A.
The teacher is easy-going, and she often __participates_____ in the pupils'games.
翻译：老师非常容易相处,她经常参与到学生的游戏中.
participates表参与,此句时态应为一般现在时,故participate变为participates.
选D绝对错误,因为有often,所以不应用过去时took,而应用take,而选项没有,故应选A.