Lesson video

Hiya, my name's Ms. Lambell.

Thank you so much for popping along today to do some maths.

I hope you enjoy it.

Welcome to today's lesson.

The title of today's lesson is Securing Understanding of Arithmetic Procedures with Integers and Decimals, and that's within our unit Arithmetic Procedures of Integers and Decimals.

Main focus of today's lesson is being able to use our calculator efficiently to check our answers.

So by the end of this lesson we will be able to add, subtract, multiply, and divide with integers and decimals and we will be able to use our calculators to help us check.

So at this point it would be useful to pause the video and go and get yourself a calculator if you don't already have one with you.

Just one word that we will be looking at today.

And that is decimal form.

So like I said, we will be looking at numbers in decimal form, and remember those are numbers that have a decimal point and that there are digits to the right of the decimal point.

Today's lesson is going to be split up into two learning cycles and we're going to firstly just concentrate on integer calculations, so whole number calculations.

And like I said, we'll be looking at checking our answers with our calculators.

And the second learning cycle, we'll be doing exactly the same but with decimals.

Let's get started then on that first learning cycle and we're going to look at using our calculator for integer calculations, but I what I'd like you to do, just pop your calculator to one side, put it face down 'cause we're not going to use it straight away.

Here we have the cost of a car and the cost of a house.

What is the total cost of the car and the house? Remember that calculator is to one side and face down.

Like I said, we don't want to be using calculators just yet.

Sofia, Jacob and Laura have each worked out the answer to this question.

They each claim that they must be right because they've used a calculator.

So they are adamant, my answer's right.

It must be 'cause the calculator said that that's what the answer was.

Let's have a look and see what answers they got.

Without calculating, that's why I said keep that calculator off one side, can you tell who is right? So not even working this out with pencil and paper, just looking at the reasonableness of these answers, can you tell who is right? Let's have a look.

Well, the car is fairly close, I think you'll agree, to 17,000 pounds and the house is fairly close, although still quite a way off, but we could say it's around 300,000 pounds.

The total of those is 317,000.

Who's can we rule out at this stage then, hmm? Jacob said 43,000, that can't definitely be right.

That's less than the cost of just the house alone.

It looks though that Sofia and Laura's answers could both be right.

They both have an answer which is in the 100,000s, whose answer of Sofia's and Laura's do you think must be right? If we look at both of the costs, the car has a one's digit of zero and the house has a one's digit of zero.

So therefore the total must also have a one's digit of zero.

And we can see that Sofia's one digit is nine and Laura's is zero.

So Laura is the correct one.

The total cost of the car and the house is 281,890 pounds.

Well done, Laura.

We are now going to have a look and see if we can see what mistake that Sofia and Jacob have made.

'Cause remember they said they used a calculator.

They were adamant that that answer must be right because the calculator said so.

So we're sticking with that same questions.

We're just going to leave it there at the top to remind us we are finding the total cost of the car and the house.

This is a calculator that I will be using throughout this lesson and it's a Casio fx-991EX.

Yours may look similar to this, it may look totally different.

There will be certain buttons that your calculator may have in a different place when you come to use your calculator, but don't worry, you'll be able to look up and see how to do particular things on your own calculator.

You can now turn your calculator over and like I said, if it looks similar to this one, need to make sure it's on calculate and press your EXE button.

You may not have to do this if you've got a slightly different calculator, just make sure that it's ready to do some calculations.

What mistake do you think Sofia has made? So just have a think a moment.

Can you see what mistake she may have made? Well, here's her calculator display.

I'm very lucky to have been able to see what Sofia had typed into her calculator.

So I'm going to show you what it is and what I'd like you to do is to think and see what her mistake was.

So here's her calculation.

What what mistake has Sofia made? Brilliant, yeah, I can see you all saying she's missed the zero.

She's missed the zero off the end of 16,790.

She's actually found the total of 1,679 on the cost of the house.

So that was Sofia's mistake.

