1. Transition Algebra Manuel Navarro and Dirk Hodges Austin, TX May 6 th and 7 th, 2011

3. TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA

4. TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA 10. “Baseball is ninety percent mental and the other half is physical.” (percentage)

5. TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA 9. “Half the lies they tell about me aren't true.” (fractions)

6. TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA 8. “I knew I was going to take the wrong train, so I left early.” (distance formula)

7. TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA 7. “You better cut the pizza in four pieces because I'm not hungry enough to eat six.” (fractions)

8. TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA 6. “I take a two hour nap, from one o'clock to four.” (subtraction)

9. TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA 5. “90% of the putts that are short don't go in.” (percentage)

10. TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA 4. “You give 100 percent in the first half of the game, and if that isn't enough in the second half you give what's left.” (percentage)

11. TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA 3. “The towels were so thick there I could hardly close my suitcase.” (Volume)

12. TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA 2. “A nickel ain't worth a dime anymore.” (value of money)

13. TOP TEN QUOTES FROM THAT GREAT MATHEMATICIAN, YOGI BERRA 1.“He hits from both sides of the plate. He's amphibious.” (okay it’s a biology question)

14. WHY DO ADULT LEARNERS STRUGGLE WITH “TRANSITIONAL” ALGEBRA? Bonnie Goonen national trainers for the Leadership Excellence Academy

15. Adult learners are encouraged to learn math from a “hands on, real world” perspective - Concrete learning.

16. But when they show up in the college classroom, they encounter the world of Abstract learning – rules, facts, theorems…

17. Strategy Fluency and Fluidity

18. Teach fluidity between the world of the abstract and the concrete, not just fluency in one.

19. Fluency = Accuracy with little effort

20. Fluidity = Ability to change with ease

21. 8 Simple Rules to exist in the fluid world of solving equations.

22. 1 st Simple Rule The goal of algebra is to find the value of an unknown.

23. X must be… Isolated – like Beyonce’ (single ladies) Positive – not like Country and Western music.

24. The answer needs to look like this: x Not like this: 2xor- x

25. 2 nd Simple rule A prerequisite for learning algebra is understanding balance.

26. 4x =8

27. 4 = 8

28. 4 = 8 4

29. x=2

30. 3 rd Simple rule Distributive Property If there are parentheses in an equation, then multiply across the parentheses distributing evenly.

31. Using the Distributive Property a.) 2(x + y) = 2x + 2y Example: Find each product by using the distributive property to remove the parentheses. b.) 7(x + 2y – 5z) = 7x + 14y – 35z c.) – 4(3a – 3b – 10c) = – 12a + 12b + 40c a.) 2(x + y) b.) 7(x + 2y – 5z)c.) – 4(3a – 3b – 10c)

32. 4 th Simple rule Addition Property of Equality Collect like terms by moving variables to one side of the fence and non-variables to the other side (making sure to change the sign if they cross over).

33. Much like corralling cattle and sheep. 3x = 6

34. +2 = x-4-2 -x

35. Combining Like Terms 6x 2 + 7x 2 19xy – 30xy 13xy 2 – 7x 2 y 13x 2 – 11xy Can’t be combined (since the terms are not like terms) Terms Before CombiningAfter Combining Terms

36. Combining Like Terms We cannot combine a chicken and a goat and create a Chickengoat

37. Combining Like Terms Or a Zonkey??

38. 5 th Simple rule Multiplication Property of Equality Divide (or multiply) both sides of an equation to get the variable isolated and positive.

39. 6x =18 6 6 x = 3

40. 6 th Simple rule Multiplication Property of Inequality If the problem is an inequality, then all rules apply with 2 exceptions: 1)When dividing by a negative number the direction of the arrow must be changed. 2)When there is a compound inequality each set of terms must be applied.

41. -6x >18 -6 x < 3

42. 0 < 20 8 < -4x20 -20 < -4x < -12 -4

43. 5 > x > 3

44. 7 th Simple rule Systems of equations If problem has 2 variables then must substitute the value of one of the variables (which is many times a polynomial) for the other.

45. Solve the following system using the substitution method. 3x – y = 6 and – 4x + 2y = –8 Solving the first equation for y, 3x – y = 6 –y = –3x + 6 y = 3x – 6 Multiply both sides by – 1.) Substitute this value for y in the second equation. –4x + 2y = –8 –4x + 2(3x – 6) = –8 Replace y with result from first equation. –4x + 6x – 12 = –8 Use the distributive property. 2x – 12 = –8 Simplify the left side. 2x = 4 Move 12 to the other side and change sign. x = 2 Divide both sides by 2. The Substitution Method Continued. Example:

46. Substitute x = 2 into the first equation solved for y. y = 3x – 6 = 3(2) – 6 = 6 – 6 = 0 Our computations have produced the point (2, 0). Check the point in the original equations. First equation, 3x – y = 6 3(2) – 0 = 6 true Second equation, –4x + 2y = –8 –4(2) + 2(0) = –8 true The solution of the system is (2, 0). The Substitution Method Example continued :

47. 8 th Simple rule Square Root Property If problem has a quadratic (square) then utilize square root.

48. Square Root Property If b is a real number and a 2 = b, then

49. Solve x 2 = 49 Solve (y – 3) 2 = 4 Solve 2x 2 = 4 x 2 = 2 y = 3  2 y = 1 or 5 Square Root Property Example :

50. Solve (x + 2) 2 = 25 x =  2 ± 5 x =  2 + 5 or x =  2 – 5 x = 3 or x =  7 Square Root Property Example :

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