Multiplication and Division Concepts 175Successful Strategies
While the equal products concept can be used in any
multiplication situation, it is most effi cient when the newly
created expression invites mental math. We need to teach
students to get a feel for the numbers they are working with. Is
the multiplicand (or multiplier) a number that is easier to work
with when it is doubled? Is the multiplier (or multiplicand)
even? Students must learn how to analyze multiplication
equations to help them fi gure out which concept is preferred.
For some students the equal products concept is a mystery.
If they do not understand why the doubling and halving
procedures work, they will not build conceptual understanding
of multiplication. One of the best ways to model the equal
products concept is with arrays. If we have a paper array that is
25 x 6, we can cut the array and slide part of it to show 50 x 3.
product, multiplicand,
multiplier, multiplication,
multiply, equal, equation,
expressionMath Words to Use
Questions at Different Levels of Cognitive Demand
Recall: What is 25 x 8?
Comprehension: How would you solve 35 x 6?
Application: Where would you cut and how would
you move the array to show an equal product?
Analysis: How would you compare and contrast the
products?
Evaluation: Is equal products always the most effi cient
way to solve an equation? Why?
Synthesis: What if we quadrupled the multiplier?EASYCOMPLEX