Central in the frameworks that describe algebra from K-12 is the idea that algebraic thinking is not a single construct, but consists of several algebraic thinking strands. Validation studies exploring this idea are relatively scarce. This study used structural equation modeling techniques to analyze data of middle school students' performance on tasks that correspond to four algebraic thinking strands: (i) Generalized Arithmetic, (ii) Functional Thinking, (iii) Modeling Languages, and (iv) Algebraic Proof. The study also examined the role that cognitive abilities play in students' algebraic thinking. Results emerging from confirmatory factor analysis showed that the proposed model adequately explains students' algebraic thinking. Additionally, results emerging form latent path analysis showed that students are first able to solve Functional Thinking tasks and only when this is achieved, they proceed to solve Generalized Arithmetic tasks, then Modeling Languages tasks, and finally Algebraic Proof tasks. Lastly, the quantitative analyses indicated that students' cognitive abilities (analogical, serial, and spatial reasoning) predict students' algebraic thinking abilities.