FOIL’ing through Math: A Blast from the Past!
Remember those days in math class when you learned the acronym FOIL as a mathematical tool? This method was used to help us multiply two binomials, but with the advent of newer methods like the AREA MODEL & BOX METHOD, the FOIL method might seem like a thing of the past to some. However, let's take a step back & reminisce about this classic technique to better understand its evolving role in the world of mathematics education.
FOIL stands for First, Outer, Inner, Last & is a systematic way to multiply two binomials. Take a look at the #MathGIF below. Watch it a couple times - does FOIL seem familiar? Questions you may ask yourself as you watch:
What is meant by First? What is meant by Outer? What is meant by Inner? What is meant by Last?
What is happening mathematically when the left piece & right piece are each pulled down & seemingly combined?
How does FOIL relate to previous topics discussed here at Mister Marx’s Math Corner?
While FOIL can be a useful tool for finding the product of two binomials, its sole use does run the risk of leaving students with a lack of a true understanding of the distributive property occurring. The reason being that FOIL is limited strictly to finding the product of two binomials, making it insufficient for finding the product of varying numbers of polynomials with any number of terms. As a result, students who rely solely on FOIL may struggle to make the leap to more advanced multiplication concepts & might miss out on a deeper understanding of the distributive property.
That being said, it is crucial to recognize that FOIL remains a valuable tool for students to learn. However, for students to fully develop a deep understanding of mathematics, it's important to expose them to multiple approaches & techniques beyond just FOIL. The BOX METHOD & the AREA MODEL - both of which I have written about previously - are examples of modern approaches that incorporate visual aids & organized structures, & are adaptable as students progress in their mathematical understanding.
In conclusion, FOIL may be a classic technique for multiplying binomials, but it can leave students with a limited understanding of the distributive property. Newer methods like the AREA MODEL & the BOX METHOD provide the visual representation & organized structure of the distributive property & can help students gain a deeper understanding of multiplication. So, let's not forget tried & true FOIL, but let’s also embrace newer methods like the BOX METHOD & the AREA MODEL to help us fully grasp the concept of distributive property in mathematics.
What do you think? Share your thoughts on FOIL, the BOX METHOD & the AREA MODEL in the comments section below!
