This Research to Practice Full Paper presents the development of the algorithmic expressions for the assessment tools for assessing algorithmic thinking ability of elementary school children. In Japan, elementary school children will be required to learn computer programming as an interdisciplinary element appearing throughout the curriculum in 2020. The purpose of this programming education is to nurture Computational Thinking (CT) for elementary school children in Japan. However, almost no discussion has been conducted in Japan on how to measure the level of CT an elementary school child has acquired. Since the definition of CT is not very firm, it is not easy to measure the levels of CT. Therefore, several organizations have issued operational definitions of CT. Among the concepts of CT in those operational definitions, Algorithmic Thinking was chosen as a representative of CT, and the assessment tools for evaluating Algorithmic Thinking ability have been developed in this research. The assessment tool was conducted in the experimental Computer Science Unplugged classes and in the control classes in two elementary schools in Japan. There were in total 152 children in the classes, and all of them were 5th grade children. By answering the questions in the assessment tool, each child got a score between 0 and 15. The scores were statistically analyzed.