Math Strategy: Using strategic and efficient methods in both addition & multiplication

Math strategy: Using strategic and efficient strategies in addition, subtraction, multiplication & division
Math strand: Number Sense and Numeration

Overview: 
Not all problems should be solved in the same way.  Students need to have a variety of strategies that they can use proficiently when solving problems, yes, this may include the standard algorithm.

This handy checklist can help students know which strategy to use:
• easy to understand?
• easy to apply?
• easy to remember?
• easy to perform accurately?

With experience, students can learn to apply these criteria to their own strategies and develop ways for improving their efficiency and effectiveness.

Over-reliance on memorized addition and subtraction, multiplication and division procedures prevents students from using mathematical reasoning.
For example in subtraction students may persist with regrouping procedure to solve 2000-50, come up with 1050, and not reason that one step of the used procedure is missing, and their answer is wrong by a significant amount.

For example in multiplication a student using standard algorithm for 3x149 may come up with 327, forgetting to add the carrying numbers, and getting a wrong answer.



Students who learn the basic facts using a variety of strategies (i.e., making tens, using doubles, skip counting, using familiar facts) will be able to extend these strategies and their understanding of number to multi-digit computations and problem solving in more efficient ways. (Guide to effective instruction in mathematics, K-6, Vol. 5)

http://www.eworkshop.on.ca/edu/resources/guides/Guide_Math_K_6_Volume_5.pdf 


How this supports student learning:
Student-developed strategies are not necessarily efficient and effective.
For example, a student-generated strategy may require more steps and time than is appropriate. However, students develop and use these strategies because they make sense to them. As students share and compare their strategies, they will become better at finding methods that are both efficient and effective.

An efficient method is one that does not require a page of calculations and more than a reasonable amount of time to produce an answer. An effective method is one that works for all problems of a particular type (i.e., one that is generalizable to many problems using the same operation). Students need to learn to evaluate their own strategies and algorithms on the basis of the following criteria.

Is the strategy:
• easy to understand?
• easy to apply?
• easy to remember?
• easy to perform accurately?

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