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 today's lesson, you are going to be using the relationship between the 4 and 8 times tables to solve problems. Your keywords are on the screen now and I'd like you to repeat them after me.

So multiple, doubling and halving.

Fantastic.

Let's move on.

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

Doubling is that act of becoming twice as many.

Halving means to divide into two equal parts.

So for this first lesson cycle, we are going to be looking at finding the missing number.

In this lesson, you will meet Andeep and Izzy.

I find these questions really interesting because ultimately what we're doing, we're trying to balance the equation by finding the missing number.

So whatever products you get on one side, the other side must also equal the same.

So in this case you've got 4 times 4 and that is 16.

So 2 times something else must also equate to 16.

I wonder what that could be.

Could we possibly use our knowledge of the 2 times tables or use the array to help us? So Izzy is solving missing number problems "Andeep's rubbed off my number." The equation that she's got is 4 times 4 is equal to 2 times something.

And there's a array there to help us.

So what advice would you give to Izzy? Explain your reasoning to your partner.

Well, if I know that 4 times 4 equals 16, then I know that 2 times 8 is equal to 16.

This is because four groups of 4 is equal to two groups of 8.

So there's your four groups of 4 and there's your two groups of 8.

So the product 16 does not change.

So 4 times 4 is equal to 2 times 8.

So she continues to solve missing number problems. 4 times 10 is equal to 8 times something.

What advice again would you give to Izzy? And I'd like you to explain your reasoning to your partner.

Let's have a look.

So if you know that 4 times 10 is 40, then you also know that 8 times 5 is 40.

This is because five groups of 8 is equal to 10 groups of 4.

There's your 10 groups of 4, and you can see that there's five groups of 8 there.

So again, the product has not changed.

The product is 40, but you've got two multiplication equations there that have the same product.

Over to you.

You are going to find the missing number.

You're going to show the relationship using an array.

You can pause the video here.

So how did you do? Well, we know that 4 times 6 is 24, so whatever is on the other side must also, when multiplied together, give us a product of 24.

So have a think 8 times something is 24.

If you know that 4 times 6 is 24, then you also know that 8 times 3 is 24.

This is because four groups of 6 is equal to eight groups of 3.

And there's your four groups of 6, and here's your three groups of 8.

Pairs of facts can help us to quickly solve multiplication equations.

So we've got 4 times 12, which is equal to 48, and then you've got 8 times 12, which is equal to 96.

What do you notice? When one factor doubles, so does the product.

So 48 doubles to 96.

And in this case the 4 has doubled to 8, so the product has doubled to 96.

When one factor halves, so does the product.

The 8 has halve to 4, so the product has halved to 48.

What do you notice about this factor pair? Well, when one factor doubles, so does the product, and this time we can see that the position of the factors have changed.

But even then, if one of the factors has doubled, the product will still double.

And if one of the factors halves, so does the product.

So in this case, the 8 has halved to 4.

So the product has halved to 8.

Over to you.

I'd like you to fill in the gap.

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

So how did you do? So if you know that 5 times 4 is 20, then you also know that 5 times 8 is 40 because if one of the factors has doubled and in this case it has, we've got 4 that's doubled to 8, then our product has also doubled.

Let's move on.

Izzy is collecting data for science.

An axolotl lot has four legs, an octopus has eight legs.

What strategy could Izzy use to calculate the total number of legs for two octopuses? Have a think.

Well, if one octopus has eight legs, then two octopuses will have 16 legs.

This is because when one factor doubles then so does the product.

Over to you.

What strategy could Izzy use to calculate the total number of legs for four octopuses? Justify your thinking to your partner.

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

So how did you do? Well there are four octopuses with eight legs, that's 4 times 8, so that's 32.

But also if you already know that two octopuses have 16 legs, if we double the factor 2 to 4, we know that we just need to double 16 to get 32 legs altogether.

Let's move on.

Andeep is collecting data for both axolotls and octopuses and he's going to begin to fill in this data now.

What pattern do you notice? Well, octopuses have double the number of legs compared to axolotls.

Axolotls have half the number of legs compared to octopuses.

So over to you.

Using the information provided in the table, find the missing number.

You can pause the video here.

How did you do? Well, for six axolotls.

Let's have a look at that first.

If there are six axolotls, we know that axolotls have four legs.

Now we can use the information in the table to help us.

