Mathematics
What to know
Candidates need number sense and operations, fractions and decimals, ratios and proportional reasoning, algebraic thinking, geometry, measurement, data and statistics, and probability. Understand place value, the meaning of operations, and multiple representations (concrete, pictorial, symbolic). Know properties (commutative, associative, distributive), order of operations, and the relationship among fractions, decimals, and percents. Geometry covers shapes, angles, area, perimeter, and volume; data covers mean, median, mode, and graphs.
Traps to watch
- Adding denominators when adding fractions (must find a common denominator).
- Confusing area (square units) with perimeter (linear units).
- Reversing mean and median, or forgetting the median requires ordered data.
- Misapplying order of operations, especially with parentheses and exponents.
- Confusing ratio (part-to-part) with proportion (equal ratios).
Rule of thumb
Estimate first to catch unreasonable answers, and label units-most errors in word problems come from the wrong operation or unit, not arithmetic.
Worked example
Add 1/3 + 1/4. Find a common denominator (12): 4/12 + 3/12 = 7/12. Estimating first (about 0.33 + 0.25 ≈ 0.58) confirms 7/12 ≈ 0.58 is reasonable, so the answer is not 2/7.