It is important that children are given the opportunity to devise their own strategies to help them gain understanding of the concepts they are learning. Van de Walle and Folk (194-196) discuss many of the invented strategies that are common amongst many students when dealing with larger numbers. They include:

**Useful Representations:**Children will often use a visual model to represent the problem they are presented with. This is often shown by using arrays.

**Complete-Number Strategies:**Students who are not comfortable with breaking a number down into its tens and ones, will resort to other methods when multiplying larger numbers. For example, they may use addition (23 x 6 = 23 + 23 + 23 +23 + 23 + 23 = 138).

**Partitioning Strategies:**When given higher number to multiply, students will sometimes break the numbers down in a variety of different ways. For example, some students may divide the numbers into tens and ones (32 x 3 : 10 x 3 = 30; 10 x 3 = 30; 10 x 3 = 30; 2 x 3 = 6; 30 + 30+ 30 + 6 = 96). Others may decide to partition by decades ( 30 x 3 = 90; 2 x 3 = 6), while others may find even more ways to divide the numbers.

**Compensation Strategies:**Children often find ways to manipulate numbers to allow for easier calculations (48 x 3 : 50 x 3= 150; 2 x 3 = 6; 150 - 6 = 144).

**Using Multiples of 10 and 100:**When presented with multiples of 10 and 100, students will often use the beginning part of the number to find the product. For example, for 300 x 12, students will often first multiply 3 x 12 and then use that to help them figure out 300 x 12. It is important to ensure students are not simply adding zeros to the end but are actually understanding why they are doing that.

Reference

Van de Walle, John, and Folk, Sandra. Elementary and Middle School Mathematics - Teaching Developmentally. Canadian ed. Pearson Education Canada, 2005.

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