Algebra I
Recommended Prerequisite: None
Grades Offered: 9-12
Credit: ½ - 1
SDE Course Code: 3102
MNPS Course Code: MTH4111
Course Description:
Algebra I provides students with a transition from thinking about patterns and operations using concrete quantities to their abstraction as variables, expressions, equations, inequalities, and functions. Students should become adept at translating between verbal, symbolic, and graphical forms for representing algebraic ideas. While most of the Gateway indicators will be covered in the first semester of this course, the second semester topics will provide the foundation for a student’s further study of mathematics. Technology and manipulatives are used to develop and extend algebraic thinking and to engage student reasoning. Students will take the Gateway Mathematics Test upon completion of this course.
Outline of Content:
· The student will recognize, represent, model and apply real numbers and operations verbally, physically, symbolically, and graphically by …
o Demonstrating an understanding of the relative size of rational and irrational numbers
o Articulating, modeling, and applying the concept of inverse (e.g., opposites, reciprocals, powers and roots)
o Describing the understanding of the subsets, elements, properties, and operations of the real number system, modeling, and applying inverse operations
o Applying number theory concepts (e.g., primes, factors, divisibility and multiples) in mathematical problem solving
o Connecting physical, graphical, verbal, and symbolic representations of absolute value
o Using real numbers to represent real-world applications (e.g., slope, rate of change, probability, and proportionality)
o Using a variety of notations appropriately (e.g. exponential, functional, square root).
· The students will apply appropriate tools and units of measurement; develop effective estimation and computation strategies for producing reasonable results; and calculate using appropriate tools such as mental mathematics, technology, manipulatives and pencil-and-paper by …
o Selecting and applying an appropriate method (i.e. mental arithmetic, paper and pencil, or technology) for computing with real numbers and evaluate the reasonableness of the results
o Communicating the concepts and strategies being used in estimation, measurement, and computation
o Performing operations on algebraic expressions and informally justify the procedures chosen
o Using concepts of length, area, and volume to estimate and solve real world problems
o Applying measurement concepts and relationships in algebraic and geometric problem-solving situations
o Demonstrating an understanding of rates and other derived and indirect measurements (e.g., velocity, miles per hour, revolutions per minute, cost per unit)
o Using matrices with appropriate technology in real-world problem solving
o Using estimation to make predictions and test reasonableness of results.
· The student will describe, extend, analyze, and create a wide variety of patterns and functions using appropriate materials and representations in real-world problem solving by …
o Recognizing, extending, and creating geometric, spatial, and numerical patterns
o Analyzing mathematical patterns related to algebra and geometry in real-world problem solving
o Using algebraic thinking to generalize a pattern by expressing the pattern in functional notation
o Solving linear systems using a variety of techniques, including matrices
o Solving problems in number theory, geometry, probability, statistics, and measurement and estimation using algebraic thinking and symbolism
o Communicating the meaning of variables in algebraic expressions, equations, and inequalities
o Identifying and representing a variety of functions
o Applying the concept of rate of change
o Analyzing graphs to describe the behavior of functions
o Interpreting results of algebraic procedures
o Applying the concept of variable in simplifying algebraic expressions, solving equations, and solving inequalities
o Interpreting graphs that depict real-world phenomena
o Modeling real-world phenomena using functions and graphs
o Articulating and applying algebraic properties in symbolic manipulation
o Identifying relationships which can and which cannot be represented by a function
o Graphing inequalities and interpreting graphs of inequalities
o Describing the domain and range of functions and articulating restrictions imposed either by the operations or by the real-life situations which the functions represent
o Describing the transformation of the graph that occurs when coefficients and/or constants of the corresponding linear equations are changed.
· The student will collect, organize, represent, and interpret data; make inferences and predictions; present and evaluate inferences and predictions; present and evaluate arguments based on data analysis, and model situations to determine theoretical and experimental probabilities by …
o Collecting, representing, and describing linear and nonlinear data sets developed from the real world
o Making predictions from a linear data set using a line of best fit
o Interpreting a set of data using the appropriate measure of central tendency
o Choosing, constructing, and analyzing appropriate graphical representations for a data set
o Applying the Law of Large Numbers and the concept of randomness in sampling
o Applying counting principles of permutations and combinations using appropriate technology.
· The student will investigate, model, and apply geometric properties and relationships by …
o Applying geometric properties, formulas, and relationships to solve real-world problems
o Using inductive reasoning to make conjectures
o Applying right triangle relationships including the Pythagorean Theorem and the distance formula.
Reading: Students will develop appropriate reading strategies for understanding mathematical texts, as well as a variety of sources including maps, charts, graphs, and technical writings.
Writing: Students will write regularly using correct mathematical symbols and terminology. Suggested written assignments include: journals, descriptions, comparisons, and logically ordered processes.
Standards Links
MNPS Standards:
http://www.mnps.org/PageFactory.aspx?PageID=3403
State Standards:
http://www.state.tn.us/education/ci/cistandards2001/math/cimath.htm
Gateway Mathematics Test Standards and Item Sampler:
http://www.state.tn.us/education/tssamplers.htm
Textbooks
Basal: Larson, et al, McDougal Littell Algebra 1, 2nd Edition, 2004, McDougal Littell
Online Textbook:
http://www.classzone.com/books/algebra_1/index.cfm
Adapted: Siegfried Haenisch, Algebra, Circle Pines, MN: AGS Publishing, 2004.
(Adopted 2004)
Recommended Resources:
TI 83+ Graphing Calculator or TI 84+ Graphing Calculator
CBR or CBL with probes
A variety of manipulatives: graph paper, rulers, protractors, two-color counters, fraction bars, centimeter cubes or linking cubes, geoboards, miras, pattern blocks, algebra tiles, meter sticks, etc.
Tennessee Gateway Coach: Algebra I, Merv Edwards, Educational Design, 2002.