Course Title: Algebra Integration
Curriculum Guide: This course is meant to build algebra readiness for Algebra 2 and to allow students the opportunity to
build statistics and probability knowledge. Students who take this course will have passed both Algebra and Geometry and
need a 3rd year math course to complete high school graduation requirements. Work samples and state testing
opportunities will be given throughout the year as well. Topics studied in this course will include investigating patterns,
monomial, binomial, and polynomial functions, introduction to trigonometry, statistics, and applications of geometry.
Scope and Sequence
Unit Topic
Or Framing
Questions
Or Project Topic
Unit 1
(Semester 1)
Investigating
Patterns
How do various
patterns present
themselves and
how can
mathematical
models be used
to represent this
data?
Unit 2
(Semester 1)
Graphing
Linear
Equations
How do you plot
points, graph
lines, and
represent data
in a visual
Core Academic and Professional Knowledge & Skills
What do you want students to know and do?
A.2.1 Identify, construct, and extend patterns in a linear sequence or table.
A.A.1.1 Demonstrate an understanding of the concept of a function, use
function notation, evaluate a function, determine whether or not a given
relation is a function and determine whether or not a given function is one-toone.
A.A.1.2 Determine the domain and range of a relation included those with
restricted domains.
A.A.1.10 Collect and analyze data to make predictions and to investigate
scatterplots and to determine the equation for a curve of best fit including
linear, power, exponential, and logarithmic functions.
A.A.1.12 Find the x and y-intercepts of a function if they exist.
A.2.1 Identify, construct, and extend patterns in a linear sequence or table.
A.2.2 Given a rule, two points, table, graph or situation, state, describe, and explain
the rate of change and verify the result.
A.2.3 Fluently convert among all forms of linear relationships.
A.2.4 Identify and distinguish graphically and symbolically between x and y intercepts
of a line, and interpret their contextual meanings.
A.2.5 Translate between slope-intercept, point-slope, and standard forms of linear
equations.
A.2.6 Represent and solve linear equations and inequalities in a single variable using
algebraic methods and justify the mathematical reasoning used to determine the
Student Activities
What will students do
to demonstrate their
learning? What
products and/or
performances will
students complete?
Assessment
Tools
What criteria or tools will
you, the teacher, use to
measure student progress
and achievement?
* Students will investigate
patterns modeling growth
and decay specifically in
regards to loans and
savings.
*Students will begin to
investigate the concept of
limits in regards to real life
values by examining
exponential growth or
decay. Topics might
include the amount of
medicine in the body over
time or car depreciation.
*Students will learn and
use function notation.
*Students will practice
graphing linear equations
and interpreting
contextual meanings.
*Students will create
scatter plots with lines of
best fit to predict future
information. Extensions
will be explored through
graphing calculators.
Begin with review of graphing.
Formative assessment will be
ongoing. Students will be
expected to categorize
sequences as arithmetic or
geometric. This ability to
distinguish between patterns as
well as use function notation will
be monitored. Students will also
be given formative assessment
around constructing linear
sequences from patterns or
tables.
Unit test
One completed work sample.
Formative assessment will be
ongoing around algebra skills.
These include, graphing,
understanding the properties of a
linear equation, solving for a
variable and interpreting the
meaning of intercepts. These
skills lend themselves to quick
formative assessments that
teachers can evaluate as a
manner?
Unit 3
(Semester 1)
Quadratic
Equations
How do you
graph, solve,
and apply
quadratic
equations?
solution(s).
A.2.7 Solve a system of linear equations graphically and algebraically and interpret
the solution appropriately.
A.2.8 Solve real-world problems using linear equations, linear inequalities, and
systems of linear equations and interpret, verify, and determine the reasonableness
of the solution.
A.3.4 Identify and distinguish between linear, quadratic and/or exponential functions
through the interpretation of tables, equations or graphs.
A.A.1.1 Demonstrate an understanding of the concept of a function, use
function notation, evaluate a function, determine whether or not a given
relation is a function and determine whether or not a given function is one-toone.
A.A.1.2 Determine the domain and range of a relation included those with
restricted domains.
