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David Achen Retired Teacher South Middle School Grand Forks dave.achen@gmail

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  1. David AchenRetired Teacher South Middle School Grand Forksdave.achen@gmail.com

  2. Three Subjects : Or One for $30 1st one regular price plus half price for each extra one Algebra Pre-Algebra Math 116 139 108 Total All for $60 363

  3. Full Version Contains: Total Algebra Geometry 326 142 47 Math Jeopardy Games Writing 114 3 Word Problems Quizzes 20

  4. Using a Virtual Textbook for Tutoring • Develops understanding using Visual connections • Develops understanding using Conceptual connections • Easy to navigate, use and coordinated with Lessons • Can be used to learn, practice and review concepts

  5. Features of Virtual Textbook • Use of Color & Shapes • Develop Understanding using Visual Keys • Making Connections using Examples • Showing Relationships in Geometry • Developing Formulas in Geometry • Making Connections • Instruction and Practice • Visual Demonstration • Setting up Word Problems

  6. Fractions (Using Shapes & Colors)

  7. How many red trapezoids are in the yellow hexagon? How many green triangles are In the yellow hexagon? How many blue rhombuses are In the yellow hexagon?

  8. Integers (Using Cubes & Colors)

  9. -3 2 = + -5

  10. Understanding Polynomials (Using Visual Keys)

  11. Visual Keys -1 1 -x x -x2 x2 -x3 x3

  12. Add these Polynomials - 3 + 4x + 2x2 3x3 (+) - x + 2 2x3 - 1 + 3x 5x3 + 2x2

  13. Making Connections (Distributive Property)

  14. Dry Erase Board Dry Erase Marker Dry Erase Eraser $6.25 $1.50 + $1.25 + ( ) 20 $6.25 + $1.25 + $1.50 = = + $30 $125 $25 + $180

  15. Dry Erase Board Dry Erase Marker Dry Erase Eraser b + m + e ( ) 20 b + m + e = + 20 e 20 m 20 b +

  16. Showing Relationships (Corresponding Angles)

  17. Corresponding Angles. 1 2 4 3 145o 35o 145o 35o

  18. Developing Formulas (Surface Area)

  19. Top 12 units2 4 4 4 4 6 6 6 6 2 2 2 2 Bottom 12 units2 Front 24 units2 Back 24 units2 Side 8 units2 Side 8 units2 + 88 units2

  20. Rectangular Solid 2 LH units2 2 WH units2 H 2 LW units2 L W 2LH + 2WH + 2LW units2

  21. length = d d r2 2 r2 r2 Area Circle = r2 C = d r h h + h

  22. Making Connections (Simultaneous Equations)

  23. Subtracting 5 footballs + 3 baseballs $170 = 1 football 3 baseballs $70 + = 4 footballs + 0 baseballs $100 = 1 football = $25 3 baseballs 1 baseball = $45 $15

  24. Subtracting 5 f + 170 3 b = 1 f 3 b 70 + = 100 4 f + 0 b = 1 f = 25 3 b 15 1 b = 45

  25. If terms don’t match: **Change to Equivalent Equation 4 books + 6 binders $170 = (-) ( ) 1 books 2 binders + 3 books 6 binders $45 3 $135 = 1 book + 0 binders $35 $35 = $30 $170 6 binders 1 binder $5 $140 + = 4*

  26. Instruction & Practice (Multiplying Polynomials Using Algebra Tiles)

  27. 1 1 x 1 x x 1 x 1 1 1 (x + 3) (2x + 1) 2x2 + 7x + 3 = x x x x x x x2 x2

  28. Write Mutiplication Problem and Answer:

  29. Visual Demonstrations (Writing Equations & Working with Exponents )

  30. ( , ) 5 - 2 Equations from Ordered Pairs ** First we need to find the Slope! Now, using y = mx + b ( , ) ( , ) - 8 5 - 2 8 - 6 3 - 6 - 2 3 = y 8 - 2 - 2 x -10 + = * 5 ____

  31. y y y y y y (x2y3)2 x x x x . x2y3 x2y3 y6 x4

  32. Word Problems (Setting up Equations)

  33. Percent Whole Part x = 1. A family went out to dinner. They paid for the dinner and also left a 15% tip. The total including the tip was $41.40. How much was the dinner by itself?

  34. 115% 15% Tip? $41.40 Dinner + Tip? + Price of Dinner: ? 100% 0%

  35. Percent Whole Part x = 1. A family went out to dinner. They paid for the dinner and also left a 15% tip. The total including the tip was $41.40. How much was the dinner by itself? n 115% 41.40

  36. 2. Jim is three years older than twice Bill’s age now. If the sum of their ages is 42, how old is Bill? 42 + Jim Bill = Jim = 3 + 2b b ( ) + 2b 3 + 42 = b Bill = 42 3b + 3 = 39 = 3b 13 yrs old & 29 yrs old

  37. X 3. The tortoise and the hare decided to race. The tortoise left the starting line at 6 am. The hare didn’t begin until 10 am. When he started, he ran 4 mph faster than the tortoise and caught him at 10:30 am. How fast was each going? t mph ? mph 4.5 hours ? hours Tortoise (t + 4) mph .5 hours ? hours ? mph Hare (t + 4) 4.5 t .5 =

  38. Solving the Equation X 4.5 t = .5 (t + 4) 2 4.5 t .5t + = 2 4t = t ½ 2/4 mph =

  39. X Check the Solution: The tortoise and the hare decided to race. The tortoise left the starting line at 6 am. The hare didn’t begin until 10 am. When he started, he ran 4 mph faster than the tortoise and caught him at 10:30 am. How fast was each going? .5 mph ? mph 4.5 hours ? hours Tortoise ? hours .5 hours 4.5 mph ? mph Hare 2.25 2.25 (4.5) 4.5 (.5) = .5

  40. The End!