Lesson video

Hello, I'm Miss Sew, and I'm going to be your math teacher for today.

How are you feeling? I hope you're doing really well.

Today in maths we're going to be multiplying decimals using short multiplication, make sure you become quite space ready, and let's get started with our learning today.

Welcome to today's math lesson where we are multiplying decimals using a formal written method.

You will have encountered this method in other math lessons and in previous units, but today might be the first time that you are multiplying decimals with short multiplication.

For today's lesson, you will need a pencil and some paper, pause the video now and go and get them if you don't have them yet.

Once you have all your equipment, make sure that you are ready to load in a calm, quiet space.

If you have any apps running, make sure to turn off notifications so that you can finish this lesson without distraction.

Today we're going to start with a warm up with some speedy timetables, then we're going to be doing our short multiplication with decimals, then it will be your turn after I've shown you, and we'll finish off the lesson with an independent task and quiz so that you can show what you know.

Let's get started with our speedy times tables.

If you haven't seen a grid like this before, this is a times table chart.

So for example, I could do two multiplied by seven, the answer is 14.

Two multiplied by six, the answer is 12.

I want you to do the equations on this grid on your paper and see if you can do it as quickly as you can.

Three, two, one, go.

Pause the video and do as many as you can.

Right, it's now time for the answers.

Ever the archetype timetables square, have a look at your work and see what you got correct.

Whew, that was a lot of times table questions, your hand, my heart, but you should feel really proud of yourself because your brain is now ready to be multiplying decimals.

So, before we start looking at the formal method, when might we choose a formal method for multiplication? How to think? Why would we use this method rather than anything else? So I could use formal multiplication, or I could use things like my area method, I could use things like my known facts, if I know that I know, I could also roll my numbers and say my times tables.

So these are all valid methods I would use at different times.

And I might use a formal method of calculating like this for a number of reasons.

Maybe it is going to be a way to check one of my other methods, or maybe I'm multiplying a number that requires a lot of regrouping and I don't know all my timetables by heart, so I want to check it using a formal written method.

I might be quicker.

This method, there might be other methods I previously said.

So we might use a formal method of multiplication for different reasons.

Remember, this is not the only way of solving a multiplication question.

When we choose our methods, we try to use whichever is most efficient.

That means whichever is quickest with the least mistakes, think about which method is most efficient for you when you are encountering different multiplication problems. Let's start by having a look at short multiplication with whole numbers.

Now, how do I know the answer will be a little over 120? I had a go estimating my answer, and I think 40 times three is 120, and so 42 times three will probably be a bit over 120, 42 is greater than 40, and if 40 multiplied by three is 120, 42 multiplied by three is going to be a little bit greater.

So that's my estimate.

I'm looking for a number around here.

Let's start by laying out my short multiplication, I'm going to write 42 multiplied by three.

Now, first, I'm going to do three multiplied by two.

I've got my place value chart here to represent what I'm doing with my equation.

So three, multiply by two.

I've got two ones here for 42, and I need three sets of 42, three lots of 42, or three groups of 42.

Let's first start by multiplying the ones.

So I've got one group of two here, two groups of two, and three groups of two.

Three groups of two is equal to six and I've written this into my formal written method.

Now let's look at the 10s.

I now need to do three multiplied by four 10s or three multiplied by 40.

Here I've got 10, 20, 30, 40.

I've represented the 10s of my place value chart.

Three multiplied by four, I've got two groups of 40, and now I have three groups of 40; 40, 80 and 120.

I can write 12 for 12 10s inside my formal written method, and now I've got my answer, which is 126.

Now looking at my estimate, I was close, it is a little bit greater.

It's over 120.

So my estimate helps me, it shows me where my answer should be, and I can tell if I've made a mistake.

Now, let's have a look at short multiplication with our decimals.

And I've got a word problem here to help me understand the context.

Sean is putting up six shelves, each shelf is 1.

4 metres long, how much wood does he need? Now I need to estimate this question again.

I've got 1.

4 multiplied by six.

I made around 1.

4 down to one and just do one multiplied by six.

One multiplied by six is equal to six.

Now, although that was a really easy equation, this helps me because I know that my answer should definitely probably be in the ones, it shouldn't be 60 or 600, it should be close to six, probably less than 10.

I know it'll be a little bit greater than six because 1.

4 is greater than one, but it shouldn't be anything much greater than this.

So let's start off and I'll be showing you what I'm doing in my equation on my place value grid on the right hand side.

So first of all, I've got six multiplied by 4/10.

I've got 4/10 represented here by my green place value counters, six groups of 4/10 is what I need.

I've got one group of 10ths, two groups of 10ths, three groups of 10ths, four groups of 10ths, five groups of 10ths, and six groups of 10ths stop, I now have six lots of 10ths.

This is equal to 24.

Now, if I have 24/10, I could regroup some of these and place them into my ones column.

So instead of having 20/10, I could just have two ones, and I've done that here.