What about Jacob's mistake? Before we look at what he typed into the calculator, do you think you can spot what Jacob did wrong? Again, I was lucky enough to be able to see what he typed into his calculator, so here it is.

What was his mistake? Very similar, wasn't it, to Sofia's? He's missed a zero.

He reckons that house is 26,510 pounds.

If only, I'd definitely be buying it.

So we've missed a zero off of the end.

It is really, really important.

Lots and lots of people always say, oh, my answer must be right, the calculator told me, but we must always double if not triple check that the calculation you have inputted into the calculator is what you should have.

It would've been really easy here for Sofia and Jacob to have checked that they'd written the correct values for the car and the house into the calculator in the first place and come up with exactly the same answer as Laura did.

Checking what you've put into the calculator is so important.

Quick check for understanding, right, calculator to one side, face down.

No calculators for this one.

I want you to decide which of those values will be closest to 43,872 subtract 245.

Pause the video, remember no calculator, just want you to use your mathematical knowledge of the size of numbers and decide which of those is the only sensible answer.

Which one of those will it be closest to? Pause a video and come up when you're ready.

Great work, so if we look, we have that's roughly 40,000 takeaway 200-ish.

Our answer has to be closest to 40,000.

Well done, I'm sure you got that right.

And a second check, again without a calculator, I want you to decide which of the following is the correct answer this time.

So last time we were looking at which one is closest, this one I want you to think about which of those is the correct answer.

And remember, no cheating, no writing it down with pen and paper and working it out.

No tapping into your calculator.

Just use your mathematical knowledge to work out which of those could only be the one possible answer.

Pause a video, come up when you're ready.

Super, we had a 300,000 roughly plus another, that's roughly 100,000, isn't it? So it is got to be around 400,000.

So my only sensible answer there B.

I'm sure that the other ones probably came from a miss slip on the type on the calculator of missing out a digit maybe.

We're ready to have a go at Task A now.

So this is a little bit of an interesting problem.

We've got to find one answer in each row that is the only possible correct answer to the question, but unfortunately somebody has had a bit of a mishap with their pen and there are ink splats all over the questions and all over the answers.

Maybe that's what your homework might look like.

So let's some a look, we've got something, three, eight, add four, something, something.

What I want you to do is to decide which is the only possible correct answer to that.

Even though we don't know all of the digits, we don't know the exact answer, only one of those could possibly be correct.

Is it answer one, answer two, or answer three? You are going to do that for each of the questions and you'll notice the right hand end of each of the answer columns is a letter.

When you've decided which is the only correct answer in each row, I want to write down the letter and then you are going to have a go at rearranging those letters to make a word that is associated with today's lesson.

Good luck with this.

Don't worry if you don't get the word.

The most important bit is being able to work out which of those is the only correct answer.

So pause the video and when you're ready, come back.

Good luck with this.

Let's hope you find that magic word.

Here are our answers then.

So the first one, it was answer two, which gave us an I.

The second one, it was answer one, which gave us an R.

The third one was answer three, which gave us an E.

The fourth one was answer three, which was another E.

The next one was answer one, which was a T.

The next one was answer two, which was a G, and the final one was answer three, which was an N.

Now some of you might have been saying that doesn't spell anything, but remember I said you needed to rearrange the letters to create a word, rearrange the letters to create a word.

Remember it was associated with today's lesson.

Absolutely superb if you managed to rearrange those letters to make the word integer, well done.

We're now going to move on to look at our next learning cycle.

Very similar to the first one, we're going to be using our calculator, but this time for decimal calculations.

Andeep buys three pens, four pencils, two highlighters.

He says it's going to cost him 311 pounds and 22 pence.

Hmm, do you think Andeep is right? What did you say? I would've said no, Andeep is not right.

If he was right, I certainly wouldn't be buying my pens and highlighters and pencils from that shop.

How did you make your decision that Andeep was wrong? Maybe you did it by saying, well, a pen is roughly one pound 50.

A pencil is roughly a pound and a highlighter is roughly a pound.

