Mathematics
What the test rewards
Elementary math questions probe your grasp of number sense, operations, fractions, geometry, measurement, and the progression of algebraic thinking. You must also know how children build understanding-concrete to representational to abstract-and be able to diagnose common errors.
Concepts to master
- Place value as the foundation of algorithms; regrouping (borrowing/carrying) is a place-value idea, not a trick.
- Operations and properties: commutative, associative, distributive, identity, and inverse properties.
- Fractions: equivalent fractions, comparing with common denominators or benchmarks, and the meaning of the numerator (parts) and denominator (size of parts).
- Geometry and measurement: perimeter vs. area, unit conversion, and properties of shapes.
- Data and algebraic reasoning: patterns, variables, and interpreting graphs.
Traps
Distractor answers often reflect a predictable misconception-adding numerators and denominators, treating area and perimeter interchangeably, or misapplying a property. Questions may ask which manipulative or model best supports a concept; area models suit multiplication and fractions, number lines suit magnitude and rounding.
Worked example
Compare 3/4 and 5/8. Find a common denominator (8): 3/4 = 6/8, and 6/8 > 5/8, so 3/4 is larger. Alternatively, use the benchmark 1/2: both exceed it, but 3/4 is closer to 1. Rule of thumb: when comparing fractions, either make the denominators the same or compare each to a familiar benchmark.
Rule of thumb
If a student's wrong answer is consistent, identify the underlying misconception before choosing a remediation strategy.