#! perl -slw
use strict;

sub nWordsMatch {
    my( $str1, $str2 ) = @_;
    my $p = 0; 
    $p++ while substr( $str1, $p, 1 ) eq substr( $str2, $p, 1 );
    my @words = substr( $str1, 0, $p-1 ) =~ m[\b(\w+)\b\W+]g;
    return @words;
}

my @matchWords = nWordsMatch( 
    'This is a sentence', 
    'This is another sentence.' 
);
print "@matchWords";

my $count = @matchWords;
print $count;

@matchWords = nWordsMatch( 
    'The quick brown fox jumps over the lazy dog', 
    'The quick brown fox jumps over teh lazy dog', 
);
print "@matchWords";
print scalar @matchWords;


__END__
c:\Perl\test>test2
This is
2
The quick brown fox jumps over
6
[download]

my @sentences = (
    'This is a sentence',
    'This is another sentence',
);
my $matches = grep /\bthis is\b/i , @sentences;
[download]

• The number of words that are the same in each sentence
• How many words are the same starting at the beginning of each sentence
• How many sentences does the phrase "This is" appear in (my first solution)
• Something else entirely

print Start_In_Common( 'This is a sentence', 'This is another sentence
+' );
sub Start_In_Common {
    my ($first, $second) = @_;
    ($first, $second) = ($second, $first) if length $first > length $s
+econd;
    my @word = ( [split /\s+/, $first ], [split /\s+/, $second ] );
    my @fragment;
    for ( 0 .. $#{ $word[0] } ) {
        if ( $word[0][$_] eq $word[1][$_] ) {
            push @fragment, $word[1][$_];
        }
        else {
            return join ' ', @fragment, scalar @fragment;
        }
    }
}
[download]

use strict;

my $a = "This is a sentence";
my $b = "This is another sentecne";

my @matches = match_words($a,$b);
print join(" ",@matches),"\n";
print scalar(@matches);


sub match_words{
     my @word_list1 = split(/\s+/,$_[0]);
     my @word_list2 = split(/\s+/,$_[1]);

     my $i = 0;
     while(defined($word_list1[$i]) && defined ($word_list2[$i])
           && $word_list1[$i] eq $word_list2[$i]){
        ++$i;
     }
     return splice @word_list1, 0, $i;
}

__END__
This is
2
[download]

    my @result = splice @word_list1,0,$i;
    return @result;
[download]

Algorithm::HowSimilar or Algorithm::LCSS may be what you are after.