Hempfield School District Curriculum: Unit Template
Course Title:
Unit Title: Tools of Algebra
Names of Teachers who Developed Unit:
Dates Developed:
Approximate Dates when Taught During School Year:
Approximate Number of Periods:
Summary:
Print Materials Needed:
Resources:
Internet Resource Links:
Stage 1: Desired Results
Essential Questions (Include PA Standards, Anchors & Eligible Content)
Big Ideas:
• Numbers, measures, expressions, equations, and inequalities can represent mathematical
situations and structures in many equivalent forms.
• There are some mathematical relationships that are always true and these relationships
are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of
expressions and solving equations and inequalities.
• Probability expresses the likelihood that a particular event will occur. Data can be used to
calculate an experimental probability, and mathematical properties can be used to determine
a theoretical probability. Either experimental or theoretical probability can be used to make
predictions or decisions about future events. Various counting methods can be used to
develop theoretical probabilities.
Essential Questions:
• What are the relationships among the numbers sets in the real number system?
• How can the properties of real numbers be used in mathematics?
• Why is the order of operations important and necessary?
• How can properties be used to simplify algebraic expressions?
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Hempfield School District Curriculum: Unit Template
• Why is evaluating expressions important in the real world?
• What does it mean to “solve an equation”?
• How can you use an equation to solve a real world problem?
• Why are inequalities necessary when solving some real world problems?
• How does solving inequalities differ from solving equations?
• How can compound inequalities help describe real world situations?
• How do you write absolute value inequalities as compound inequalities?
• How do you solve absolute value inequalities algebraically and graphically?
• How are probability and odds different?
• How do we use probability and odds in everyday life?
• What is the difference between experimental probability and theoretical probability?
Assessment Anchors:

Eligible Content:

Know
Vocabulary:
Rational number
Irrational number
Integer
Whole Number
Natural Number
Opposite
Additive inverse
Reciprocal
Commutative Property
Associative Property
Identity Property
Inverse Property
Distributive Property
Multiplicative inverse
Understand
Students will understand:
• Various types of
numbers are necessary
in the real world
depending on the
problem or the situation
• Properties of real
numbers can be used to
rewrite mathematical
expressions in
equivalent forms
• Order of operations is
important to ensure
consistency and
Do
The Students will be Able to:
• Locate real numbers on the number
line
• Order real numbers
• Identify to which set(s) of numbers a
number belongs
• Find the opposite of a number
• Find the reciprocal of a number
• Use properties of real numbers
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Hempfield School District Curriculum: Unit Template
Absolute value
Variable
Algebraic expression
Variable expression
Evaluate
Term
Coefficient
Solution of an equation
Compound inequality
Interval Notation
Absolute value
Extraneous solution
Experimental probability
Theoretical probability
Sample space
Simulation
accuracy when
simplifying expressions
• Properties of real
numbers can be used to
rewrite mathematical
expressions in
equivalent forms and
simplify algebraic
expressions
• Many real-world
situations and problems
can be modeled with
algebraic expressions
and then used to solve
real-world problems
• A solution(s) of an
equation is a number(s)
that makes the equation
true
• Equations can be used
to solve real-world
problems by defining a
variable(s) to represent
the unknown value(s)
and using the given
information in the
problem to write an
equation
• Solutions of an
inequality are the
numbers that make the
inequality true
• Inequalities can be
used to solve real-world
problems by defining a
variable(s) to represent
the unknown value(s)
and using the given
information in the
problem to write an
• Find the absolute value of a number
• Evaluate algebraic expressions
• Use properties of real numbers to
simplify algebraic expressions
• Combine like terms
• Evaluate real-world algebraic
expressions
• Solve an equation with a variable on
both sides
• Use the distributive property
• Solve a formula for a given variable
• Solve an equation for a variable
• Write and solve equations that model
real-world problems
• Solve and graph inequalities
• Solve and write compound
inequalities containing either and or or
• Write and solve inequalities that
model real-world problems
• Write the solution set of an inequality
in interval notation
• Solve absolute value equations
• Check for extraneous solutions
• Solve absolute value inequalities
• Graph the solution set of an absolute
value inequality on a number line
• Write the solution set of an absolute
value inequality in interval notation
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Hempfield School District Curriculum: Unit Template
inequality or compound
inequality
• Inequalities are
necessary to use in real
world problems that may
have many solutions or
an infinite number of
solutions
• An absolute value
quantity is nonnegative.
• Find the experimental probability
• Find the theoretical probability
• Find the odds
• Solve real-world problems using
probability or odds
• Find geometric probability
• Since opposites have
the same absolute value,
an absolute value
equation can have two
solutions.
• Inequalities can be
used to solve real-world
problems by defining a
variable(s) to represent
the unknown value(s)
and using the given
information in the
problem to write an
inequality or compound
inequality.
• Absolute value
inequalities can be
written as compound
inequalities without
absolute value signs.
• The probability, p, of
an event is a number
such that 0≤p≤1. The
probability of an
impossible event is 0.
The probability of a
certain event is 1.
• Experimental
probability is determined
by dividing the number
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Hempfield School District Curriculum: Unit Template
of times the event
occurred by the total
number of trials. Data is
gathered from the actual
trials or a simulation.
• Theoretical probability
is determined by
dividing the number of
outcomes in which an
event occurs by the total
number of outcomes. It
can be used to predict
the experimental
probability.
Stage 2: Assessment Evidence
Assessments/Performance Tasks
Rubric Titles
Benchmark(s) for Course: Unit’s key Assessments
Self-Assessments
Other Evidence, Summarized
Stage 3: Learning Activities
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Hempfield School District Curriculum: Unit Template
Differentiation:
Readiness

.
Profile: Learning Styles /
Multiple Intelligences

Interest

Accommodations for ELLs:

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