Mathematics, Science, and Social Studies (PreK–4)
Mathematics
Counting rests on principles: one-to-one correspondence, stable order, cardinality, order irrelevance, and abstraction. Cardinality is the understanding that the last number named tells how many there are. Place value and base-ten composition underpin regrouping, and fraction understanding begins with equal partitioning of a whole or a set. Geometry (shape attributes, composing and decomposing shapes), measurement (iterating units, comparing lengths), and data (sorting, tallying, graphing) appear through classroom vignettes. Problem-solving items reward child-generated strategies such as counting on, making ten, or decomposing numbers over answer-getting alone, and manipulatives should support reasoning rather than replace it.
Science and Social Studies
Science items test process and inquiry skills (observing, predicting, classifying, measuring, communicating) alongside content, and the 5E sequence runs Engage, Explore, Explain, Elaborate, Evaluate. Distinguish a misconception, such as assuming heavier objects always fall faster, from a simple gap in knowledge; strong instruction elicits and confronts the misconception. Social studies includes civics (rules, roles, responsibilities), geography (maps, globes, relative location, scale), economics (needs versus wants, goods versus services), history (timelines, primary versus secondary sources), and culture.
Trap: area versus perimeter questions often hide behind "cover" or "border" language, and "more than" comparisons can be reversed in wording. In science, a teacher who explains the concept before students explore has inverted the 5E sequence.
Rule of thumb: ask whether the task measures the space inside (area) or the distance around (perimeter); if the unit is a square tile, it is area.