Difference between revisions of "AlgebraicFractions"

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m (New page: <h2>Algebraic Fractions for Student Answers</h2> <!-- Header for these sections -- no modification needed --> <p style="background-color:#eeeeee;border:black solid 1px;padding:3px;"> ...)
 
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<em>This code shows how to format questions in which the answer is an algebraic fraction that has separate answer blanks for the numerator and denominator.</em>
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<em>This code shows how to format questions in which the answer is an algebraic fraction that has separate answer blanks for the numerator and denominator. This is useful for fractional answers that you want students to simplify as much as possible.</em>
 
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<b>Initialization:</b>
  
<b>Initialization:</b>
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To do ..(what you are doing)........., we don't have to change the
 
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We include the macros file <code>PGunion.pl</code> to be able to display the answer boxes on top of each other (as a fraction).
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tagging and documentation section of the problem file.
 
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In the initialization section, we need to include the macros file <code>-------.pl</code>.
  
 
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Context("Numeric");
  
Context("Numeric");
   
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$a = random(3,7,1);
  
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$b = random(3,7,1);
  
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while ($a == $b) { $b = random(3,7,1); }
  
   
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$apb = $a + $b;
  
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$frac = "\frac{d}{dx} \left( \frac{-(x^2+4)}{(x^2-4)^2} \right)";
   
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$frac = "\frac{$a}{x} + \frac{$b}{x-1}";
  
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$num = Formula("2 * x * (x**2 + 12)")->reduce;
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$den = Formula("(x**2 - 4)**3")->reduce;
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$num = Formula("$apb * x - $a")->reduce;
  
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$den = Formula("x*(x-1)")->reduce;
  
   
 
#
 
#
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<p>
  
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<b>Setup:</b>
 
<b>Setup:</b>
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We specify that the Context should be <code>......</code>, and define the answer to be a formula.
 
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We define a string <code>$frac</code> that will be displayed in TeX mode. We define MathObjects formulas <code>$num</code> and <code>$den</code> that are the correct numerator and denominator for the answer.
 
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Notes: on using this and related Contexts.
  
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We define a mode-dependent string <code>$displayfrac</code> that will be the nicely formatted fraction and answer blanks. To display the fraction nicely in TeX mode, we use displaystyle math <code>\[ ... \]</code> and append two concatenated answer blanks to the string <code>$frac</code>. In other modes (such as html), we use a <code>ColumnTable</code> from <code>PGunion.pl</code> macros to display the answer blanks as a fraction.
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<p>
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For fractions over fractions, to keep the font size large use the display fraction <code>\dfrac{}{}</code> option in TeX. For example, <code>\( \dfrac{ \dfrac{a}{b} }{ \dfrac{c}{d} } \)</code>.
 
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BEGIN_TEXT
  
BEGIN_TEXT
   
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Write the expression as a single fraction. Simplify your answer.
  
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Calculate the indicated derivative.
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Simplify your answer as much as possible.
 
$BR
  
$BR
 
$BR
  
$BR
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<p>
  
<p>
 
<b>Main Text:</b>
  
<b>Main Text:</b>
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The problem text section of the file is as we'd expect.
  
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Everything is as usual. Insert the fraction and answer blanks using <code>$displayfrac</code>.
 
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<p>
  
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<b>Answer Evaluation:</b>
  
<b>Answer Evaluation:</b>
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As is the answer.
  
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If you want to give students feedback on whether their numerator and denominator are correct, set <code>$showPartialCorrectAnswers = 1;</code>, otherwise set it to 0 to withhold feedback. If you want to withhold credit until both answer blanks are correct, use the standard problem grader, otherwise omit it to use the default (average problem grader).
 
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Revision as of 12:08, 11 January 2010

Algebraic Fractions for Student Answers


This code shows how to format questions in which the answer is an algebraic fraction that has separate answer blanks for the numerator and denominator. This is useful for fractional answers that you want students to simplify as much as possible.

Problem Techniques Index

PG problem file Explanation 
DOCUMENT();

loadMacros(
"PGstandard.pl",
"PGunion.pl",
"MathObjects.pl",
"PGcourse.pl",
);

TEXT(beginproblem());

Initialization: We include the macros file PGunion.pl to be able to display the answer boxes on top of each other (as a fraction). 

Context("Numeric");


$frac = "\frac{d}{dx} \left( \frac{-(x^2+4)}{(x^2-4)^2} \right)";

$num = Formula("2 * x * (x**2 + 12)")->reduce;
$den = Formula("(x**2 - 4)**3")->reduce;

# 
#  Display the fraction and answer blanks nicely
#
if ($displayMode eq 'TeX') {
  $displayfrac =
  "\[ $frac = ".ans_rule(10).ans_rule(10)." \]";
} else {
  $displayfrac =
  ColumnTable(
  "\( \displaystyle $frac = \)",
  ans_rule(20).$BR.$HR.ans_rule(20),
  indent => 0, separation => 10, valign => "MIDDLE"
  );
}

Setup: We define a string $frac that will be displayed in TeX mode. We define MathObjects formulas $num and $den that are the correct numerator and denominator for the answer.

We define a mode-dependent string $displayfrac that will be the nicely formatted fraction and answer blanks. To display the fraction nicely in TeX mode, we use displaystyle math \[ ... \] and append two concatenated answer blanks to the string $frac. In other modes (such as html), we use a ColumnTable from PGunion.pl macros to display the answer blanks as a fraction.

For fractions over fractions, to keep the font size large use the display fraction \dfrac{}{} option in TeX. For example, \( \dfrac{ \dfrac{a}{b} }{ \dfrac{c}{d} } \). 

Context()->texStrings;
BEGIN_TEXT

Calculate the indicated derivative.
Simplify your answer as much as possible.
$BR
$BR
$BCENTER
$displayfrac
$ECENTER

END_TEXT
Context()->normalStrings;

Main Text: Everything is as usual. Insert the fraction and answer blanks using $displayfrac. 

$showPartialCorrectAnswers = 1;

install_problem_grader(~~&std_problem_grader);

ANS($num->cmp);
ANS($den->cmp);

ENDDOCUMENT();

Answer Evaluation: If you want to give students feedback on whether their numerator and denominator are correct, set $showPartialCorrectAnswers = 1;, otherwise set it to 0 to withhold feedback. If you want to withhold credit until both answer blanks are correct, use the standard problem grader, otherwise omit it to use the default (average problem grader).

Problem Techniques Index

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