How to use the lattice multiplication worksheet generator
- Choose the number of problems (1 to 12) and the digits in the first and second numbers.
- The seed decides the problems: the same seed always gives the same worksheet. Choose Pick a new seed for different problems.
- Tick Add an answer key page if you want filled-in grids after the problems.
- Check the list of problems on the page, then choose Download PDF.
How lattice multiplication works
In the lattice (gelosia) method, the digits of one number are written across the top of a grid and the digits of the other down the right side. Each cell is split by a diagonal. The product of the two digits for that cell is written with its tens digit above the diagonal and its ones digit below it. Then the numbers are added along each diagonal, starting from the lower right corner, carrying when a sum passes 9. The sums, read from the top left down and around to the bottom, give the answer.
For 58 x 23 the cells are 5 x 2 = 10, 8 x 2 = 16, 5 x 3 = 15 and 8 x 3 = 24. The diagonals add up to 4, then 6 + 5 + 2 = 13 (write 3, carry 1), then 0 + 1 + 1 + 1 = 3, and 1, which read as 1334. The page checks every product it prints against exact integer multiplication.
Making and using the worksheet
Problems have the number of digits you choose and no leading zeros. They are drawn from a seeded generator, so a worksheet can be rebuilt later and a teacher can keep only the seed. Each problem has an empty grid with the digits already written, a line for the answer, and, if you ask for a key, a filled grid with the diagonal sums and the answer. Cells are 40 points (about 0.56 inch) wide, so students have room to write.
For standard practice sheets, see the math worksheet generator, and for the step-by-step view of the usual method, the long multiplication calculator. The multiplication chart and hundreds chart help with facts. The worksheet is made on your device and nothing is uploaded.
Assumptions and limits
- The first number has 2 to 4 digits and the second 1 to 3 digits.
- Problems use plain whole numbers with the first digit not zero. Zeros can appear inside a number.
- The seed is a whole number between 0 and 4,294,967,295. The page picks a random seed only when you ask for one.
- The answer key shows the digit pair in each cell and the diagonal digits, which read left to right form the answer.
Frequently asked questions
Why is it called lattice or gelosia multiplication?
The grid with its diagonals looks like a lattice or a window shutter, called a gelosia in Italian. It comes from medieval arithmetic and is still taught as an alternative to the standard algorithm.
How many problems fit on a page?
It depends on the size of the grids. Six problems of 3 digits by 2 digits fit on one page, and more spill onto new pages. The answer key follows after the problem pages.
Can I get the same worksheet again?
Yes. Use the same seed and the same settings. The problems are generated by a seeded generator, so they repeat exactly, which also lets two people share a worksheet by sharing a number.
Why do carries matter in the diagonals?
A diagonal can add up to 10 or more. You write the ones digit and carry the tens digit into the next diagonal. Forgetting a carry is the most common error, and the answer key shows the result.