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FOR MULTIPLICATION

LATTICE ALGORITHM. FOR MULTIPLICATION. Created by Paula Cantera Elk Neck Elementary. The lattice algorithm for multiplication has been traced to India, where it was in use before A.D. 1100. Many students find that this is one of their favorites. It helps them keep track

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FOR MULTIPLICATION

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  1. LATTICE ALGORITHM FOR MULTIPLICATION Created by Paula Cantera Elk Neck Elementary

  2. The lattice algorithm for multiplication has been traced to India, where it was in use before A.D. 1100. Many students find that this is one of their favorites. It helps them keep track of all the partial products without having to write extra zeros - and it helps them practice their multiplication facts!

  3. With this algorithm, numbers are placed around and within a lattice - a special kind of grid in which the dotted-line “rails” within the cells help form diagonals.

  4. Write one factor along the top outside of the grid, one digit per cell. X 26 35 3 5

  5. Write the other factor along the outer right side of the grid, one digit per cell. 35 X 26 3 5 2 6

  6. Begin with the first digit from the side factor, and multiply it by each digit in thetop factor. 35 X 26 3 5 2 6

  7. Record the product in the upper right-hand cell. Multiply 2 x 5. 3 5 1 2 0 6

  8. Multiply 2 x 3. Record the product in the upper left-hand cell. 3 5 0 1 2 0 6 6 **Since 6 is a product less than 10 you must enter a zero in the top half of the cell!

  9. Record the product in the lower right-hand cell. Multiply 6 x 5. 3 5 0 1 2 0 6 3 6 0

  10. Multiply 6 x 3. Record the product in the lower left-hand cell. 3 5 0 1 2 0 6 1 3 6 8 0

  11. Now, add along the diagonal. Begin with the bottom right diagonal and work toward the upper left diagonal. 3 5 0 1 2 0 6 1 3 6 8 0 Regroup each tens digit to the top of the next diagonal as needed.

  12. 3 5 0 1 2 0 6 1 3 6 8 0 0

  13. Notice we needed to regroup this time! 3 5 1 0 1 2 0 6 1 3 8 + 3 + 0 = 11 6 8 0 1 0

  14. 3 5 1 0 1 2 0 6 1 + 6 + 1 + 1 = 9 1 3 8 + 3 + 0 = 11 6 8 0 9 1 0

  15. 3 5 1 0 1 2 0 6 0 1 + 6 + 1 + 1 = 9 1 3 8 + 3 + 0 = 11 6 8 0 9 1 0

  16. The product of 35 x 26 is 910 ! 3 5 1 0 1 2 0 6 0 1 + 6 + 1 + 1 = 9 1 3 8 + 3 + 0 = 11 6 8 0 9 1 0

  17. Of course you can use the Lattice Algorithm for any number of digits. Simply adjust your lattice grid to fit the factors that you are multiplying!

  18. Three digit by a two-digit: 251 x 36 2 5 1 3 6

  19. Shall we try to solve this one? 2 5 1 0 3 3 6

  20. 2 5 1 1 0 3 5 3 6 So far so good! Keep going!

  21. 2 5 1 0 1 0 3 6 5 3 6 Excellent work so far! You have the hang of it!

  22. 2 5 1 0 1 0 3 6 5 3 0 6 6

  23. 2 5 1 0 1 0 3 6 5 3 3 0 6 0 6 You’re almost there! Keep going!

  24. 2 5 1 0 1 0 3 6 5 3 1 3 0 6 2 0 6 Wasn’t that easy? Do you remember what to do next?

  25. Of course! You add the diagonals! 2 5 1 1 0 1 0 3 6 5 3 0 3 1 0 6 2 0 6 9 0 6 3

  26. The product of 251 x 36 is 9,036 ! 2 5 1 1 0 1 0 3 6 5 3 0 3 1 0 6 9 2 0 6 0 6 3

  27. Lattice Multiplication is lots of fun! Give it a try!

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