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 use unitizing and multiplying by 10 to scale multiplication facts.

And you know this is going to be a good lesson because we will be scaling.

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

Scale, scaling.

Now some of you might be thinking, "Oh, we're going to get the weights out and we're going to use the scales to measure things to help us with multiplication." Not for this lesson.

And I'm going to show you what scaling and scale means.

And believe me, once you find out how to scale, you're then going to find it so easy to calculate equations that you think might be a bit tricky, especially when they've got bigger numbers involved.

So scaling is when a given quantity is made times the size.

In this lesson, scaling will involve making values 10 times the size.

This lesson is all about scaling known multiplication facts by 10.

We've got two lesson cycles here.

Our first lesson cycle is all to do with scaling multiplication facts and our second lesson cycle is to then solve problems using the knowledge we've learned in our first lesson cycle.

So make sure you pay attention and do not skip that first lesson cycle, let's go.

In this lesson you will meet Andeep and Izzy.

Now you can use your multiplication facts to solve other multiplication facts.

Izzy is saying, "If you know that four times three is.

, then you can also calculate four times 30 and 40 times three." In today's lesson, you'll be exploring how to scale to help you solve these calculations.

Oh, now you may have seen this type of chart in your classroom.

If not, don't worry, I'm going to explain what this chart does.

It would be even more helpful if you had something like this in front of you.

Now this is known as a Gattegno chart and it can help you explore the relationship when scaling by 10.

Scaling by 10 means you are multiplying a number by 10.

So let's have a look.

We've got a lovely Gattegno chart here all the way up to nine.

So let's look at the first row only.

We can see that it's all, it's in our ones.

So we've got one, two, three, four, five, six, seven, eight, nine.

Now I want you to point to the ones, I want you to point to the number one.

Now if we move our finger up to 10, we've actually multiplied our one by 10 to get 10.

So that means if we scale one by 10, we end up with 10 and that is the same as saying one times 10.

Now I want you to move your finger across to the number two and I want you to move it up.

So you should have ended up with 20.

So two scaled by 10 gives us 20.

So two times 10 is 20.

Now I want you to move your finger back down to the number three and I walk, and I'd like you to scale three by 10.

What did you get? If you got 30, you are correct.

So you can see that moving one up in the Gattegno chart means that you are multiplying by 10.

This means your product has been scaled by by 10.

So three goes to 30, it is now 10 times bigger.

Now there are two jars of marbles and 30 marbles in each jar.

How many marbles are there altogether? Okay, let's think about the facts we know.

Izzy says that if there are two jars of three marbles instead, there would be six marbles altogether.

Now that is key because Izzy's used a fact that she knows, instead of thinking about 30 marbles in a jar, she's thought about, "Okay, what if I've had two jars of three marbles instead?" We can represent this using an array.

So we've got two times three, we know that's six.

So in this case we've got two jars of 30 marbles.

So there are 10 times as many marbles in each jar.

I wonder how we could represent this.

I'm sure that array would look the same, but I think something else would change.

Ah, that's right, the value.

So instead of one each, we're now going to have tens.

So tens.

Now we can see that we've represented two times 30 there.

So knowing that two times three is six, we can scale the product six by 10, which gives us 60.

So if two groups of three is six, 30 is 10 times the size of three, so two groups of 30 would give us 60.

The size of the group is 10 times greater, so the product is also going to be 10 times greater.

Over to you.

Which known multiplication fact can help us solve four times 50, right? You've got got three equations here, you've got four times 10, you've got four times five and you've got 40 times 50.

You can pause the video here to have a think and click Play when you're ready to rejoin us.

So how did you do? If you got B, you are correct.

And the reason to why you should have gotten B is because there are four groups of 50.

So one of the factors has been scaled by 10 and we can see that that's five.

Five has been scaled by 10.

It also means it's 10 times the size, so four times five can be used to help you and that's key.

If you do come across equations where one of the factors has been scaled by 10, always think back, "Okay, but what other multiplication fact do I know where the numbers have not been scaled?" And in this case it's four times five.

