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To be able to think of numbers in factored form one must master the multiplication facts. Students should not only know that 8 x 7 = 56, but also should recognize when given the number 56 that it factors (breaks up) as 8 x 7. Requiring this next level motivates the student to get beyond using repeated addition to do multiplication problems. Being able to think this factoring way obviously makes division much easier.
After learning some divisibility rules, how to divide with a one-digit number, and the relationship between multiplication and division, students can factor numbers like 65. First they recognize that since it ends in the digit 5, it is divisible by 5. Dividing 65 by 5 yields 13, so they know that 65 = 5 x 13.
The REAL benefit of factoring comes in working with fractions. Fractions are so much easier to work with when we use factoring to help. We can use factoring to help reduce fractions to lowest terms, to help simplify multiplication and division problems, to find a common denominator when adding and subtracting fractions, and then to complete the addition and subtraction problems.
Working with fractions in this way helps students make the transition from basic mathematics to algebra. In algebra we factor algebraic expressions and use this to solve, not only problems involving fractions, but also problems in simplifying radical expressions and solving polynomial equations of degree two or higher.
The factoring idea, together with its prerequisite skills should be emphasized more in the elementary grades beginning in about the 3rd or 4th grades. Playing with the PrimePak deck of cards is a way to make this happen.
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