A.A.1.12 Find the x and y-intercepts of a function if they exist.
A.A.8.3 Analyze an inconsistent system of equations.
*Students will solve
systems of linear
equations and interpret
solutions. Students will
determine break-even
points in real life situations
and interpret the meaning.
*Students will learn and
use function notation.
team.
Students will make an informed
recommendation in regards to
cost comparisons.
Students will complete at least
one work sample.
See attached.
Unit test.
A.1.2 Evaluate numeric expressions that include absolute values, integer exponents,
and square roots and use estimation to verify the reasonableness of the results.
A.1.3 Recognize, represent, generate and justify equivalent forms of polynomials and
exponential expressions, including the use of simplifying and expanding techniques
to manipulate such expressions.
A.1.4 Evaluate the value of rational, polynomial, and exponential expressions and
use estimation to determine the reasonableness of the result.
A.2.4 Identify and distinguish graphically and symbolically between x and y intercepts
of a line, and interpret their contextual meanings.
A.3.1 Given a quadratic function, produce a table of values and graph (by hand and
with appropriate technology).
A.3.2 Using quadratics of the form x2 + bx +c with integer roots, identify the vertex,
the axis of symmetry, and identify the zeros using graphing and factoring.
A.3.4 Identify and distinguish between linear, quadratic and/or exponential functions
through the interpretation of tables, equations or graphs.
A.A.1.11 Connect the relationships among the solution of an equation, zero of
a function, x-intercept of a graph and the factors of a polynomial expression.
A.A.3.1 Perform operations on complex numbers and represent, apply and
discuss the properties of complex numbers.
A.A.3.3 Solve quadratic equations using the zero product property, completing
the square, the quadratic formula, and graphing.
A.A.3.4 Graph and analyze quadratic functions and relate the zeros to the
discriminant.
A.A.5.2 Perform arithmetic operations to simplify radical expressions.
A.A.5.3 Solve radical equations.
*Students will distinguish
and convert between
congruent forms of
quadratic equations.
*Students will learn and
apply the quadratic
formula.
*Students will be able to
factor simple quadratic
equations.
*Students will learn and
use function notation.
Students will identify
quadratic elements
(vertex and roots) and
explain their real life
application.
Students will use their
knowledge of quadratics
to investigate physical
situations.
Students will need to
demonstrate the skills of:
graphing, using the quadratic
formula and understand the
meaning of the answer, translate
between quadratic forms, As
these skills are essential, they
will be assessed formatively as
well in the summative
assessment.
Unit test
Work sample.
Unit 4
(Semester 1)
Exponents
How do you
apply rules of
exponents to
solve for
unknown
variables?
Unit 5
(Semester 2)
Probability and
Statistics
How do you
represent and
interpret
statistics and
resulting data?
A.1.2 Evaluate numeric expressions that include absolute values, integer exponents,
and square roots and use estimation to verify the reasonableness of the results.
A.1.3 Recognize, represent, generate and justify equivalent forms of polynomials and
exponential expressions, including the use of simplifying and expanding techniques
to manipulate such expressions.
A.1.4 Evaluate the value of rational, polynomial, and exponential expressions and
use estimation to determine the reasonableness of the result.
A.2.4 Identify and distinguish graphically and symbolically between x and y intercepts
of a line, and interpret their contextual meanings.
A.3.3 Recognize, compare and contrast exponential growth and decay in the form of
y=abx using graphs, equations, tables, and verbal descriptions.
A.3.4 Identify and distinguish between linear, quadratic and/or exponential functions
through the interpretation of tables, equations or graphs.
A.A.1.13 Identify, distinguish between, and describe the characteristics of the
following functions in tabular, verbal graphical or symbolic form: polynomial,
power, absolute value, rational, radical, logarithmic, exponential, algebraic,
piece-wise, and step.
A.A.7.3 Solve exponential and logarithmic equations.
A.A.7.4 Graph and analyze exponential and logarithmic functions.
PS.1.1 Describe strengths and limitations of a particular survey, observational study,
or experiment and critically analyze the results.
PS.1.2 Interpret a variety of data displays to make and justify inferences and
predictions.
