The alternative methods to teaching multiplication are to be used only when students are experiencing difficulty using the traditional algorithm. Prior to using the alternative method, many experiences should be provided with concrete/hands on manipulatives. Students should understand that four groups of four is 16, they should see it visually before representing it symbolically. When a child is ready for 2 digit multiplication yet experiences difficulty, this alternative method should be explained clearly, it should be modeled for ten to fifteen questions and the child should be exposed to the alternative method for several days. A worksheet a day for 2 or 3 weeks will help the child better understand multiplication.
When is a child ready for two digit multiplication?
Typically, a child should know the multiplication facts to at least 10, 12 is preferable. They should be able to represent the facts concretely, in other words, they should be able to show the facts using bingo chips, beans or buttons and arrange the facts into groups. From there, try two digit numbers by one digit number, then move to two digit numbers by two digit numbers. If there is difficulty, it is worth trying the alternative method. The alternative method is not for everyone, it's a method to try with struggling learners.
Why does the alternative method work?
The alternative method maintains place value easier than the traditional algorithm. In the sample given, 27 x 36, the 2 and the 3 are always referred to correctly, as twenty and as thirty, similarly, the 7 and the 6 are always referred to as 7 and 6. When we are teaching young learners, this is extremely important.