1. MTH 232 Section 3.3 Algorithms for Multiplication and Division of Whole Numbers

2. Overview Multiplication and division of whole numbers are confusing for some elementary students, largely because the rules are: 1.Confusing; 2.Taught with the expectation of memorization rather than understanding. It is often the case that the first one happens because of the second one.

3. Multiplication is Repeated Addition

4. But… While the concept of repeated addition works on a one-digit level, larger numbers are difficult to execute. To be clear, one-digit multiplication facts should be memorized. The key to larger-digit multiplication is establishing a deep understanding of positional systems and notation, in conjunction with the distributive property of multiplication over addition.

5. Multiplication Algorithms 1.Expanded Notation 2.Instructional – similar to Expanded Notation except the products are written vertically. 3.Final – the “traditional” method.

6. Multidigit Multiplication The Instructional and Final Algorithms are frequently used. Consider the Lattice Algorithm:

7. Division Algorithms The Partition Method can be used to model one-digit division (particularly with base-ten blocks or mats, strips, and units). The other algorithms are based on the Repeated Subtraction Method (using 100s and 10s of your divisor rather than individual subtractions of your divisor). The Long Division Algorithm is the “traditional” method of division.