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KenR

Posted: Sun Jun 03, 2007 7:25 pm 

Joined: Fri Mar 17, 2006 5:12 pm Posts: 1301 Location: Birmingham

Thought I would just mention this as an issue that my son is having with his year 7 calculator work.
He has been doing some trig SIN work with a calculator and has found a few examples where different calculators compute BIDMAS in different ways.
The example I have is from a work sheet with an expression:
87SIN90 div 2SIN87
Using a Casio fx85ES recommended by the school this gives an answer of 43.44 (to 2 places). (Where 90 and 87 after the SIN are angles)
Whereas using a Sharp EL531W (also with a recommend sticker for KS3/GCSE) gives an answer of 43.56 (to 2 places)
(Note: the casio automatically generates a bracket after the SIN button which you need to close after entering the angles. The Sharp just allows you to enter SIN87 etc.
It appears the casio is computing the expression as:
(87SIN(90) div 2) x SIN(87)
Whereas the SHARP is computing this as:
(87SIN(90)) div (2SIN(87)
Has anyone come across issues like this before?
Can the BIDMAS Mathematical experts tell me which one is computing the correct answer?
This totally threw my son particularly as the worksheet gave specific procedural instructions of what to press on the calculator and of course my son followed them to the letter and got the wrong answer!
PS I checked and he was in the correct degree mode.
Regards
Ken


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Guest55

Posted: Sun Jun 03, 2007 8:28 pm 

Joined: Mon Feb 12, 2007 1:21 pm Posts: 11952

Why is he using the sine rule like this!! sin 90 should never appear in a calculation ... can you explain the question in more detail before I comment?


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KenR

Posted: Mon Jun 04, 2007 6:58 am 

Joined: Fri Mar 17, 2006 5:12 pm Posts: 1301 Location: Birmingham

Hi Guest
This is a bonefide question in a IGSE worksheet that teaches them how to use a calculator in Trigonometry situations.
The specific situation I quote was a worked example that they were supposed to follow all about the Sine function.
I know that SIN90=1 but no doubt part of the reason was to demonstarte that fact.
Regards


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Guest

Posted: Mon Jun 04, 2007 4:46 pm 


Re: 87sin90 div 2sin87
How is the actual question written? This is the important part to notice. Is it written as a fraction, whereby 2sin87 is the denominator? If that is the case, then to check your answer calculate the numerator and the denominator separately before tackling the division.
To calculate the correct answer straight away, this is one method of typing the question into your calculator:
87sin90 div (2sin87) = 43.56 (2dp)
It is useful knowing how to use your calculator efficiently [have been doing this with one of my KS3 classes], and sometimes a question may not have brackets in it but to answer it correctly on your calculator, brackets have to be inserted.
Different makes and now different models of calculators require different input.
Hope this is helpful to you. Interestingly, using Casio 83MS, typing the sum is as it stands also gives 43.56.


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KenR

Posted: Mon Jun 04, 2007 5:44 pm 

Joined: Fri Mar 17, 2006 5:12 pm Posts: 1301 Location: Birmingham

Hi Guest
The question is actually written as a fraction (not a div sign) but the problem is that it is a worked example and they have an example box section entitled "how to use your calculator" with procedural instructions of what to enter and what key functions to press to get the correct answer.
I think the problem is that calculators do vary  the issue is that my son takes teacher or written instructions very literally and without variation.
I personally have always over bracketed
Thanks


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Guest55

Posted: Mon Jun 04, 2007 7:55 pm 

Joined: Mon Feb 12, 2007 1:21 pm Posts: 11952

This is NOT a realistic use of trig functions ....
If it is a fraction then the value of the numerator should be calculated then divided by the value of the denominator. This worksheet is flawed in a second respect as NO two brands of calculator work the same  this is why schools often don't lend out calculators as pupils need to learn to use their own.


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Guest

Posted: Mon Jun 04, 2007 9:05 pm 


Evening Ken R,
As you say, the example may well be written for a different model of calculator so as long as your son is confident knowing how to use his calculator to ascertain the correct answer, that is the most important thing.
I must admit, teaching 'using your calculator efficiently' requires a great deal of patience as I do not produce a worksheet as students don't all have the same make of calculator, so I go through the various options and then the students write down the key sequence that works for them [that way they have a few notes to refer to later on]. Modelling a few different examples also helps. Has your son discovered calculator words made answering sums using various function keys?
If a student understands the question and how the order of operations works within the question, then that helps with the calculator work.


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KenR

Posted: Tue Jun 05, 2007 1:41 pm 

Joined: Fri Mar 17, 2006 5:12 pm Posts: 1301 Location: Birmingham

Hi Guest and Guest55,
Thanks for this.
I agree it's not a typical trig example, however I still think that there is a flaw in the particular casio calculator model that we bought for my son.
In essence, the mathematical expression we are keying into the calculator is 87a/2b where a is SIN(90) and b is SIN(87).
Keying in an expression like this I would not expect a calculator to compute this as ((87 x a) / 2 ) x b which the Casio does!
I've now given my son the Sharp which works ok.
I guess there must be a moral somewhere in all of this!
Regards


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solimum not logged in

Posted: Tue Jun 05, 2007 2:31 pm 


I suspect the moral is "always use brackets to avoid ambiguity". I must confess I would always have assumed that a calculator would simply perform operations in the order entered, so that if you press div 2 it will instantly divide the previous total by 2 and not assume there is another expression to modify the 2 unless a bracket has been inserted. Certainly when writing formulae in Excel spreadsheets brackets are vital. Calculators have obviously developed minds of their own since my O Level days!


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SunlampVexesEel

Posted: Thu Jul 19, 2007 9:16 pm 

Joined: Fri Jul 06, 2007 8:31 pm Posts: 1192


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