** Using WeBWorK **

The problem here is that when the student doesn't enter units, the NumberWithUnits answer checker already creates the message "Your answer doesn't look like number with units", and so the line

      return $ans if $ans->{ans_message};

causes the rest of the post-filter to be skipped. So you never do the check for partial credit. The first step is to change that line to

      return $ans if $ans->{ans_message} && $ans->{ans_message} ne 
            "Your answer doesn't look like a number with units";

so that you will continue in the case where the student entered only a number (and lots of other cases as well, but we'll deal with that later).

Unfortunately, when this error occurs, the $ans->{student_value} will be undefined, since no MathObject gets created when the answer isn't of the correct form. So you will have to create it yourself. Here is on way:

    $cmp = $A->cmp->withPostFilter(sub {
      my $ans = shift;
      return $ans if $ans->{ans_message} && $ans->{ans_message} ne "Your answer doesn't look like a number with units";
      my $correct = $ans->{correct_value};
      my $student = $ans->{student_value};
      if (!defined($student)) {
        my $num = "^ *".Context()->{pattern}{signedNumber}." *~~$";
        $student = Compute($ans->{student_ans}) if $ans->{student_ans} =~ m/$num/;
      }
      return $ans unless defined($correct) && defined($student);
      if ($student->{units} ne $correct->{units}) {
        if ($correct->{value} == $student->value) {
          $ans->{score} = .75;
          $ans->{ans_message} = "Has the correct number but incorrect units.";
        } else {
          $ans->{score} = 0;
        }
      }
      return $ans;
    });

Here, we check for whether the student value isn't defined, and if not, check if it looks like a signed number (the $num variable is set to a pattern that checks for a number, and then if the student answer matches that pattern, we parse it into a MathObject using Compute().

The rest of the filter is the same, and will handle the case of a student answer with no units.