Correlation Between the Texas Essential Knowledge and Skills and the eTAP Lessons TAKS Preparation with eTAP Lessons Click here for summary test on all skills. Below are the eTAP lessons covering each TAKS. Click on the eTAP lesson for access to the links to video. Topics marked by yellow are accessible from the Demo. You need to become a subscribing Member to access other lessons. Pre- Test   Post- Test Objective 1 The student will describe functional relationships in a variety of ways. A(b)1: Foundations for functions: The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. Q&A (A) The student describes independent and dependent quantities in functional relationships. 10. Linear Relations Ordered Pairs Q&A Q&A (B) The student {gathers and records date, or} uses data sets, to determine functional (systematic) relationships between quantities. 13. Functions Functions and Graphs http://www.learner.org/vod/login.html?pid=1545 Q&A Q&A (C) The student describes functional relationships for given problem situations and writes equations or inequalities to answer questions arising from the situations. 13. Functions Functions and Graphs Graphing Linear Equations I. Inequalities http://www.eduplace.com/math/mathsteps/3/e/index.html Q&A Q&A (D) The student represents relationships among quantities using {concrete} models, tables, graphs, diagrams, verbal descriptions, equations and inequalities. 13. Functions Functions and Graphs Graphing Linear Equations I. http://www.inspiration.com/productinfo/inspirati on/using_insp/index.cfm?fuseaction=math Q&A Q&A (E) The student interprets and makes inferences from functional relationships. 13. Functions Number Relations Graphing Linear Equations I. http://mathforum.org/library/drmath/sets/high_functions.html Q&A Objective 2 The student will demonstrate an understanding of the properties and attributes of functions. A(b)2: Foundations for Functions: The student uses the properties and attributes of functions. Q&A (A) The student identifies (and sketches) the general forms of linear (y = x) and quadratic (y = x2) parent functions. 10. Linear Relations * Graphing Linear Equations I. Graphing Linear Equations II. Quadratics http://id.mind.net/~zona/mmts/functionInstitut e/linearFunctions/linearFunctions.html Q&A Q&A (B) For a variety of situations, the student identifies the mathematical domains and ranges and determines reasonable domain and range values for given situations. 13. Functions * Number Relations http://www.regentsprep.org/Regents/math/A LGEBRA/AP3/LFunction.htm Q&A Q&A (C) The student interprets situations in terms of given graphs (or creates situations that fit given graphs). Visual Representation of Data Comparing Data Seeking Trends with Line Graphs Functions as Graphs http://people.hofstra.edu/steven_r_costenoble/Graf/Graf.html Q&A Q&A (D) In solving problems, the student (collects and) organizes data, (makes and) interprets scatter plots, and models, predicts, and makes decisions and critical judgments. Visual Representation of Data Comparing Data Seeking Trends with Line Graphs Functions as Graphs http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=data Q&A A(b)3: Foundations for Functions: The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. Q&A (A) The student uses symbols to represent unknowns and variables. 2. The Language of Algebra * Changing Words into Math http://www.mathleague.com/help/algeb ra/algebra.htm#variables Q&A Q&A (B) Given situations, the student looks for patterns and represents generalizations algebraically. 24. Mathematical Induction * http://standards.nctm.org/document/eexamp les/chap4/4.1/index.htm Q&A A(b)4: Foundations for Functions: The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. Q&A (A) The student finds specific function values, simplifies polynomial expressions, transforms and solves equations, and factors as necessary in problem situations. 4. Factoring Polynomials * Monomials and Polynomials http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=polyadd Q&A Q&A (B) The student uses the commutative, associative, and distributive properties to simplify algebraic expressions. Properties http://www.purplemath.com/modules/numbprop.htm Q&A Objective 3 The student will demonstrate an understanding of linear functions. A(c)1: Linear Functions: The student understands that linear functions can be represented in different ways and translates among their various representations. Q&A (A) The student determines whether or not given situations can be represented by linear functions. (B) The students translates from among and uses algebraic, tabular, graphical, or verbal descriptions of linear functions. 