Long division on graph paper, with every digit in its own box

I watched a fourth grader get 457 divided by 3 wrong three times in a row, and each time the division was right. What went wrong was a 1 drifting into the tens column, a partial product written under the wrong digit, a subtraction done on numbers that were not lined up. Her math was fine. Her columns were not.

What the sheet looks like

The long multiplication and division generator covers eight skills, from 2-digit × 1-digit multiplication up to 3-digit × 2-digit, and from 2-digit ÷ 1-digit division up to 4-digit ÷ 1-digit and 3-digit ÷ 2-digit. Plain gives the problem and a space. Graph-paper boxes gives one cell per digit and exactly the number of rows the algorithm needs, no more. Labelled steps, for division only, adds a column beside the problem reading divide, multiply, subtract, bring down. Remainders can be off or allowed, 4, 6 or 9 problems fit a page, and the answer key shows every partial product and quotient digit.

Why it works

• A cell per digit makes a misaligned column impossible. There is only one place the 1 can go.
• Having exactly the rows the algorithm needs tells the child how many steps there are. If there are two empty rows left, they are not done.
• The divide, multiply, subtract, bring down column turns a half-remembered procedure into a checklist, which is how it gets remembered.

Who it suits

2-digit × 1-digit on graph-paper boxes is where grade 3 starts. 3-digit ÷ 1-digit with labelled steps is the core grade 4 sheet. 3-digit × 2-digit and 3-digit ÷ 2-digit on plain are grade 5. This tool assumes the times tables are already fluent; if not, the multiplication worksheet is the step before. A child who understands partial products but not the stacked algorithm might prefer the area model multiplication sheet first.

Move from boxes to plain one skill at a time, not all at once. The boxes are a tool, not a crutch.