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 will be able to use estimation to support accurate calculation.

These are your keywords.

Expanded multiplication, short multiplication, and estimate.

I'd like you to repeat these after me.

Expanded multiplication.

Short multiplication.

estimate.

Fantastic.

Let's move on.

Expanded multiplication is a way of recording the steps of a calculation, focusing on partitioning one or more factors and showing partial products.

A way of recording using columns to set out and calculate a multiplication is called short multiplication.

To find a value that is close enough to the right answer, usually with some thought or calculation involved, is known as estimation.

In this lesson, you will use estimation to support accurate calculation.

And in this first lesson cycle, you will use estimation.

You will also meet Andeep and Izzy.

Why estimate? Estimation is a skill for life.

Imagine if you could easily estimate how much a bill will be, which item is the best value for money.

Personally, for me, when I go shopping, I'm always looking for the best deals.

So when it comes to estimation, this is super important because it's a key skill that you will use throughout your life.

Estimation is finding a number that is close enough to the right answer.

There are various methods that can be used to solve this calculation, including informal and mental strategies, expanded, and short.

Now, you might have a preference.

I definitely do.

For me it's short multiplication.

What is your favourite method? Have a think.

Now, during this lesson, you're going to think about which method will be most efficient for each calculation.

Let's begin.

Andeep has three bags of 243 marbles.

How many does he have altogether? What multiplication equation is needed and what is your estimate? Our equation that we are calculating is 243 multiplied by three.

243 is between 200 and 300.

This can also be written like this, using our inequality symbol.

Three multiplied by 200 is 600.

Three multiplied by 300 is 900.

The answer will be between 600 and 900.

Which number do you think the answer will be closest to and why? The answer will be closer to 600 because 243 is closer to 200.

Now, you're probably thinking that, well, I know that 243 is also between 240 and 250.

This can also be written as this expression shown here, using our inequality sign.

Now, whilst rounding to the nearest multiple of 10 will result in a more accurate estimate, it may not always be as efficient, and it may take you a bit of time to calculate this.

So this is why rounding to a simpler value, such as a multiple of a hundred, may be better.

Over to you.

I'd like you to fill in the gaps.

You can pause the video here.

So how did you do? 347 is between 300 and 400.

Well done if you got that correct.

347 is between 300 and 400.

So knowing this, I'd like you to continue with the equations shown on the screen now.

You can pause the video here.

So how did you do? If you got the numbers here, you are correct.

You can give yourself a tick.

So, ultimately, the answer will be between 1,800 and 2,400.

Let's move on.

Andeep believes that 200 multiplied by three is less than 243 multiplied by three.

Well, there's 200 groups of three in this equation.

This sign means that it is less than.

And in my second equation, it's 243 groups of three.

So Andeep is correct 'cause the factor 200 is less than the factor 243, and 243 is 43 more than 200.

So the product would be greater.

Back to you.

True or false.

Five multiplied by 300 is less than five multiplied by 350.

Is it true or false? And I'd like you to justify your answer.

You can pause the video here.

So what did you get? It's true.

So, ultimately, your product will also be greater as well.

Izzy has four bags of 383 marbles.

When playing with them, she loses 21 marbles.

How many does she have altogether? So I'd like you to think about what multiplication equation is needed and what is your estimate? Well, the multiplication equation is going to have to be four multiplied by 383 because we are calculating four groups of 383.

Now, she loses 21 marbles, so we must then subtract 21 from our product.

So let's calculate this together.

Begin by estimating an answer to your calculation.

So 383 is between 300 and 400.

This can also be written like this.

So we then multiply 300 by four, which is 1,200, and we multiply four by 400, which gives us 1,600.

So the answer will be between 1,200 and 1,600.

For the first part, Izzy solve this problem using expanded multiplication.

Do the answers match the estimation? Have a think.

So the answer should have been between 1,200 and 1,600.

So 1,200 is less than 1,532, and 1,600 is greater than 1,532.

So 1,532 is in between 1,200 and 1,600.

Both answers in this case match their estimation, which means the answers could be correct.

So Andeep carries on.

He now needs to subtract 21.

He says that he can use a mental strategy because it is more efficient.

So this is what he does.

So instead of subtracting 21 Andeep first subtracts 20.

This leaves him with 1,512.

He then subtracts the remaining one which gives him a final answer of 1,511.

So Izzy has 1,511 marbles altogether.

Now, Izzy solved this problem using expanded multiplication.

Andeep is saying that he can use both methods.

It's very important to note that if you do know both methods, that's great because that means you've got a toolkit with so many tools that you can use and you can use these tools effectively for different questions, but it's really important to remember that short multiplication is more efficient than the expanded method.

