Difference between revisions of "AlgebraicFractions"

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−
$frac = "\frac{d}{dx} \left( \frac{-(x^2+4)}{(x^2-4)^2} \right)";
 +
$fraction = "\frac{d}{dx} \left( \frac{-(x^2+4)}{(x^2-4)^2} \right)";
   
 
$num = Formula("2 * x * (x**2 + 12)")->reduce;
  
$num = Formula("2 * x * (x**2 + 12)")->reduce;
Line 60: Line 60:
 
#
  
#
 
if ($displayMode eq 'TeX') {
  
if ($displayMode eq 'TeX') {
−
$displayfrac =
 +
$showfraction =
−
"\[ $frac = ".ans_rule(10).ans_rule(10)." \]";
 +
"\[ $fraction = ".ans_rule(10).ans_rule(10)." \]";
 
} else {
  
} else {
−
$displayfrac =
 +
$showfraction =
 
ColumnTable(
  
ColumnTable(
−
"\( \displaystyle $frac = \)",
 +
"\( \displaystyle $fraction = \)",
 
ans_rule(20).$BR.$HR.ans_rule(20),
  
ans_rule(20).$BR.$HR.ans_rule(20),
 
indent => 0, separation => 10, valign => "MIDDLE"
  
indent => 0, separation => 10, valign => "MIDDLE"
Line 76: Line 76:
 
<p>
  
<p>
 
<b>Setup:</b>
 
<b>Setup:</b>
−
We define a string <code>$frac</code> that will be displayed in TeX mode. We define MathObjects formulas <code>$num</code> and <code>$den</code> that are the correct numerator and denominator for the answer.
+
We define a string <code>$fraction</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.
 
</p>
  
</p>
 
<p>
  
<p>
−
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>$frac</code>. In other modes (such as html), we use a <code>ColumnTable</code> from <code>PGunion.pl</code> macros to display the answer blanks as a fraction.
+
We define a mode-dependent string <code>$showfraction</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>$fraction</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.
 
</p>
  
</p>
 
<p>
  
<p>
  +
To get fractions that have a large font size, be sure to use the LaTeX command <code>\( \displaystyle \frac{a}{b} \)</code>.
 
For fractions over fractions, to keep the font size large use the LaTeX commands
  
For fractions over fractions, to keep the font size large use the LaTeX commands
 
<pre>
  
<pre>
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$BR
  
$BR
 
$BCENTER
  
$BCENTER
−
$displayfrac
  
  +
$showfraction
 
$ECENTER
  
$ECENTER
   

Revision as of 22:12, 11 January 2010

Algebraic Fractions in 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 that are stacked on top of each other like a fraction. Stacking the answer blanks is nice formatting that simplifies how to ask students for the parts of a fraction separately. In addition, having two separate answer blanks is useful for requiring students to simplify their answer 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");


$fraction = "\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') {
  $showfraction =
  "\[ $fraction = ".ans_rule(10).ans_rule(10)." \]";
} else {
  $showfraction =
  ColumnTable(
  "\( \displaystyle $fraction = \)",
  ans_rule(20).$BR.$HR.ans_rule(20),
  indent => 0, separation => 10, valign => "MIDDLE"
  );
}

Setup: We define a string $fraction 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 $showfraction 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 $fraction. In other modes (such as html), we use a ColumnTable from PGunion.pl macros to display the answer blanks as a fraction.

To get fractions that have a large font size, be sure to use the LaTeX command \( \displaystyle \frac{a}{b} \). For fractions over fractions, to keep the font size large use the LaTeX commands 

\( 
\displaystyle\frac{ 
  \displaystyle\frac{a}{b} 
  }{ 
  \displaystyle\frac{c}{d} 
} 
\)


Context()->texStrings;
BEGIN_TEXT

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