So if we have six and look at how many legs three axolotls have, that's 12.

So in order to calculate how many legs six axolotls have, we just need to double 12 to get 24.

We can use that information to calculate how many legs six octopuses have.

We know that axolotls have half the number of legs of octopuses.

So if six axolotls have 24 legs, six octopuses would have double the amount.

So that's 24 doubled.

Or in other words, instead of multiplying 6 by 4, we will multiply 6 by 8, which is 48.

So remember when you double one factor, the product doubles.

Onto your task for Lesson Cycle 1.

Question 1, you're going to be finding the missing numbers.

And can you see a pattern? For question 2, you're going to be completing the table using your knowledge of the 4 and 8 times tables.

And do remember that if you double one factor, the product also doubles.

You could pause the video here to have a go.

And when you're ready, click play to rejoin us.

So how did you do? So for question 1a, this is what you should have got.

So you missing number was 1, then 2, 3, 4, and 5.

And for question 1b, those are the answers that you should have got.

In order to balance the equation, you should have remembered that as the factors doubled, the product also doubles.

So, when you're ready, tick your work and then we can move on.

And this is what you should have got for question 2.

So we'll start off with the total number of legs for axolotls and I'll read the answers and you can mark them as we go along.

So we've got three axolotls will have 12 legs, four axolotls will have 16, five axolotls lots will have 20.

And I'm going to pause here for six axolotls with 24 legs.

Now we could have either multiplied all by 6 or we could have used our knowledge of what? Of how many legs three axolotls had, which is 12, and then doubled it to get the answer.

Seven axolotls have 28 legs, eight axolotls have 32 legs.

And we're going to pause here again because we could have used the fact that we already know, which is, if we have 8, we get 4.

Four axolotls have 16 legs, eight axolotls is double that.

So we would need to double 16 to get the answer there.

So that's 32 legs.

Let's carry on.

So nine axolotls would have 36 legs, 10 would have 40, 11 was already filled in.

And then 12 axolotls would have 48 legs.

Now when it comes to the number of legs for octopuses, what you should have done was look at the number of legs for the axolotls and double it.

So for example, if we have a look at the first missing number, which was how many legs two octopuses would have, if we looked above to how many legs two axolotls would've had, that's 8.

So what we could have done is doubled 8 to get 16 because octopuses have doubled the amount of legs.

And then using that information, if you knew that four axolotls had 16 legs, then you know that four octopuses would have 32 legs because you would double 16 to get 32.

Next, you could also do the same for the rest of those even numbers.

So I'm going to read out the rest of the answers.

You can tick them as we go along.

So six octopuses would have 48 legs, seven would have 56, 8 would have 64, 9 octopuses would have 72 legs altogether, 10 octopuses would have 80, 11 octopuses would have 88 and 12 octopuses would have 96 legs altogether.

Let's move on to Lesson Cycle 2, which is to solve worded problems. Now when you solve problems, you need to decide what operation to use.

Sometimes there will be more than one step with different operations.

The language in a worded problem can help us decide on the operation.

Sometimes you may come across worded questions which involve multiplication or division, right? This is the ultimate question to divide or to multiply.

Let's go.

Equal parts usually means I need to divide, groups of usually means you need to multiply, halving means dividing by 2, double and twice of 10 mean we need to multiply by 2 split and cut of 10 means a division question, times and lots of mean we will be multiplying our factors.

Now identifying the key words will help you to find which operations to use.

Let's look at this question in detail.

Pencils are sold in packs of four or eight.

Andeep wants to buy four packs of four, but the shop has run outta four packs.

How many packs of eight should he buy to get the same number of pencils? So in this example you will have to multiply.

We've got four or eight, which is key information.

Packs of tells us we are finding the whole or total, which tells us that we are multiplying.

So 4 times 4 is equal to 16.

So four packs of four is the same as 4 times 4.

So Izzy says that she knows that 8 times 2 is 16, which means Andeep will need to buy two packs of eight pencils instead.

Let's look at another example.

Andeep has 40 metre length of ribbon being used to wrap gifs for a party.

If 10, 4 metre lengths can be made, how many 8 metre lengths can be made? Well, in this example you'll have to divide.

Seeing how many usually means you need to divide.

So to find how many 8 metre lengths we can make from 40 metres means we are dividing by 8.