So there's no way that that can all come to over 300 pounds.

Now I want you to think, just like I did previously with Sofia and Jacob, what mistake do you think Andeep has made? Hmm, maybe you're not so sure on that one.

Let's take a look and see what mistake Andeep may have made.

Let's start with the pens.

Andeep buys three pens.

They're one pound 56 each, so we need to calculate three multiplied by one pound 56.

Now we can use our calculators.

So using the calculator I've got, I've typed in three multiplied by 1.

56, but unfortunately my calculator has given me an answer as a fraction and you may find that your calculator has done this too.

Now, if you have a calculator similar to my one, then this is what you need to do to get that into a decimal answer.

We need to change this into a decimal and this is how we do it.

We press the format button so you can see that the format button is down on the bottom row next to that EXE button, you press the format button and then you press the down arrow, and then you can press okay.

So format, down, 'cause that will take you to decimal, and then okay, and it you should get four pound, 68.

What I'd like you to do now is to pause the video and just check you know how to enter the calculation three multiplied by one pound 56 into your calculator.

Remember to press equals or EXE, and then make sure you know on your calculator how you need to turn that into a decimal and check that you get four pound 68.

So pause the video, check you've got that and when you're done, come back.

Great, hopefully now you know how to do that on your particular calculator if it's not the same as mine, the one I'm using here.

Now let's look at the cost of the pencils.

This is where I think that Andeep made its mistake.

Maybe you thought that too.

And I think the mistake he probably made was not realising that he'd started with the pens in pounds, but this is in pence.

We must make sure that all of our values are in the same unit so that we can combine them for a total cost at the end.

So we need to make sure the price is in pounds.

Instead of doing four multiplied by 76 pence, we're going to do four multiplied by 0.

76 pounds.

So I'd like you to do this along with me on your calculator so you know how to do it on your particular model.

On my calculator, I typed in four multiplied by 0.

76 and that gave me a fraction answer of 76 over 25.

Don't worry if this is the first time that you've been working on your calculator and changing things from fractions to decimals.

By the end of this lesson, you'll be an expert at it.

On my calculator, I press format, down arrow, okay, 'cause the down arrow takes me to decimal.

You may have to do something slightly different on your calculator, but you should get an answer of 3.

04.

So the cost of four pencils is three pounds and four pence.

Now we'll look at the highlighters.

We want the cost of two highlighters, so that's two multiplied by one pound 27.

This time I get a fractional answer of 127 over 50.

Now we're going to change that to a decimal and I get two pounds 54.

Please just check for me that you've got that correct on your calculator and that you are confident with how to change if it's a fractional answer on your calculator display to a decimal answer, because I know that if I looked at 127 over 50 pounds, I wouldn't have a clue how much I was paying for those highlighters, but I do now, two pounds 54.

Here are our total costs of the pens, the pencils, and the highlighters.

We want to find the total cost that Andeep thought he was going to pay, 311 pounds something.

We can clearly see now that Andeep had made a mistake.

So let's work out actually the total cost of all of those items. To find the total cost, we would add together all of those items. What I'd like you to do now on your calculator is check that you also get 10 pounds and 26 pence, but I want you to leave that on your calculator display.

Just remember to make sure that everything we are working for, working with is in the same unit so that we can make sense of the result, okay? Andeep probably did four multiplied by 76 pence, which meant then that his final calculation for what he needed to pay was way off.

So hopefully you've done that.

You've checked for me that you end up with 10.

26 and that is on your calculator screen and I don't want you to get rid of it 'cause we are now going to have a look at a nifty little button that allows us to keep what's on the calculator display and use it in another calculation.

It saves us having to write down things and particularly when we get onto very, very complex decimals, it allows us to just use that exact value rather than writing down maybe an approximation of it.

The total cost is this calculation, and like I said, you should have that now on your calculator screen.

Now we're introducing the fact that Andeep is actually paying for his pens and pencils and he's going to do that with a 20 pound note.

What I want us to do is to work out how much change he gets.

