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

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

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**David AchenRetired Teacher South Middle School Grand**Forksdave.achen@gmail.com**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**Full Version Contains:**Total Algebra Geometry 326 142 47 Math Jeopardy Games Writing 114 3 Word Problems Quizzes 20**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**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**Fractions**(Using Shapes & Colors)**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?**Integers**(Using Cubes & Colors)**-3**2 = + -5**Understanding Polynomials**(Using Visual Keys)**Visual Keys**-1 1 -x x -x2 x2 -x3 x3**Add these Polynomials**- 3 + 4x + 2x2 3x3 (+) - x + 2 2x3 - 1 + 3x 5x3 + 2x2**Making Connections**(Distributive Property)**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**Dry Erase Board**Dry Erase Marker Dry Erase Eraser b + m + e ( ) 20 b + m + e = + 20 e 20 m 20 b +**Showing Relationships**(Corresponding Angles)**Corresponding Angles.**1 2 4 3 145o 35o 145o 35o**Developing Formulas**(Surface Area)**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**Rectangular Solid**2 LH units2 2 WH units2 H 2 LW units2 L W 2LH + 2WH + 2LW units2**length = d**d r2 2 r2 r2 Area Circle = r2 C = d r h h + h**Making Connections**(Simultaneous Equations)**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**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**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***Instruction & Practice**(Multiplying Polynomials Using Algebra Tiles)**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**Visual Demonstrations**(Writing Equations & Working with Exponents )**( , )**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 ____**y**y y y y y (x2y3)2 x x x x . x2y3 x2y3 y6 x4**Word Problems**(Setting up Equations)**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?**115%**15% Tip? $41.40 Dinner + Tip? + Price of Dinner: ? 100% 0%**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**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**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 =**Solving the Equation**X 4.5 t = .5 (t + 4) 2 4.5 t .5t + = 2 4t = t ½ 2/4 mph =**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