Lesson video

Hi, everyone, my name is Miss Ku, and I'm really happy to be learning with you today.

It's going to be a fun, interesting, and challenging lesson in parts, but don't worry, I am here to help.

You will come across some new keywords and maybe some keywords you've already come across before.

We're going to work really hard today, but I am here to help and we can learn together.

In today's lesson from the unit Arithmetic Procedures with Integers and Decimals, we'll be looking at using a calculator efficiently.

And by the end of the lesson you'll be able to fluently use certain calculator functions and use a calculator appropriately.

So let's have a look at some keywords, starting with the word evaluate.

And evaluate means to find the value of a numerical or algebraic expression.

For example, if a question wanted you to evaluate 100 divided by 2 and 5, it would be 55.

If a question wanted you to evaluate the square root of 64, add 2 cubed, it'd be 8 + 8, which is 16.

So we evaluate simply means to find the value of a numerical or algebraic expression.

Now today's lesson will be broken into two parts.

The first is where we'll be using negatives and operations, and the second is where we'll be using brackets and operations.

So let's start with the first part of our lesson, using negatives and operations.

There are lots of different scientific calculators out there, but they all have very similar functionality and notation.

When turning on your calculator, there will be different applications available.

Ensure the calculate is selected and then press OK or execute or EXE.

Now from here, to return back to all the applications, you simply press the home button, and that will take you back to all these wonderful applications.

Now what we're going to do is we're going to go through the main operations with the Casio FX-570 or the 991 Classwiz.

What I want you to do is look at the calculator, and can you find the four main operations, addition, subtraction, multiplication, and division? Now hopefully you've spotted they're right here, so it's important to know where those operations are.

Now do you think you can find the negative button on your calculator? Well, hopefully you spot it.

You can actually use the subtraction as a negative.

Another way in which you can access the negative is by pressing shift and the subtraction, and you'll see the little minus come up.

Now this will show the proper negative sign.

For example, if you pressed shift and subtract, it'll show you it's a negative sign with the six.

But just we also remember, you can use the subtraction or the minus key, and the calculator will know and adjust the number to a negative.

So don't worry which method to use to access that negative.

Now what I want you to do is have a look at your calculator and I want you to find the button that will execute the calculation.

Well, there are two buttons.

You can actually use the OK or the EXE for execute.

Either one of those are fine to make sure you can work out the value of your calculation.

Next, I want to see if you can find the square button on your calculator.

Hopefully you've spotted it's this button here.

They do look different on different calculators, but using our calculator, it's this button.

Now can you find the brackets? Well, hopefully you can spot the brackets right here.

And we'll be using brackets to illustrate the negative numbers and group numbers together.

So they're really powerful and important to know where they are in the calculator.

Next I want you to have a look to see if you can find the square root button.

Well, for me, it's right here.

So it's important to know where the functions are on your calculator.

Can you find the power button? For me, it's right here.

Well done if you found that.

What about the fraction button? Can you see where the fraction button is on your calculator? For me, it's right here.

Well done if you found it.

And the next buttons to find are the cursor buttons.

These are really important buttons.

Can you find them in your calculator? Well, hopefully you can see it's right at the top here.

And these are really important keys, as they allow you to move around the calculator screen and your calculation, as well as access different applications.

Well done if you found that.

Now what we're going to do, we're going to have a look to see if you can find the format button.

Can you see that anywhere? Well, the format is indicated here, and this is a really powerful key, as it allows you to change the format of your answer.

So there are many more different applications and operations in our calculator, but these are the main buttons that we'll be using in our lesson.

The OK or the execute will execute the calculation.

We have the operations multiply, divide, add, and subtract, but also remember subtraction, we can use that to represent the negative.

Remember the cursor keys will allow you to scroll around the screen, the square buttons used will also be using the square root button and our brackets.

If we're asked to change the format, we press this format button.

The fraction button is illustrated here as well as the power button.

So we'll be using lots of different buttons in our lesson today.

Now the cursor key will allow you to move around the functions, applications, and calculations on your calculator screen.

