Lesson Plan (Teaching Demo) - Rational Inequalities

Lesson Plan: May Plan: May 17, 2018 Topic: Rational Inequalities Objectives: 1. To teach the difference of rational equations and rational inequalities 2. To properly introduce the concept of rational inequalities 3. To teach how to solve rational inequalities in an orderly manner Time: 1 hour Materials: Pen and paper (taking notes and answering activities) Procedure: 1.  Ask the students if they are familiar with rational rational expressions and and equations and the factoring and special products methods. If they are not familiar, provide a  short review. Rational Expressions is Expressions  is a fraction where the numerator and denominator are polynomials. Difference from a polynomial expression : variable is present in the denominator for a rational expression. Polynomial Expression

Rational Expression    2 2  1

   2  1

2

Rational Equations are equations containing at least one fraction whose numerator and denominator are polynomials. Difference from a polynomial equation: equation : variable is present in the denominator of at least one fraction for the rational equation. Polynomial Equation    2  1 =

Rational Equation



1

7

2

2=

5 

Factoring and Special Products is commonly used in solving rational equations and inequalities. FACTORING Common Monomial Factor Difference of Two Squares Factoring of a Trinomial Etc. SPECIAL PRODUCTS FOIL Method

   =  (  )     = (  )( )(  )    3  2 = (  2)( 2)(   1) 1) 

(  2)(  1) =     2  1 =    3  2

2. Provide the difference between rational equation and rational inequalities. Rational Equation:  +

 = 3 → 1 = 3(  3) → allowed

Rational Inequalities:  +

 ≥ 1 → 2 ≥ 1(  3) → not allowed, the sign of x+3 is still unknown. If it turns out

to be negative, we need to change ≥  ≤. 3. Explain concepts of solving rational inequalities and enumerate general steps on how to solve it. a. Goals i. Find the value/s of x which makes the inequality true. ii. Find the value/s of x which makes the inequality undefined. b. General Steps on how to solve Rational Inequalities i. If the left or the right side of the inequality contains addition and subtraction, combine them to a single fraction with the use of LCD. ii. Factor all the factorable polynomials in the numerator and denominator in both sides of the inequality. iii. Cancel all similar factors in the numerator and the denominator. Do it for the left side and the right side of the inequality. Note: if a similar factor is found in the left side and the right side of the inequality, DO NOT CANCEL IT. iv. Find all the value/s of x which will make the numerator and denominator equal to zero. These are the values where the rational expression might change signs. v. From the number line, choose one test points in each region, solve for the inequality. If the inequality is true, the region is a solution set of the rational inequality. The value/s of x obtained in iv. is included in the solution set if the inequality has either ≥  ≤., otherwise, it is not. The value/s of x which will make the rational inequality undefined is NOT INCLUDED in the solution set. •

•

•

4.  Show examples on how to solve rational inequalities following the general steps. Examples: •

•

+

 ≤ 0 (show solutions following the general steps)→Answer: [-1,5)

−  +4+ −

> 0  (show solutions following the general steps) →Answer: (-3,-

1)U(1, ∞)

5. Let the students answer some exercises and after around 10 minutes, explain how to answer the problems in the board. Exercises: •

•

•

+

≥1

+4   −6

(−) −8 

→Answer:



(-∞,-4)U[ , ∞) 

 < 0 →Answer: (-4,1)U(1,4) →Answer:

< 3 

(-∞,-2)U(0,4)

6. Provide some items they can answer at home. Homework: •

•

•

+ +6 −

>0

 < 2

+  +9+4 −

≤0

Prepared by: CHRISTIAN S. GALOPE For teaching demonstration purposes only.