Lattice Multiplication Worksheets

Lattice multiplication worksheets with an answer key. One factor runs along the top of the grid, the other down the side, and every cell holds a single digit-by-digit product split by its own diagonal. Add down each diagonal channel and the answer reads off the left side and along the bottom.

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Other methodsStepping upLong multiplication

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Other methods

Box methodLattice

Stepping up

2 by 1 digit2 by 1, carrying2 by 2, easy

Long multiplication

2 by 2 digits3 by 2 digits3 by 3 digits

Box method multiplication. Split each factor by place value and fill the grid.Lattice multiplication. Multiply each pair of digits, then add down the diagonals.Two digits by one digit. Forty problems, the first step past the facts.Two by one, carrying. Every problem needs a carry, for practising regrouping.Two by two, no carrying. Two-digit problems that need no regrouping. A gentle start.Two digits by two digits. The full two-by-two set, with room to show the working.Three digits by two digits. Two partial products under every problem.Three digits by three digits. Long multiplication in full, with a worked answer key.

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The problems

MethodLong multiplicationBox method / area modelLatticeMultiply each pair of digits, then add down the diagonals.

Digits in the top number

Digits in the bottom numberSets how much room each problem gets to be worked in, so it also sets how many fit.

CarryingAnyNeeds carryingNo carrying

Allow zeros in the bottom number

The sheet

How many problemsEach grid takes a lot of room, so fewer fit than on a long-multiplication sheet.

Answer keyScore box

Different versionsUp to 8, each with different problems and its own key.

Title and instructions

Title

Instructions

The page

Margin

incm

Name and date line Border DadsWorksheets logo at the foot

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Lattice multiplication · 2 by 2 digits · 9 problems · with answer key

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How the Lattice Works

Every cell is one fact. For 36 × 86, the cell where 3 meets 8 holds 24 — the 2 above the diagonal, the 4 below it. Nothing larger than a single times-table fact is ever multiplied, which is the point: a student who knows the facts can do a four-digit answer without carrying anything during the multiplying.

The carrying happens once, at the end, adding down the diagonals. The diagonals on these sheets run past the edge of the grid on purpose — that is where each column of the answer is written.

Who It Helps

The lattice separates the two things the standard algorithm asks a student to do at once: recall a fact, and keep track of place value. The grid holds the place value, so all that is left is the facts. For a student who knows the facts but loses the columns, it often works when nothing else has.

It is worth saying that it is not a shortcut, and it is not how most adults multiply. It is a way in. Plenty of classrooms teach it alongside the box method and move to the standard algorithm once both have done their job.

Where to Go Next

For the stacked form, see multiple digit multiplication. For the facts the lattice depends on, see multiplication worksheets and the Spaceship Math series.

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