As technology becomes increasingly prominent in modern mathematics education, there's a growing need to understand the essential knowledge mathematics teachers need to effectively integrate technology in algebra instructions. This study therefore enhances the current Knowledge of Algebra for Teaching (KAT) framework, which theorises teachers' knowledge for teaching algebra, by introducing technological knowledge as a requisite teacher knowledge for interactive teaching of algebra. Through the narrative review methodology, the study builds on the Expanded KAT framework to develop the Technological Knowledge of Algebra for Teaching (T-KAT) model as a structured framework that projects technological knowledge as crucial teacher knowledge for interactive and effective teaching of algebra using technology. The study showed that mathematics teachers need not just Algebra Teaching Knowledge (ATK) to pedagogically drive the teaching of algebra, as hypothesised in the Expanded KAT framework, instead, an Algebra Teaching Knowledge (ATK) redefined in the light of technology (Technological Algebra Teaching Knowledge - TATK) to meet the technological demands of 21st century mathematics education. The study further resulted in the identification of four distinct technological knowledge domains (TATK, TSATK, TAATK, and TPCKA) within the proposed T-KAT framework. These findings provide valuable insights for teacher professional development and further research.