An Investigation on the Effective Method of Multiplying 2 Digits With 2 Digits

1. Grouping Method

It works because it follows a systematic ways of arranging the numbers according to the place value system.

Why the grouping method is interesting:
The method is straightforward, easy to understand and an efficient way to solve the problem.

2. Vertically and crosswise method

Why the vertically crosswise method works:
At each stage, you are computing those partial products whose place value matches the place value of the digit you are computing.

Why the vertically method is interesting:
There are relatively few intermediate results to keep track of (and all of those involve at most two-digit numbers). With a little practice, one can do all of the arithmetic in one’s head, and when presented with a multiplication problem of any complexity proceed directly to writing down the digits of the answers.


3. Grid multiplication

Why the grid multiplication works:

The numbers are arranged in a unique way before multiplying and adding the product together. The secret to why it works rest on the numbers arrangements and the grid box.

Why the grid multiplication is interesting:

This method provides a grid to use which systematically arranged the numbers to come to the conclusion and a fun way to solve the problem.


references:
References
Chamberlain, N. (2005). Long multiplication and percentage without a calculator. Mathematics In School Journal, 34 (2), 22-23.

Curriculum Development Department. (2006). Mathematics Syllabus For Lower Primary Schools. Bandar Seri Begawan: Curriculum Development Department.

Curriculum Development Department. (2007). Smart Mathematics Primary 4. Singapore City: EPB Pan Pacific.

Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities,
37(1), 4-15.

Glover, J. T. (2002). Vedic Mathematics for Schools Book 3. New Delhi: Motilal Banarsidass Publishers.