Over to you again.

Which multiplication will help Andeep solve 80 times nine.

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

So what did you get? Well, if you got eight times nine, you are correct.

And that's because if you know that eight times nine is 72, you can then scale the product 72 by 10 to get the answer of 720 or 80 times nine.

One times nine wouldn't help.

Nine times nine would not help.

Okay, moving on.

There are four jars of marbles and 30 marbles in each jar.

How many marbles are there all together? Now if there were four jars of three marbles, there would be 12 marbles altogether, but there are four jars of 30 marbles.

So there are 10 times as many marbles in each jar and you can see that's represented in the array in the right hand side.

So if I know that four groups of three is 12, 30 is 10 times the size of three, so four groups of 30 is 120.

The size of the group is 10 times greater, so the product is also going to be 10 times greater.

Over to you.

I'd like you to fill in the blanks.

You can see an equation there with an array which represents it.

So four times six is equal to 24.

So four times is equal to? Think about how many times greater the group is compared to the group on the left.

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

So how did you do? If you got four times 60 is equal to 240, you are correct.

Well done.

And that's because we can see that the group has been scaled by 10.

It is 10 times greater.

Four groups of six is 24 and the six has been scaled by 10.

It is 10 times the size, so four groups of 60 is 240.

Back to you.

Four times nine can help Andeep to solve which other multiplication expression? Are there any other facts which you know of that can help solve this? So you've got four times 90, three times one, and five times 12.

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

So what did you get? Well, four times 90 was the correct answer because using the fact four times nine, Andeep can scale his product by 10 and other facts that you could have had were 90 times four.

Onto the main task for this lesson cycle.

For question one, you are going to be completing the tables that you see on the screen by using the multiplication facts.

One has been completed for you and I'll talk you through this.

So your first table, we can see that we are focusing on our twos because we've got two times one which is two, two times three, which is six, two times six, which is 12 two times seven, which is 14, two times nine, which is 18, two times 11, which is 22 and two times 12 is 24.

Now if two times one is two, we can see that if we multiply by 10 we get 20.

So we have scaled by 10 to get 20.

Then if we look at the middle row, we've got our four times tables and then lastly we've got our eight times tables.

You're going to have to scale by 10.

Now there are some missing gaps that come in for your four times tables and then for your eight times tables, make sure you fill those out first and then multiply your product by 10.

And by doing this, you are scaling by 10.

And then for question two, you're going to use your knowledge of the times tables to match up the pairs of calculations to solve the problems and the product.

So you can see that you've got four equations on the left.

I can use this calculation.

So six times two, four times seven, two times nine and eight times seven to help me with this calculation.

80 times seven, 60 times two, 20 times nine and four times 70.

So make sure you match the calculations first.

And then once you've done that, you're then going to match it to the correct product.

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

Off we go, good luck.

So how did you do? Let's have a look at question one.

So for the first row we were looking at multiples of two.

If you knew your multiplication facts for the two times tables, you were then scaling that product by 10.

So for example, for the first row you should have got 20, then you should have got 60 because six multiplied by 10 would've given you 60.

Then you should have got 120 because 12 scaled by 10 is 120.

Then you should have got 140 and then 180, then 220 and then lastly 240.

Now some of you might say, "Well that's easy.

Whenever you multiply by 10 you add a zero." But that's not always the case.

We're not adding a zero, we're placing a zero because we know that when we multiply by 10, the numbers on our place value chart move to the left, which means the product is now 10 times the size.

Now let's look at the second row, but this table we were looking at our four times table.

So this is what you should have got.

We'll go through the missing products first, four, four times three is 12, four times six is 24, four times seven is 28, four times nine is 36, four times 11 is 44 and four times 12 is 48.

Now because we are scaling the product by 10 or in other words multiplying by 10, we then would get 40, 12 times 10 is 120, 24 times 10 is 240.

28 times 10 is 280.

36 times 10 is 360.

44 times 10 is 440 and 48 times 10 is 480.