And it's an important key to leave or enter an operation.

So for example, what buttons do you need to press to get this calculation on your screen? We have 5 to the 4 + 6 x 2, and the answer is 637.

But what buttons do you need to press in order to access this calculation? Well, the buttons are 5 and then to the power button, 4, then you must scroll to the right because it allows you to leave the exponent function and then you can press the addition of the 6 x 2.

So the cursor will allow you to leave a function or operation, and it's very important.

So let's have a look at a check question.

Alex is asked by his teacher to square -8.

So Alex showed this on his calculator.

He thinks he's put it incorrectly to give the answer of -64.

What should have Alex inputted it into the calculator, and how did the calculator get an answer of -64? Have a little look and look at your calculator as well.

Let's see if we can figure it out.

Press pause if you need.

Well done.

Well, Alex should have inputted into the calculator (-8) squared.

Remember to show those negatives using brackets, then we would've got an answer of 64.

So it's important to remember negatives should be inputted within brackets.

But how did the calculator get the answer of -64? Well, scientific calculators have the priority of operations installed in their programming, and the calculator is performing the exponent first, and then the multiplication.

In other words, the calculator works out 8 squared, and then multiplies it by the -1, thus giving -64.

Now let's have a look at another check question.

We have three students, and they were given the same question.

6 cubed, add to the square root of 9 + 16 - 200.

Aisha says, "My answer's 21." Andeep says, "My answer's 23." And Izzy says, "I got a math error." Who's correct, and what buttons need to be pressed to work out the correct answer? See if you can give it a go and press pause if you need.

So let's see how you got on.

Aisha is correct, and the correct answer is 21.

The buttons which needed to be pressed are 6 power of 3.

Scroll to the right to exit the exponent function, add the square root of 9 + 16.

Don't forget to scroll to the right again to exit that square root function.

Then you subtract the 200.

The next check question says we have to match the correct calculation on the calculator with the correct answer.

So which calculation represents Aisha's, which calculation represents Andeep's, and which calculation represents Izzy's? Well, hopefully you've spotted Aisha got an answer of -5 is found through this calculation.

Andeep who got an answer of -3 is this calculation, and the math error is found with Izzy's, which is this calculation.

Well done if you got this one right.

So just remember, your calculator may give you an answer in a different format than you might want.

Let's work out the answer to 80 subtract the square to 2.

25 + -4, all squared.

But I want the answer as a decimal.

See if you can work it out and look at the answer that's on your screen.

Well, hopefully when you've inputted it into your calculator, the calculation will pretty much look the same on your calculator screen.

Now once you press OK or execute, you'll actually get your answer as a fraction.

But the question stated we wanted our answer as a decimal.

So what do we have to do to change the fractional answer into decimal form? Well, we simply press format.

And when you press format, it'll give you some options of how to represent your answer.

We need to scroll down, select decimal, and then press execute.

Here, it changes the answer into a decimal.

So that format button allows you to change the format of your answer.

The great thing is, once an answer is obtained from a calculation, you can select it in any format available.

So now let's move on to your task.

Question one wants you to work out the following on your scientific calculator, but give your answer in decimal form.

So remember to use that format button.

See if you can give it a go and press pause if you need.

Great work.

Well done.

So let's move on to question two.

Question two wants you to work out the following with your scientific calculator, but giving your answer in fractional form.

See if you can give it a go and press pause if you need.

Well done.

So let's move on to question three.

Question three wants you to insert any number to make the answer 6.

5.

But you might notice you have to use certain operations here.

Something cubed, subtract the negative of what squared, add something over something, subtract something, and I want the answer to be 6.

5.

Same here, something cubed, subtract the square root of something, subtract something.

And lastly, something squared, add the square root of something, subtract something.

See if you can give it a go.

This is a hard question, so certainly press pause if you need more time.

Really well done.

So let's move on to these answers.

For question 1A, we should have got 719.

4.

For B, 454.

5, and for C, 1.

175.

Remember to scroll to the right to leave that function whether it's a square root or an exponent or a fraction.

Well done if you got those right.

