Laying the Foundation: 2007

Sunday, November 11, 2007

TEKS

Strand 1: Number, Operation, and Quantitative Reasoning
ALG2.1.01
Use complex numbers to describe the solutions of quadratic equations. (2B) (Ab2B)
Use complex numbers to describe the solutions of quadratic equations.
ALG2.1.02
Analyze and interpret the number and types of solutions of quadratic equations using discriminants. (8B) (AdeB)
Analyze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula.
Strand 2: Patterns, Relationships, and Algebraic Reasoning
ALG2.2.01
Identify the mathematical domains and ranges of functions, determine reasonable domain and range values for continuous and discrete situations, and describe situations given domain and range values. (1A) (Ab1A)
Identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations.
TAKS Exit Level – Obj. 2
ALG2.2.02
Use tools including factoring and properties of exponents to simplify expressions and to transform and solve equations and inequalities. (2A) (Ab2A)
Use tools including factoring and properties of exponents to simplify
expressions and to transform and solve equations.
TAKS Exit Level – Obj. 2
ALG2.2.03
Analyze situations and formulate systems of equations in two or more unknowns or inequalities in two unknowns to solve problems. (3A) (Ab3A)
Analyze situations and formulate systems of equations in two or more unknowns or inequalities in two unknowns to solve problems. TAKS Exit Level – Obj. 4
ALG2.2.04
Use algebraic methods including substitution or linear combination, graphs, tables, or matrices, to solve systems of equations or inequalities. (3B) (Ab3A)
Use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities.
TAKS Exit Level – Obj. 4
ALG2.2.05
Interpret and determine appropriate domain and range values and the reasonableness of solutions to systems of equations or inequalities for given contexts. (3C) (Ab3C)
Interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts.

TAKS Exit Level – Obj. 4
ALG2.2.06
Describe and analyze the relationship between a function and its inverse using concrete representations, tables of values, graphs, and symbolic representations. (4C) (Ac1C)
Describe and analyze the relationship between a function and its inverse.

ALG2.2.07
Make generalizations from patterns in both equation and graphical form to identify a conic section from the general equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. (5D) (Ac2D)
Identify the conic section from a given equation.
ALG2.2.08
Determine the reasonable domain and range values of a quadratic function represented by a table of values, graph, function rule, or a contextual situation. (6A) (Ad1A)
Determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to quadratic equations and inequalities.
TAKS Exit Level – Obj. 2
ALG2.2.09
Determine the reasonableness of solutions to quadratic equations and inequalities.
ALG2.2.10
Identify and relate quadratic functions that are represented in written, tabular, graphical, and symbolic forms. (6B) (Ad1B)
Relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions. TAKS Exit Level – Obj. 1
ALG2.2.11
Determine a quadratic function from its roots or a graph. (6C) (Ad1C)
Determine a quadratic function from its roots or a graph. TAKS Exit Level – Obj. 5
ALG2.2.12
Analyze situations involving quadratic functions and formulate quadratic equations or inequalities to solve problems. (8A) (Ad3A)
Analyze situations involving quadratic functions and formulate quadratic equations or inequalities to solve problems.
TAKS Exit Level – Obj. 5
ALG2.2.13
Solve quadratic equations using the quadratic formula. (8B) (Ad3B)
Analyze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula.
ALG2.2.14
Compare and translate between algebraic solutions and graphical solutions of quadratic equations, and describe the relationship between the roots of a quadratic equation and the zeros of the corresponding quadratic function.
(8C) (Ad3C)
Compare and translate between algebraic and graphical solutions of quadratic equations. TAKS Exit Level – Obj. 5
ALG2.2.15
Solve quadratic equations using graphs, tables, and algebraic methods. (8D) (Ad3D)
Solve quadratic equations and inequalities using graphs, tables, and algebraic methods. TAKS Exit Level – Obj. 5
ALG2.2.16
Solve quadratic inequalities using graphs, tables, and algebraic methods
ALG2.2.17
Relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions.

(9B) (Ad4B)
Relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions.

