Download Accelerated Coordinate Algebra Syllabus

Accelerated Algebra I/Geometry A Syllabus
Unit 1(2 weeks): RELATIONSHIPS BETWEEN QUANTITIES AND EXPRESSIONS
Use units of measure as a way to understand problems and interpret units in the context of the
problem; Convert units and rates using dimensional analysis; Identify the different parts of the
expression or formula and explain their meaning; Operate with polynomials with an emphasis on
expressions that simplify to linear or quadratic forms; Rewrite (simplify) expressions involving
radicals; Use and explain properties of rational and irrational numbers.
Unit 2(4 – 5 weeks): REASONING WITH LINEAR EQUATIONS AND INEQUALITIES
Solve linear equations and inequalities in one variable; Rearrange formulas to highlight a
quantity of interest; Solve a system of two equations in two variables by using multiplication and
addition; Solve a system of two equations in two variables graphically; Graph a linear inequality
in two variables; Analyze linear functions using different representations; Interpret linear
functions in context; Investigate key features of linear graphs; Recognize arithmetic sequences as
linear functions.
Unit 3(5 – 6 weeks): MODELING AND ANALYZING QUADRATIC FUNCTIONS
Focus on quadratic functions, equations, and applications; Explore variable rate of change;
Factor general quadratic expressions completely over the integers and to solve
general
quadratic equations by factoring; Find the vertex of the graph of any polynomial
function and to convert the formula for a quadratic function from standard to vertex form; Apply
the vertex form of a quadratic function to find real solutions of quadratic equations that cannot be
solved by factoring; Explore only real solutions to quadratic equations; Explain why the graph of
every quadratic function is a translation of the graph of the basic function f(x) = x2; Apply and
justify the quadratic formula
Unit 4(3 – 4 weeks): MODELING AND ANALYZING EXPONENTIAL FUNCTIONS
Analyze exponential functions only; Build on and informally extend understanding of integer
exponents to consider exponential functions; Interpret exponential functions that arise in
applications in terms of the context; Analyze exponential functions and model how different
representations may be used based on the situation presented; Recognize geometric sequences
as exponential functions; Construct and compare exponential models and solve problems;
Investigate key features of exponential graphs; Investigate a multiplicative change in
exponential functions; Create and solve exponential equations; Apply related linear equations
solution techniques and the laws of exponents to the creation and solution of simple
exponential equations.
Unit 5(3 – 4 weeks): COMPARING AND CONTRASTING FUNCTIONS
Deepen their understanding of linear, quadratic, and exponential functions as they compare and
contrast the three types of functions; Understand the parameters of each type of function in
contextual situations; Analyze linear, quadratic, and exponential functions and model how
different representations may be used based on the situation presented; Construct and compare
characteristics of linear, quadratic, and exponential models and solve problems.; Distinguish
between linear, quadratic, and exponential functions graphically, using tables, and in context;
Recognize that exponential and quadratic functions have a variable rate of change while linear
functions have a constant rate of change; Observe using graphs and tables that a quantity
increasing exponentially eventually exceeds a quantity increasing linearly, quadratically.
Unit 6(2 – 3 weeks): DESCRIBING DATA
Assess how a model fits data; Choose a summary statistic appropriate to the characteristics of the
data distribution, such as the shape of the distribution or the existence of extreme data points;
Use regression techniques to describe approximately linear relationships between quantities; Use
graphical representations and knowledge of the context to make judgments about the
appropriateness of linear models; Look at residuals to analyze the goodness of fit (Students take
a more sophisticated look at using a linear function to model the relationship between two
numerical variables.)
In addition to Units 1 – 6 of Algebra 1, students will also complete the 1st three units of
Geometry.
Unit 7 (1 – 2 weeks): TRANSFORMATIONS IN THE COORDINATE PLANE
Use and understand definitions of angles, circles, perpendicular lines, parallel lines, and line
segments based on the undefined terms of point, line, distance along a line and length of an arc;
Describe and compare function transformations on a set of points as inputs to produce another
set of points as outputs, including translations and horizontal or vertical stretching; Represent
and compare rigid and size transformations of figures in a coordinate plane; Compare
transformations that preserve size and shape versus those that do not; Describe rotations and
reflections of parallelograms, trapezoids or regular polygons that map each figure onto itself;
Develop and understand the meanings of rotation, reflection and translation; Transform a figure
given a rotation, reflection or translation; Create sequences of transformations that map a figure
onto itself or to another figure.
Unit 8 (4 – 5 weeks): SIMILARITY, CONGRUENCE AND PROOFS
Use the idea of dilations to develop the definition of similarity; Determine whether two figures
are similar; Use similarity theorems to prove triangles are similar; Prove geometric figures, other
than triangles, are similar and/or congruent; Use the definition of congruence, based on rigid
motion, to show two triangles are congruent if and only if their corresponding sides and
corresponding angles are congruent; Prove theorems pertaining to lines and angles; Prove
theorems pertaining to parallelograms; Make formal geometric constructions with a variety of
tools and methods
Unit 9 (2 – 3 weeks): RIGHT TRIANGLE TRIGONOMETRY
Explore the relationships that exist between sides and angles of right triangles; Build upon
previous knowledge of similar triangles and of the Pythagorean Theorem to determine the side
length ratios in special right triangles; Understand the conceptual basis for the functional ratios
sine and cosine; Explore how the values of these trigonometric functions relate in
complementary angles; Use trigonometric ratios to solve problems