Gakko tosho’s textbooks [2005,2011]. In Figure 9 (p. 11, Grade 4,2005 edition), Task 5 is about the area os the L shape(gnomon). The child may have a question: “I can use the formula if….” This is the problematic, the objective of this class. Next (p. 12), various solutions are shown, All answers are appropriate for Task 5. Then, the teacher can summarize by saying that the area does not change by moving, adding, and subtracting. For the next step in application, the children face the challenge of solving Task 6. Then, they recognize that there are applicable ideas and non-applicable ideas. Takeshi’s idea does not work. The children appreciate what they have learned at Task 5 and learn the applicability of ideas. Testing the applicability to other cases is the viability of mathematical ideas, which was enhanced by von glasersfeld (1995). The Japanese textbook employs the sequence of extension based on what the children have learned before and teaches the children how to extend mathematical ideas using the sequence for extension