Mathematics
What to know
Mathematics for P-5 centers on number sense and operations, algebraic thinking, geometry, measurement and data, and fractions. Understand the base-ten system and place value, the meaning of the four operations, and the relationship between them (inverse operations, fact families). Know the progression of strategies: concrete (manipulatives) → representational (drawings, number lines) → abstract (symbols). For fractions, know that a fraction is a number on a number line, that equivalent fractions come from multiplying by a form of one, and that operations require common denominators for addition and subtraction. In geometry, distinguish polygons, classify by attributes, and know area vs. perimeter. In measurement, know unit conversions within a system and the difference between customary and metric. In data, know mean, median, mode, and range and when each is useful. Understand the Standards for Mathematical Practice-reasoning, modeling, precision, and using structure.
Traps
Questions bait confusion between area and perimeter, or between mean and median when outliers are present. Another common trap: applying a procedure without the conceptual reason (e.g., "keep-change-flip" for division without understanding). Watch for place-value errors in regrouping and for problems where the operation is embedded in language ("how many more" signals subtraction). Distractors often show a right answer computed with a wrong operation.
Worked example
A student adds 3/4 + 2/3 and writes 5/7. The error is adding numerators and denominators. Correct reasoning: find a common denominator (12), convert to 9/12 + 8/12 = 17/12 = 1 5/12. Rule of thumb: denominators must match before adding or subtracting fractions; multiply by a form of one to create equivalent fractions.