Lesson video

Hello, I'm Miss Miah 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 adjacent multiples of seven.

Your keywords are on the screen now and I'd like you to repeat them after me.

Multiple.

Adjacent.

Fantastic.

Let's find out what these words mean.

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

Adjacent means next to each other.

An adjacent multiple is a multiple next to another.

It could be before or after.

Now this lesson is all about explaining the relationship between adjacent multiples of seven, and we have two lesson cycles here.

Our first lesson cycle is all to do with adjacent multiples of seven, and then in our second lesson cycle we're going to be finding the adjacent multiples of seven.

Now understanding the relationship between adjacent multiples of seven is important because it helps you see the patterns in numbers.

For example, if you know that seven times three is 21, then you can quickly figure out seven times four is just seven more, which is 28.

This makes it easier to solve maths problems faster, especially when you don't have a calculator.

It also helps you to understand how numbers grow and connect, making math feel more like a fun puzzle than just memorising facts.

So are you ready? Let's get started.

Now in this lesson, you will meet Aisha and Laura, who are going to be helping us with our mathematical thinking.

Let's begin.

Aisha and Laura are filling in their seven times table chart.

"I almost filled in all of the chart, but I don't know the other products." And we can see that she's got some gaps there.

In this lesson, you will learn how to find adjacent multiples of seven to help you identify the missing products.

Now Aisha and Laura are helping me with the summer fair.

Aisha recalls the number of sweets which come in packs of seven.

She recalls the multiples of seven in order.

Now I remember sorting this out when I was teaching in school and it was a very busy time, but knowing our multiple facts really helped sorting things out quite quickly.

Here I've got four packs of seven sweets.

So Aisha's table now shows adjacent numbers.

These are numbers next to each other.

"Seven has one more group of seven than zero.

14 has one fewer group of seven than 21.

Adjacent multiples of seven have a difference of seven." So basically when moving down the column, the product increases by seven, so that's a difference of seven.

And then when moving up the column, the product decreases by seven.

So in other words, we are subtracting by seven to find the previous adjacent multiple.

Now Aisha is trying to find the adjacent multiple of seven.

"To find the adjacent multiple, I need to add seven because it is the next multiple." Something has one more group of seven than 35.

Now remember when moving down the column, the product increases by seven.

So 35 add seven equals 42.

42 has one more group of seven than 35.

Over to you.

I'd like you to find the adjacent multiple of seven.

So we've got a number of packs here, six packs, which is 42 sweets altogether.

So what would seven packs be? You could pause the video here and click play when you're ready to rejoin us.

So how did you do? Well, to find the next multiple of seven, you need to add seven.

And also remember when you're moving down the table, the product is increasing by seven.

So actually to the product 42, you're adding seven.

So 42 add seven is equal to 49.

So 49 has one more group of seven than 42.

Did you get that? Well done if you did.

Let's move on.

Aisha is trying to find that adjacent multiple of seven.

Now Aisha says, "To find the adjacent multiple, I need to subtract seven because it's the previous multiple." So we've got a number of packs, eight and that is 56 sweets altogether.

We need to find how many sweets there will be for seven packs.

So I should suggest we subtract seven.

So something has one fewer group of seven than 56.

Now remember when moving up the column, the product decreases by seven.

49 has one fewer group of seven than 56.

Back to you.

The previous multiple to 63 is.

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

So what did you get? Well, the previous multiple to 63 is 56.

Now remember when you're going up the table, we need to decrease by seven.

So in this case we are subtracting seven from 63.

So 56 has one fewer group of seven than 63.

Now Aisha continues to look at multiples of seven on a number line.

Oh, she's added seven there from zero to get to seven and then we're adding on another seven.

So every time you make a jump on the line to the right, it is seven more.

We add a group of seven to get to the adjacent multiple of seven.

So adding seven to a multiple of seven gives the next multiple of seven.

The adjacent multiple of seven to 14 is 21.

Now Aisha continues to look at multiples of seven on a number line.

And this time, she's subtracting seven each time.

So subtracting seven from a multiple of seven also gives an adjacent multiple of seven.

Each time you make a jump on the line to the left, it is seven less.