Okay, over to you.

Choose an appropriate estimation equation for 271 multiplied by four.

Is it A, B or C? You can pause the video here.

Okay, so how did you do? If you got A, you are correct, and that's because the answer is in between 800 and 1,200.

The multiples of a hundred that 271 is in between are 200 and 300.

You multiply both by four to find your range of estimation.

Back to you.

So you're going to now choose the right equation for this multi-step word problem.

And I'll read this out to you.

Andeep has collected four bags of 231 marbles.

Izzy gives him 51 more marbles.

How many does he have all together? So you've got three options here.

You can pause the video now to select the correct answer.

How did you do? If you got A, you are correct.

And that's because four bags of 231 marbles means our multiplication equation is four multiplied by 231.

Izzy gives him 51 marbles.

So we need to add this to our product.

Onto the tasks for lesson cycle one.

For task one, you are going to be completing the table.

For each equation, you are going to be writing down the inequalities equation, and then you're also going to be writing down an estimation.

For task two, you're going to estimate the answer to each of these calculations.

You can pause the video here, off you go.

So how did you do? For task one, this is what you should have got.

You can pause the video here to mark your work.

For task two, this is what you should have got for each estimate.

So for 2a, you should have got between 2,100 and 2,800 For task b, you should have got 2,400 and 2,800.

And for task c, you should have got between 4,000 and 4,800.

Let's move on.

So for lesson cycle two, you'll now be recording multiplication using an efficient strategy.

You'll now be picking that efficient strategy for the different problems that you'll be coming across.

Izzy and Andeep are working out 201 multiplied by four.

by Izzy says that she will use short multiplication, and you can see her recording there.

Andeep method is below.

Have a look at both.

Now, sometimes mental strategies are more efficient, especially in calculations which do not involve too many instances of regrouping.

As there is no need to regroup, I would argue that and Andeep's method is more efficient.

Over to you.

Which calculation would be more efficient to use a mental method? Explain your thinking to your partner.

You've got three options here.

You can pause the video.

So how did you do? If you got C, you are correct, and that's because there is no need to regroup.

Back to you again.

Which calculation would be more efficient to use a short multiplication method? And this time I'd like you to explain your thinking to your partner as well.

So you've got three options here.

You can pause the video now.

So how did you do? If you got A, you are correct, and that is because you will need to regroup in the ones column.

So it would be best to use short multiplication in this example.

Let's move on.

Izzy has five small bags, each containing 271 marbles and one larger bag of 99 marbles.

How many marbles are there altogether? Now, I think you may have noticed that this is a multi-step problem.

The second part of the question also means that we have to add on a certain amount of marbles.

So what multiplication equation do you think is needed for the first part and what more do we need to add on? And secondly, what would your estimate be? So the equation is five multiplied by 271 or it could be the other way.

You could have also had 271 multiplied by five.

Now, 271 is between 200 and 300, and this can be written like this.

200 multiplied by five is 1,000.

300 multiplied by five is 1,500.

The answer will be between 1,000 and 1,500.

That's just for the multiplication equation.

We've not factored in the second part.

So to begin with, you're going to place the largest factor at the top, and you're going to place the smallest factor underneath in the ones column.

You're going to start off by multiplying with the ones.

So five multiplied by one one is five ones.

Well done if you got that correct.

We place the five in the ones column.

We then move on our tens column.

So five multiplied by seven tens is 35 tens.

35 is regrouped as three hundreds and five tens.

Now where do we place the three hundreds? Do you remember? Yes, we must place it underneath in the hundreds column.

We then put the five tens in the tens column.

So what do you think we do next? We then move on to the hundreds column.

Well done if you got that correct.

So five multiplied by two hundreds is equal to 10 hundreds.

What do we do now? We must regroup.

So not only do we have to regroup.

We also have to add the regroup three hundreds, and that is 13 hundreds.

13 hundreds which can be regrouped as 1,000 and three hundreds.

Where do you think the 1,000 will be placed? You could point to the screen.

So yeah, it has to be placed in the thousands column.

And then you put your three hundreds in the hundreds column.

So Izzy has 1,355 marbles altogether, but that's only part of the equation.

Don't forget.

And here's Andeep reminding us of that.

So do remember to add the larger bag of marbles? How many marbles was that? It was 99.

So Izzy and Andy both added 99 to the product.

Have a look at both.

Which method do you think is more efficient? And I'd like you to explain your thinking to your partner.

