La Cañada High School
Course Outline – LC Math 1
I.
Course Title – Math 1
II.
Grade Level(s) – Grades 9-12
III.
Length/Credit – 1 Year - 10.0 units Satisfies Traditional Algebra I Graduation
Requirement
IV.
Preparations – Completion of CC Math 8 or its equivalent
V.
Course Description
This is the first course in a common core based college preparatory math sequence. This course
builds on, and deepens, the conceptual understanding of linear function from CC Math 8. The
main purpose of LC Math 1 is to develop students’ fluency with linear, quadratic and exponential
functions. The critical areas of instruction involve deepening and extending students’
understanding of linear and exponential relationships by contrasting them with each other and by
applying linear models to data that exhibit a linear trend. In addition, students engage in methods
for analyzing, solving, and using exponential and quadratic functions. Some of the overarching
ideas in the LCM1 course include: the notion of function, solving equations and inequalities,
rates of change and growth patterns, working with sequences, understanding absolute value
relationships, graphs as representations of functions, and modeling. Since the Standards for
Mathematical Practice will be woven throughout each unit of the course, students will analyze
each other’s work, make and prove conjectures, use tools to experiment and validate conclusions,
and problem solve.
VI.
Standards Addressed
1. Standards for Mathematical Practices
 Make sense of problems and persevere in solving them.
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Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
2. Number and Quantity
The Real Number System
Standards Abbreviation: N-RN
 Extend the properties of exponents to rational exponents.
 Use properties of rational and irrational numbers.
Quantities
Standards Abbreviation: N-Q
 Reason quantitatively and use units to solve problems.
3. Algebra
Seeing Structure in Expressions
Standards Abbreviation: A-SSE
 Interpret the structure of expressions.
 Write expressions in equivalent forms to solve problems.
Arithmetic with Polynomials and Rational Expressions
Standards Abbr.: A-APR
 Perform arithmetic operations on polynomials.
Creating Equations
Standards Abbreviation: A-CED
 Create equations that describe numbers or relationships.
Reasoning with Equations and Inequalities
Standards Abbreviation: A-REI
 Understand solving equations as a process of reasoning and explain the reasoning.
 Solve equations and inequalities in one variable.
 Solve systems of equations.
 Represent and solve equations and inequalities graphically.
4. Functions
Interpreting Functions
Standards Abbreviation: F-IF
 Understand the concept of a function and use function notation.
 Interpret functions that arise in applications in terms of the context.
 Analyze functions using different representations.
Building Functions
Standards Abbreviation: F-BF
 Build a function that models a relationship between two quantities.
 Build new functions from existing functions.
Linear, Quadratic, and Exponential Models
Standards Abbreviation: F-LE
 Construct and compare linear, quadratic, and exponential models and solve problems.
 Interpret expressions for functions in terms of the situation they model.
5. Statistics and Probability
Interpreting Categorical and Quantitative Data
Standards Abbreviation: S-ID
 Summarize, represent, and interpret data on a single count or measurement variable.
 Summarize, represent, and interpret data on two categorical and quantitative
variables.
 Interpret linear models
VII.
Brief Course Outline
Essential Course Concepts: Quarter 1: Quantities, Functions, and Linearity
 Introduction to variables, quantities, functions, and equations
 Properties of real numbers
 Solving linear equations and inequalities
Common Core State Standards Addressed: N-RN.3, N-Q.1, N-Q.2, N-Q.3, A-SSE.1, A-CED.1, A-CED.2, ACED.3, A-CED.4, A-REI.1, A-REI.3, A-REI.10.
Course Concepts Description: Create and solve linear equations and inequalities, model reallife contexts with linear functions, use function notation, perform operations on functions, use
proportional reasoning to solve problems involving business, geometry and other real-life
applications, extend solving linear equations and inequalities to problems involving absolute
value expressions.
Essential Course Concepts: Quarter 2: Applying and Extending Linearity
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Graph linear functions
Apply rate of change and slope to describe linear function behavior
Analyze lines of best fit and linear regression
Problem solving with systems of linear equations and inequalities
Common Core State Standards Addressed: N-Q.1, N-Q.2, N-Q.3, A-SSE.1, A-SSE.2,
A-CED.2, A-CED.3, AREI.5, A-REI.6, A-REI.10, A-REI.11, A-REI.12, F-IF.1, F-IF.2, F-IF.3, F-IF.4, F-IF.5, F-IF.7, F-IF.9, F-BF.1, F-BF.2, F-BF.3,
F-LE.1, F-LE.2, F-LE.5, G-GPE.5, S-ID6, S-ID.7, S-ID.8, S-ID.9
Course Concepts Description: Use function notation to describe (algebraically or graphically) a
situation or pattern, create recursive and explicit function rules for arithmetic and geometric
sequences, and determining whether a situation is a function or relation, describe the domain and
range of a function, use rate of change to create, graph and analyze linear functions, transform
between forms of linear functions and understand applications for each form, use slope to
determine geometric properties of linear functions, create and analyze scatter plots for bivariate
data, find trend lines and analyze residuals for linear regression, graph linear absolute value
functions, solve problems using a system of linear equations and inequalities.