It also means you are finding the missing part or quotient.

So our division equation is 40 divided by 8, which is 5.

Over to you.

I'd like you to think about what equation you are calculating and how you know.

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

So how did you do? Well, you know the hole is 24 metres and the value of the jump is 8 metres.

So the division equation that you're calculating is 24 divided by 8.

The divisor was 8.

The snow leopard made three jumps because 24 divided by 8 is 3.

Andeep bakes four cupcakes a day for a party.

Izzy bakes eight cupcakes.

If Izzy bakes 40 cupcakes in five days, how many days did it take Andeep to bake the same amount? Izzy thinks that we need to halve because Andeep baked four cakes a day.

Do you agree? Let's read this question carefully because sometimes we may get it a little bit confused.

So Andeep says that he's baked half the amount, so that means it will take him double the time.

So actually we're multiplying by 4.

So 10 days times 4 gives us 40 days.

So that means we actually have to multiply.

So 10 days multiply by 4 equals 40 cupcakes, he would've taken double the amount of time to get that done.

Back to you.

What is the equation you are calculating? Andeep bakes four cupcakes a day for a party.

Izzy bakes eight cupcakes.

If Izzy bakes 24 cakes in three days, how many days did it take Andeep to bake the same amount? So think about the keywords that have been used in this question to help you find the equation that you will be calculating.

You can pause the video here.

So how did you do? Well, you know, that Izzy bakes 24 cupcakes because she bakes eight cupcakes a day.

You also know that Andeep bakes half the amount, so that means it will take him double the time, which means it would take him six days to bake the same amount.

Right.

Over to you.

These are your tasks for this lesson cycle.

So for question 1, you're going to be completing the word problems. 1a, Izzy is wrapping present, she has of ribbon.

If 10, 4 metre lengths can be made, how many 8 metre lis can be made? 1b, pencils are sold in packs of four or eight.

Andeep wants to buy five packs of eight, but the shop has run out of eight packs.

How many packs of four should he buy to get the same number of pencils? 1c Andeep has 64 metre length of ribbon being used to wrap gifs for a party.

If eight 8 metre lengths can be made, how many 4 metre lengths could be made? And 1d, Izzy and Andeep both bake four cakes every day.

How many weeks will it take both of them to bake 96 cakes? And for question 2, Izzy has created some digital designs during her computing classes using octagons and squares.

Complete the questions below, thinking about the total number of sides.

So you've got three designs there.

You know that octagons have eight sides and you know that squares have four sides.

Using this information, I want you to calculate how many sides are used within each design and to also identify the factors.

Lastly, if Andeep made Design 1 using squares, how many sides would there be? And 1B, if Design 3 was remade using octagons, how many sides would there be? You can pause the video here.

Off you go.

Good luck.

Now for question 1a, Izzy would've needed five 8 metre lengths if she was cutting the ribbon into 8 metre lengths.

For 1b, Andeep will have needed 10 packs of four.

For 1c, Andeep will need 16, 4 metre lengths.

And for 1D, it would've taken both Andeep and Izzy 12 weeks.

For question 2, we're going to look at this in a little bit more detail.

So for Design 1, we know that an octagon has eight sides.

So if there are three octagons, that's 3 eight times.

So that's 24.

We know that a square has four sides, so let's look at Design 2 and 3 now.

Now if we know that there are three squares, that's 4, 3 times, so that's 12 sides.

You could have also used your answer from Design 1 to help you with this because if we know that a square has half the amount of sides that an octagon has, we could have half 24 to get 12.

And then for Design 3, there are five squares with four sides.

So that's 4, five times, so that's 20 sides altogether.

For question a, you would've had 12 sides, so that's 3 times 4.

And then for question b, if Design 3 was remade using octagons, well we would've doubled the amount.

so that's 5 times 8, so we would've got 40 sides altogether.

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

Well done.

Good job.

I hope you really enjoyed it.

Now we're going to summarise our learning.

So we use knowledge of the relationship between the 4 and 8 times tables to solve problems. You now understand that multiples of 8 are all multiples of 4, but not all multiples of 4 are multiples of 8.

You also understand that multiples of 8 are double the multiples of 4 and that multiples of 4 are half the multiples of 8.

And lastly, you can use this knowledge to solve problems. I really hope that you enjoy that lesson and I hope to see you in the next one.