This unit template from the Hempfield School District covers tools of algebra. It includes the unit title, teachers who developed it, dates, and topics to be covered such as the real number system, order of operations, algebraic expressions, equations, inequalities, and probability. Students will understand properties of real numbers and how to use them to simplify expressions and solve equations and inequalities. They will also learn about experimental and theoretical probability. The unit will be assessed through benchmarks, self-assessments, and performance tasks.

1. 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?
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2. Hempfield School District Curriculum: Unit Template
• 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?
• 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:
•
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3. Hempfield School District Curriculum: Unit Template
Know Understand Do
Vocabulary: Students will understand: The Students will be Able to:
Rational number • Various types of • Locate real numbers on the number
Irrational number numbers are necessary line
Integer in the real world
Whole Number depending on the • Order real numbers
Natural Number problem or the situation
Opposite • Identify to which set(s) of numbers a
Additive inverse • Properties of real number belongs
Reciprocal numbers can be used to
Commutative Property rewrite mathematical • Find the opposite of a number
Associative Property expressions in
Identity Property equivalent forms • Find the reciprocal of a number
Inverse Property
• Order of operations is
Distributive Property • Use properties of real numbers
important to ensure
Multiplicative inverse
consistency and
Absolute value • Find the absolute value of a number
accuracy when
Variable
simplifying expressions • Evaluate algebraic expressions
Algebraic expression
Variable expression
• Properties of real • Use properties of real numbers to
Evaluate
numbers can be used to simplify algebraic expressions
Term
rewrite mathematical
Coefficient
expressions in • Combine like terms
Solution of an equation
equivalent forms and
Compound inequality
simplify algebraic • Evaluate real-world algebraic
Interval Notation
expressions expressions
Absolute value
Extraneous solution
• Solve an equation with a variable on
• Many real-world
Experimental probability
both sides
situations and problems
Theoretical probability
can be modeled with
Sample space
• Use the distributive property
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4. Hempfield School District Curriculum: Unit Template
Simulation algebraic expressions
and then used to solve • Solve a formula for a given variable
real-world problems
• Solve an equation for a variable
• A solution(s) of an
equation is a number(s) • Write and solve equations that model
that makes the equation real-world problems
true
• Solve and graph inequalities
• Equations can be used
• Solve and write compound
to solve real-world
inequalities containing either and or or
problems by defining a
variable(s) to represent
• Write and solve inequalities that
the unknown value(s)
model real-world problems
and using the given
information in the
• Write the solution set of an inequality
problem to write an
in interval notation
equation
• Solve absolute value equations
• Solutions of an
inequality are the
• Check for extraneous solutions
numbers that make the
inequality true
• Solve absolute value inequalities
• Inequalities can be
• Graph the solution set of an absolute
used to solve real-world
value inequality on a number line
problems by defining a
variable(s) to represent
• Write the solution set of an absolute
the unknown value(s)
value inequality in interval notation
and using the given
information in the • Find the experimental probability
problem to write an
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5. Hempfield School District Curriculum: Unit Template
inequality or compound • Find the theoretical probability
inequality
• Find the odds
• Inequalities are
necessary to use in real • Solve real-world problems using
world problems that may probability or odds
have many solutions or
an infinite number of • Find geometric probability
solutions
• An absolute value
quantity is nonnegative.
• 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
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6. Hempfield School District Curriculum: Unit Template
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
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.
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7. Hempfield School District Curriculum: Unit Template
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
Differentiation:
Readiness Profile: Learning Styles / Interest
Multiple Intelligences
• . • •
Accommodations for ELLs:
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8. Hempfield School District Curriculum: Unit Template
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