These lattice multiplication worksheets arrive with the lattice already drawn, diagonals included, which is the slow part to rule by hand. Sheets run from a one-row lattice for 47 × 6 up to 3 by 3, then decimals and blank templates.
Read the full guide
How a lattice works, cell by cell
Write one number across the top and the other down the right side. Each cell holds its column digit times its row digit: tens above the diagonal, ones below, so 2 × 4 is written 08. Add along each diagonal from the bottom right, carrying when a sum passes 9. Read the answer down the left side and along the bottom. For 68 × 47 the cells are 24, 32, 42 and 56, and the answer is 3,196.
What the lattice hides
A lattice is long multiplication in another layout. The top-left cell of 47 × 36 says 12 but stands for 40 × 30 = 1,200.
Begin with Fill the cells only, and check every product under 10: 08, not 8.
Lattice, then check with columns sets both methods side by side: for 68 × 47, rows 476 and 2,720 total 3,196.
When the top-left diagonal comes to 0, as in 12 × 13, the lattice reads 0156. Pupils write 156.
Questions and answers
Is there a blank lattice multiplication worksheet for my own numbers?
Yes, three. Blank 2 by 2 lattice template has 9 lattices a page, the 3 by 2 has 6 and the 3 by 3 has 4. Diagonals are drawn, digit spaces are empty, and the print is 1 page with no answer key.
Which grade is lattice multiplication for?
Grades 4 and 5, going by problem size. The Common Core sets 2-digit × 2-digit in grade 4 (4.NBT.5) and the standard algorithm in grade 5 (5.NBT.5). Texas sets 3-digit × 2-digit in grade 5 (5.3(B)). Neither document names the lattice.
How do decimals work in a lattice?
Multiply as if the points were not there. Draw a line down from the point in the top number and across from the point in the side number. The diagonal through their crossing ends where the point goes: 4.7 × 3.6 = 16.92.
All 25 sheet types
One-row lattices 4
One-row lattice with a carry58 × 7 has cells 35 and 56. The middle diagonal is 5 + 5 = 10, so write 0 and carry 1 to the next diagonal: 3 + 1 = 4. The answer is 406.
One-row lattice, 2-digit × 1-digit47 × 6 needs two cells: 24 and 42. The diagonals give 2, then 4 + 4 = 8, then 2, so the answer reads 282. A first lattice, with only one row to fill.
One-row lattice, 3-digit × 1-digit217 × 4 has cells 08, 04 and 28. Write 08, not 8: a product under 10 still needs a 0 above the diagonal. The diagonals read 0, 8, 6, 8, so the answer is 868.
One-row lattice, 4-digit × 1-digit3,241 × 3 has cells 09, 06, 12 and 03, and the diagonals read 0, 9, 7, 2, 3: the answer is 9,723. Four cells in a row is the widest lattice a grade 4 size needs.
Show all 25 sheet types (21 more)
2 by 2 lattices 5
2 by 2 lattice with a 3-digit answer12 × 13 has cells 01, 02, 03 and 06. The top-left diagonal comes to 0, so the lattice reads 0156 and the answer is 156. A 0 at the front of the answer is not written.
2 by 2 lattice with a multiple of 1064 × 30 has cells 18 and 12 in the top row and 00 and 00 in the bottom row. The row of zeros is still filled in, because it moves every other digit one diagonal along: 1,920.
2 by 2 lattice with carrying68 × 47 has cells 24, 32, 42 and 56. The third diagonal is 4 + 3 + 4 = 11: write 1 and carry 1, so the last diagonal is 2 + 1 = 3. The answer is 3,196. The page opens on this sheet.
2 by 2 lattice with digits 6 to 989 × 98 has cells 72, 81, 64 and 72, and two diagonals carry: 1 + 4 + 7 = 12, then 2 + 8 + 6 + 1 = 17. The answer is 8,722. Large digits make every cell a hard fact.
2 by 2 lattice, no carrying47 × 36 fills four cells: 12 and 21 in the top row, 24 and 42 below. No diagonal reaches 10 (2, then 1 + 4 + 4 = 9, then 2 + 2 + 2 = 6, then 1), so the answer reads 1,692.
Larger lattices 5
2-digit × 3-digit, three rows58 × 213 puts 58 across the top and 213 down the side, so the lattice is 2 wide and 3 tall: 10, 16, then 05, 08, then 15, 24. The answer is 12,354. Turning it to 213 × 58 gives the same digits.
3 by 2 lattice with a zero inside507 × 38 has a whole column of 00 cells under the 0. Fill them in anyway: leaving the column out turns 19,266 into a 4-digit answer.
