Tag Archives: CASIO fx-83GT PLUS

Game – Prime Number Recognition

You will need:

2 dice and a pen and paper.

Take in turns to:

  • Throw the dice
  • From the dice, construct 2 or perhaps 3 numbers. For example, if you throw a two and a three, you can make 5, 23 and 32 (3+2=5, two followed by three is 23 and three followed by two is 32)
  • Score one point for each prime number you have made (so this example scores one for the 5 and one for the 23, scoring two points in total).
  • If you need to use a calculator, then a Casio fx-83GT PLUS can tell you whether a number is prime. This is *not* cheating – students will soon start to recognise the primes they need, rather than having to check using the calculator!

The Winner Is:

The person who has the most points.

Things to discuss:

  • Why are two even numbers always such bad news? (even+even=even and the only even prime number is two)
  • Is it possible to score three points with one throw?
  • If there is a six in your throw, what happens?

This sample space diagram may help:

Sample Space Diagram for 2 Dice

1

2

3

4

5

6

1

(1,1)

(2,1)

(3,1)

(4,1)

(5,1)

(6,1)

2

(1,2)

(2,2)

(3,2)

(4,2)

(5,2)

(6,2)

3

(1,3)

(2,3)

(3,3)

(4,3)

(5,3)

(6,3)

4

(1,4)

(2,4)

(3,4)

(4,4)

(5,4)

(6,4)

5

(1,5)

(2,5)

(3,5)

(4,5)

(5,5)

(6,5)

6

(1,6)

(2,6)

(3,6)

(4,6)

(5,6)

(6,6)

 

 

 

How to Factorise a Number (Or Check that is Prime) using a CASIO fx-83GT PLUS calculator

On the CASIO fx-83gt PLUS factorising is done like this:

  • Entering the number,
  • press equals,
  • SHIFT and ., ,,, (this has “FACT” written above it in yellow).
  • The Prime Factor Form is displayed as the answer.
  • If the number is Prime, then the number itself is displayed.

This is a natural way to introduce what indices mean, because the CASIO gives the answers in index form eg 34 rather than 3x3x3x3

Pythagoras and Dyscalculia

This approach:

  • Uses a calculator.
  • Uses just one single approach for all problems (long side or short)
  • Reduces the number of steps by rooting and adding in the same step.
  • Keeps to an absolute minimum, the need to compare sizes, because Dyscalculia makes this challenging.
  • Uses a mnemonic to recall the steps.

Method:

Normally in a problem involving Pythagoras, you are given 2 of the sides of a right angled triangle and asked to find the third. You need to Root the Add of the Squares (R.A.S, end of PythagoRAS). Always key in the larger number first….wpid-20150422_133239.jpg

This will give the answer 8.0622..

but Perhaps You Takeaway (PYThagoras) so mouse back to the plus (+) and change it to a take away (-)… and this gives  5.7445..

Now it’s decision time – using the picture, which answer looks most sensible, 8.0622 or 5.7445? The length of the 3rd side in this example is clearly longer than 7 so the correct answer is 8.0622.

 

The power of practice

multiply out and simplifyDear M,

You are making great progress with algebra, I think. The crucial link between the written symbols and what they actually MEAN is not easy to make, but you are putting the hours of practice that you need, in order to become confident. 

Here are some more questions. I know we discussed the idea that I could build an interactive game for you that would check each piece of your working, and your answers, but on reflection, I think you are getting sufficiently fluent with algebra now, that this level of feedback would actually be unhelpful, like bolting stabilizers back onto a bicycle after you have begun to balance it by yourself. 

You are already in the (excellent) habit of keying the question into your calculator, keying in the answer, and comparing the two, What I would like you to focus on this week, is actually writing down the “easy version” and, if the question and answer DON’T match, then key in these workings out as well to narrow down the problem.

The huge advantage of you and the calculator (rather than the computer) doing the checking, is that you are able to use your calculator throughout the IGCSE exam, so you are practicing really useful skills, not using a tool that will be taken away from you.

After working on the last worksheet with you, we both realised that the sums were too densely packed on the page, and a bit dazzly. I hope this version is easier. I have left gaps for you to write the “easy version” out directly below the sum.

As you work, it may be worth being aware of the commonest errors you were making in the lesson (which are errors most people make, you are not alone 🙂  )

  • If there was a minus sign in front of the first bracket, you were not always “seeing it” clearly when you keyed expressions into your calculator
  • If there was a minus in front of the bracket as well as one inside it, you sometimes made the wrong decision (although you had pretty much stopped doing that by the end of the lesson, errors have a nasty habit of creeping back in a few days later!)
  • You made more errors when you did everything mentally, and fewer when you jotted the “easy version” as a working step.

Jargon-wise, what we are doing is called “multiplying out brackets and simplifying”. That’s the terms the examiner would use (instead of “writing down the easy version and writing down the answer”.

So here are three more worksheets:

multiply out and simplify 1

multiply out and simplify 2

multiply out and simplify 3

 

 

Substitution into a formula (calculator method)

Using formulae to solve problems can be fraught with difficulties if some of the numbers are negative. If the calculator is given the values of the letters, then the formulae is keyed in using those letters, accurate results can be achieved every time. The work is also easier to check.

Click here to see a film of the calculator being used to solve this problem.

To set the letter A to the value 12 , B to -3.6 and C to 15

  • 2   Shift   RCL(Sto)   (-)A
  • 7  Shift   RCL(Sto)   ..”’ B
  • -12 Shift   RCL(Sto)   hyp C

Once that is done you can type entire algebra phrases into the calculator and find their values.  Here is an example of using the calculator to use a formula. You will see that the formula is written with capital letters to match the way the calculator sees the alphabet.

Quadratic Formula 001

How to use your calculator to understand Standard Form.

These instructions work on a CASIO fx-83GT PLUS, which is widely used in schools and will, if you learn to drive it with confidence, do a tremendous number of different sorts of Maths.

If you want the calculator to give all its answers in standard form, follow this sequence:

  1. shift mode 7
  2. it will offer you a choice of Sci 0~9 and this means how accurately it will display the answers. 3 is OK, but you might want to experiment with 4 and 5 as well, to see for yourself what difference it makes.
  3. Try it, type in 23×3000= and you will get 6.90×10^4   (sorry! the ^ means to the power!!! The calculator is designed to display Maths properly and computers aren’t)
  4. To make your calculator display your answers normally again, shift mode 8 1 will do the trick. mode 8 is “Norm”, normal mode.
Red ring round the standard form button
Red ring round the standard form button

To type in a number that is in standard form, for example 4.5 x 10^12, use the button with x10x on it (it’s in the middle of the bottom row of buttons, and I will use square brackets to mean button) so the keystrokes you need, are    4.5 [x10x]12