In this article, multiplication is taught using the Lattice method. Lattice multiplication is a simple method of multiplying large numbers using a grid. It is equivalent to regular long multiplication, but breaks the multiplication process into smaller steps. The Lattice method was first introduced in Europe in 1202 by Leonardo Fibonacci in his Liber Abaci.
Objective:
Lattice multiplication
Lattice, or sieve, multiplication is algorithmically equivalent to long multiplication. It requires the preparation of a lattice (a grid drawn on paper) which guides the calculation and separates all the multiplications from the additions.
Step 1:
Ask the students how they think multiplication is different from simple addition. (Explain that it is actually adding a number to itself a specified number of times. Encourage them to share examples to get a clear idea of the concept.)
Begin by asking them to multiply single digit numbers. After a brief session move on to multiplication of two-digit numbers. Tell them an easy and interesting way of multiplying bigger numbers is the Lattice multiplication.
Step 2:
Use the blackboard to draw and explain what a lattice is.
Ask the students to choose any two-digit numbers to be multiplied. Let’s say that they want to multiply, say 22, by another two-digit number, say 13. The product of the two is actually 286. Let’s see how this can be obtained by the lattice method.
The lattice is drawn on the basis on the number of digits in each number. The first number gives us the number of columns, while the second gives us the number of rows. Since we have two double-digit numbers, we draw a lattice consisting of two rows and two columns.
Write the digits of the first number individually over individual columns, beginning left to right. Each of the two columns now has ‘2’ written over it. Now write the second number,’13’ to the right of the lattice, going top to bottom. So we have ‘1’ beside the first row and ‘3’ beside the second.
We then draw diagonals in each box, as in the figure:
The partial products of the digits are now found out. The ones are put below the diagonal, while the tens are put above it. If the product is a single digit, we write a zero in the tens place. The partial products in the first row will therefore be 1 x 2, and 1 x 2, while those in the second row will be 3 x 2 and 3 x 2. After filling in the partial products, the lattice will look like this.
Now we add the numbers along each diagonal and write them close to where the diagonal ends, as below. Any carry over from a diagonal is taken to the one above it.
Reading the figures from the top let to bottom right, we get the answer: 286!
Step 3
Let’s now find the product of two three-digit numbers, say, 254 and 193. This gives us the answer: 49022! While adding the numbers along the diagonals, we get carry-over. The illustration show these carry-overs (represented in little boxes) taken from one diagonal to the next.
Try the lattice method for yourself!
- To introduce students to an algorithm of multiplication, the Lattice method.
- To teach the students an easy and workable alternative to long multiplication.
- To enable students to solve multiplication problems that involve more than a single digit.
- To help students learn to multiply two or more digit numbers in smaller and simpler steps. The students can perform the three steps of multiplication (to multiply, add and carry) separately, thereby avoiding confusion and errors.
Lattice multiplication
Lattice, or sieve, multiplication is algorithmically equivalent to long multiplication. It requires the preparation of a lattice (a grid drawn on paper) which guides the calculation and separates all the multiplications from the additions.
Step 1:
Ask the students how they think multiplication is different from simple addition. (Explain that it is actually adding a number to itself a specified number of times. Encourage them to share examples to get a clear idea of the concept.)
Begin by asking them to multiply single digit numbers. After a brief session move on to multiplication of two-digit numbers. Tell them an easy and interesting way of multiplying bigger numbers is the Lattice multiplication.
Step 2:
Use the blackboard to draw and explain what a lattice is.
Ask the students to choose any two-digit numbers to be multiplied. Let’s say that they want to multiply, say 22, by another two-digit number, say 13. The product of the two is actually 286. Let’s see how this can be obtained by the lattice method.
The lattice is drawn on the basis on the number of digits in each number. The first number gives us the number of columns, while the second gives us the number of rows. Since we have two double-digit numbers, we draw a lattice consisting of two rows and two columns.
Write the digits of the first number individually over individual columns, beginning left to right. Each of the two columns now has ‘2’ written over it. Now write the second number,’13’ to the right of the lattice, going top to bottom. So we have ‘1’ beside the first row and ‘3’ beside the second.
We then draw diagonals in each box, as in the figure:
The partial products of the digits are now found out. The ones are put below the diagonal, while the tens are put above it. If the product is a single digit, we write a zero in the tens place. The partial products in the first row will therefore be 1 x 2, and 1 x 2, while those in the second row will be 3 x 2 and 3 x 2. After filling in the partial products, the lattice will look like this.
Now we add the numbers along each diagonal and write them close to where the diagonal ends, as below. Any carry over from a diagonal is taken to the one above it.
Reading the figures from the top let to bottom right, we get the answer: 286!
Step 3
Let’s now find the product of two three-digit numbers, say, 254 and 193. This gives us the answer: 49022! While adding the numbers along the diagonals, we get carry-over. The illustration show these carry-overs (represented in little boxes) taken from one diagonal to the next.
Try the lattice method for yourself!
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