GPS Algebra Version: 2011-2012

Scholastic Area that Course Is Active In: Mathematics

Strand: Number and Operations

Students will represent and operate with complex numbers.
Element: MM2N1.a
a. Write square roots of negative numbers in imaginary form.
Element: MM2N1.b
b. Write complex numbers in the form a + bi.
Element: MM2N1.c
c. Add, subtract, multiply, and divide complex numbers.
Element: MM2N1.d
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: MM1A2.a
a. Represent functions using function notation.
Element: MM1A1.b
Graph the basic functions f(x) = xn, where n = 1 to 3, f(x) = x , f(x) = |x|, and f(x) = x 1 .
Element: MM1A1.c
c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.
Element: MM1A1.d
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: MM1A1.e
e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.
Element: MM1A1.f
f. Recognize sequences as functions with domains that are whole numbers.
Element: MM1A1.g
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: MM1A1.h
h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.
Element: MM1A1.i
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: MM1A2.a
a. Simplify algebraic and numeric expressions involving square root.
Element: MM1A2.b
b. Perform operations with square roots.
Element: MM1A2.c
c. Add, subtract, multiply, and divide polynomials.
Element: MM1A2.d
d. Expand binomials using the Binomial Theorem.
Element: MM1A2.e
e. Add, subtract, multiply, and divide rational expressions.
Element: MM1A2.f
f. Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas below. (x + y)2= x2 + 2xy + y2 (x - y)2= x2 - 2xy + y2 (x + y)(x - y) = x2- y2 (x + a)(x + b) = x2 + (a + b)x + ab (x + y)3= x3 + 3 x2y + 3xy2+ y3 (x - y)3= x3 - 3x2y + 3xy2€“ y3
Element: MM1A2.g
g. Use area and volume models for polynomial arithmetic.

Students will solve simple equations.
Element: MM1A3.a
a. Solve quadratic equations in the form ax2+ bx + c = 0, where a = 1, by using factorization and finding square roots where applicable.
Element: MM1A3.b
b. Solve equations involving radicals such as x + b = c, using algebraic techniques.
Element: MM1A3.c
c. Use a variety of techniques, including technology, tables, and graphs to solve equations resulting from the investigation of x2+ bx + c = 0.
Element: MM1A3.d
d. Solve simple rational equations that result in linear equations or quadratic equations with leading coefficient of 1.

Students will investigate step and piecewise functions, including greatest integer and absolute value functions.
Element: MM2A1.a
a. Write absolute value functions as piecewise functions.
Element: MM2A1.b
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: MM2A1.c
c. Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

Students will analyze quadratic functions in the forms f(x) = ax2+ bx + c and f(x) = a(x €“ h)2+ k.
Element: MM2A3.a
a. Convert between standard and vertex form.
Element: MM2A3.b
b. Graph quadratic functions as transformations of the function f(x) = x2.
Element: MM2A3.c
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: MM2A3.d
d. Explore arithmetic series and various ways of computing their sums.
Element: MM2A3.e
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: MM2A4.a
a. Solve equations graphically using appropriate technology.
Element: MM2A4.b
b. Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.
Element: MM2A4.c
c. Analyze the nature of roots using technology and using the discriminant.
Element: MM2A4.d
d. Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

Strand: Data Analysis and Probability

Students will determine the number of outcomes related to a given event.
Element: MM1D1.a
a. Apply the addition and multiplication principles of counting.
Element: MM1D1.b
b. Calculate and use simple permutations and combinations.

Students will use the basic laws of probability.
Element: MM1D2.a
a. Find the probabilities of mutually exclusive events.
Element: MM1D2.b
b. Find the probabilities of dependent events.
Element: MM1D2.c
c. Calculate conditional probabilities.
Element: MM1D2.d
d. Use expected value to predict outcomes.

Students will relate samples to a population.
Element: MM1D3.a
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: MM1D3.b
b. Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.
Element: MM1D3.c
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: MM2D2.a
a. Gather and plot data that can be modeled with linear and quadratic functions.
Element: MM2D2.b
b. Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and €œeyeballing.€
Element: MM2D2.c
c. Understand and apply the processes of linear and quadratic regression for curve fitting using appropriate technology.
Element: MM2D2.d
d. Investigate issues that arise when using data to explore the relationship between two variables, including confusion between correlation and causation.

Strand: Process Standards

Students will solve problems (using appropriate technology).
Element: MM1P1.a
a. Build new mathematical knowledge through problem solving.
Element: MM1P1.b
b. Solve problems that arise in mathematics and in other contexts.
Element: MM1P1.c
c. Apply and adapt a variety of appropriate strategies to solve problems.
Element: MM1P1.d
d. Monitor and reflect on the process of mathematical problem solving.

Students will reason and evaluate mathematical arguments.
Element: MM1P2.a
a. Recognize reasoning and proof as fundamental aspects of mathematics.
Element: MM1P1.b
b. Make and investigate mathematical conjectures.
Element: MM1P3.c
c. Develop and evaluate mathematical arguments and proofs.
Element: MM1P2.d
d. Select and use various types of reasoning and methods of proof.

Students will communicate mathematically.
Element: MM1P3.a
a. Organize and consolidate their mathematical thinking through communication.
Element: MM1P3.b
b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
Element: MM1P3.c
c. Analyze and evaluate the mathematical thinking and strategies of others.
Element: MM1P3.d
d. Use the language of mathematics to express mathematical ideas precisely.

Students will make connections among mathematical ideas and to other disciplines.
Element: MM1P4.a
a. Recognize and use connections among mathematical ideas.
Element: MM1P4.b
b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
Element: MM1P4.c
c. Recognize and apply mathematics in contexts outside of mathematics.

Students will represent mathematics in multiple ways.
Element: MM1P5.a
a. Create and use representations to organize, record, and communicate mathematical ideas.
Element: MM1P5.b
b. Select, apply, and translate among mathematical representations to solve problems.
Element: MM1P5.c
c. Use representations to model and interpret physical, social, and mathematical phenomena.

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