Lattice was first introduced in Europe in the early 13th century by Fibonacci and has remained a useful method of multiplication today. Lattice involves drawing what appears to be several windows or a latticed fence. For double digit multiplication, first draw a window (a square with a horizontal and vertical lines across the center) and write the two-digit factors along the top and right side of the figure. Draw diagonal lines from the top right corners to the bottom left to bisect each square. Each digit aligns with another digit in the opposite factor across the rows and columns. Their products are written inside the four small squares created by the shape of the window. The products are added along the diagonal lines to reach the final answer.
The partial products method is similar to lattice but does not utilize the shape of the window or fence. Each digit is multiplied by another digit in the opposite factor and the products are added together. For example, in 25 times 36, first solve for 20 times 30, which equals 600. Then solve for 20 times 6, which equals 120. Next, solve for 5 times 30, which is 150. Finally, solve for 5 times 6, which is 30. The last step is to add all products, which totals 900.
The traditional method of multiplication is similar to partial products but involves carrying. It is also known as long multiplication. For the same problem, 25 times 36, the factors are aligned vertically. Each digit of 25 is first multiplied by the 6 in 36. If a product has a number in the 10s place, it is carried over to the next column and added to the next product. The final products are added together to reach the answer.
Using base 10 blocks to learn multiplication can be highly beneficial for those kids who are hands-on learners. A base 10 block set comes with individual cubes with a volume of one cubic centimeter, rods of 10 connected cubes, squares of 100 connected cubes, and a large cube made up of 1,000 centimeter cubes. To illustrate the problem 20 times 15, students take 20 cubes (2 of the rods), then think about what 15 times that amount would look like. They end up with 15 sets of 2 rods. Students add the total number of cubes by counting by tens (each single rod) to reach 300.