Very good introduction of Modern Math concept “Group” to secondary school math students by an American high school teacher.

https://www.quantamagazine.org/symmetry-algebra-and-the-monster-20170817/

Summary:

• Symmetry of a Square
• Isometry (*) or Rigid Motion (刚体运动) = no change in shape and size after a transformation
• What is a Group (群 “CAN I” ) ? = Closure Associative Neutral Inverse
• Monster Group = God ?
• String Theory: Higgs boson (玻色子) aka “God Particles”

Note (*): “保距映射” (Isometry），是指在度量空间 (metric space) 之中保持距离不变的”同构“关系 (Isomorphism) 。几何学中的对应概念是 “全等变换”。