The teaching sequence focuses on helping children learn the "oi" sound through various activities. It starts by showing pictures of words containing the "oi" sound and singing a nursery rhyme. Children are taught to cup their hands around their mouth when saying words with "oi" to help identify the sound. Later activities involve identifying words with and without "oi", segmenting and blending words, and filling in missing letters to practice writing the sound. The overall goal is for children to distinguish and become familiar with the "oi" sound through listening, speaking, and writing activities.