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 reappreciate what they have learned at 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.
Like the sample in Figure 9, generally, Gakko Tosho's textbooks [2006 , 2011] have the following features: