Box Method Multiplication Worksheets

Box method worksheets, also called the area model, with an answer key. Each factor is split by place value along the edges of a grid, and every cell holds one part-product. Add the cells and you have the answer — the same partial products the traditional algorithm writes under the rule, laid out where you can see what each one is.

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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 modelLatticeSplit each factor by place value and fill in the grid.

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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Box method multiplication · 2 by 2 digits · 9 problems · with answer key

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Box Method and Area Model Are the Same Thing

Two names for one worksheet. "Area model" comes from the picture: a rectangle 23 units by 45 units, cut into four smaller rectangles whose areas are 800, 120, 100 and 15. "Box method" is the same grid without the claim that it is drawn to scale. A classroom that says one will recognise the other, so this page serves both.

Why Teach It Before the Standard Algorithm

The traditional algorithm is faster, and it hides what it is doing. A student who writes 180 under 18 × 11 is multiplying by ten and may not know it. The grid makes every part-product visible and labelled: the row is 10, the column is 18, the cell is 180. Nothing is carried, nothing is shifted, and nothing has to be taken on trust.

It is also where a wrong answer becomes findable. A missing carry in the standard algorithm looks like a wrong digit; a wrong cell in the grid looks like one wrong multiplication.

Where to Go Next

Once the grid is secure, move to multiple digit multiplication, which uses the same partial products in the stacked form. Lattice multiplication is a third arrangement of the same arithmetic, and some students take to it when neither of the others has stuck. For the facts underneath all of it, see multiplication worksheets.

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