PS.1.3 Determine and explain the general effect of outliers on the mean, median,
mode, and range of a data set.
PS.1.4 Identify types of distributions and recognize populations that have normal
distributions.
PS.2.1 Compare and contrast experimental probability to theoretical probability.
PS.2.2 Compute theoretical probabilities for dependent, independent,
complementary and compound events; determine and explain the reasonableness of
your results.
PS.2.3 Determine and explain the sample space of a particular event and the total
number of arrangements of objects in a given set by applying counting strategies,
combinations, or permutations.
A.S.1.1 Construct, interpret, and summarize numerical characteristics of
univariate data sets to describe patterns and departure from patterns, using
measures of center, spread, and position.
A.S.2.2 Plan, analyze, and conduct a survey, and/or observational study;
describe characteristics of a well-designed and well-conducted survey; explore
various sampling methods including investigations sources of bias.
A.D.5.1 Produce all combinations and permutations of sets.
*Students will identify and
graph exponential
equations.
*Students will learn and
use properties of
exponential and power
functions.
*Students will evaluate
and interpret solutions to
exponential equations.
*Students will identify and
convert between various
forms of exponential
equations.
Students will investigate
such topics as financial
situations, population
growth and decay and use
equations to describe
these situations.
*Students will learn the
differences and
similarities between
theoretical and
experimental probability.
*Students will explore
randomness and
probability in various
scenarios such as political
polls, health surveys, and
game theory.
*Students will learn and
apply rules of
permutations and
combinations.
*Students will calculate
and interpret probabilities.
Formative assessment will occur
around the rules of exponents,
graphing, and distinguishing
between growth and decay.
Applying exponential ideas to
real world applications will also
be monitored.
Unit test
Project around exponential
growth to be developed.
Work sample
The essential skills for this unit
are interpreting data, calculating
probabilities, using combinations
and permutations and
interpreting probability and
statistics presented in various
forms. Teachers will continually
monitor these skills in class and
work on formative assessments
as a team.
Unit test
Work sample.
Unit 6
(Semester 2)
Trigonometry
How do you
apply and solve
trigonometric
equations and
scenarios?
Unit 7
(Semester 2)
Applied
Geometry
How do you
translate
problems into
mathematical
models and
apply geometry
formulas to
solve them?
A.D.5.2 Calculate the number of combinations and permutations of sets of m
items taken n at a time.
A.D.5.5 Find the odds that an event will occur given the probabilities and vice
versa.
G.2.5 Identify, apply and explain using trigonometric ratios of right triangles to solve
for missing lengths and angle measurements.
A.T.1.1 Develop and apply the properties of special right triangles.
A.T.1.2 Develop, define, and apply right triangle trigonometric ratios.
A.T.1.3 Develop and apply the Law of Sines and the Law of Cosines.
A.T.1.4 Develop and apply the area formulas of a triangle.
G.2.6 Identify, calculate and verify missing dimensions of polygons, circles or
combinations of two or more shapes.
G.2.7 Identify and classify polygons by their angles and sides.
G.3.1 Recognize, model, sketch, and label representations of three-dimensional
objects from different perspectives.
G.3.2 Identify, apply, and modify the formulas for surface area and volume of prisms,
pyramids, cones, cylinders, spheres and compositions thereof to solve problems and
determine the reasonableness of solutions.
G.3.3 Identify, calculate, and verify missing dimensions of prisms, pyramids, cones,
cylinders or spheres.
*Students will use right
triangle trigonometry to
solve for missing values.
Students will use right
triangle trigonometry for
measurement.
*Students will spend time
building background
knowledge of basic
geometry formulas.
*Students will calculate
and solve for missing
dimensions for 2-D and 3D shapes.
*Students will apply
geometric formulas to
solve story problems.
Students need to know when to
use the rules of sines, cosines,
and tangents as well as
understand special triangle
relationships. This will be
assessed throughout the unit as
well as in the unit test.
Work sample.
Students need to correctly
identify and apply the formulas
for 2D and 3-D shapes.
Unit project to be developed.
Work sample.