How to Teach Lattice Multiplication

Lattice multiplication gets its name because the box used to set up a problem resembles a lattice fence. This multiplication strategy first appeared in the 1200s in Europe. The advantage to using lattice multiplication is that is makes it simpler for students to multiply larger numbers with two- and three-digits. It also focuses on place value and organizing a math problem.

Things You'll Need

• Paper
• Pencils
• Ruler

Instructions

How to Teach Lattice Multiplication

1. Explain to students the meaning of the word lattice. Review the words product and factors. Tell the students that factors are the numbers being multiplied in a problem and product is the answer to a multiplication problem.

2. Give the students a multiplication problem with factors that have two-digits each. An example of this is 24 x 32.

3. Make a 2 by 2 table. This will look like a square with two rows and two columns, creating 4 boxes inside total.

4. At the top of the box, write the numbers 2 and 4. The number 2 will be on top of the first column, and 4 on top of the second column.

5. On the right side, outside of the box, write the numbers 3 and 2 vertically. The 3 will be next to the first row and the 2 next to the second row.

6. Draw diagonals through each box that extend outside of the table. Start with the upper right-corner of each box down to the lower left-hand corner of the box. Explain that doing this makes a place holder for the tens and ones place values in each box. Go to the Cool Math 4 Kids or Dr. Math website to see a diagram of a lattice multiplication box.

7. Demonstrate to the students how to multiply the number on top of the second column, 4, by the number next to the first row, 3. The product of 4 x 3 is 12, so in the left half of that box write a 1 (for the tens place) and in the second half of that same box a 2 (for the ones place).

8. Tell the students to multiply the number on top of the first column, 2, by the number in the first row, 3. The product of 2 x 3 is 6, so in in the left half of that box write a 0 (there are no tens in the number 6) and in the second half of that same box write a 6 (for the ones place).

9. Tell the students to multiply the number on top of the first column, 2, by the number next to the second row, 2. The product of 2 x 2 is 4 so in the left half of the box write a 0 (there are no tens in the number 4) and in the second half of the same box write a 4 (for the ones place value).

10. Show students the last step for multiplication. Multiply the number on top of the second column, 4, by the number next to the second row, 2. The product of 2 x 4 is 8 so in the left half of that box write a 0 (there are no tens in the number 8) and in the second half of that same box, write an 8 (for the ones place value).

11. Add up the numbers in each diagonal. In the first diagonal from the left the only number is a 0. In the second is 0 + 6 + 1 = 7, so write the 7 down at the bottom of that diagonal outside the table. Next, add the numbers in the third diagonal. 2 + 0 + 4 = 6, so write the 6 at the bottom of that diagonal outside the table. Finally, in the fourth column the only number is an 8, so write that at the bottom of that diagonal.

12. At the bottom of the table, show students that you wrote the numbers 7, 6 and 8. Put the numbers in that order to make the product 768. This is the answer to the multiplication problem 24 x 32.

13. Ask your students to multiply 24 x 32 using the traditional method they were previously taught. Show the students that the answers are the same and that they can use either method to find the correct answer.

14. Practice several more problems with two-digit factors. When students are comfortable with two-digits, introduce three-digit factors.

References

• Dr. Math
• Cool Math 4 Kids