Math Problem Generator

“No regrouping” is a promise, and it has to be checked

A worksheet labelled two-digit addition without regrouping is not a worksheet about addition. It is a worksheet about one specific step of the written algorithm, given to children who have not been taught the next step yet. If three problems in thirty need a carry, those three children stall, and the sheet has quietly become a different lesson. So the constraint here is not a hint to the random number generator; every candidate problem is put through the written method digit by digit and rejected if it breaks the rule.

For addition the test is whether any column total exceeds nine. For subtraction it is whether any column of the smaller number is larger than the column above it, taking earlier borrows into account. Multiplication is the awkward one, because regrouping can happen in two different places: inside a partial product, when a digit times the multiplier comes to more than nine, and again when the partial products are added up. Both are checked, so 21 × 3 passes a “no regrouping” filter and 27 × 3 does not. Division has no carrying to speak of, so its equivalent control is the remainder: divide exactly, allow a remainder, or insist on one in every problem so nobody can coast.

How many different problems your settings can make

The line under the controls that reads something like 4,455 distinct problems available is the part worth reading before you press print. It is not an estimate. Where the search space is small enough the tool walks every combination of first and second number, applies your constraints, and counts what survives; where the space runs into millions it says so rather than guessing.

That number matters because the constraints bite harder than people expect. Ask for two-digit addition where every problem regroups and a large slice of the grid disappears — every pair whose units digits sum to nine or less is gone. Ask for sums within twenty from addends up to twenty and most of the grid goes too. If the pool ends up smaller than the number of problems you asked for, the sheet is shortened and you are told why, because the alternative — repeating a problem twice on one page — is worse than a short sheet. No problem appears twice on the same version.

Four versions, four keys, one code

Two children sitting next to each other with identical sheets is a known problem with a boring solution: give them different problems from the same pool. Set Versions to two, three or four and you get parallel sheets marked A, B, C and D, each with its own answer key on its own page. They are drawn from the same constraint pool, so the skill is the same, but the numbers are not.

Every sheet prints a short worksheet code in its header, and the key repeats it. Type that code back into the code box, with the same settings, and the same problems come back in the same order — useful when one child was absent, or when a sheet gets marked and the key has gone missing. Change the range or the regrouping rule and the code no longer reproduces the old sheet, because the code identifies the shuffle, not the settings.

Questions that come up after the first print run

Why does the answer key say “7 r 3” instead of a fraction?

Because remainder notation is what the long-division layout is teaching. A quotient of seven remainder three is written the way a child writes it under the bracket. If your class has moved on to expressing the remainder as a fraction or a decimal, set remainders to divide exactly and use the quotient range to control the difficulty instead.

Can I control the dividend directly in division?

Not directly, and that is deliberate. You set the divisor range and the quotient range, and the dividend is built from them, so the numbers land where you want them instead of producing a page of awkward divisions that happen not to work out. The help line under the range boxes relabels them when you switch to division so it is clear which is which.

Does the working space affect what fits on a page?

Yes, and it is the main lever. Twenty column-format problems in four columns with working space fill roughly one side; turn the working space off, or move to five columns, and thirty fit comfortably. The browser handles the page breaks, and problems are not allowed to split across a break, so a long sheet simply flows onto a second side.

Where is any of this calculated?

Entirely inside the page, on your own machine. Pressing the button sends no request anywhere; nothing about the worksheet leaves the browser, and once the page has loaded it keeps working with the network switched off. Nothing is stored either, so the code in the header is the only thing worth writing down.

What it deliberately does not do

There are no fractions, decimals, negatives beyond a simple subtraction toggle, no word problems, no algebra and no number lines — this is drill on the four written operations and nothing else. Numbers are capped at four digits, which is past the point where a written algorithm is still teaching anything new. There is no PDF button: the browser's own print dialogue has a “Save as PDF” destination that produces a smaller, sharper file than an in-page PDF library would. The four versions are equivalent in the properties the tool controls, but they are not statistically matched test forms, so use them for practice rather than for grading one child against another.