Circle, square, triangle — found in street signs, blocks, and around the room. Pure perception and vocabulary.
Shapes gain sides, angles, symmetry. Kids combine shapes to build things — tangrams, a square folding into a cube.
Geometry proper: area, perimeter, angle relationships, intro coordinate geometry. Shapes become measurable and provable.
Architecture and drafting: shapes as functional constraints — scale, load, blueprints, intro CAD. Geometry serves a real structural purpose.
Concrete, observable, sensory. Talk about it, read about it, see a photo mural, draw it, watch it happen live if a chrysalis is on hand. The wow is the whole point.
Frogs, plants, seasons. Kids start predicting ("what comes next?") and sequencing independently.
Personal identity change, historical "before/after" transformation, mitosis and puberty as biological change.
Social movements, phase transitions, paradigm shifts — analyzed as systems-level, multi-variable, causal change.
Concrete. Sensory. Observable. What can a 3-year-old touch, watch, or point to that IS this concept — no abstraction allowed?
The concept gains a property or a pattern. Kids start predicting, sorting, or combining — not just noticing.
It gets named. Abstraction begins — this is where vocabulary catches up to intuition.
Systems-level. Multi-variable. The concept becomes a lens for analyzing something real and complex.