Now if you are not used to using this next button, this nifty little button, you probably would've before written down 10.

26 so you could remember how much he'd spent, and then done 20 subtract 10.

26.

But there is a button that saves us having to write in that 10.

26 again and it's the Ans button.

So pause the video and find your Ans button.

My Ans button is above the seven.

Have you found your Ans button? Brilliant, now if you look at my calculator display, I've got 20 takeaway Ans.

So I pressed 20, subtract Ans.

The Ans button basically just copies whatever your last answer was to save you typing it out again.

It's really, really not a problem if you struggle to use the Ans button.

It just means that later on when we are looking, like I said, at horrible decimals, we can make sure our answers are as accurate as we can.

So if for today's lesson we are going to make sure we try and practise using it if we possibly can.

So let's just repeat what we did.

We worked out the total cost, which was 10.

26, 10 pounds and 26 pence that was left on our calculator display.

We wanted to work out how much change he gets.

We could have done 20, take away 10 pounds 26, but the most efficient way is to use that Ans button.

So 20, subtract Ans, and it's going to use the 10 pounds 26 and then equals.

And now I know you will have changed that into a decimal because you're expert at that by now, which is nine pounds 74.

So the change that Andeep will get is 9 pounds 74.

Here's a check for understanding.

So this time, normally I say no calculators, this time I'd like you to use your calculator.

And what I'd like you to do is to find the total cost of two of each item, two pens, two pencils, and two highlighters.

Good luck with that.

Come back when you're ready, pause the video.

Great work, did you rule out any of those answers before you even started? Maybe you did, maybe you looked and said, oh dear, I think maybe A has done an Andeep and actually not changed the 76 pence into 0.

76 pounds.

The correct answer was seven pounds 18.

I'm sure you've got that right and hopefully you are getting used to using that calculator and changing your answer from a fraction to a decimal if that's required.

Now you're going to have a go at working out the answers to these questions.

So we are sticking with the same items, the pen, the pencil, and the highlighter, and we're sticking with the same costs.

I'd like you, if you please, to work out the total cost of each of those using your calculator.

And then when you are ready, you can come back.

So pause the video now, good luck.

Come back when you are ready.

Here are our answers then.

So A was nine pounds 32, B, 12 pounds and seven pence, C, 10 pounds 95, D, 16 pounds 74, E, 20 pounds and nine pence, and F, 628 pounds 25.

I'm just wondering if you spotted maybe a slight shortcut to that final question.

If we work at the total cost of all three, we could then multiply that total cost by 175.

Wonder if you did it like that.

Don't worry if you didn't.

It was just something I thought I might mention.

Now we can summarise our learning from today's lesson.

One of the most important things we can ever do in maths is to consider the reasonableness of our answers.

Is my answer sensible? Because we can correct so many of our own mistakes by just considering whether our answers are sensible or reasonable.

We should be able to now have the ability to check if an answer appears too big or too small.

So just like we did with the car and the house, Jacob's answer was way too small.

His answer was less than just the cost of the house.

And then Andeep, when he tried to work out the total cost of all of those items, the pens, the pencils, and the highlighters, we clearly knew that 311 pounds something was way too big.

Really important because like I said, we can really catch our own mistakes.

Remember also, the calculator does not guarantee the correct answer.

You must remember to double check and maybe triple check that what you think you've entered into the calculator is what you actually have.

It doesn't take long, a few seconds just to double check what's on your calculator display is what you've written down as a calculation you are trying to find the answer to.

And then the use of that Ans button 'cause that Ans button can be more efficient, particularly if we've got a long number that we need to be reusing, and it can allow for greater accuracy.

So I mentioned that when we get into later on, some decimals or some just some very, very big numbers or very, very small numbers, it can allow for greater accuracy because it means that we can use that exact value rather than just writing down a few of the digits.

You've done superbly well today.

Hopefully you've got a little bit more confident with using your calculator.

The more you use it, the more confident you will get.

Fantastic, well done, thank you, bye.