Now for the last row, we were looking at are eight times tables and multiplication facts for our eights.

So again, this is what you should have got for the first row.

Eight times one is eight, eight times three is 24, 8 times six is 48, eight times seven is 56, eight times nine is 72, eight times 11 is 88 and eight times 12 is 96.

And then for the products you should have got 80 because eight times 10 is 80, 24 times 10 is 240.

48 times 10 is 480, 56 times 10 is 560, 72 times 10 is 720, 88 times 10 is 880 and 96 times 10 is 960.

Now let's look at question two.

We're going to look at this in a bit more detail.

So let's look at six times two first.

You should have matched this to 60 times two, and that's because six has been scaled by 10 to 60.

So 60 is 10 times the size of six.

If you know that six times two is 12, then you also know that 60 times two is 120.

So you should have matched 60 times two to 120.

Now four times seven should have been matched to four times 70, and that's because 70 has been multiplied by 10 or scaled by 10.

Now if you know that four times seven is 28, then you also know that four times 70 is 280.

Next two times nine should have been matched to 20 times nine.

And that's because we can see that the two has been scaled by 10.

So 20 times nine is 180.

And lastly eight times seven should have been matched to 80 times seven because we can see that the eight has been multiplied by 10 to give us 80, 80 times seven should have been then matched to 560 because eight times seven is 56, 80 times seven is 560.

If you got all of those questions correct, good job because you are on your way of being able to scale by 10 and use your multiplication facts when doing this.

Let's move on to our second lesson cycle.

And this is all about solving problems now.

So using everything you've learned in the first lesson cycle, you're now going to apply this knowledge.

So using knowledge of your multiplication allows you to scale and solve problems more efficiently, so more quickly.

For example, you may come across worded problems like this.

"Each child in a class gets four books.

There are 70 children altogether.

How many books are needed?" Well, let's look at this in more detail.

So if there's a class and each child in each class gets four books, there are 70 children altogether.

So how many books are needed? And what is the equation needed for this problem? Well, if you know that if seven children got four books, that's seven times four, which is 28.

So seven times four is equal to 28, there are seven groups of four.

If you know that fact, then you also know that 70 children with four books each, is equal to 70 times four, which is equal to 280.

280 books are needed altogether.

Over to you.

Which multiplication expression is needed to solve this problem? "A barrel can hold 60 litres of honey.

How many can eight barrels hold?" So is it A, six times eight? Is it B, 60 times eight? Or is it C, 600 times eight? You could pause the video here, talk to your friend if you need to and then click Play to rejoin us.

So what did you get? Well, the correct answer was 60 times eight.

And that's because we know each barrel holds 60 litres of honey and there are eight barrels altogether.

So our correct multiplication expression was 60 times eight.

Now this is a guinea card.

They come in different pack sizes.

So for this example we've got one pack of three.

They can be other packs.

So they could be one pack of five, they could be one pack of seven or even one pack of eight.

This is important information because you're going to need to use this later on.

So keep this in mind.

Sometimes you may come across a two step problem.

This usually involves calculating two equations before finding the answer.

That sounds tricky.

I used to find these questions so tricky because I just didn't know what the equations were to help me calculate the answer.

But don't worry, we are going to be breaking down the steps to help us find the correct equations to then let us solve the problem, and we'll do this slowly.

Here's our question.

"Andeep has collected five packets of eight guinea cards.

Izzy has collected 10 times as many.

How many guinea cards does Izzy have?" What is the equation needed for this problem? Well first of all, this is a two step problem, five packets of eight guinea cards.

So that means we need to calculate what that is first.

So if there are five packets of eight guinea cards, you know that five times eight is 40.

10 times as many means you actually have to scale by 10.

So 40 times 10 gives you 400.

So that means Izzy has actually collected 400 cards altogether.

Over to you.

Which words suggest you have to scale by 10? So Andeep has collected seven packets of eight guinea cards.

Izzy has collected 10 times as many.

How many guinea cards does Izzy have? You can pause the video here and click Play when you're ready to rejoin us.