If I was not feeling confident, I would probably choose column addition, but I think it would work against me because of the amount of regrouping, and sometimes, when we are regrouping, that can expose us to making a lot more mistakes than we want to.

So, ideally, I think, Andy's method is far more efficient.

So we can see here he's rounded 99 to a hundred, and then he's adjusted by taking away one, which has given him his answer.

So two steps there.

Your turn.

Use information from the word problem to fill in the gaps.

Eric buys four tickets to attend a football game.

Each ticket costs 373 pounds.

What is the total? You can pause the video here.

How did you do? If you got this as your answer, you are correct, and that is because Eric is buying four tickets.

That's one of our factors, and it's our smallest factor that cost 373 pounds, and that is our largest factor.

So we need four groups of 373, and this is how we would arrange it in short multiplication.

So Eric buys five tickets.

Each cost 205 pounds.

He also buys a discounted, which costs 98 pounds.

What is the total cost of tickets? So I'd like you to think about what multiplication equation is needed, and is there anything else that you have to do in this question? And what is your estimate? So five groups of 205, which means our multiplication equation is five multiplied by 205.

He then buys another ticket at 98 pounds, which means you need to add 98 to the product.

So now that we know what we have to do, let's have a look at what Izzy's done.

Izzy's completed part of the calculation so far, and you can see that she's got her short multiplication recording there.

You can use estimation to instantly check if she's close to the answer or not.

So using estimation then, is she correct? I'd like you to explain your thinking to your partner.

Let's calculate the estimation together.

205 is between 200 and 300.

This can also be written like this.

So 200 multiplied by five is 1,000.

300 multiplied by five is 1,500.

The answer will be between 1,000 and 1,500.

But have a look at Izzy's calculation.

It is nowhere near.

So we know straight away that she's incorrect.

So Izzy corrects this, she moves on, and now she needs to add the remaining 98 to the product.

What method would you choose to add 98? Would you choose column addition or would you choose to round and adjust? Andeep is saying that he can use a mental strategy because it's far more efficient.

For example, he's chosen to round and adjust.

He's added 100 to 1,025, which gives him one than 1,125.

Because he added too many more, he now needs to take that away.

So 1,125 takeaway two is 1,123.

So Eric spent 1,123 pounds altogether on the tickets.

Over to you.

Andeep has completed a calculation.

Is he correct? I'd like you to explain your thinking to your partner.

You can pause the video here.

So how did you do? Well, Andeep actually forgot to regroup.

So if we have a look, four multiplied by three ones is 12 ones.

He should have placed the regrouped one ten underneath the tens column.

And because he didn't, his calculation is incorrect.

Onto our final tasks.

For this learning cycle, what you will be doing is completing the word problems below by, number one, estimating an answer and then recording your calculation as an informal or formal strategy.

So you need to think which tool you're going to use from your toolkit to efficiently answer these questions, and that's what a good mathematician does.

They pick the most efficient method.

So let's look at A.

Izzy has four small bags, each containing 176 marbles, and one larger bag of 96 marbles.

How many marbles are there altogether? Question B.

Andeep has six small bags each containing 236 marbles.

Izzy then gives him another smaller bag of 98 marbles.

How many marbles does Andeep have altogether? Question C, Eric buys seven football tickets at 303 pounds each.

He then sells one of those tickets at a discounted price of 297 pounds.

How much did he spend altogether? And lastly, question D.

Andeep has collected 594 packs of football cards.

Each pack contains four cards.

When Andeep is playing against his friends, he loses 19 cards.

So how many cards does Andeep have now? You can pause the video here to answer the questions.

Off you go.

Good luck.

So how did you do? If, for question A, you got to 800 marbles altogether, you are correct.

And the best option to use for both parts of the question was short multiplication for the first part because there was quite a bit of regrouping involved, and then using rounding and adjusting to calculate the rest of the answer.

For B, Andeep has 1,540 marbles altogether.

Similar to the previous question, short multiplication for the first part would've been the most efficient method to use, and then mental strategy of rounding and adjusting to calculate the extra marbles that were given.

For question C, the answer is 1,824 pounds.

If you got that correct, well done.

Let's move on to question D.

So for question D, Andeep has 2,357 cards altogether.

If you got that correct, give yourself a tick.

Fantastic.

We've made it to the end of the lesson, and I really enjoyed teaching you that lesson as well.

So to summarise our learning, you used estimation to support accurate calculation.

You can now hopefully estimate and use expanded and short multiplication to multiply a three-digit by a one-digit number.

You can also choose an efficient method to use to multiply.

Thank you for joining me in this lesson.

And if you do find that you didn't quite understand something, do go back and re-listen to the method that was explained.