Math practice sheets: pick the problems, print the sheet and its answers

What is on a sheet

• 12, 20 or 30 problems, each written in a line with a blank after the equals sign: 7 × 8 = ____. Each one has a small number in front of it.
• A line for a name and a date at the top, and a few words of your own if you type them.
• The sheet number and what you chose, in small print at the bottom, so a sheet and its answers can be matched.
• No line is printed twice on a sheet.
• The answer sheet is the same page with each answer in place of the blank, and the word Answers at the top.

The numbers

• Addition: answers up to 10, answers up to 20, two-digit numbers, or three-digit numbers.
• Subtraction: the same sizes. The larger number comes first, so no answer is below zero.
• Multiplication: up to 5 × 5, up to 10 × 10, up to 12 × 12, or a two-digit number times 2 to 9. Zero is one of the numbers in the first three.
• Division: the same tables turned around. Every division comes out whole, with nothing left over, and nothing is divided by zero.
• Mixed sheets have two kinds on one page, in no fixed order.

Sheet numbers

• Every sheet has a number from 1 to 9999. The page picks one by chance when it opens and when you press Another sheet. You can also type one.
• The same number with the same choices gives the same sheet every time, on any device. So the answers can be printed another day: set the same choices and type the number from the bottom of the sheet.
• A sheet of 12 or 20 is the beginning of the sheet of 30 with the same number.
• The address changes as you choose. What comes after the # sign holds the kind, the size, how many and the sheet number, so the address is a link to this exact sheet. The words you type for the top are not in it.

What this page does not do

• It does not check anyone’s work. A person compares the sheet with the answer sheet.
• It has no remainders, no fractions, no decimals and no numbers below zero, and no word problems.
• It writes every problem in a line, not with one number above the other.
• It does not say which sheet suits which age or grade. You choose.
• It keeps nothing, and it does not time anyone.
• It has been tried in one browser’s print preview (Chromium, saved as PDF), not on paper from a real printer.

Every time the page is built, a program checks 44 examples worked by hand. Then it makes every sheet this page can make, all 239,976 of them (9,999 numbers, 6 kinds, 4 sizes, 30 problems each), and works out each of the 7,199,280 answers a second way: adding back, taking away, adding again and again, multiplying back. It also checks that the numbers are the size the page says and that no line is there twice. Last, it writes 2,000 made-up sheets the way the page prints them, and a second reader takes every line back off the paper and does the arithmetic again by other means. That checks the page’s own work, not the work done on the sheet.