How our printables are made
Updated
Each worksheet page runs a small generator. You choose the settings; the generator draws problems that meet them, lays them out on a US Letter or A4 page, and draws a matching answer key.
How problems are chosen
- Seeded, repeatable randomness. Every sheet comes from a seed number. The same settings and seed always rebuild the same sheet, which is why the link in your address bar brings an exact worksheet back. New problems picks a new seed.
- Constraints are built in, not filtered by luck. A "no regrouping" addition sheet is made digit by digit so no column can carry; a "no remainders" division sheet only uses dividends that divide evenly; "whole-number answers" really are whole numbers. Where a setting allows only a few distinct problems (the 12s facts, say), the generator avoids repeats until it runs out.
- Answers use exact arithmetic. Fractions are kept as whole-number numerators and denominators and simplified with the greatest common factor; decimals are worked as scaled whole numbers so 0.1 + 0.2 is 0.3 on the key. Cylinder answers with π say whether they use 3.14 or leave π in the answer.
How grade levels are set
Each page names the grade band and the Common Core State Standards for Mathematics cluster it practices, with a link to that standard. We use the standards as a shared map of when skills are usually taught. Your curriculum may teach a skill earlier or later, so the settings let you make any sheet easier or harder.
How sheets are checked
- Automated tests build every generator thousands of times with random settings and check that no problem is malformed, that keys match the problems, and that constraints hold (no carrying where none is allowed, no negative answers on early subtraction, prime answers that really are prime).
- Print checks. Every generator is proofed as a PDF at US Letter and A4 sizes, in black and white, because most worksheets are printed that way.
- Corrections. A wrong answer key is the most serious error this site can make. Reports from the contact page are checked first, the fix is tested, and the change is logged on What changed.
How calendars are made
- Dates come from the Gregorian rules. Month lengths, leap years (every fourth year, except century years not divisible by 400) and weekdays are computed for any year from 1900 to 2100, not copied from a table.
- Holidays follow the law and the usual rules. The eleven US federal holidays follow 5 U.S.C. 6103, and a holiday on a Saturday or Sunday is also marked on the Friday or Monday it is observed, as the US Office of Personnel Management sets out. Easter uses the Gregorian computus, and the daylight saving dates use the US rule in force since 2007. Observances such as Mother's Day and Halloween are the ones most US calendars print.
- Week numbers are ISO 8601. Weeks start on Monday, and week 1 is the week with the year's first Thursday.
- Tests check the dates. Automated tests compare weekdays, Easter dates, holiday dates and week numbers against published values for many years.
Who writes the explanations
The teaching notes on each page (how to do the skill, a worked example, common mistakes) are written and edited by Paul Gunder. They describe standard methods taught in US schools; where there is more than one common method, the page says so.