Essential Course Concepts: Quarter 3: Building Exponential Functions
 Pattern recognition, arithmetic sequences, and geometric sequences
 Exponential expressions
 Graph and analyze exponential functions
Common Core Concepts Addressed: N-RN.1, N-RN.2, N-RN.3, A-SSE.1, A-SSE.2, A-SSE.3, A-APR.1, AAPR.3, A-CED.2, A-REI.11, F-IF.4, F-IF.5, F-IF.7, F-IF.8, F-IF.9, F-BF.1, F-BF.2, F-BF.3, F-LE.1, F-LE.2
Course Concepts Description: Extend exponent rules to rational exponents, understand the
distinction between rational and irrational numbers, extend properties of exponents to
exponential functions, connect geometric sequences to exponential functions, compare and
contract linear and exponential functions, graph exponential functions, apply transformations to
graph and analyze exponential functions, model situations with linear and exponential functions,
transform between forms of quadratic expressions, determine which factoring strategy best
solves quadratic equations.
Essential Course Concepts: Quarter 4: Quadratic Functions
 Quadratic expressions
 Graph and analyze quadratic functions
 Model with linear, exponential and quadratic function
 Summarize, represent, and interpret data
Common Core Concepts Addressed: N-Q.1, N-Q.2, N-Q.3, A-SSE.1, A-SSE.3, A-APR.3, A-CED.1, ACED.2, A-CED.3, A-CED.4, A-REI.1, A-REI.4, A-REI.7, A-REI.11, F-IF.4, F-IF.5, F-IF.6, F-IF.7, F-IF.8, F-IF.9,
F-BF.1, F-BF.3, F-LE.1, F-LE.2, F-LE.3, S-ID.1, S-ID.2, S-ID.3, S-ID.6
Course Concepts Description: Create quadratic models, graph quadratic functions, analyze
properties of quadratic graphs, solve quadratic equations using multiple methods (factoring,
graphing, completing the square, or the quadratic formula), determine which method for solving
quadratic equations is best, simplify radicals, transform between forms of quadratic functions,
solve real-life problems involving linear, quadratic or exponential functions, extend systems of
equations to involve applications of linear and quadratic functions, compare and contrast linear,
exponential and quadratic functions, determine when an application is linear, quadratic or
exponential, collect and analyze univariate and bivariate data, represent univariate data in
multiple formats (tables, histograms, plots, box-plots), calculate measures of central tendency
(mean, median, mode) and variation (variance, standard deviation, range) to describe data sets.
VIII. Methods of Assessment
Evaluation:
1. Examinations: Examinations are a critical component in monitoring comprehension and in
preparing students in the development of key critical thinking, operational and computational
skills, data analysis, and reading skills. The examinations in this course will follow the
district examination policies. Exams will take the form of tests and quizzes given at
appropriate instructional periods.
2. Projects: Students will be asked to complete both individual and group projects related to
key concepts of this course. .
3. Homework: Students will be assigned homework daily to provide independent practice
opportunities to practice and deepen key concepts. Homework Intensity for this course is
moderate and expects that students will complete homework that will require
approximately 30 to 60 minutes daily.
4. Final Exam: A final exam will be given at the conclusion of both first and second semester.
It will be a comprehensive exam based upon the course of study completed during the year.
Grades:
Grades are based on total points accumulated during each grading period:
Tests and Quizzes:
75%
Homework/Projects:
10-12%
Final Exam:
13-15%
Grading Scale
A = 90-100 %
B = 79-89%
C = 67- 78 %
D= 55 – 66 %
F = Below 55 %
IX.
Materials/Textbook(s)
Algebra: Structure and Method, Book 1, Richard G. Brown, et al. MCDOUGAL LITTLE, 2000.
X.
Seeking “a-f” Approval – Yes/No – Yes, this course will be submitted to the University
of California for approval for the 2015-16 academic year in the subject domain “C” for
mathematics.
XI.
Seeking AP Class Approval – Yes/No – This course does NOT seek AP approval.
C:/Course.out/Proposed Course Outline Template