Lattice Multiplication

With the introduction of Arabic numerals in the 13th century an opportunity was presented for more complex mathematical methods, such as multiplication.

Lattice multiplication was the first of its kind to use Arabic numerals for factoring.

The name of this style of multiplying comes from how the multiplication is done on a grid, which resembles the common structure used for growing ivy.

In order to execute this multiplication chart, one must first set up a grid table according to the numbers present in the multiplication problem.

The numbers to the left or on the top of the multiplication problem conclude how many boxes are in a row. The numbers to the right or on the bottom of the multiplication problem determine how many boxes are in a column.Each box has a diagonal line drawn through it from the right corner down to the left.

Once the boxes are drawn, the multiplication chart is created, for example; in the problem 123x45 a chart of three boxes across and two boxes down would be drawn, with each box containing a diagonal line crossing from right to left, creating two triangles within the box.

Now the multiplication fun begins as each number is multiplied; starting with the top two on the right and working individually down the row and column.

The answers to each multiplication problem are recorded in the boxes, and are entered by putting the tens and ones places on either side of the diagonal line.

For example: in the number 24, the 2 is in the tens place, and the 4 is in the ones place; in a lattice multiplication table the 2 would be in the left triangle and the 3 would be in the right triangle of a box.

When the multiplication is complete, simply sum up the totals of the numbers in the diagonal boxes and write the answers at the bottom of the chart, just outside the grid.

Lattice multiplication creates smaller and easier factoring within large multiplication equations, simply by charting out each number and adding up the individual factors.

This style of compartmentalizing is not only more manageable, but can also make multiplication fun for young students to learn.

Another great activity with lattice multiplication is involving the students in creating the lattice grids; create worksheets to look like a window pane or hockey goal.

Emphasize order and tidiness when working with the lattice multiplication grids, as numbers that are not lined up correctly may result in a wrong answer.

This insistence of order on the grid will also instill a sense of discipline for students to use when factoring multiplication problems.
Lattice multiplication was a major advancement for quantifying numbers in the Middle Ages, and still has use in learning multiplication facts today.