For question two, we had to write our answer in fractional form.

So for A, 1,532/25, for B, 6,427/64 and for C, 511/20.

Great work if you got that one right.

Now for question three, there's an infinite number of calculations.

This was a hard one.

I'm just going to give you some examples of some numbers I've used.

Very well done if you've got any number working out to be 6.

5.

Well done, everybody.

So let's move on to the second part of our lesson, which is brackets and operations.

Now sometimes we use brackets to see the grouping of numbers together, and this can be used with a fraction button to show division.

For example, if we're asked to work out this calculation with your calculator, (5 X 8 + 8 squared) divided by (2 + 3 X 2).

What answer do you get if you input this into your calculator? Well, hopefully you've got 13.

Now what I'm going to do, is say I want you to press the fraction button, and I want you to insert the calculation for the top of the fraction and then use those scrolling keys to input the bottom of the calculation so it looks exactly the same as what I'm displaying on the screen.

What answer did you get? See if you can give it a go and press pause if you need more time.

Well, hopefully you've got an answer of 13.

So this is quite interesting.

So what I want to do is just really remind you that division can be inputted using the divide or the fraction button.

But I also want you to have a think.

Do you think the answers would be different if we use brackets? Well, given the fact that they're both 13, sometimes we don't need to show this grouping with the brackets if the grouping is shown through the operation.

So you can see the grouping does not need to be expressed here with brackets because of the extended division line.

But what about these calculations? What do you think? Do you think we need brackets here? You have 10 to the power of 2 X 3 + 4, and 10 to the power of (2 X 3 + 4).

Do you think we need brackets? The grouping does not need to be expressed with brackets, because they are all grouped by the exponent function.

So we don't need to use our brackets here.

And this is an important thing for you to see in a calculation as well as to input into your calculator.

So let's do a quick check.

I want you to identify if these calculations are equal without a calculator.

You need to identify if they're equal and if the grouping is the same with or without brackets.

So see if you can give it a go and press pause if you need.

This was a tough one, so let's have a look.

Well, 20 subtract the root of 13 + 14.

One has one pair of brackets and the other one doesn't.

Are they the same? Well, yes they are.

Because we have the extended line which indicates the grouping of 13 and 14, so we didn't have to put in those brackets.

What about the second one? 293 - 282 in brackets, divided by the 39 X 4 - 1.

Is that the same as 293 - 282 on the top of our fraction over 39, multiply by 4 - 1? Yes, it is.

We didn't need those brackets, because the fractional line indicates the grouping.

What about the third one? Is -3 to the power of 4 + 9 X 4, is that the same as (-3) to the power of 4 + 9 X 4? No, it's not.

And that's important for you to remember that the negative should always be put in brackets.

How about the last one? Here we have 80 + 4 X 10, subtract root 30, all divided by 90 - 8 squared.

Is that the same as 80 + 4 X 10 - root 30 on the top of our fraction over 90 - 8 squared? No, it's not, because on the left hand side, we only have our 80 and that's not the same as 80 over that 90 - 8 squared.

Now let's have a look at your task.

Here, you need to work with the following with your scientific calculator, giving your answer in decimal form.

See if you can give it a go and press pause if you need.

Great work.

So let's move on to question two.

Question two wants you to insert any number as long as you get an answer of 4.

5.

See if you can give it a go.

Press pause if you need more time.

Great work.

So let's go through our answers.

For question one, giving our answer in decimal form for A, we should have got 46.

51.

For B, you should have got 0.

4.

And for C, you should have got 22.

15.

These were great questions and notice how I've used the fraction button for part C to show that division.

You didn't have to, but it was just another option for you.

Well done if you got that one right.

Now there are an infinite number of calculations.

I've just put down a few here just for you to refer to.

A huge well done today.

So in summary, just remember those cursor keys will help you navigate around the different functions, applications, and calculations on a calculator screen.

Division can be inputted by the fraction button or with the division button.

Brackets do help isolate those negative numbers and improve accuracy.

And sometimes brackets are optional if the operation groups the calculation.

A huge well done.

It was great learning with you today.