We subtract a group of seven to get to the previous multiple of seven.

So you can see here on the number line, every time you've subtracted seven, you're moving to the left of the number line to find the previous multiple of that factor.

So the adjacent multiple of 70 is 63 and that's because we've subtracted seven.

Back to you.

The adjacent multiples of seven to 42 are something and something.

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

So what did you get? Did you use the number line to help you? Well, we've got 42 here.

To find the next multiple of seven to 42, we would add seven and that would give us 49.

So Aisha says, "I knew the next multiple here is 49 because it is seven more and seven more than 42 is 49." And remember because we're counting to the right of the number line, we are adding on seven more.

She also says that she knew the previous multiple here is 35 because it is seven less and seven less than 42 is 35.

She's correct.

And if we have a look at the number line, because we're going to the left of the number line, we are subtracting seven.

Onto the main task for this lesson cycle.

So for question one, you're going to work with a partner, you're going to pick a multiple of seven and place it in the correct place on the number line.

You're going to explain your choice.

So the numbers that you will be placing are 63, seven, 28, 49, and 84.

And for question two, you're going to find the missing multiples and complete the sequences.

Now remember if you're finding the next multiple of seven, you need to add seven and if you're finding the previous multiple of seven, you need to subtract seven.

Use this to help you.

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

So how did you do? Well, here is the completed number line and I'm going to read you out the numbers.

So we're going to start at zero.

Zero, seven, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, and 84.

Now let's have a look at what Aisha's saying.

So she started off with seven, she put seven here because it is seven more than zero.

So seven is the next multiple.

Now if we have a look at placing the number 28, we know that 28 can be placed just before 35 and that's because seven less than 35 is 28.

28 is the previous multiple.

Well done if you manage to place your multiples of seven correctly on the number line using your knowledge of adjacent multiples.

Now for question two, you were finding the missing multiples and completing the sequences.

So this is what you should have got.

So for A, you should have got 14 and that's because seven add seven is 14.

We added seven there because we were finding the next multiple of seven.

Then you should have got 21 because adding seven to 14 would've given you 21.

Now with the next one, so 28 blank 42, you should have got 35.

Now there were two ways of calculating this.

So you could've added seven to 28 to find the next adjacent multiple, which is 35 or you could have subtracted seven from 42 to also get 35.

If you manage to get all of those sequences correct.

Fantastic work.

Let's move on.

Now lesson cycle two is all to do with finding the adjacent multiples of seven.

Laura and Aisha are helping me to get ready for the summer fair.

Aisha gives Laura another pack of sweets.

Three groups of seven is equal to 21.

Four groups of seven is one more group of seven.

So here we've added seven.

So we can write this as four times seven is equal to three times seven add seven.

There are 28 sweets altogether.

So four times seven is equal to 28.

Over to you.

Aisha gives Laura another pack of sweets.

How many sweets are there altogether? I'd like you to use the image below to help you and complete the equations.

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

So what did you get? Well, here we can see that there are four groups of seven which have been marked with a circle.

Now five times seven is adding on one more group of seven.

So five times seven is equal to four times seven add seven.

So five times seven is equal to 35.

Well done if you manage to get that correct.

Now Laura gives away a pack of sweets to one of her friends.

Three groups of seven is equal to 21.

And you can see that there are three packs of seven sweets.

Two groups of seven is one less group of seven because we're taking away a group.

So here we are, we've subtracted a group of seven or we've subtracted seven sweets.

So two times seven is equal to three times seven subtract seven.

So there are 14 sweets altogether now.

Two times seven is equal to 14.

Over to you.

So Laura gives away a pack of sweets.

How many sweets are there altogether? I'd like you to use the image on the screen to help you to fill in the blanks.

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

So what did you get? Well, on the screen I can see five packs of seven sweets.

Here we can see that we've subtracted seven and that's one pack of seven sweets.

So four times seven is equal to five times seven subtract seven.

Four times seven is equal to 28.

Well done if you manage to get that correct.

Aisha is trying to find the adjacent multiple of seven.

She says, "To find the next multiple after 35, I need to add seven.

So it's five groups of seven plus one group of seven." So something has one more group of seven than 35.

