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

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David AchenDavid Achen Retired Teacher Retired Teacher

South Middle School South Middle School Grand ForksGrand Forks

dave.achen@gmail.comdave.achen@gmail.com

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Pre-AlgebraPre-Algebra

116MathMath

108AlgebraAlgebra

139

Three Subjects :Three Subjects :

TotalTotal

363

11stst one regular price plus half price for one regular price plus half price for each extra one each extra one

One for $30One for $30 OrOr

All for $60All for $60

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AlgebraAlgebra

142GeometryGeometry

47MathMath

114Word ProblemsWord Problems

20

WritingWriting

3QuizzesQuizzes

Jeopardy Jeopardy GamesGames

Full Version Full Version Contains:Contains:

TotalTotal

326

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Using a Virtual Textbook for Tutoring

Easy to navigate, use and coordinated with Lessons

Develops understanding using Visual connections

Can be used to learn, practice and review concepts

Develops understanding using Conceptual connections

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Features of Virtual TextbookFeatures 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

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Fractions (Using Shapes & Colors)

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How many red trapezoids are in the yellow hexagon?

How many blue rhombuses areIn the yellow hexagon?

How many green triangles areIn the yellow hexagon?

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Integers (Using Cubes & Colors)

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-3-5 + 2 =

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Understanding Polynomials

(Using Visual Keys)

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x

x2

x3

-x

-x2

-x3

1 -1

Visual KeysVisual Keys

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3x3

(+)

- 3+ 4x

+ 22x3

+ 2x2

- x

5x3 + 2x2 + 3x - 1

Add these Add these PolynomialsPolynomials

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Making Connections

(Distributive Property)

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Dry Erase Board

Dry Erase Eraser

Dry Erase Marker

$6.25 $1.25 $1.50

$25$125 $30

+

+

+

+

20 =$6.25 + $1.25 + $1.50( )

=

$180

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Dry Erase Board

Dry Erase Eraser

Dry Erase Marker

b m e

20 m20 b 20 e

+

+

+

+

( )20 =b + m + e

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Showing Relationships

(Corresponding Angles)

XX FeaturesCorresponding Angles.

3535oo

11

145145oo

2233 44

3535oo 145145oo

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Developing Formulas

(Surface Area)

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44

2266

44

2266

44

2266

44

2266

Top 12 unitsTop 12 units22

Bottom 12 unitsBottom 12 units22

Front 24 unitsFront 24 units22

Back 24 unitsBack 24 units22

Side 8 unitsSide 8 units22

++88 units88 units22

Side 8 unitsSide 8 units22

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Rectangular

Solid

LL WW

H H

LH unitsLH units22 WH unitsWH units22 LW unitsLW units22

2LH + 2WH + 2LW units2LH + 2WH + 2LW units22

222222

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Area Circle = rArea Circle = r22

hh

dd

C = dC = d

++

rr22

hh

hh

rrlength = dlength = d

2 r2 r22

rr22

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Making Connections

(Simultaneous Equations)

XX Features

5 footballs + 3 baseballs = $170

1 football + 3 baseballs = $70

4 footballs + 0 baseballs = $100

Subtracting

1 football = $253 baseballs = $451 baseball $15

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5 f + 3 b = 170

1 f + 3 b = 70

4 f + 0 b = 100

Subtracting

1 f = 253 b = 451 b 15

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$140 + 6 binders = $170

( )

4 books + 6 binders = $170

1 books + 2 binders = $45

1 book + 0 binders = $35

If terms don’t match:If terms don’t match:

3 books 6 binders $1353(-)

$354* $301 binder $5

**Change to Equivalent Equation**Change to Equivalent Equation

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Instruction & Practice

(Multiplying Polynomials Using Algebra Tiles)

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x

x 1 1 1

x

1

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

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Write Mutiplication Problem and Answer:

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Visual Demonstrations(Writing Equations &

Working with Exponents )

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( , ) 5 - 2 ( , )8 - 8

Equations from Ordered Pairs

3 - 6

3- 6 = - 2

____- 2 x=y + - 2 * 5 8 -10

( , ) 5 - 2

** First we need to find the Slope!Now, using y = mx + b

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xx xx

(x(x22yy33))22

xx22yy33 xx22yy33..

xx44 yy66

yy yyyyxx xx yy yyyy

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Word Problems(Setting up Equations)

XX Features 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?

=xPartPartWholeWholePercentPercent

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115%115%

100%100%

Price of Price of Dinner:Dinner:

++

0%0%

Dinner + Tip?Dinner + Tip?

??

Tip?Tip? 15%15%$41.40$41.40

XX Features 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?

=xPartPartWholeWholePercentPercent

115%115% nn 41.4041.40

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( )( )BillBill == bbJimJim == 3 + 2b3 + 2b BillBill JimJim++ == 4242

== 42423b + 33b + 3 == 4242

3b3b == 3939

bb 33++ 2b2b++

13 yrs old13 yrs old

2. Jim is three years older than twice Bill’s age now. If the sum of their ages is 42, how old is Bill?

29 yrs old29 yrs old&&

== .5.5 (t + 4)(t + 4)

TortoiseTortoise

HareHare

4.5 t4.5 t

? mph? mph

(t + 4) mph(t + 4) mph

? hours? hours4.5 hours4.5 hours

.5 hours.5 hours? hours? hours

t mpht mph

? mph? mph

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?

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.5t.5t4.5 t4.5 t ==

4.5 t = .5 (t + 4)4.5 t = .5 (t + 4)

Solving the EquationSolving the Equation

22 4t4t ==

++ 22

½ ½ tt == mphmph2/4 2/4

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== .5.5 (4.5)(4.5)

TortoiseTortoise

HareHare

4.5 (.5)4.5 (.5)

? mph? mph

4.5 mph4.5 mph

? hours? hours4.5 hours4.5 hours

.5 hours.5 hours? hours? hours

.5 mph.5 mph

? mph? mph

2.252.25 2.252.25

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?

XX

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The The End!End!