I've regrouped 20 of these 10ths and put two of them into ones column, and I will have four of them back in my 10ths column, now I am going to multiply six by one.

I've got one one in my column, and I need six.

One group of one, two groups of one, three groups of one, four groups of one, five groups of one and six groups of one, stop.

Six multiplied by one is equal to six.

However, I've regrouped 20 of those 10ths for two ones.

So I have those two ones here underneath my line, I'd add these as well.

Six add two is equal to eight, and my answer is 84.

Let me remember, I'm multiplying decimals because I'm multiplying decimals, I need to add my decimal point.

This is really important.

The other thing that helps me is my estimate.

I know my answer should be close to six, definitely not close to 60, like 84.

I told you earlier, my answer should be less than 10, and I know that 84 would definitely be the wrong answer.

I haven't added my decimal point, and it needs to go in line, in a straight line underneath the decimal point in my question, so the answer is 8.

4.

Sean needs 8.

4 metres of wood to do all of his shelving.

I have shown you the multiplication for 1.

4 multiplied by six, the answer was 8.

4.

Now what's the same and what's different about these two equations that I've shown you here? What do you notice that's difference and what do you notice that similar? Pause the video and write down what you notice.

Okay time for the answers, listen to me because I will be explaining them.

First, what's the same and what's different? I can see the digits in these numbers are the same.

However, I can see from these digits that 1.

4 is 10 times smaller than 14.

If 1.

4 is 10 times smaller than 14, I would expect the answer to also be 10 times smaller.

84 is 10 times greater than 8.

4.

I also have here a decimal point.

In this equation, I have no decimal point.

And in this equation, I have a decimal point.

And this decimal point changes the value of the numbers considerably.

Let's imagine a real life example.

If I had 8.

4 centimetres, that would be the length of maybe a bracelet or around my wrist but if I had a leg with 84 centimetres, that would be like a dress or a skirt would go all the way down to my feet, too much greater length, it's 10 times longer, or if I imagine the temperature 8.

4 degrees would be really cold.

I'd be wanting to put in a scarf and hats and wear the gloves.

I'd be pretty chilly if it was 8.

4 degrees.

But if it was 84 degrees, I don't think a human can live in that temperature.

84 degrees might be the temperature that I use for cooking, or that I might use on the way to making a cup of tea.

It would be really, really hot.

It is 10 times hotter than 8.

4 degrees.

Now it's your turn to have a go at short multiplication.

I've got a question for you here and I want you to have a go.

I've given you some steps to success to help you on your way.

Follow these steps to make sure you don't miss anything.

If you need some help, I'm going to be giving you some clues in the next five seconds.

If you want the challenge and have it go on your own, pause the video and I'll see you later.

Okay, if you want to clue I'm going to start to show you.

To start with make sure you lay out your numbers correctly.

After you've done your estimation, so I've got 42.

9 and I'm going to write my three underneath my nine in my ones and draw my lines to that my working out is nice and neat.

Next we need to multiply from the smallest to the greatest, which means starting at three and multiplying nine first.

Three multiplied by nine, I'm going to say my times tables is 27.

Three multiplied by two is six, and three multiplied by four is 12.

Make sure you put these digits underneath and check to make sure you have regrouped if necessary.

Right, I think we're ready for the answers now.

First, I calculated my estimate.

I estimated the answer to be close to 120, next we multiply from smallest to greatest.

27, we have to regroup at the six and remember to add the two that we regrouped which is eight, and three multiplied by four is equal to 12.

Now this answer is 1287.

Oh, what do you remember? Our estimate was 120.

What are we missing? The decimal point.

The answer is 128.

7, which is much more reasonable, especially when I've used my estimate to check.

Now it's time for you to get ready for your independent task.

If you found any parts today are a bit tricky and you want to rewind and have another watch, go ahead before you start working on your own.

For your independent task today, you're going to solve each of these equations using the most efficient method.

Remember to estimate, check it by drawing your own place value counters or using a method that you're familiar with.

If you finish these equations, have a go at the math story, which I've given you an example for here.

A maths story is when you create a story with your questions.

For example, Miss Sew went shopping.

She bought three teapots for £16.

70.

How much did she spent? And the equation will be 16.

70 multiplied by three.

That is equal to £50.

10.

Pause the video and complete your task.

It's time to show you the answers now.

Well done finishing your independent work.

There are the answers to the independent work.

Did you check your answers with any other method? Can you write a math story for any of these questions? Thank you so much for joining in with your math lesson today.

If you'd like to, please ask your parent or carer to share your work with Instagram, Facebook or Twitter tagging @OakNational and #LearnwithOak.

It's now time for you to go ahead and complete the quiz where I have even more, short multiplication problems for you.

I am sure that you are going to be brilliant because you have joined me until the end of the lesson.

I hope you have a wonderful day and enjoy the rest of your lessons at Oak Academy, bye.