Lesson Topic: Literal Equations & Inequalities

1. Lesson Topic: Literal Equations & Inequalities Ms. Valencia’s Algebra Class Grade: 8th 10/19/2010

2. Moving Forward To New & Better Equations teacherspayteachers.com, qwickstep.com, green-planet-solar-energy.com, www.mathsteacher.com.au/.../Image1404.gif, prep.math.lsa.umich.edu/pmc/images/8.1.e.5.gif

3. Prior Knowledge: You should know that…. • Literal equations • Contain several letters • Are formulas • Inequalities • Are equations • Result in a set of numbers which we will use to graph • Absolute of a negative number is always positive

4. You should know how to….. • Literal Equations • Solve numerical equations • Solve for the given variable • Simplify equations • Inequalities • Know the difference between <, >, ≤, ≥ • Graph equations • Find absolute value

5. What are Literal Equations? • Literal equations consist primarily of letters . • FORMULAS. • Each variable in an equation “literally” represents an important part expressed by the equation. • For example: Perimeter of a rectangle P=2L+2W

6. What are Inequalities? • An Inequality is an equation with three differences. • It is solved just like an equation, except it has NO exact answer. • It will have many answers that satisfy that inequality. • We will now use the >, <, ≥, ≤ signs. • For example: 4+x>1-x; solve for x

7. In this lesson, you will learn that….. • Literal Equations • Equations without constants are solved the same way as equations with numbers only • Inequalities • Are solved just like ordinary equations • The <, >, ≥, ≤ signs have meanings & play a role when graphing its solution set • The solution set determines direction on the number line • Equations with absolute value will result in two answers

8. In this lesson, you will learn how to…. • Literal Equations • Solve literal equations with variables only as well as literal equations with numbers • Inequalities • Solve single, compound, & absolute value inequalities • Distinguish the meanings between <, >, ≤, ≥ signs • Graph inequality sets based on its direction

9. How to Solve Literal Equations? EXAMPLE 1 F= ab – ap; solve for a F= a(b – p) F = a(b – p) b – p b – p F = a(b – p) b – p b – p F = a b – p EXAMPLE 2 C= Kh + j; solve for K h h*(C= Kh + j)*h h Ch= Kh + j -j -j Ch – j= Kh Ch – j= Kh h h Ch-j= K h

10. How to Solve Inequalities? Single Inequality 6x – 3 < 7 + 4x 6x – 3 < 7 + 4x +3 +3 6x < 10 + 4x 6x< 10 + 4x -4x -4x 2x< 10 2x< 10 2 x< 2 Meaning of < ??? Open circle

11. How to Solve Inequalities? Compound Inequality -3 ≤ x – 2 < 4 -3 ≤ x – 2 x – 2 < 4 -3 ≤ x – 2 x – 2 < 4 +2 +2 +2 +2 -1 ≤ x x < 6 -1 ≤ x < 6 Meaning of ≤ and < ?? Closed and open circle

12. How to Solve Inequalities? Absolute Value Inequality 10 – 2k ≥ 6 10 – 2k ≥ 6 10 – 2k ≤ -6 10 – 2k ≥ 6 10 –2k ≤ -6 -10 -10 -10 -10 -2k ≥ -4 -2k ≤ -16 -2k ≥ -4 -2k ≤ -16 -2 -2 -2 -2 k ≤ 2 k ≥ 8 k ≤ 2 or k ≥ 8 k

13. Worksheet Time • Activity 1: This worksheet will provide extra practice on Literal Equations. It is time for your first activity get prepared to further your learning….YEAH!!!! Let me know if you need help!!! Click icon to see worksheet!! panther.moundsparkacademy.org/.../eqtn-11.gif

14. Who Is My Partner? • Activity 3: We are going to play a game that will help you review <, >, ≤, ≥ signs. The mathematical sign in inequalities plays a crucial role when it comes to graphing. • The game will go like so. I will divide the class into two big groups. One group will have flash cards that will contain different integers (positive, negative, and absolute value integers). The other group will have flash cards that contain the different mathematical signs (<, >, ≤, ≥). Due to the fact that there are only four signs, the groups will take turns. Student will say > Student with correct sign will say “ I am.’ ≤ NO Sol. -31___-27 Who is my Partner? ≥ <

15. Who Wants To Be A Millionaire • Activity 2: Students to further your knowledge on Inequalities we are going to play a FUN game of Who Wants To Be A Millionaire. The game will consist of various inequality problems. At this point, please break into your groups of four. Quietly, Thanks. Are you prepared to WIN A $1,000,000? Let’s Start..Click on the number line algebralab.org

16. Internet Resources Available • Extra Help on Literal Equations • Extra Help on Inequalities WEB PAGE Click Me VIDEO TUTORIALS Click Here MINI INEQUALITY GAME This webpage also contains useful videos. Take a LOOK. Click Me More Practice Problems Click Here http://www.youtube.com/watch?v=SKHQFPIOqNk&p=C042AB30BD21BC80&index=1&feature=BF, http://www.regentsprep.org/regents/math/algebra/AE4/litless.htm , http://www.math-play.com/Inequality-Game.html , sacbee.com

17. End Of Lesson • This is the end of our lesson. Now you are experts when it comes to Solving Literal Equations & Inequalities! • NOTE: Please let me know if you need extra help…I am here.

18. Resources • Algebra 1 Online. (2002-2010). Class work: Solving Inequalities Worksheet. In Module- Solving Inequalities. Retrieved October 18, 2010, from http://teachers.henrico.k12.va.us/math/hcpsalgebra1/module4-1.html • Schultzhie, L. (1998-2010). Literal Equations. In Algebra Lesson Page. Retrieved October 18, 2010, from http://www.regentsprep.org/regents/math/algebra/AE4/litless.htm • Ttor68. (2007). A16.15 Inequlity Example. In YouTube. Retrieved October 18, 2010, from http://www.youtube.com/watch?v=SKHQFPIOqNk&p=C042AB30BD21BC80&index=1&feature=BF • Popovici, D. (2007). Inequality Game. In Middle School Games. Retrieved October 18, 2010, from http://www.math-play.com/Inequality-Game.html • Valencia, J. How Wants To Be A Millionaire • Brown, R., Dolciani, M., Sorgenfrey, R., Cole, W. (2004). Inequalities CH 10. In Algebra: Structure and Method- Book 1

19. Resources Cont.. • Images • Sacbee.com • Algebralab.org • panther.moundsparkacademy.org/.../eqtn-11.gif • teacherspayteachers.com • qwickstep.com, green-planet-solar-energy.com • www.mathsteacher.com.au/.../Image1404.gif • prep.math.lsa.umich.edu/pmc/images/8.1.e.5.gif • evanborkowski.com