One- Year Integrated Algebra Outline Feb 2013
Total Days = 164
* - Indicates topics introduced in previous courses. See curriculum for
specific performance indicators.
I. Real Numbers ≈ 6 days
1. Review Prior Knowledge* (  4 days)
a. Number Sets *
b. Operations with Real Numbers*
c. Order of Operations*
d. Evaluating Algebraic Expressions*
2. Set Theory (  2 days)
a. Review subsets of Real Numbers*
b. Use set builder and/or interval notation
( Ex: {x | x > 4}, {x | -4 < x < 10}, {x | x < -3 or x > 11})
c. Define and solve graphic, letters and numbers in problems using
the following:
1. roster notation
2. subset
3. universal set
4. complement
5. null set
6. intersection
7. union
3. Properties of Real Numbers (  1 days)
a. Commutative*
b. Associative*
c. Identity*
d. Inverse*
e. Distributive*
f. Zero Property*
g. Closure
4. Review and Assessment (  1 days)
II.
Polynomials ≈ 13 days
1. Operations With Monomials and Polynomials (  9 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)*
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One- Year Integrated Algebra Outline Feb 2013
Total Days = 164
h. Divide a polynomial by a monomial or binomial, where the
quotient has no remainder*
2. Scientific Notation (  2 days)
a. Convert to scientific notation
b. Convert from scientific notation to standard form
c. Compute products and quotients involving scientific notation
d. Solve word problems involving products and quotients
3. Review and Assessment (  2 days)
III.
Linear Equations ≈ 22 days
1. Translate Among Verbal, Written, and Algebraic ( 2 days)
a. Represent words with mathematical expressions and equations
(and vice versa)*
b. Distinguish between an algebraic expression and an algebraic
equation
c. Write algebraic equations to represent a situation
2. Solve Linear Equations (  12 days)
a. Solve one-and two-step equations with one unknown (include
fractions and decimals)
1. Combine like terms*
2. Use Distributive Property*
3. Variables on opposite sides of the equal sign*
4. Fractional equations
5. Variable in the denominator
6. Equations with an infinite number of solutions
such as 2x+4 = 2(x+2)
7. Equations with no solutions such as 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)
3. Algebra Problems and Word Problems with Fractions, Decimals,
Percents and Proportions ( 4days)
a. Analyze and solve word problems whose solution requires
solving a linear equation with one unknown (consecutive
integer, perimeter, and so on).
b. Solve algebraic problems arising from situations that involve
fractions, decimals, percents (decrease/increase and
discount), and proportionality/direct variation*
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One- Year Integrated Algebra Outline Feb 2013
Total Days = 164
4. Calculate Rates Using Appropriate Units (  1 day)
h. Determine appropriate units*
i. Compare rates using proportions*
5. Conversions Within Measurement Systems (  1 day)
j. Convert between units*
k. Solve measurement problems given more than one unit*
6. Review and Assessment ( 2 days)
Common Assessment # 1
IV.
Linear Inequalities ≈ 4 days
1. Solve Linear Inequalities (  3 days)
a. Solve linear inequalities with one variable (include multiplying
and dividing by a negative number)*
b. Translate among verbal, written and algebraic*
1. Represent words with mathematical inequalities
2. 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 word problems whose solution requires
solving a linear inequality with one variable
2. Review and Assessment  1 day
V.
Graphs of Linear Equations and Inequalities ≈ 14 days
1. Graphs of Lines (  10 days)
a. Graph a line using a table of values*
b. Define a function*
1. Ordered pairs
2. 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*
1. Define slope as the rate of change*
2. Find slope between two points using the graph.*
3. Find slope between two points using the slope formula.
4. Identify different slopes (positive, negative, zero and
undefined)
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One- Year Integrated Algebra Outline Feb 2013
Total Days = 164
f.
Intercepts (x and y)
1.
Find the x- and y-intercepts (*y-intercept only)
2.
Write an equation and graph lines parallel to the axes
3.
Graph a line using the x and y intercepts (optional)
g. Slope-Intercept Form
1. Write the equation of a line given its slope and
y-intercept*
2. Convert an equation into slope-intercept form
3. Graph equations using slope-intercept form* (include
investigating and generalizing how changing the slope
and y-intercept affects the graph)
4. Determine if two lines are parallel, given their equations
in any form
5. 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 (  2 days)
a. Determine if reference line is dashed or solid
b. Determine where to shade
3. Read and interpret graphs.
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VI.
Review and Assessment (  2 days)
Systems of Linear Equations and Inequalities ≈ 10 days
1. Systems of Equations (  6 days)
a. Solve algebraically and check
1.
substitution method
2.
elimination method
b. Solve graphically and check*
c. Solve word problems
2. Systems of Inequalities (  2 days)
a. Solve graphically
b. Determine whether a given point is in the solution set
3. Review and Assessment (  2 days)
Common Assessment # 2
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One- Year Integrated Algebra Outline Feb 2013
Total Days = 164
*** Order of Chapters VII and VIII left to the discretion of the teacher.
VII. Factoring and Algebraic Fractions ≈ 13 days
1. Factoring (  4 days)
a.
b.
c.
d.
e.
f.