"Remember, when counting down the column, the product increases by seven." So 35 add seven gives us 42.

And we can represent this like this.

So we can say six groups of seven is equal to this equation below and that six times seven is equal to seven times five plus seven.

So six times seven is equal to 42.

42 has one more group of seven than 35.

Back to you.

You are going to find the adjacent multiple of seven to 63 and I'd like you to complete the equation.

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

So what did you get? Well, to find the next multiple of seven, you needed to add seven and that's because we were going down the table.

Remember when moving down the column, the product increases by seven.

So you should have got 10 times seven is equal to nine times seven add seven.

And 10 times seven which is equal to 70.

70 has one more group of seven than 63.

Aisha is representing the adjacent multiple in a different way.

Aisha says, "To find the previous multiple, I need to subtract seven.

When moving up the column, the product decreases by seven." So here we started off with 56, we subtracted seven, we end up with 49 as our product.

We can also write this as seven times seven is equal to eight times seven subtract seven.

So seven times seven is equal to 49.

And 49 has one fewer group of seven than 56.

So can you see here how we're using our knowledge of adjacent multiples to quickly help us solve these problems? Over to you.

I'd like you to find that adjacent multiple of seven for 84.

Now have a look.

We already know what 12 packs of sweets are.

We need to find out what 11 packs of sweets are.

Can you use your knowledge of the adjacent multiples of seven to help you? You could pause the video here and click play when you're ready to rejoin us.

So what did you get? Well, 'cause we were going up the column, we needed to subtract seven from 84.

So 77 has one fewer group of seven than 84.

So what you should have got was 11 times seven is equal to 12 times seven subtract seven.

And that's 11 times seven, which is equal to 77.

Well done if you manage to get that correct.

Over to you.

This is your main task for this lesson cycle.

So for question one.

In pairs you will play a game.

You will need a set of cards up to 12.

So partner A will pick a card.

Partner A will also multiply that number by seven.

Remember you can skip count in sevens to find the product.

Partner B will identify the two adjacent multiples of seven.

So for example, Aisha here has picked a three.

So Aisha says, "I picked a three.

Three times seven is equal to 21." So now Laura has to find the adjacent multiples of seven to 21.

So she says, "The previous multiple of seven to 21 is 14.

And the next multiple of seven to 21 is 28." How did she get that? Well, to find the previous multiple, she subtracted seven from 21 to get 14.

And to find the next multiple, she added seven to 21, which is 28.

"Yes, that is correct," Aisha says.

For question two, you're going to find the next and previous multiples of seven to the numbers in the circles.

Can you find any more? And then I'd like you to fill in the gaps.

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 may have picked the card seven.

Aisha says, "I picked seven.

Seven times seven is equal to 49." Laura says, "The previous multiple is 42 and the next multiple is 56." Now we know that is correct because to find the previous multiple, we must subtract seven from 49 and that is 42.

And to find the next multiple of 49, we have to add seven.

And that's 56.

"Yes, that is correct." Now for question two, this is what you may have got.

The adjacent multiples of seven would've been zero and 14.

For 35, you should have got 28 and 42.

For 70, the previous multiple for 70 is 63 because 70 subtract seven is 63.

And the next multiple is 77, and that's because 70 add seven is 77.

And for 56, you should have got 49 and 63.

These are the equations that you should have got as well.

So seven is equal to zero times seven add seven.

Seven is equal to two times seven subtract 7.

21 is equal to two times seven add seven.

And 21 is equal to four times seven subtract 7.

42 is equal to seven times seven subtract seven.

And 42 is also equal to five times seven add seven.

And lastly 77 is equal to seven times 10 add seven.

And 77 is equal to 12 times seven subtract seven.

Did you manage to get all of those correct? Well done if you did.

Fantastic.

We've made it to the end of this lesson.

And now we're going to summarise our learning.

In this lesson, you were able to explain the relationship between adjacent multiples of seven.

You should now understand that adjacent multiples of seven have a difference of seven.

You also know that if you add seven to a multiple of seven, you get the next multiple seven.

And if you subtract seven from a multiple seven, you get the previous multiple of seven.

Thank you so much for joining me in this lesson and I look forward to seeing you in the next one.

Bye.