Mathematics: Number Sense, Geometry, and Problem Solving
The skill map
Number sense and operations (whole numbers, fractions, decimals, percents, integers) carry the most items; then measurement (units, perimeter, area, volume, time, money), geometry (angles, triangles, circles, coordinate plane), data analysis (tables, line and bar graphs, mean/median/mode/range, simple probability), patterns and beginning algebra (expressions, one-step equations), and multi-step word problems that combine two or more of these.
Traps worth naming
- Unit mismatch. A rate given per hour with a time given in minutes; a length in centimeters with the answer requested in meters.
- Order of operations. Parentheses first, then multiplication and division, then addition and subtraction, left to right. So 12 − 3 × 2 equals 6, not 18.
- Rounding too early. Carry full precision to the final step, then round as instructed.
- The negative stem. Underline words like not, except, and least.
- Leftover information. Word problems often include a number you never use; that is deliberate.
- Percent traps. Increasing a value by 20% and then decreasing it by 20% does not return it to the original value.
Rule of thumb
Write the question as a sentence with a blank, list each given quantity with its unit, and decide on the operation before computing. Estimate first; if the exact answer lands far from the estimate, the setup is wrong, not the arithmetic.
Worked example
A recipe uses 3/4 cup of oil per batch. How much oil is needed for 2 1/2 batches? Convert the mixed number: 2 1/2 = 5/2. Multiply 3/4 × 5/2 = 15/8 = 1 7/8 cups. Estimate check: three-quarters of about two and a half is a little under 2 cups, so the result is reasonable.