ALG2.2.18
Determine the reasonable domain and range values of square root functions. (9C) (Ad4C)
Determine the reasonable domain and range values of square root functions, as well as interpret and determine the reasonableness of solutions to square root equations and inequalities.
ALG2.2.19
Interpret and determine the reasonableness of solutions to square root equations and inequalities.
ALG2.2.20
Determine solutions of square root equations using graphs, tables, and algebraic methods. (9D) (Ad4D)
Determine solutions of square root equations using graphs, tables, and algebraic methods.
ALG2.2.21
Determine solutions of square root equalities using graphs, tables, and algebraic methods. (9E)
Determine solutions of square root inequalities using graphs and tables.
ALG2.2.22
Analyze situations modeled by square root functions, formulate equations or inequalities, select a method including tabular, graphical, or algebraic and solve problems. (9F) (Ad4E)
Analyze situations modeled by square root functions, formulate equations or inequalities, select a method, and solve problems.
ALG2.2.23
Connect and express the inverses of square root functions with quadratic functions from tabular, graphical, and algebraic representations. (9G) (Ad4F)
Connect inverses of square root functions with quadratic functions.
ALG2.2.24
Analyze various representations of rational functions including tabular, verbal, symbolic, and graphical with respect to problem situations. (10B) (Ae2)
Analyze various representations of rational functions with respect to problem situations.
ALG2.2.25
Determine the reasonable domain and range values of rational functions.
(10C) (Ae3)
Determine the reasonable domain and range values of rational functions, as well as interpret and determine the reasonableness of solutions to rational equations and inequalities.
ALG2.2.26
Interpret and determine the reasonableness of solutions to rational equations and inequalities.
ALG2.2.27
Determine the solutions of rational equations using graphs, tables, and algebraic methods. (10D) (Ae4)
Determine the solutions of rational equations using graphs, tables, and algebraic methods.
ALG2.2.28
Determine solutions of rational inequalities using graphs and tables. (10E)
Determine solutions of rational inequalities using graphs and tables.

ALG2.2.29
Analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or quadratic function, and solve the problem. (10F) (Ae5)
Analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or quadratic function, and solve the problem.
ALG2.2.30
Use functions to model and make predictions in problem situations involving direct and inverse variation. (10G) (Ae6)
Use functions to model and make predictions in problem situations involving direct and inverse variation.
ALG2.2.31
Develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses using concrete functions, tables and symbolic expressions. (11A) (Af1)
Develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses.

ALG2.2.32
Determine the reasonable domain and range values of exponential and logarithmic functions including subsets of the domain and range which have meaning in a given situation. (11C) (Af3)
Determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities.
ALG2.2.33
Interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities.
ALG2.2.34
Determine solutions of exponential and logarithmic equations using the graph, trace, and table features on a graphing calculator as well as algebraic methods. (11D) (Af4)
Determine solutions of exponential and logarithmic equations using graphs, tables, and algebraic methods.
ALG2.2.35
Determine solutions of exponential and logarithmic equations using the graph, trace, and table features on a graphing calculator as well as algebraic methods. (11E)
Determine solutions of exponential and logarithmic inequalities using graphs, tables, and algebraic methods.
ALG2.2.36
Analyze a situation modeled by an exponential function, formulate an equation or inequality, solve the problem, and relate the solution to the domain and range that have meaning in the context of the situation.
(11F) (Af5)
Analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem.
Strand 3: Geometry and Spatial Reasoning
ALG2.3.01
Identify and sketch graphs of parent functions, including linear (f(x) = x), quadratic (f(x) = x2), exponential (f(x) = ax), logarithmic (f(x) = logax), absolute value of x (f(x) = lxl), square root (f(x) = √x), and reciprocal of x (f(x) = 1/x) functions. (4A) (Ac1A)
Identify and sketch graphs of parent functions, including linear (f(x) = x), quadratic (f(x) = x2), exponential (f(x) = ax), logarithmic (f(x) = logax), absolute value of x (f(x) = lxl), square root (f(x) = √x), and reciprocal of x (f(x) = 1/x) functions. TAKS Exit Level – Obj. 2
ALG2.3.02
Extend parent functions with parameters including a in g(x) = a[f(x)], k in g(x) = f(x) + k , and h in g(x) = f(x – h). (4B) (Ac1B)
Extend parent functions with parameters such as a in f(x) = a/x and describe the effects of the parameter changes on the graph of parent functions. TAKS Exit Level – Obj. 3
ALG2.3.03
Describe a conic section (circle, ellipse, parabola, and hyperbola) as the intersection of a plane and a cone by comparing ά, the acute angle the plane forms with the axis of the cone and β, the acute angle the face of the cone forms with its axis. (5A) (Ac2A)
Describe a conic section as the intersection of a plane and a cone
ALG2.3.04
Sketch graphs of conic sections to relate simple parameter changes in the equations of circles, (x – h)2 + (y – k)2 = r2, parabolas y = (x – h)2 +k or x = (y – k)2 + h, ellipses (x – h)2/a2 + (y – k)2/b2 = 1, and hyperbolas
(x – h)2/a2 - (y – k)2/b2 = 1 or (y – k)2/a2 - (x – h)2/b2 = 1. (5B) (Ac2B)
Sketch graphs of conic sections to relate simple parameter changes in the equation to corresponding changes in the graph.
ALG2.3.05
Identify symmetries from graphs of conic sections. (5C) (Ac2C)
Identify symmetries from graphs of conic sections.

