Algebraic Thinking (AT) and Computational Thinking (CT) are pivotal competencies in modern education, fostering problem-solving skills and logical reasoning among students. This study presents the initial hypotheses, theoretical framework, and key steps undertaken to explore characterized learning paths and assign practice-relevant tasks. This article investigates the relationship between AT and CT, their parallel development, and the creation of integrated learning paths. Analyses of mathematics and computer science/informatics curricula across six countries (Finland, Hungary, Lithuania, Spain, Sweden, and Türkiye) informed the development of tasks aligned with consolidated national curricula. Curricula were analysed using statistical methods, and content analysis to identify thematic patterns. To validate the effectiveness of the developed tasks for AT and CT, an assessment involving 208 students in K-12 across various grade levels (students aged 9-14) was conducted, with results analysed both statistically and qualitatively. Subsequently, a second quantitative study was carried out among teachers participating in a workshop, providing further insights into the practical applicability of the tasks. The research process was iterative, encompassing cycles of analysis, synthesis, and testing. The study also paid special attention to unplugged activities -- tasks that help students learn CT without using computers or digital tools. A local workshop in Hungary, where 26 tasks were tested with students from different grade levels, showed that developing CT and AT effectively requires more time and practice, especially in key topics. The findings underscore the importance of integrating AT and CT through thoughtfully designed learning paths and tasks, including unplugged activities, to enhance students' proficiency in these areas. This study contributes to the development of innovative educational programs that address the evolving digital competencies required in contemporary education.