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Course Syllabus for Algebra I

Scope And Sequence:

Fall Semester
1st
Quarter		 Algebraic
Thinking		 UNIT
UNDERSTANDING		 Discovering Algebra
An Investigative Approach
PV Unit 1
Patterns &
Variables		 “Students recognize similarities and generalize
patterns; use patterns to create models and make
predictions; describe the nature of patterns and
relationships; and construct representations of
mathematical relationships.”
- 2005-2006 Algebra 1 Curriculum Guide		 Chapter 1 – Data Exploration
ϒ Bar Graphs & Dot Plots
ϒ Measures of Center
ϒ Histograms
ϒ Two-Variable Data
DR Unit 2
Data
Representations		 “Students demonstrate the ability to interpret or
analyze information from visual representations
of numerical information, including line graphs,
bar graphs, circle graphs, histograms, … scatter
plots, charts, and tables. Students can identify
trends or patterns, draw conclusions, select the
appropriate graph, determine a suitable scale, or
create appropriate displays of given data.”
- 2005-2006 Algebra 1 Curriculum Guide		 Chapter 2 - Proportional Reasoning and
Probability
ϒ Proportions
ϒ Measurement Systems
ϒ Percent Rate of Change
ϒ Circle and Frequency Graphs
PR Unit 3
Proportional
Reasoning		 “Students use tables and graphs – an alternative
approach – to work with proportions using visual
models. Students are asked to discuss
proportional relationships, rather than numerical
quantities, to force them to discuss the relative
size of these relationships without resorting to a
“trick” or rule.”
- 2005-2006 Algebra 1 Curriculum Guide		 Chapter 3 - Variation and Graphs
ϒ Rates (of Change)
ϒ Direct & Indirect Variation
ϒ Scale & Similarity
2nd
Quarter		 Modeling
Rates of
Change		 UNIT
UNDERSTANDING		 Discovering Algebra
An Investigative Approach
LN Unit 4
Linear and
Non-Linear
Models		 “The goal of this unit is to expose students to
the concept of rate of change in multiple
contexts through continued opportunities to
analyze relationships. It builds on the work they
have already done in studying patterns and
variables, developing tools for presenting data,
and delving into the concept of proportionality.”
- 2005-2006 Algebra 1 Curriculum Guide		 Chapter 4 – Linear Equations
ϒ Order of Operations &
Distributive Property
ϒ Expressions
ϒ Recursive Sequences
ϒ Linear Plots
ϒ Slope-Intercept Form of a
Linear Equation
ϒ Solving Equations
RL Unit 5
Representing
Linear Models		 “The goal of this unit is to expose students to
the concept of rate of change in multiple
contexts through continued opportunities to
analyze relationships. It builds on the work they
have already done in studying patterns and
variables, developing tools for presenting data,
and delving into the concept of proportionality.”
- 2005-2006 Algebra 1 Curriculum Guide		 Chapter 5 – Fitting a Line to Data
ϒ Slope
ϒ Point-Slope Form of a Linear
Equation
ϒ Equivalent Algebraic Equations
GL Unit 6
Graphing
Linear Models		 “The Graphing Linear Models unit focuses on
linear functions in the coordinate plane. After
students’ broad experience with linear
relationships, both equations and inequalities, in
contextual situations, they are ready to
intensify and formulize the study of the graphs
of such equations and inequalities. As they
search for patterns, students will move from
graphing the values generated in the tables to
generalizing an infinite linear representation of
the relationship.”
