Mathematics
Mathematics tests number sense, operations, algebraic thinking, geometry, measurement, and data in PreK–2. Items ask you to interpret a child’s strategy, select a developmentally appropriate task, or correct a misconception.
Core rules
- Counting principles: one-to-one correspondence, stable order, cardinality (last number = total), abstraction, order irrelevance. Rote counting without cardinality is not full number sense.
- Subitizing (instantly seeing small quantities) supports addition and place value.
- Place value: bundle ten ones into one ten; use base-ten blocks, ten-frames, and number lines.
- Operations: join/separate, part-part-whole; fact fluency grows from strategies (make ten, doubles, counting on) to recall.
- Algebraic thinking: patterns, sorting, comparing, unknown addend (5 + ? = 8).
- Geometry: recognize and describe 2-D and 3-D shapes by attributes; orientation and size do not change shape identity.
- Measurement: compare attributes (length, weight, capacity) with nonstandard units; no gaps or overlaps.
- Data: sort, tally, picture graphs; ask and answer questions.
Worked example
A child counts ten counters, then when asked how many recounts. Reasoning: the child can produce the counting sequence but has not consolidated cardinality. The teacher should play hiding games, model touch-counting, and state the final number as the total with small sets-not drill to 100.
Traps
- Equating fast recitation with number understanding.
- Teaching column addition before concrete place-value work.
- Calling a rotated square not a square.
- Using nonstandard units without consistent spacing, then treating the result as precise.