QUARTER
TWO
QUARTER ONE
Overarching
Algebra 1: Mathematics
Year-at-a-Glance
Overarching Unit: Analyzing and Graphing Data
(Taught Throughout the School Year)
Throughout the year, students will extend their understanding of central
tendency to how the mean and is affected by the distribution (spread) of data.
Specifically, students will learn the importance of a line of best fit. They will
also learn that standard deviation is a quantified measure of a distribution and
that z-scores relate standard deviation to the area under a normal bell curve.
Standards of Learning:
Unit 1: Patterns and Tools of Algebra
This unit gives students an opportunity to explore numerical patterns in a
multi-representational manner while reviewing past material such as the
order of operations, evaluating expressions, and operations with real
numbers.
Activities for exploring numerical patterns can be found in the Stage Three
Learning Plan of this unit.
Standards of Learning:
Unit 2: Solving Equations
In this unit, students will solve equations in one and two variables using
concrete, pictorial representations and the symbolic. Students will learn to
solve increasingly, challenging problems over the course of this unit such as
variables on both sides of the equations; equations requiring distribution and
combining like terms; and word problem. Practice with solving equations will
lead to solving inequalities and an understanding of the difference between
the solution to an equation and a solution to an inequality.
Standards of Learning:
A.1
A.4
Unit 3: Solving Inequalities
In this unit, students will simplify and solve inequalities. Students will learn to
solve increasingly, challenging problems over the course of this unit such as
variables on both sides of the inequality requiring distribution and combining
like terms; and word problem. Practice with solving equations and inequalities
will build a strong understanding of the difference between the solution to an
equation and a solution to an inequality.
Standards of Learning:
Unit 4: Solving & Applying Proportions
Students will extend their prior knowledge of proportions by solving realworld problems involving equations. They will apply proportions to percent
equations, to probability situations, and to compound interest problems.
Standards of Learning:
A.4
Suggested Time
Frame:
Year long
A.9
A.10
A.1
A.7
Suggested Time
Frame:
2-3 weeks
Suggested Time
Frame:
3-4 weeks
A.5
Suggested Time
Frame:
2 weeks
Suggested Time
Frame:
2 weeks
QUARTER THREE
QUARTER
FOUR
Unit 5: Graphs and Functions
In this unit, students will make connections between and among multiple
representations of functions including concrete, verbal, numeric, graphic, and
algebraic. They will analyze a relation to determine whether a direct or
inverse variation exists, and represent a direct variation algebraically and
graphically and an inverse variation algebraically.
Standards of Learning:
A.7
A.8
Unit 6: Linear Equations and Their Graphs
Students will learn to graph linear equations within the context of realistic
situations. Students will learn about slope, x- and y-intercepts, and the various
forms of a line. Further, students will learn to write the equation of a line
given its graph and/or table of values.
Standards of Learning:
A.6
A.11
Unit 7: Systems of Equations and Inequalities
Students will learn the practical applications of solving systems of linear
equations and see how graphical and algebraic means of solving such
problems yield the same solution. Students will learn how to solve systems of
linear equations graphically, by substitution, and elimination. Further,
students will learn how to solve systems of linear inequalities and understand
that solution sets represent the values of x and y that yield true statements
for both inequalities in a system.
Standards of Learning:
A.4
A.5
Unit 8: Exponents and Exponential Functions
In this unit, students will learn how to apply the laws of exponents to perform
operations on expressions. They will also express square roots and cube roots
of whole numbers and the square root of a monomial algebraic expression in
simplest form. Students will understand the use of exponential functions
within the context of compound interest problems. Further, students will be
able to distinguish between linear and exponential functions and explain the
difference between the two. Finally, students will learn to graph basic
exponential functions.
Standards of Learning:
A.2
A.3
Unit 9: Polynomials and Factoring
In this unit, students will learn to add, subtract, multiply, and divide
polynomials. They will also factor first-, and second-degree binomials and
trinomials in one or two variables. Graphing calculators will be used as a tool
for factoring and for confirming algebraic factorizations.
Standards of Learning:
A.2
Unit 10: Quadratic Equations and Functions
Students will learn to solve quadratic equations algebraically and graphically.
They will factor quadratic equations. They will solve equations by completing
the square and they will be introduced to the quadratic formula.
Standards of Learning:
A.4
Suggested Time
Frame:
2-3 weeks
Suggested Time
Frame:
3-4 weeks
Suggested Time
Frame:
3-4 weeks
Suggested Time
Frame:
2-3 weeks
Suggested Time
Frame:
3-4 weeks
Suggested Time
Frame:
3-4 weeks
Unit 11: Direct and Inverse Variations (Optional Unit)
Students will extend their prior knowledge of proportionality by relating it to
linear functions in the form y = kx. Further, students will learn how direct and
inverse variations differ, and they will identify both forms of variation given a
table, function, or graph.
*This material may be introduced in Unit 5 with expectations for mastery in
subsequent study of Algebra.)
Standards of Learning:
A.8
Suggested Time
Frame:
1 week