ALG2.3.06
Use the method of completing the square to transform quadratic equations and functions.
(5E) (Ac2E)
Use the method of completing the square.
ALG2.3.07
Use characteristics of the quadratic parent function to sketch the related graphs and connect between the f(x) = ax2 + bx + c and the f(x) = a (x – h)2 + k symbolic representations of quadratic functions, and write the quadratic function in f(x) = ax2 + bx + c or f(x) = a (x – h)2 + k given the graph of the function. (7A) (Ad2A)
Use characteristics of the quadratic parent function to sketch the related graphs and connect between the y = ax2 + bx + c and the y = a (x – h)2 + k symbolic representations of quadratic functions. TAKS Exit Level – Obj. 5
ALG2.3.08
Use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x – h)2 + k form of a function in applied and purely mathematical situations. (7B) (Ad2B)
Use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x – h)2 + k form of a function in applied and purely mathematical situations. TAKS Exit Level – Obj. 5
ALG2.3.09
Use the parent function to investigate, describe, and predict the effects of parameter changes, a, h, and k on the graphs of square root functions represented in the form y = a√ (x – h)2 + k and describe limitations on the domains and ranges. (9A) (Ad4A)
Use the parent function to investigate, describe, and predict the effects of parameter changes on the graphs of square root functions and describe limitations on the domains and ranges.

ALG2.3.10
Use quotients of polynomials to describe the graphs of rational functions, predict the effects of parameter changes, describe limitations on the domains and ranges, examine asymptotic behavior including both vertical and horizontal asymptotes, and explain the relationship of the domain and a on the x-axis if a vertical asymptote occurs at x = a. (10A) (Ae1)
Use quotients of polynomials to describe the graphs of rational functions, predict the effects of parameter changes, describe limitations on the domains and ranges, and examine asymptotic behavior.
ALG2.3.11
Use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges including why the domain and range are limited to positive numbers, and identify and write the equations of asymptotes.
(11B) (Af2)
Use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior.
Strand 4: Measurement
(none)
Strand 5: Probability and Statistics
ALG2.5.01
Collect and organize data in a table or list, make and interpret scatterplots using graphing calculators, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments.
(1B) (Ab1B)
Collect and organize data, make and interpret scatterplots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments. TAKS Exit Level – Obj. 2

Strand 6: Underlying Processes and Mathematical Tools
ALG2.6.01
Identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. (8.14A)
Identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. TAKS Grades 9, 10, Exit – Obj. 10
ALG2.6.02
Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. (8.14B)
Use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. TAKS Grades 9, 10, Exit – Obj. 10
ALG2.6.03
Select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem or working backwards to solve a problem. (8.14C)
Select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem or working backwards to solve a problem. TAKS Grades 9, 10, Exit – Obj. 10
ALG2.6.04
Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. (8.14D)
Select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.
ALG2.6.05
Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. (8.15A)
Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. TAKS Grades 9, 10, Exit – Obj. 10
ALG2.6.06
Evaluate the effectiveness of different representations to communicate ideas. (8.15B)
Evaluate the effectiveness of different representations to communicate ideas.
ALG2.6.07
Make conjectures from patterns or sets of examples and nonexamples. (8.16A)
Make conjectures from patterns or sets of examples and nonexamples. TAKS Grades 9, 10, Exit – Obj. 10
ALG2.6.08
Validate conclusions using mathematical properties and relationships.
(8.16B)
Validate conclusions using mathematical properties and relationships. TAKS Grades 9, 10, Exit – Obj. 10

Saturday, November 10, 2007