Mathematics
What the test asks
Math items test number sense, operations, fractions and decimals, proportional reasoning, algebraic thinking, geometry, measurement, data/probability, and-critically-the pedagogy of how children build these ideas. Expect questions on place value, the meaning of operations, and developmental progressions (concrete → representational → abstract).
Concepts to master
- Place value underpins regrouping, decimals, and algorithms.
- Fraction meaning: part-whole, measurement, division; equivalent fractions and common denominators.
- Operations: properties (commutative, associative, distributive) and inverse relationships.
- Proportional reasoning: unit rates, ratios, percent.
- Geometry/measurement: area vs. perimeter, volume, unit conversion.
- Data: mean, median, mode, range; reading graphs accurately.
Traps
Misreading the question's unit is common-area in square units, perimeter in linear units. Fraction items often hinge on whether the whole is the same size (comparing 1/2 of a small pizza to 1/3 of a large one). Order of operations and integer sign errors are frequent. Pedagogy traps: confusing a manipulative activity with an algorithmic one, or selecting a strategy that skips the conceptual stage.
Rule of thumb
For word problems, identify the unknown and the relationship before computing. For fractions, find a common denominator or benchmark (0, 1/2, 1) to compare.
Worked example: Compare 3/5 and 5/8. Cross-multiply: 3×8=24, 5×5=25, so 5/8 > 3/5. Benchmark check: both near 0.6, consistent.