Revised 3/8/2016
Algebra Two Year Outline
First Year
162 Total Days
Days allotted for “Application, Review and Assessment” should be used
throughout the unit as needed.
I.
Real Numbers (  12 days)
1. Properties of Real Numbers (  3 days)
a. Commutative
b. Associative
c. Identity
d. Inverse (Include inverse operations (Ex: add/subtract,
multiply/divide, square root/square))
e. Distributive
f. Zero Property
g. Closure
2. Review Prior Knowledge (  5 days)
a. Number Sets
b. Operations with Real Numbers
c. Order of Operations
d. Evaluating Algebraic Expressions
3. Scientific Notation (  1 day)
a. Convert from standard form to scientific notation
b. Convert from scientific notation to standard form
4. Calculate Rates Using Appropriate Units (  1 day)
a. Determine appropriate units
b. Compare rates using proportions
c. Problems with mpg
5. Application, Review and Assessment (  2 days)
II.
Polynomials (  22 days)
1. Properties of Exponents (  4 days)
a. Addition (Combine Like Terms)
b. Multiplication
c. Division
d. Zero
e. Negative
f. Power to a Power
g. Product to a Power
h. Quotient to a Power
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2. Operations With Monomials and Polynomials (  12 days)
a. Add and subtract monomials
b. Add and subtract polynomials
c. Multiply and divide monomials (include negative exponents)
d. Distributive Property (include combining like terms)
e. Multiply two binomials
f. Multiply two polynomials
g. Multiply and divide monomial expressions with a common base
using the properties of exponents (use integers as exponents)
h. Divide a polynomial by a monomial or binomial, where the
quotient has no remainder
3. Scientific Notation (  2 days)
a. Compute products and quotients involving scientific notation
4. Application, Review and Assessment (  4 days)
III.
Linear Equations (  34 days)
1. Translate Among Verbal, Written, and Algebraic (  10 days)
a. Numeric/Word Problems
a. Fractions
b. Decimals
c. Percents
d. Proportions
b. Represent words with mathematical expressions and equations
(and vice versa)
c. Distinguish between an algebraic expression and an algebraic
equation
d. Write algebraic equations to represent a situation
2. Solve Linear Equations (  20 days)
a. Solve one and two-step equations with one unknown (include
fractions and decimals)
a. Combine like terms
b. Use distributive property
c. Variables on opposite sides of the equal sign
d. Fractional equations
e. Variable in the denominator
f. Equations with an infinite number of solutions (Ex:
2x + 4 = 2(x + 2))
g. Equations with no solutions (Ex: x + 4 = x + 5)
b. Solve an algebraic proportion with one unknown that results in a
linear equation
c. Determine whether a value is a solution to a given linear
equation
d. Solve literal equations for a given variable (Ex: pq + r = n, solve
for q)
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e. Analyze and solve basic word problems whose solution requires
solving a linear equation with one unknown (consecutive integer,
perimeter, d=rt, scientific notation, ratio, and so on)
f. Solve algebraic problems arising from situations that involve
fractions, decimals, percents (decrease/increase and discount),
and proportionality/direct variation
3. Applications, Review and Assessment (  4 days)
IV.
2.
V.
Linear Inequalities (  8 days)
1. Solve Linear Inequalities (  6 days)
a. Solve linear inequalities with one variable (include multiplying
and dividing by a negative number)
b. Translate among verbal, written and algebraic
a. Represent words with mathematical inequalities
b. Write algebraic inequalities that represent a situation
c. Determine whether a given value is a solution to a linear
inequality with one variable
d. Analyze and solve basic word problems whose solution requires
solving a linear inequality with one variable
Review and Assessment (  2 days)
Graphing Linear Equations and Inequalities (  26 days)
1. Graphs of Lines (  18 days)
a. Graph a line using a table of values
b. Define a function
a. Ordered pairs
b. Vertical line test
c. Determine whether a given point is on a line, given an equation
(Ex: Given (3, 2) is on the graph of x + 3y = k, find k)
d. Solve for an unknown in an equation (or for a coordinate) given
a point on a graph (Ex: Given (k, 7) is on the graph of x – 7y =
10, find k)
e. Slope
a. Define slope as the rate of change
b. Find slope between two points using the formula and
using a graph
c. Identify different slopes (positive, negative, zero and
undefined)
f. Intercepts (x and y)
a. Find the x- and y-intercepts
b. Write an equation and graph lines parallel to the
axes
c. Graph a line using the x and y intercepts (optional)
g. Slope-Intercept Form
a. Write the equation of a line given its slope and
y-intercept
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b. Convert an equation into slope-intercept form
c. Graph equations using slope-intercept form (include
investigating and generalizing how changing the
slope and y-intercept affects the graph)
d. Determine if two lines are parallel, given their
equations in any form
e. Write the equation of a line, given the coordinates of
two points on the line
h. Write the equation of a line given the slope and the coordinates
of a point (point-slope form)
i. Write the equation of a line, given the coordinates of two points
on the line
2. Graphs of Linear Inequalities (  4 days)
a. Determine if the reference line is dashed or solid
b. Determine where to shade
3. Applications, Review and Assessment (  4 days)
VI.
