Algebra I/Data Analysis Essential Curriculum
UNIT I: Patterns and Functions
Goal. The student will demonstrate the ability to summarize patterns by
examining the relationship between variables using various methods. This unit
will provide a foundation for the student as they study specific models of
change such as linear, quadratic and exponential models in later units.
Objectives – The student will be able to:
a. Recognize, describe, represent and/or extend patterns and functional
relationships that are expressed numerically, algebraically, and/or geometrically.
b. Represent and interpret relations and functions in a real-world context
using numbers, graphs, tables, oral/written descriptions, equations, and
technology.
UNIT II: Solving Linear Equations and Inequalities
Goal. The student will demonstrate the ability to solve linear equations and
inequalities and apply these concepts to solve real-world problems.
Objectives – The student will be able to:
a. Simplify and evaluate numerical and algebraic expressions.
b. Apply additiona, subtraction, multiplication, and/or division of algebraic
expressions to mathematical and real-life problems.
c. Solve one-variable equations for the unknown.
d. Solve literal equations for a specific variable.
e. Solve and graph a one-variable inequality for the unknown, interpret it in
the context of the problem, and apply the solution to a real-world application.
f. Solve and interpret absolute value expressions and equations.
UNIT III: Linear and Non-Linear Functions, Inequalities, and Graphs
Goal. The student will demonstrate the ability to graph and write linear
equations and inequalities and apply these concepts to solve real-world
problems.
Objectives – The student will be able to:
a. Describe the graph of a non-linear function and discuss its appearance in
terms of basic concepts of maxima and minima, zeros (roots), rate of change,
domain and range, and continuity.
b. Describe how the graphical model of a non-linear equation represents a
given problem and estimate the solution.
c. Recognize and describe linear functions that are expressed numerically,
algebraically, and/or graphically.
d. Represent linera functions numerically, algebraically, and/or graphically.
e. Determine the equation for a line, solve linear equations, and/or describe
the solutions using numbers, symbols, and/or graphs.
f. Determine and interpret properties of linear functions, including slope,
intercepts, dependent and independent variables, and continuity, in the
context of a real-world situation.
g. Interpret data and/or make predictions by finding and using a line of best
fit and by using a given curve of best fit.
h. Identify, describe, and apply properties of direct variation.
i. Solve linear inequalities and describe the solutions using numbers,
symbols, and/or graphs.
j. Write, solve, graph, and/or interpret an inequality in the context of a
real-world problem.
k. Interpret and solve absolute value equaltions and inequalities.
UNIT IV: Statistics, Probability, and Proportional Reasoning
Goal. The student will demonstrate the ability to apply probability and
statistical methods for representing data, interpreting data, and
communicating results.
Objectives - The student will be able to:
a. Use the concept of ratio, rate, percent, and proportion to solve problems.
b. Determine the experimental probability of an event usign real-world data.
c. Calculate theoretical probability and use simulations or statistical
inference from data to estimate the probability of an event.
d. Represent, interpret, and manipulate data in matrices to solve real-world
problems.
e. Use measures of central tendency and/or variability to draw informed
conclusions.
f. Organize and analyze data using a histogram, stem-and-leaf plot or
box-and-whisker plot.
g. Make informed decisions and predictions based upon the results of
simulationss and data from research.
h. Design and/or conduct an investigation that uses statistical methods to
analyze data and communicate results.
i. Investigate and communicate the use and misuse of statistics.
UNIT V: Linear Systems
Goal. The student will demonstrate the ability to develop systems of linear
equations to model real-world situations. Systems of liner equations will be
solved using a variety of methods and the solutions will be interpreted in the
context of the problem.
Objectives - The student will be able to:
a. Organize and interpret graphs of systems of linear equations with two unknowns.
b. Solve and describe using numbers, symbols, and/or graphs if and where two
straight lines intersect.
c. Write a system of equations for a real-world situation that is expressed
verbally, numerically, algebraically, and graphically.
d. Write, solve, and/or interpret a system of linear inequalitiess in the
context of a real-world problem.
UNIT VI: Exponents and Exponential Functions
Goal. The student will demonstrate the ability to perform operations involving
exponents. They will explore exponential growth and decay through realworld
models.
Objectives - The student will be able to:
a. Apply addition, subtraction, multiplication and/or division of algebraic
expressions to mathematical and real-world problems.
b. Simplify expressions using laws of exponents.
c. Read and write numbers in scientific notation.
d. Recognize and describe exponentail functions that are expressed
numerically, algebraically, and/or graphically.
e. Represent exponential functions numerically, graphically, and/or algebraically.
f. Solve real-world problems involving an exponential function.
UNIT VII: Polynomials and Quadratics
Goal. The student will demonstrate the ability to perform operations with
polynomial expressions and to solve and interpret quadratic functions and
apply these concepts to real-world problems.
Objectives - The student will be able to:
a. Write polynomials in standard form.
b. Add and subtract polynomials.
c. Multiply polynomials.
d. Represent polynomials as a product of a monomial and a polynomial.
e. Represent a quadratic polynomial as the product of two linear factors.
f. Recognize and describe quadratic functions thast are expressed numerically,
algebraically, and/or graphically.
g. Identify the properties of a quadratic function represented numerically,
algebraically, and/or graphically.
h. Represent quadratic functions numerically, algebraically, and/or graphically.
i. Solve a quadratic function using a graph, factors, and the quadratic formula.
j. Evaluate expressions by adding, subtracting, multiplying, dividing, and
simplifying radicals.
k. Solve a quadratic equation using the quadratic formula.
l. Solve a real-world problem involving a quadratic function.
