Mathematics - Number Sense and Operations
What this domain asks you to do
Number Sense and Operations covers place value, the four operations with whole numbers, fractions, decimals, integers and rational numbers, factors and multiples, order of operations, ratios, proportions, percents, exponents, and scientific notation - along with estimation and reasonableness.
Concepts to master
- Place value and regrouping across whole numbers and decimals, including how multiplying or dividing by powers of ten shifts the decimal point.
- Fraction operations: common denominators for addition and subtraction; multiply straight across; divide by multiplying by the reciprocal.
- Integer rules: subtracting a negative adds; a negative times a negative is positive.
- Order of operations: grouping symbols, then exponents, then multiplication and division left to right, then addition and subtraction left to right.
- Ratios and percent: part-to-whole vs. part-to-part; percent of a number; percent increase and decrease.
Traps the test sets
Working left to right regardless of operations; flipping the sign incorrectly with integers; adding denominators in fraction addition; confusing percent of with percent increase; lining up decimal digits incorrectly; forgetting that the reciprocal is used only in division; misreading a ratio as a fraction of the wrong whole.
Rule of thumb and worked example
Estimate first, compute second, compare third. If your exact answer is far from the estimate, find the error before moving on.
Worked example: evaluate 3 + 4 × (5 − 2)². Parentheses give 3; the exponent gives 9; multiplication gives 36; addition gives 39. A student who works strictly left to right gets 63 - a classic order-of-operations trap. As a check, note that 4 × 9 alone is 36, so a final answer near 40 is reasonable.