Factoring and Solving Quadratics (  14 days)
1. Factoring (  8 days)
a. Factor algebraic expressions using the GCF
b. Factor a trinomial into two binomials, given a = 1
c. Factor a trinomial into two binomials, given a >1 (optional)
d. Identify and factor the difference of two perfect squares
e. Factor a trinomial into binomials that requires factoring out a
GCF first
f. Factor a trinomial into two binomials that requires factoring out a
negative GCF first (Ex: –x2 – 3x – 4)
2. Solve Quadratic Equations (  3 days)
a. Understand and apply the multiplication property of zero to solve
quadratic equations whose coefficients and roots are integers
3. Applications, Review and Assessment (  3 days)
VII. Statistics and Regression (  26 days)
1. Categorize Data (  1 day)
a. Qualitative
b. Quantitative
c. Univariate
d. Bivariate
2. Biased Data (  1 day)
a. Evaluate reports and graphs for accuracy, appropriateness,
experimental design and soundness of the conclusion
b. Identify and describe sources of bias and its effect, drawing
conclusions from data
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3. Measures of Central Tendency (  4 days)
a. Mean
b. Median
c. Mode
d. Appropriate choice of measure
e. Range
f. Recognize how linear transformations of one-variable data affect
the data’s mean, median, mode and range
4. Histograms (  5 days)
a. Generate a frequency table
b. Construct a frequency histogram
c. Construct a cumulative frequency histogram
d. Analyze data from a frequency table, histogram, cumulative
frequency table or cumulative frequency histogram
5. Percentiles/Quartiles (  3 days)
a. Definition
b. Find the percentile rank of a value in a set of a data
c. Find the first, second and third quartiles
6. Box-and-whisker Plot (  3 days)
a. Define as a five-number summary (minimum, maximum,
quartiles)
b. Construct a box-and-whisker plot
c. Analyze data from a box-and-whisker plot
7. Scatterplots (  5 days)
a. Construct a scatterplot
b. Identify the independent and dependent variables
c. Find the relationship between the variables (positive, negative,
none)
d. Understand the difference between correlation and causation
e. Identify variables that might have a correlation but not a causal
relationship
f. Construct manually a line of best fit
g. Determine the equation of a line of best fit
h. Interpolation and extrapolation
8. Applications, Review and Assessment (  4 days)
VIII. Radicals and Pythagorean Theorem (  15 days)
1. Operations with Radicals (  9 days)
a. Simplify radicals
a. perfect square radicand
b. radicand with a perfect square factor (variable optional)
b. Add and subtract like and unlike radicands
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c. Multiply radicals (include use of distributive property)
d. Divide radicals
2. Pythagorean Theorem (  3 days)
a. Determine if a triangle is a right triangle
b. Find the third side (radical, rational and irrational) of a right
triangle, given two sides
c. Solve word problems
3. Review and Assessment (  3 days)
IX.
Review and Final Exam (  5 days)
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Algebra Two Year Outline
Second Year
159 Total Days
Days allotted for “Application, Review and Assessment” should be used
throughout the unit as needed.
I.
General Review of First Year Algebra (  3 days)
1.
II.
Possible review topics include:
a. Graphing Calculator
b. Prime and Composite Numbers
c. Radicals
d. Exponents
Set Theory and Probability (  26 days)
1. Set Theory (  6 days)
a. Review subsets of Real Numbers
b. Use set builder and interval notation
( Ex: {x | x > 4}, {x | -4 < x < 10}, {x | x < -3 or x > 11})
c. Define and solve problems using the following:
a. roster notation
b. subset
c. universal set
d. complement
e. null set
f. intersection
g. union
2. Probability (  14 days)
a. Review
a. Simplifying fractions (no variables)
b. Operations with fractions (no variables)
b. Define and solve problems using the following:
a. sample space
b. simple probability of a single event
c. probability with “and” (single event)
d. probability with “or” (single event)
e. complement
f. empirical probability (based on specific sample data)
g. impossible events
h. certain events
c. Fundamental Counting Principle
a. Factorials
b. Define factorials
c. Evaluate factorials
d. Simplify expressions with factorials (rational and
algebraic)
d. Analyze a set of events to determine when:
a. some or all are equally likely to occur
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b. one is more likely to occur
c. an event is certain to happen or not to happen
e. Conditional Probability
a. with replacement
b. without replacement
f. Probability of a series of independent and dependent events
a. and
b. or
c. mutually exclusive
d. not mutually exclusive
3. Permutations (  2 days)
a. Review definition of factorial
b. Formula
4. Applications, Review and Assessment (  4 days)
III.
