Mathematics (222)
What is tested
Mathematics items on 222 blend content and pedagogy. Content: place value and base-ten structure, the four operations and their properties, fractions as numbers on a number line, equivalence, decimals, ratio and proportional reasoning, early algebra (patterns, expressions, equations), geometry (attributes, area versus perimeter), measurement units, and data representation. Pedagogy: the concrete–representational–abstract sequence, selecting manipulatives and models, and diagnosing student thinking from work samples.
Traps
Questions rarely ask you to compute; they ask what a child's error reveals or which model fits a concept. Watch for these: treating 3/5 as larger than 2/3 because 3 > 2 (whole-number thinking); calling the longer shape larger in area when only perimeter grew; adding numerators and denominators straight across; assuming a taller stack of blocks holds more when it is narrower; and confusing the mean with the median. Also separate content from method - a correct answer reached by flawed reasoning still signals a misconception.
Worked example
Compare 3/5 and 2/3. A student who says 3/5 is bigger is comparing parts of different-sized wholes. Anchor both to one-half: 3/5 = 0.6 and 2/3 ≈ 0.67, so 2/3 is larger; or rewrite over fifteenths: 9/15 versus 10/15. Rule of thumb: when a fraction comparison fails, move to a number line or a common whole before reteaching the algorithm.