Accelerated Mathematics 1 Version: CPS 08/09

Scholastic Area that Course Is Active In: Mathematics

Strand: Number and Operations

Students will represent and operate with complex numbers.
Element: MA1N1.a.
Write square roots of negative numbers in imaginary form.
Element: MA1N1.b.
Write complex numbers in the form a + bi.
Element: MA1N1.c.
Add, subtract, multiply, and divide complex numbers.
Element: MA1N1.d.
Simplify expressions involving complex numbers.

Strand: Algebra

Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.
Element: MA1A1.a.
Represent functions using function notation.
Element: MA1A1.b.
Graph the basic functions , where n = 1 to 3, , , and .
Element: MA1A1.c.
Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.
Element: MA1A1.d.
Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.
Element: MA1A1.e.
Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.
Element: MA1A1.f.
Recognize sequences as functions with domains that are sets of whole numbers.
Element: MA1A1.g.
Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.
Element: MA1A1.h.
Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.
Element: MA1A1.i.
Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

Students will simplify and operate with radical expressions, polynomials, and rational expressions.
Element: MA1A2.a.
Simplify algebraic and numeric expressions involving square root.
Element: MA1A2.b.
Perform operations with square roots.
Element: MA1A2.c.
Add, subtract, multiply, and divide polynomials.
Element: MA1A2.d.
Expand binomials using the Binomial Theorem
Element: MA1A2.e.
Add, subtract, multiply, and divide rational expressions.
Element: MA1A2.f.
Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas below.

Element: MA1A2.g.
Use area and volume models for polynomial arithmetic.

Students will analyze quadratic functions in the forms and .
Element: MA1A3.a.
Convert between standard and vertex form.
Element: MA1A3.b.
Graph quadratic functions as transformations of the function .
Element: MA1A3.c.
Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.
Element: MA1A3.d.
Explore arithmetic series and various ways of computing their sums.
Element: MA1A3.e.
Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

Students will solve quadratic equations and inequalities in one variable.
Element: MA1A4.a.
Solve equations graphically using appropriate technology.
Element: MA1A4.b.
Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.
Element: MA1A4.c.
Analyze the nature of roots using technology and using the discriminant.
Element: MA1A4.d.
Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

Students will investigate step and piecewise functions, including greatest integer and absolute value functions.
Element: MA1A5.a.
Write absolute value functions as piecewise functions.
Element: MA1A5.b.
Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.
Element: MA1A5.c.
Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

Strand: Data Analysis and Probability

Students will determine the number of outcomes related to a given event.
Element: MA1D1.a.
Apply the addition and multiplication principles of counting.
Element: MA1D1.b.
Calculate and use simple permutations and combinations.

Students will use the basic laws of probability.
Element: MA1D2.a.
Find the probabilities of mutually exclusive events.
Element: MA1D2.b.
Find the probabilities of dependent events.
Element: MA1D2.c.
Calculate conditional probabilities.
Element: MA1D2.d.
Use expected value to predict outcomes.

Students will relate samples to a population.
Element: MA1D3.a.
Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.
Element: MA1D3.b.
Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.
Element: MA1D3.c.
Understand that a random sample is used to improve the chance of selecting a representative sample.

Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

Students will determine an algebraic model to quantify the association between two quantitative variables.
Element: MA1D5.a.
Gather and plot data that can be modeled with linear and quadratic functions.
Element: MA1D5.b.
Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and "eyeballing."
Element: MA1D5.c.
Understand and apply the processes of linear and quadratic regression for curve fitting using appropriate technology.

Strand: Geometry

Students will investigate properties of geometric figures in the coordinate plane.
Element: MA1G1.a.
Determine the distance between two points.
Element: MA1G1.b.
Determine the distance between a point and a line.
Element: MA1G1.c.
Determine the midpoint of a segment.
Element: MA1G1.d.
Understand the distance formula as an application of the Pythagorean theorem.
Element: MA1G1.e.
Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

Students will understand and use the language of mathematical argument and justification.
Element: MA1G2.a.
Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proof as appropriate.
Element: MA1G2.b.
Understand and use the relationships among a statement and its converse, inverse, and contrapositive.

Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.
Element: MA1G3.a.
Determine the sum of interior and exterior angles in a polygon.
Element: MA1G3.b.
Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.
Element: MA1G3.c.
Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).
Element: MA1G3.d.
Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.
Element: MA1G3.e.
Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

Students will understand the properties of circles.
Element: MA1G4.a.
Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
Element: MA1G4.b.
Understand and use properties of central, inscribed, and related angles.
Element: MA1G4.c.
Use the properties of circles to solve problems involving the length of an arc and the area of a sector.
Element: MA1G4.d.
Justify measurements and relationships in circles using geometric and algebraic properties.

Students will find and compare the measures of spheres.
Element: MA1G5.a.
Use and apply surface area and volume of a sphere.
Element: MA1G5.b.
Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

Strand: Process Standards

Students will solve problems (using appropriate technology).
Element: MA1P1.a.
Build new mathematical knowledge through problem solving.
Element: MA1P1.b.
Solve problems that arise in mathematics and in other contexts.
Element: MA1P1.c.
Apply and adapt a variety of appropriate strategies to solve problems.
Element: MA1P1.d.
Monitor and reflect on the process of mathematical problem solving.

Students will reason and evaluate mathematical arguments.
Element: MA1P2.a.
Recognize reasoning and proof as fundamental aspects of mathematics.
Element: MA1P2.b.
Make and investigate mathematical conjectures.
Element: MA1P2.c.
Develop and evaluate mathematical arguments and proofs.
Element: MA1P2.d.
Select and use various types of reasoning and methods of proof.

Students will communicate mathematically.
Element: MA1P3.a.
Organize and consolidate their mathematical thinking through communication.
Element: MA1P3.b.
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
Element: MA1P3.c.
Analyze and evaluate the mathematical thinking and strategies of others.
Element: MA1P3.d.
Use the language of mathematics to express mathematical ideas precisely.

Students will make connections among mathematical ideas and to other disciplines.
Element: MA1P4.a.
Recognize and use connections among mathematical ideas.
Element: MA1P4.b.
Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
Element: MA1P4.c.
Recognize and apply mathematics in contexts outside of mathematics.

Students will represent mathematics in multiple ways.
Element: MA1P5.a.
Create and use representations to organize, record, and communicate mathematical ideas.
Element: MA1P5.b.
Select, apply, and translate among mathematical representations to solve problems.
Element: MA1P5.c.
Use representations to model and interpret physical, social, and mathematical phenomena.

Strand: Reading Across the Curriculum

Students will enhance reading in all curriculum areas by:
Element: MRC.a
Reading in all curriculum areas: Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areas; Read both informational and fictional texts in a variety of genres and modes of discourse; Read technical texts related to various subject areas.
Element: MRC.b
Discussing books: Discuss messages and themes from books in all subject areas; Respond to a variety of texts in multiple modes of discourse; Relate messages and themes from one subject area to messages and themes in another area; Evaluate merit of texts in every subject discipline; Examine author's purpose in writing; Recognize the features of disciplinary texts.
Element: MRC.c
Building vocabulary knowledge: Demonstrate an understanding of contextual vocabulary in various subjects; Use content vocabulary in writing and speaking; Explore understanding of new words found in subject area texts.
Element: MRC.d
Establishing context: Explore life experiences related to subject area content; Discuss in both writing and speaking how certain words are subject related; Determine strategies for finding content and contextual meaning for unknown words.

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