Systems of Linear Equations and Inequalities (  24 days)
1. Review (  8 days)
a. Slope
b. Writing the equation of a line
a. Given slope and y-intercept
b. Given slope and a point on the line
c. Given two points on a line
d. Solving linear equations and inequalities
e. Graphing linear equations and inequalities
f. Evaluating expressions
2. Systems of Equations (  9 days)
Note: Include examples where
a. both equations are in standard form
b. one equation is in standard form and the other is in
slope intercept form
c. both equations are in slope intercept form
a. Solve algebraically and check
a. substitution method
b. elimination method
b. Solve graphically and check
c. Solve word problems
3. Systems of Inequalities (  2 days)
a. Solve graphically
b. Determine whether a given point is in the solution set
4. Applications, Review and Assessment (  5 days)
IV.
Non-Linear Functions (  29 days)
1. Graph Quadratic Equations (  5 days)
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a. Recognize general form of a quadratic
b. Determine the axis of symmetry using the formula from the
graph
c. Determine the vertex algebraically or graphically
d. Find the table of values for an equation
e. Graph the equation
2. Solve Quadratic Equations (  12 days)
a. Identify the relationship between the roots of a quadratic equation
and the x-intercepts on the graph of the parabola
b. Find the roots of a parabolic function graphically (integer
solutions)
c. Identify the relationship between the number of roots and the
number of x-intercepts
d. Review factoring
e. Understand and apply the multiplication property of zero to solve
quadratic equations whose coefficients and roots are integers
f. Analyze and solve word problems that involve quadratic equations
g. Solve algebraic proportions with one unknown that result in
quadratic equations
3. Solve Systems of Linear and Quadratic Equations (  4 days)
a. Solve graphically
b. Solve algebraically using substitution
4. Exponential Functions (  3 days)
a. Identify and graph an exponential function (given an unknown in
the base or as an exponent)
b. Analyze and solve word problems that involve exponential growth
and decay
5. Absolute Value Functions (  1 day)
a. Identify and graph an absolute value function
6. Applications, Review and Assessment (  4 days)
V. Algebraic Fractions (  10 days)
1. Algebraic Fractions (  8 days)
a. Review properties of exponents (with emphasis on division)
b. Find the value for which an algebraic fraction is undefined
a. monomial and binomial denominators
b. factorable binomial denominators
c. Simplify fractions with polynomials in the numerator and
denominator by factoring both and reducing to lowest
terms
d. Add or subtract fractional expressions
a. like and unlike monomial denominators
b. like binomial denominators
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e. Multiply and divide algebraic fractions and express the product
or quotient in simplest form
a. monomial divided by monomial
b. polynomial divided by monomial
c. polynomial divided by polynomial
2. Applications, Review and Assessment (  2 days)
VI.
Plane and Solid Geometry (  24 days)
Note: Include problems that require linear and quadratic equations
1. Perimeter (  4 days)
a. Triangle
b. Rectangle
c. Square
d. Parallelogram
e. Rhombus
f. Trapezoid
g. Circle
h. Semi-Circle
i. Quarter- Circle
j. Other Regular Polygons
k. Figures composed of polygons and/or circles or sectors of a
circle
2. Area (  8 days)
a. Triangle
b. Rectangle
c. Square
d. Parallelogram
e. Rhombus
f. Trapezoid
g. Circle
h. Semi-Circle
i. Quarter-Circle
j. Figures composed of polygons and/or circles or sectors of a
circle
k. Shaded regions
3. Volume (  2 days)
a. Cube
b. Rectangular Prism
c. Cylinder
4. Surface Area (  4 days)
a. Cube
b. Rectangular Prism
c. Cylinder
5. Relative Error (  2 days)
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a. Calculate the relative error in measuring square and cubic units,
where there is an error in the linear measure
6. Applications, Review and Assessment (  4 days)
VII.
Trigonometric Functions (  11 days)
1. Review (  1 day)
a. Simplifying Radicals
b. Pythagorean Theorem
2. Applications (  8 days)
a. Sine
b. Cosine
c. Tangent
d. Inverse Trigonometric Functions
e. Find all sides and angles of a right triangle using trig. and/or
Pythagorean Theorem
f. Solve word problems (include angle of elevation and
depression)
3. Review and Assessment (  2 days)
VIII. Word Problems Involving Linear Equations and Inequalities (  12
days)
1. Conversions Within Measurement Systems (  2 days)
a. Convert between units
b. Solve measurement problems given more than one unit
2. More in-depth word problems including but not limited to (  8 days)
Note: Include word problems that can be solved using one linear
equation and one that can be solved using a system of linear
equations.
a. Consecutive integer
b. Perimeter
c. Area
d. Volume
e. Motion (d=rt, proportions)
f. Age
g. Weighted Averages (Ex: Coin, Ticket, Mixtures)
h. Scientific Notation
3. Review and Assessment (  2 days)
IX.
Regents Review (  20 days)
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