Mathematics
The Mathematics subarea emphasizes number and operations, fractions, geometry, measurement, data, and early algebraic reasoning. You need conceptual explanations, not just procedures, because answer choices often contrast a correct model with a memorized shortcut.
Core rules
- Place value underlies the standard algorithms; the area model shows why partial products work.
- Fractions are numbers on a number line; equivalence means the same value with different partitions. Multiply by a fraction equal to 1 to find equivalent fractions.
- To divide by a fraction, ask how many groups of the divisor fit in the dividend; multiplying by the reciprocal is the shortcut.
- Perimeter is a linear measure; area is in square units. Classify shapes by properties, not by appearance.
Worked example
Compute 3/4 ÷ 1/2. Reasoning: the question is "how many one-halves are in three-fourths?" One-half equals two-fourths, so three-fourths contains one full half plus one-fourth left over, which is half of a half. The quotient is 1 1/2. The algorithm agrees: 3/4 × 2/1 = 6/4 = 1 1/2. Notice that the answer is larger than 3/4 because dividing by a number less than 1 gives a larger quotient.
Traps that cost marks
- Adding denominators in fraction addition.
- Flipping the dividend instead of the divisor when dividing fractions.
- Confusing area and perimeter units.
- Applying operations left to right while ignoring grouping symbols.