3 by 2 lattice, 3-digit × 2-digit345 × 12 has three columns and two rows: 03, 04, 05 above 06, 08, 10. The diagonals come to 0, then 14, then 10 plus the carried 1, so two of them carry. The answer is 4,140.
3 by 3 lattice, 3-digit × 3-digit586 × 274 has nine cells. The middle diagonal holds five digits, 2 + 6 + 4 + 0 + 3 = 15, and the next comes to 20 with the carry. The answer is 160,564. Four lattices fill the page.
4 by 2 lattice, 4-digit × 2-digit3,168 × 45 fills eight cells: 12, 04, 24, 32 above 15, 05, 30, 40. Two of the diagonals hold four digits each, and the answer is 142,560.
Decimal lattices 3
Decimal lattice, tenths × hundredths5.8 × 2.13 is the lattice of 58 × 213 with two lines drawn from the decimal points. One place plus two places gives three in the answer: 12.354.
Decimal lattice, tenths × tenths4.7 × 3.6 uses the same cells as 47 × 36. Draw a line down from the point in 4.7 and a line across from the point in 3.6. The diagonal through the place where they meet marks the point in the answer: 16.92.
Decimal lattice, tenths × whole number6.8 × 47 uses the cells of 68 × 47, which makes 3,196. The whole number has no point, so there is one line to follow: straight down from the point in 6.8, then out along the diagonal. The answer is 319.6.
Blank templates and part-done lattices 8
Add the diagonals onlyEvery cell is already filled. The pupil adds along the diagonals from the bottom right, carries where a sum passes 9, and reads the answer. For 76 × 58 the diagonals come to 8, then 10, then 13 plus the carried 1, then 3 plus the carried 1: 4,408.
Blank 2 by 2 lattice templateNine empty 2 by 2 lattices with the diagonals drawn and room for the digits along the top and right side. For problems from a textbook, the board or a pupil's own numbers. No answer key, because there are no set problems.
Blank 3 by 2 lattice templateSix empty lattices, 3 columns wide and 2 rows tall, for any 3-digit × 2-digit problem. For a 2-digit number times a 3-digit number, write the 3-digit number across the top: the product is the same.
Blank 3 by 3 lattice templateFour large empty 3 by 3 lattices. A 3-digit × 3-digit product has up to six digits, so the template leaves three answer spaces down the left side and three along the bottom.
Cell facts warm-up, tables 2 to 940 facts from the 2 to 9 times tables, up to × 10, written across the page, such as 8 × 7 = 56. A lattice cell is one digit times another, so the × 10 facts are extra practice no cell needs.
Fill the cells onlyThe numbers are in place and the pupil fills the cells, with no adding. For 76 × 58 that means 35, 30, 56 and 48. It isolates the two-digit cell rule before any adding.
Find the mistake in a finished latticeEach lattice is complete, but one cell holds a wrong product, such as 48 where 7 × 8 = 56 belongs. The pupil circles the cell, corrects it and writes the right answer. The key names the cell.
Lattice, then check with columnsEach problem has a lattice and, beside it, space for the standard algorithm. Both must agree. For 68 × 47 the two column rows are 476 and 2,720, and they total 3,196, the same as the lattice.
How this list was compiled: Sheet types, wording and worked examples are own work. Every worked example (the cell products, each diagonal sum, each carry and the product) was computed twice by script on 2026-09-19. The layout of the method (first number across the top, second number down the right side, tens digit above the diagonal and ones digit below, a 0 in the tens place for a product under 10, diagonals added from the bottom right, the answer read down the left side and along the bottom), the decimal point rule, the example 58 × 213 = 12,354, the other names of the method and its history were checked 2026-09-19 against https://en.wikipedia.org/wiki/Lattice_multiplication. The example 345 × 12 and the statement that lattice multiplication is equivalent to long multiplication were checked the same day against https://en.wikipedia.org/wiki/Multiplication_algorithm. Number sizes and standard numbers were checked 2026-09-19 against the full text of the Common Core State Standards for Mathematics (national copy, https://learning.ccsso.org/wp-content/uploads/2022/11/ADA-Compliant-Math-Standards.pdf, read again 2026-09-20) and the Texas Essential Knowledge and Skills for Mathematics, 19 TAC chapter 111 subchapter A (https://tea.texas.gov/laws-and-rules/sboe-rules-tac/sboe-tac-currently-effect/ch111a.pdf). Neither document names the lattice method. The examples 217 × 4 = 868 and 3,241 × 3 = 9,723 (their cells, diagonal sums and products) were computed by script on 2026-09-20. The two standards texts and the two Wikipedia articles were read again on 2026-10-03. Licence: own work