The discriminant of a quadratic equation, ax2 + bx + c = 0 is D = b2 – 4ac. If D>0, the quadratic equation has two distinct roots; if D<0, then the equation has no real roots; and, if D=0, the we have two equal roots. Let’s apply it in the following problem. Continue reading “Application of the Discriminant”
Category: Algebra
Types of Problem Solving Tasks
The phrase ‘problem solving’ has different meanings in mathematics education. Even its role in mathematics teaching and learning is not clear cut. Some view problem solving as an end in itself. Others see it as starting point for learning. Nevertheless, here are some of the types of problem solving tasks we would see in textbooks and teaching. They are arranged according to cognitive demand. Remember that learners will only consider something a problem if they experience some sort of barrier in a situation they are curious about. There’s a difference between an exercise and a problem. Continue reading “Types of Problem Solving Tasks”
When is it algebra and when is it arithmetic?
In the post Algebra vs Arithmetic, I distinguished between arithmetic and algebra by arguing that it has nothing to do with the use of letters. That algebra is about letters and arithmetic is about numbers is an oversimplified view of algebra and can create misconceptions. Here are more ways of characterizing algebra. Continue reading “When is it algebra and when is it arithmetic?”
FOIL Method is Distributive Law
The FOIL method is not that bad really for teaching multiplication of two binomials as long as it is derived from applying the distributive law or more officially known as the Distributive Property (over addition or subtraction).
The FOIL method is a mnemonic for First term, Outer term, Inner Term, Last term. It means multiply the first terms of the factors, then the outer terms, then the inner terms and the last terms. I would suggest the following sequence of examples before the teacher introduces product of two binomials: Click here for the complete description of how to teach this with meaning.
Simplify the following expressions
- 3(2x-1)
- 3x(2x-1)
- -3x(2x-1)
- (x+3)(2x-1)
The FOIL method is also related to Line Multiplication. However, while the latter is applicable to any number of terms in the factors like the Distributive Law, the FOIL method is not. It only works for getting the factors of binomials. This is why it is not a powerful tool. The most powerful knowledge is still the distributive property of equality. Before the teacher should introduce any fancy way of calculating, he or she should make sure this knowledge is in place. Sample lesson on how to do this is presented in Sequencing Examples.
Want a more challenging problem for distributive law? Click Application of Distributive Law.