19f6ec", "lessonId": "506c22e7-9401-55c3-6393-8e370804ab59" }, { "type": "Question", "question": { "text": "Look at the image. Match the size of the group to the number of groups.", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1706169993%2Fxiahy3ljrkjyjujyd4r2.png&w=640&q=75", "imageKey": "675097c2-b952-9c76-cdcd-9b345c9168a1/question/da48987fada9efe56f3395c72235d857.png" }, "questionType": "Matching", "pairs": [ { "left": { "text": "Groups of 2 =" }, "right": { "text": "8" } }, { "left": { "text": "Groups of 4 =" }, "right": { "text": "4" } } ], "id": "6e5962cd-b75b-2246-9dbc-9590d13075d7", "lessonId": "506c22e7-9401-55c3-6393-8e370804ab59" }, { "type": "Question", "question": { "text": "Match the groups of 4 to the groups of 2." }, "questionType": "Matching", "pairs": [ { "left": { "text": "1 group of 4" }, "right": { "text": "2 groups of 2" } }, { "left": { "text": "2 groups of 4" }, "right": { "text": "4 groups of 2" } }, { "left": { "text": "3 groups of 4" }, "right": { "text": "6 groups of 2" } }, { "left": { "text": "4 groups of 4" }, "right": { "text": "8 groups of 2" } }, { "left": { "text": "5 groups of 4" }, "right": { "text": "10 groups of 2" } } ], "id": "9683b393-3e27-90e9-5769-901fe9ec8946", "lessonId": "506c22e7-9401-55c3-6393-8e370804ab59" }, { "type": "Question", "question": { "text": "Which of the statements are true?" }, "questionType": "Multiple choice", "correct": [ { "text": "All multiples of 4 are multiples of 2" }, { "text": "If a factor is doubled, the product also doubles" }, { "text": "If a factor is halved, the product also halves" } ], "choices": [ { "text": "If a factor is doubled, the product is halved" }, { "text": "All multiples of 2 are multiples of 4" }, { "text": "All multiples of 4 are multiples of 2" }, { "text": "If a factor is doubled, the product also doubles" }, { "text": "If a factor is halved, the product also halves" } ], "id": "2078ca46-37c4-281e-9d96-08ea316a3b1b", "lessonId": "506c22e7-9401-55c3-6393-8e370804ab59" }, { "type": "Question", "question": { "text": "Multiples of 4 are ______ the multiples of 2." }, "questionType": "Short answer", "correct": [ { "text": "double" }, { "text": "Double" }, { "text": "DOUBLE" } ], "id": "1d32dbf8-b071-d2f2-c8ef-ab55465f47d2", "lessonId": "506c22e7-9401-55c3-6393-8e370804ab59" }, { "type": "Question", "question": { "text": "Look at the array. Match the questions to the correct answers.", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1706169993%2Ffxfz2yduv7uy0mhth5in.png&w=640&q=75", "imageKey": "675097c2-b952-9c76-cdcd-9b345c9168a1/question/46d65e372d8ea1714c082e909cdd0fe0.png" }, "questionType": "Matching", "pairs": [ { "left": { "text": "How many groups of 4 are there?" }, "right": { "text": "6" } }, { "left": { "text": "How many groups of 2 are there?" }, "right": { "text": "12" } }, { "left": { "text": "6 x 4 =" }, "right": { "text": "24" } }, { "left": { "text": "12 x 2 = " }, "right": { "text": "24" } } ], "id": "0888d405-e845-975f-0517-61711cea09b4", "lessonId": "506c22e7-9401-55c3-6393-8e370804ab59" } ], "lessonId": "506c22e7-9401-55c3-6393-8e370804ab59", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 3", "topic": null, "unit": "2, 4 and 8 times tables: using times tables to solve problems", "lessonCount": "15", "age": [ 7, 8 ], "gradeId": "age_7_8", "gradeStage": "Key Stage 2", "lesson": "Explain the relationship between multiples of 2 and multiples of 4" } } ] }