STEP 1: To begin, put one of the numbers at the top (47) of a rectangle (that has a space for each digit in the number) and the other number along the side (32) of the same rectangle (that has a space for each digit). The method you are now going to learn is called the LATTICE METHOD and it could be used for multiplying 2 digit or 3 digit or even bigger numbers together. Multiply the two digits together and put the answer in the box with the diagonal. What is Lattice Multiplication The process of multiplication that breaks the process of traditional long multiplication method into smaller steps. Put one number on top and the other on the right of the square. But first, I’ll show you how to multiply 2 single digits together. You are going to learn a cool and easy way to multiply numbers together. Are you ready to try a couple of duplation problems of your own? Well, ready or not, here they come! Of course, because of the commutative property of multiplication, the answer is 525, no matter which way you do it. Here are two more examples for you to study. In the right hand column, start with 26 and double away. This time, in the left column, you check off numbers that add up to 17 it's coincidental that I had to double to 16 again and stop. In other words, use the duplation method to compute: \(17 \times 26\). Let's do the same problem over again, but use the commutative property of multiplication. Watch how the rest of the problem is done: It's those numbers in the right column that you add together to get the answer. And we learned up here, this part of the video, we learned that this same multiplication could also be interpreted as 3 times 4. After you check off the numbers in the left column, circle or point to their corresponding numbers in the right column. The method is so called because it requires a rectangular lattice with one of the diagonals drawn: Each cell of the lattice is split by the diagonal into two parts used to house a 1. It was introduced in Europe in 1202 by Leonardo Fibonacci in his Liber Abaci. Simply start at the bottom of the first column, and check off numbers that add up to 26 (this is like doing it in base two). Lattice multiplication is a predecessor of a more compact long multiplication scheme. Okay, now we only need to add 26 seventeens together. Isn't it neat how we know that \(16 \times 17 = 272\) and we just double a few numbers to get there? Now if \(2 \times 17\) is 34, then \(4 \times 17\) is twice as many as \(2 \times 17\), so double 34 to get 68. So, \(2 \times 17\) is simply 17 doubled. The left side keeps track of how many of some number you are adding together. Now, you may need to think about this for a few minutes. Above all, this method improved self-esteem and self-confidence in the students.\)ĭo you see the corresponding numbers? 1 corresponds with 17, because 17 is \(1 \times 17\), 2 corresponds with 34, because 34 is \(2 \times 17\), 4 corresponds with 68, because 68 is \(4 \times 17\), 8 corresponds with 136, because 136 is \(8 \times 17\), and 16 corresponds with 272, because 272 is \(8 \times 17\). Students obtained much higher scores in the test with the Lattice Method than with the traditional way of multiplication. Overall, statistically significant differences between the two tests were found on the pre-test (significant at the 0.01 level) and the post-test (significant at the 0.05 level) on the basis of the formula of Chi-square. In addition, the method was used to teach decimal multiplication to students with learning disabilities very effectively. It was also found that students were not able to multiply two or three digits in the traditional way, but they were able to multiply two or more digits with the Lattice Method in accuracy ranging from 90% to 100%. Proper instructions greatly reduced the repetition of student errors in multiplication. The method ensured that students with learning disabilities avoided misplacing place value and other errors in multiplying algorithms. Special education teachers who used the method to teach their students multiplication with whole numbers and decimals achieved great success in their classes. In the study, students with learning disabilities were able to do multiplication by the traditional way only with 15% accuracy, but they skillfully used the Lattice Method to multiply more than 2 digit numbers with more than 97% accuracy. The common errors made by learning disabled students in multiplication with whole numbers were analyzed. The purpose of the study was to help teachers understand the importance of using the Lattice Method in teaching multiplication with whole numbers and decimals to students with learning disabilities.
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