Factor algebraic expressions using the GCF*
Factor a trinomial into two binomials, given a = 1*
Factor a trinomial into two binomials, given a >1 (optional)
Identify and factor the difference of two perfect squares
Factor a trinomial into binomials that requires factoring out a
GCF first
Factor a trinomial into two binomials that requires factoring out a
negative GCF first (Ex: –x2 – 3x – 4)
2. Algebraic Fractions (  5 days)
a. Find the value for which an algebraic fraction is undefined
1. monomial and binomial denominators
2. factorable binomial denominators
b. Simplify fractions with polynomials in the numerator and
denominator by factoring both and reducing to lowest terms
c. Add or subtract fractional expressions
1. like and unlike monomial denominators
2. like binomial denominators
d. Multiply and divide algebraic fractions and express the product
or quotient in simplest form
1. monomial divided by monomial*
2. polynomial divided by monomial*
3. polynomial divided by polynomial
3. Fractional equations (2 days)
4. Review and Assessment (  2 days)
VIII. Non-linear Functions ≈ 17 days
1. Graph Quadratic Equations (  2 days)
a. Recognize general form of a quadratic*
b. Determine the axis of symmetry using the formula or from the
graph
c. Determine the vertex algebraically or graphically
d. Find the table of values for an equation
e. Graph the equation
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One- Year Integrated Algebra Outline Feb 2013
Total Days = 164
2. Solve Quadratic Equations (  7 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. Understand and apply the multiplication property of zero to solve
quadratic equations whose coefficients and roots are integers
e. Analyze and solve word problems that involve quadratic
equations
f. Solve algebraic proportions with one unknown that result in
quadratic equations
3. Solve Systems of Linear and Quadratic Equations (  2 days)
a. Solve graphically
b. Solve algebraically using substitution
4. Exponential Functions (  2 days)
a. Identify and graph an exponential function (given an un known
in the base or as an exponent )
b. Analyze and interpret graphs
c. Analyze and solve word problems that involve exponential
growth and decay (appreciation depreciation)
5. Absolute Value Functions (  1 day)
a. Identify and graph an absolute value function
6. Review and Assessment (  3 days)
IX.
Radicals and Right Triangles ≈ 15 days
1. Operations with Radicals (  5 days)
a. Simplify radicals
1. perfect square radicand*
2. radicand with a perfect square factor (no variable)
b. Add and subtract like and unlike radicands
c. Multiply radicals (include use of distributive property)
d. Divide radicals
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One- Year Integrated Algebra Outline Feb 2013
Total Days = 164
2. Pythagorean Theorem (  2 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. Trigonometric Functions (  5 days)
a.
b.
c.
d.
e.
f.
Sine
Cosine
Tangent
Inverse Trigonometric Functions
Find all sides and angles of a right triangle using trig. and/or
Pythagorean Theorem
Solve word problems (include angle of elevation and
depression)
4. Review and Assessment (  3 days)
Common Assessment # 3
X.
Plane and Solid Geometry ≈ 12 days
1. Perimeter (  2 days)
NOTE: Include problems that use algebra to find / express perimeter
of the following figures:
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
Triangle
Rectangle
Square
Parallelogram
Rhombus
Trapezoid
Circle
Semi-Circle
Quarter- Circle
Other Regular Polygons
Figures composed of polygons and/or circles or sectors of a
circle
2. Area (  4 days)
NOTE: Include problems that use algebra to find /express area of
the following figures:
a. Triangle
b. Rectangle
c. Square
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One- Year Integrated Algebra Outline Feb 2013
Total Days = 164
d.
e.
f.
g.
h.
i.
j.
Parallelogram
Rhombus
Trapezoid
Circle
Semi-Circle
Quarter-Circle
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 ( 2 days)
a. Cube
b. Rectangular Prism
c. Cylinder
5. Relative Error (  1 day)
a. Calculate the relative error in measuring square and cubic units,
where there is an error in the linear measure
6. Review and Assessment (  1 day)
XI.
Probability ≈ 10 days
1. Probability (  7 days)
a. Define and solve problems using the following:
1.
2.
3.
4.
5.
6.
7.
8.
9.
sample space
simple probability of a single event
probability with “and” (single event)
probability with “or” (single event)
complement
empirical probability (based on specific sample data)*
impossible events
certain events
Fundamental Counting Principle
b. Analyze a set of events to determine when:
1. some or all are equally likely to occur
2. one is more likely to occur
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One- Year Integrated Algebra Outline Feb 2013
Total Days = 164
3. an event is certain to happen or not to happen
c. Conditional Probability
1. with replacement
2. without replacement
d. Probability of a series of independent and dependent events
1. and
2. or
3. mutually exclusive
4. not mutually exclusive
2. Permutations (  1/2 day)
a. Review definition of factorial
b. Formula
3.
Factorials (  1/2 day)
l. Define factorial
m. Evaluate factorials
n. Simplify expressions with factorials (rational, algebraic)
4.
Review and Assessment (  2 days)
XII. Statistics and Regression ≈ 11 days
1. Categorize Data (  1 day)
a.
b.
c.
d.
Qualitative
Quantitative
Univariate
Bivariate
2. Measures of Central Tendency
a.
b.
c.
d.
e.
f.
(  1 day)
Mean
Median
Mode
Appropriate choice of measure*
Range*
Recognize how linear transformations of one-variable data affect
the data’s mean, median, mode and range
3. Histograms (  2 days)
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One- Year Integrated Algebra Outline Feb 2013
Total Days = 164
a.
b.
c.
d.
Generate a frequency table
Construct a frequency histogram
Construct a cumulative frequency histogram
Analyze data from a frequency table, histogram, cumulative
frequency table or cumulative frequency histogram
4. Percentiles (  1 day)
a. Definition
b. Find the percentile rank of a value in a set of a data
c. Find the first, second and third quartiles
5. Box-and-whisker Plot (  1 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
6. 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
7. Scatterplots (  2 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. Review and Assessment ( 2 days)
XIII. Regents Review ≈ 15 days
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