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GED® ADULT EDUCATOR
MATHEMATICAL REASONING
INSTITUTE
FOUNDATIONS OF
ALGEBRAIC
PROBLEM SOLVING
TOPIC 2
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Topic 2 - Foundations of
Linear Equations &
Inequalities
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LESSON GOALS
 A.1.c – Write linear expressions as part of word-tosymbol translations or to represent common settings.
 A.2.c – Write one-variable and multi-variable linear
equations to represent context.
 A.3.a – Solve linear inequalities in one variable with
rational number coefficients.
 A.3.d – Write linear inequalities in one variable to
represent context.
 A.6.c – Use slope to identify parallel and
perpendicular lines and to solve geometric problems.
MATHEMATICAL REASONING INSTITUTE
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WORKING WITH
THE CONTENT
Think, Pair, Share
Think & Work Alone
Cooperative
Learning In
Small
Groups
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Symbols to Words
Key Phrase
Sum, Increase, Add, All
together, Total
Math Symbols
+ (Addition)
Subtract, Decrease,
Difference Minus, Fewer
-
(Subtraction)
Times, Multiply, Product
x
(Multiplication)
Divide, Per, Quotient
÷
(Division)
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Symbols to Words Activity
Process:
Five posters numbered 1 to 5 with
linear expressions written on them
Number off 1 to 5
Start at the poster numbered with
your number
15 seconds at each poster to write
as many word phrases as you can
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Words to algebraic
expressions
Process:
Index card with a word phrase
Write the word phrase on your
poster
Reach consensus on the correct
translation to an algebraic
expression
Record translation on poster
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Try These with a Partner!
For each of the following, write an expression in terms
of the given variable that represents the indicated
quantity.
 The total cost of a mechanic to repair your car if he
spends h hours on the job and charges $39 for parts
and $45 per hour for labor.
 The sum of three consecutive numbers if the first
number is n.
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Try These with a Partner!
For each of the following, write an expression in terms
of the given variable that represents the indicated
quantity.
 The amount of money in Steve’s bank account if he put
in d dollars the first year, $600 more the second year
than the first year, and twice as much the third year as
the second year.
 The first side of a triangle is s yards long. The second
side is 3 yards longer than the first side. The third side
is three times as long as the second side. What is the
perimeter of the triangle in feet?
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Translating Words to
Linear Equations
Equations
n + 32 = 40
4x = 36
K - 7 = 15
3w = -15
6/x = 2
MATHEMATICAL REASONING INSTITUTE
Words
A number increased by 32
is equal to 40.
Four times a number is 36.
Seven less than a number is
15.
The product of a number
and 3 is -15.
Six divided by a number is
equal to 2.
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Context to
Linear Equations
Context
John called a plumber to fix
his broken toilet. In
addition to a $50 fee for
the visit, the plumber
charges $22 per hour.
Write an equation that
models this situation to
determine how many
hours the plumber took if
John’s total bill was $116.
MATHEMATICAL REASONING INSTITUTE
Equation
h = hours the plumber
worked
50 +
50 + 22h
50 + 22h = 116
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Context to
Linear Equations
Context
Jane needs $2100 for a
vacation for spring break.
She plans to save $350
per month for the trip.
Write an equation that
represents this situation
to help Jane determine
how many months it will
take her to save for the
trip at this rate.
MATHEMATICAL REASONING INSTITUTE
Equation
m = number of months to
save for trip
350m
350m = 2100
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Context to Multi-variable
Linear Equations
Context
A line on a graph represents
a ramp that extends from
the back of a moving
truck to the ground. The
line has a slope of -.5 and
passes through (8, 0).
The y-intercept
represents the height of
the back of the moving
truck. Write an equation
with two variables that
represents this situation.
MATHEMATICAL REASONING INSTITUTE
Equation
y = mx + b
y = -.5x + b
0 = -.5(8) + b
0 = -4 + b
4=b
y = -.5x + 4
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Linear Inequalities
https://www.youtube.com/watch
?v=8hhewFQ_K0w
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Inequalities vs. Equations
Activity
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Slopes of Parallel &
Perpendicular Lines
https://www.khanacademy.org/
math/algebra/linear-equationsand-inequalitie/more-analyticgeometry/v/equations-ofparallel-and-perpendicular-lines
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Try with a partner!
• Describe in your own words the
relationship of the slopes of
parallel lines.
• Describe in your own words the
relationship of the slopes of
perpendicular lines.
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Try with a partner!
Using what you know about parallel and perpendicular lines
and the relationships of their slopes and what you know
about writing the equations of lines do the following:
• Find the equation of the line that is perpendicular to
y = -4x + 10 and passes through the point (7, 2). Leave
your answer in standard form.
• Find the equation of the line that is parallel to y = -4x + 10
and passes through the point (7, 2). Leave your answer in
standard form.
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Lunch Time!
Please come back on time.
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