THE FIELD NOTES
Understand the workings.
Worked examples, common traps, and the small conventions that change an answer.
21 guides
Add or subtract calendar days from a date
Move forward or backward by a whole-day offset, verify month and year crossings, and avoid confusing offsets with inclusive day numbers.
Square feet, square meters, acres, and hectares
Convert area with squared length factors, calculate rectangular examples, and distinguish numerical area from usable or legally defined space.
Counting days between dates: start with the convention
Choose elapsed days, inclusive dates, or weekdays, and understand the endpoint rules before using a calendar result.
Date formats and time zones: keep calendar dates clear
Avoid ambiguous numeric dates, distinguish date-only values from timestamps, and keep time-zone questions out of simple calendar-day arithmetic.
Discount math: sale prices and stacked offers
Calculate the amount saved and final price, compare successive discounts, and keep tax, shipping, and eligibility separate from the arithmetic.
Inclusive date counting: when both endpoints count
See why inclusive counts add one calendar date, test same-day and weekend intervals, and document the endpoint rule clearly.
Leap years: the Gregorian rule and February 29
Apply the divisible-by-four rule with its century exception, and check day counts crossing February without assuming every year has 365 days.
Inches, feet, and centimeters: convert length clearly
Convert US customary lengths to metric, handle feet-and-inches inputs, and keep linear dimensions distinct from area and volume.
Pounds, ounces, grams, and kilograms: convert mass
Convert avoirdupois pounds and ounces to metric mass, combine mixed units correctly, and avoid confusing mass ounces with fluid or troy ounces.
Calendar months are not fixed numbers of days
Distinguish month-based schedules from day offsets, handle month-end questions explicitly, and avoid converting months to days with an unstated average.
Percentage calculations: choose the right whole
Learn when to multiply, divide, or compare values, with worked percentage examples and a checklist for choosing the right denominator.
Percentage increase and decrease: use the original value
Calculate relative changes, understand asymmetric increases and decreases, and recognize when a zero or negative starting value needs another approach.
Percentage points versus percent change
Tell an absolute change in a rate from its relative percentage change, and write comparisons that keep the starting rate visible.
Reverse percentages: recover the original amount
Work backward from a discounted or increased amount using a multiplier, and see why adding the same percentage does not restore the original.
Rounding percentages without losing the meaning
Keep precision through calculations, understand why rounded shares may not total 100%, and choose a useful way to report small differences.
Fahrenheit, Celsius, and kelvin: offsets matter
Convert absolute temperature readings with the correct offset and scale, and distinguish readings from temperature differences.
Unit conversions: match the quantity before the number
Choose compatible units, cancel conversion factors correctly, and distinguish length, area, volume, mass, and temperature before converting.
US cups, fluid ounces, gallons, and liters
Convert US customary liquid volumes to metric, distinguish cup definitions, and keep Imperial, dry, and mass measures out of liquid calculations.
Why cups do not convert directly to grams
Use density to connect volume and mass, understand ingredient and packing differences, and avoid a universal cup-to-gram conversion.
Weekdays are not always business days
Count Monday through Friday accurately, separate holiday calendars from weekend removal, and verify deadlines with the responsible organization.
Combine percentages with the right weights
Use underlying counts to combine group rates, distinguish equal and unequal denominators, and avoid averaging percentages without context.