So how did you do? That's correct.

10 times as many means you need to scale by 10.

Let's move on.

Andeep has collected seven packets of three guinea cards.

Oh, straight away.

I know this is important information because, 'cause we need to figure out how many cards there are altogether if there are seven packets.

Let's carry on reading the question.

"Izzy has collected 10 times as many." So that means we'll also be scaling by 10, right? So how many guinea cards does Izzy have? One packet has three cards.

What we need to do is figure out what is known, what is unknown, and how else can this problem be represented.

By figuring out what is known and what is unknown, this will help to form our thinking of what equation is it also needed.

Well, we know that Andeep has seven packets of three guinea cards.

That's a factor.

And Izzy has collected 10 times as many, which is the other factor.

We don't know the total amount of cards that Izzy has.

Now this problem can be represented as a bar model, but we are going to need two bar models because this is a two step problem.

So we need to figure out how many cards Andeep has collected first.

So we can see that Andeep's got seven packets of three guinea cards, which is 21 cards altogether.

Now our second bar model is going to help represent what we need to calculate.

So Izzy has collected 10 times as many packets, which is seven packs of three cards scaled by 10.

You need to scale 21 cards by 10.

21 times 10 is 210 cards altogether.

Over to you.

You're going to represent this problem using a bar model.

Andeep has collected two packets of three guinea cards.

Izzy has collected 10 times as many.

How many guinea cards does Izzy have? You can pause the video here and click Play when you're ready to rejoin us.

Well, this is what you should have got.

Two bar models, so we can see that Andeep's bar model shows us we need to figure out how many cards he has altogether.

So based on this, he's got six cards because he's got two packets of three guinea cards, which is three times two, which is this, and three times two is equal to six cards.

Then for Izzy's bar model, we've got six cards.

We then need to scale this by 10 to figure out the unknown, which is the total amount of cards.

If you've got that correct, well done.

Onto the main task for your lesson cycle.

You are going to solve the worded problems below and you're going to draw a bar model if you need to.

What multiplication fact can you use each time? So 1a, "A fish tank can hold 40 fish.

How many fish can four tanks hold?" 1b, "Four classes raised 90 pounds each in a charity fundraiser.

How much have they raised in total?" 1c, "Each crayon box holds seven crayons.

There are 80 boxes.

How many crayons are there altogether?" And 1d, "Andeep has collected eight packets of four guinea cards.

Izzy has collected 10 times as many as Andeep.

How many cards does Izzy have altogether?" You can pause the video here and when you're ready, click Play to rejoin us.

Off you go, good luck.

Let's have a look at 1a and 1b in more detail.

So for 1a, four tanks can hold 160 fish because if we know that four times four is 16, we then know that 40 times four is 160 because 40 is 10 times the size as four, which means our product also has to be 10 times the size.

And this is how you could have also represented it in the bar model.

You've got four groups of 40 and that's because that's the number of fish tanks there are, which means the total would be 160.

Let's look at 1b.

So this is what you should have got.

Well, we know that four times nine is 36, so four times 90 must be 360 because the nine has been scaled by 10 to 90, which means our product also needs to be scaled by 10, we get 360.

And this is the bar model you should have got.

If you've got something similar to that, well done, let's move on.

For 1c, you should have got 560 crayons all together because if eight times seven is 56, then you know that 80 times seven would be 560 because again, we've scaled one of the factors by 10, which means our product also needs to be scaled by 10.

And lastly, you should have got 320 cards because 32 cards multiply by 10 is 320.

And if four times eight is 32 and Izzy has 10 times as many, we need to scale 32 by 10 and that gives us 320.

If you've got all of those questions correct, well done, I'm really proud of you.

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

Let's summarise our learning.

So in this lesson you were scaling known multiplication facts by 10.

You should now understand that if thinking of a number of tens, you can scale up and work out the 20, 40 and 80 times tables.

You should also understand by thinking of a number of tens, you can scale up and work out 10 times the two, four and eight times tables.

Fantastic work, I look forward to seeing you in the next lesson.