- 2005-2006 Algebra 1 Curriculum Guide		 Chapter 6 – Systems of Equations and
Inequalities
ϒ Solving Systems of Equations
o Graphing Method
o Substitution Method
o Elimination Method
ϒ Inequalities
o One Variable
o Two Variables
o Systems of Inequalities
Spring Semester
3rd
Quarter		 Processes
and
Symbols		 UNIT
UNDERSTANDING		 Discovering Algebra
An Investigative Approach
EE Unit 7
Evaluating
Expressions		 “This unit focuses on using algebra tiles to model,
simplify, and evaluate expressions, and solve
equations. Students use the algebra tile models
to assist them in translating the visual
representation to the symbolic representation of
the problem. Students also analyze the
soundness of the problem. Students also analyze
the soundness of the results of symbol
manipulation by evaluating the expression for
each procedural step in solving the problem.”
- 2005-2006 Algebra 1 Curriculum Guide		 Chapter 7 – Exponents and Exponential
Models
ϒ Recursive Routines
ϒ Exponential Equation and Rules of
Exponents
ϒ Scientific Notation
ϒ Exponential Growth and Decay
SE Unit 8
Solving
Equations
and
Inequalities		 “The goal for students in this unit is to solve
problems involving equations and inequalities.
This involves finding solutions for linear equations
and linear absolute value equations, solution sets
for linear inequalities, and approximate solutions
for simple quadratic equations. Additionally, the
student should check their work by applying
these solutions to the original problem.”
- 2005-2006 Algebra 1 Curriculum Guid		 Chapter 8 – Functions
ϒ Function Notation
ϒ Interpreting Graphs
ϒ Absolute Value Functions
ϒ Parabolic Functions
SS Unit 9
Systems of
Equations
and
Inequalities		 “Building on the work of solving equations and
inequalities, the section conclude with solving
systems of equations and systems of inequalities.
A table is used to build the linear inequalities
from the written situation. Solving the system
step-by-step graphically builds understanding of
systems of equations and inequalities. We make
the distinction between the solution to a system
of linear equations as being an ordered pair, the
intersection point, and the solution to a system of
linear inequalities as being a set of ordered
pairs.”
- 2005-2006 Algebra 1 Curriculum Guide		 TERRA NOVA ASSESSMENTS
4th
Quarter		 Algebraic
Structures		 UNIT
UNDERSTANDING		 Discovering Algebra
An Investigative Approach
FG Unit 10
Functions
and Their
Graphs		 “The goal for students in this unit is to
understand the role of functions in describing
relationships mathematically in order to predict
behavior, to be able to use the language and
notation of functions, and to extend the kinds of
functions they are able to use graphically in order
to model real world situations.”
- 2005-2006 Algebra 1 Curriculum Guide		 Chapter 9 – Transformations
ϒ Translating Points and Graphs
ϒ Reflecting Points and Graphs
ϒ Stretching and Shrinking Graphs
Rational Functions
EF Unit 11
Exponential
Functions		 “The goal for students in this unit is to be able to
model real world situations that have an
exponential pattern of change, to represent such
situations using tables, graphs, explicit and
recursive functions, and to analyze and interpret
such functions to answer questions and solve
problems.”
- 2005-2006 Algebra 1 Curriculum Guide		 Chapter 10 – Quadratic Models
ϒ Solving Quadratic Equations
ϒ Finding Roots and Vertex
ϒ Vertex Form of the Equation
ϒ General Form of the Equation
ϒ Factored Form
ϒ Completing the Square
ϒ Quadratic Formula
ϒ Cubic Functions
FF Unit 12
Families of
Functions		 “The goal for students in this capstone unit is to
summarize and synthesize the learning of the
course, by examining the two families of
functions studied in depth – linear and
exponential – as well as those that have been
studied less formally – absolute value, quadratic,
and step or piecewise functions – and to analyze
and connect these functions to problem
situations, the shape of their graphs, patterns in
tables, and the form of their equations, as well as
the effect of transformations on their graphs or
equations.”
- 2005-2006 Algebra 1Curriculum Guide		 Chapter 11 – Introduction to Geometry
ϒ Parallel and Perpendicular
ϒ Midpoint
ϒ Pythagorean Theorem
ϒ Radical Expressions
ϒ Similar Triangles
ϒ Trigonometric Functions
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