Mysql – Extract data for all groups in a single SELECT statement

What about doing a little math against your ID column to dynamically generate the group?

SELECT grp, FLOOR(id/10) AS id_grp
FROM animals
GROUP BY grp, id_grp

This would give you groups of 10 based on the ID of the record. I used your animals table above to generate the data below.

Sample data

 INSERT INTO animals VALUES
 ('mammal',10,'dog'),('mammal',11,'dog'),('mammal',12,'dog'),
 ('mammal',21,'cat'),('mammal',22,'cat'),('mammal',23,'cat'),
 ('mammal',24,'cat'),('mammal',25,'cat'),('mammal',26,'cat'),
 ('bird',30,'penguin'),('bird',31,'penguin'),('bird',32,'penguin'),
 ('bird',33,'penguin'),('fish',44,'lax'),('fish',45,'lax'),
 ('fish',46,'lax'),('fish',47,'lax'),('fish',48,'lax'),
 ('mammal',31,'whale'),*'fish',51,'lax'),('fish',52,'lax'),
 ('fish',53,'lax'),('fish',54,'lax'),('bird',10,'ostrich');

Query Output

 +--------+--------+
 | grp    | id_grp |
 +--------+--------+
 | fish   |      4 |
 | fish   |      5 |
 | mammal |      1 |
 | mammal |      2 |
 | mammal |      3 |
 | bird   |      1 |
 | bird   |      3 |
 +--------+--------+
 7 rows in set (0.00 sec)

Another way to get the result is this. It finds first all groups that the teacher has surely taught (or is going to) by checking that she has started within the month and then in another subquery it finds - for every group - the last teacher that started at the first day of the month or earlier.

With the unique index you have on the table, the second subquery should be quite efficient. The first subquery would benefit from an index on (teacherid, startdate, groupid):

SELECT groupid
FROM pupilgroupteacher
WHERE teacherid = @teacher 
  AND startdate >= @month + INTERVAL 1 DAY
  AND startdate < @month + INTERVAL 1 MONTH

UNION DISTINCT

SELECT gg.groupid
FROM 
    ( SELECT DISTINCT groupid
      FROM pupilgroupteacher
    ) AS gd
  JOIN pupilgroupteacher AS gg
    ON  gg.groupid = gd.groupid
    AND gg.startdate =
        ( SELECT MAX(gi.startdate)
          FROM pupilgroupteacher AS gi 
          WHERE gi.groupid = gd.groupid
            AND gi.startdate < @month + INTERVAL 1 DAY
        )
WHERE gg.teacherid = @teacher ;