David Achen Retired Teacher South Middle School Grand Forks dave.achen@gmail
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Transcript of 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
[email protected]@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)
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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?
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The The End!End!