5. Linear Equations * Linear Functions http://standards.nctm.org/document/eexam ples/chap7/7.5/index.htm http://www.algebra.com/algebra/homework/functions/ Q&A A(c)2: Linear Functions: The student understands the meaning of the slope and intercepts of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. Q&A (A) The student develops the slope as a rate of change and determines slope from graphs, tables and algebraic expressions. Slope of a Line Slope Intercept Form http://people.hofstra.edu/faculty/Stefan_Wan er/RealWorld/tutorialsf0/frames1_3.html Q&A Q&A (B) The student interprets the meaning of slope and intercepts in situations using data, symbolic representations or graphs. Slope of a Line http://people.hofstra.edu/faculty/Stefan_Wan er/RealWorld/tutorialsf0/frames1_3.html Q&A Q&A (C) The student investigates, describes and predicts the effects of changes in m and b on the graph of y = mx + b. Slope of a Line Slope Intercept Form http://id.mind.net/~zona/mmts/functio nInstitute/linearFunctions/lsif.html Q&A Q&A (D) The student graphs and writes equations of lines given characteristics, such as two points, a point and a slope, or a slope and y-intercept. Point Slope and Standard Forms Slope Intercept Form of Equations Slope Intercept Form http://people.hofstra.edu/faculty/Stefan_Wan er/RealWorld/tutorialsf0/frames1_3.html Q&A Q&A (E) The student determines the intercepts of linear functions from graphs, tables, and algebraic expressions. Slope Intercept Form http://id.mind.net/~zona/mmts/functionIn stitute/linearFunctions/lsif.html Q&A Q&A (F) The student interprets and predicts the effects of changing slope and y-intercept in applied situations. Equations of Lines http://faculty.ed.umuc.edu/~swalsh/Math %20Articles/Parperp.html Q&A Q&A (G) The student relates direct variation to linear functions and solves problems involving proportional change. Direct Variation http://regentsprep.org/Regents/Math/v ariation/Ldirect.htm Q&A Objective 4 The student will demonstrate an understanding of linear functions. A(c)3: Linear Functions: The student formulates equations and inequalities based on linear functions, uses a variety of methods to solve them, and analyzes the solution in terms of the situation. Q&A (A) The student analyzes situations involving linear functions and formulates linear equations or inequalities to solve problems. 5. Linear Equations * 8. Inequalities * Properties http://regentsprep.org/Regents/math/rea lnum/properties.htm Q&A Q&A (B) The student investigates methods for solving linear equations and inequalities using (concrete) models, graphs, and the properties of inequality, selects a method, and solves the equations and inequalities. 5. Linear Equations * 8. Inequalities * Properties Equations of Lines http://www.purplemath.com/modules/solvelin.htm Q&A Q&A (C) For given contexts, the student interprets and determines the reasonableness of solutions to linear equations and inequalities. 5. Linear Equations * 8. Inequalities * Properties Equations of Lines Q&A A(c)4: Linear Functions: The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solution in terms of the situation. Q&A (A) The student analyzes situations and formulates systems of linear equations to solve problems. B) The student solves systems of linear equations using (concrete) models, graphs, tables and algebraic methods. C) For given contexts, the student interprets and determines the reasonableness of solutions to systems of linear equations 20. Systems of Equations * 21. Systems of Linear Equations * Simultaneous Linear Equations Systems of Equations http://regentsprep.org/Rege nts/math/math-topic.cfm?TopicCode=syslin Q&A Objective 5 The student will demonstrate an understanding of quadratic and other nonlinear functions. A(d)1: Quadratic and other nonlinear functions: The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions. Q&A (A) The student investigates, describes and predicts the effects of changes in a on the graph of y = ax2. 7. Quadratic Equations * Graphing Quadratic Functions Solving Quadratic Equations http://www.analyzemath.com/Graphing/Gra phingQuadraticFunction.html Q&A Q&A (B) The student investigates, describes and predicts the effects of changes in c on the graph of y = x2 + c. 7. Quadratic Equations * Graphing Quadratic Functions Solving Quadratic Equations http://orion.math.iastate.edu/algebra/sp/xcu rrent/applets/quadraticfunction.html Q&A Q&A (C) For problem situations, the student analyzes the graphs of quadratic functions and draws conclusions. 7. Quadratic Equations * Graphing Quadratic Functions Solving Quadratic Equations http://home.alltel.net/okrebs/page7.html Q&A A(d)2: Quadratic and other nonlinear functions: The student understands that there is more than one way to solve a quadratic equation and solves them using appropriate methods. Q&A (A) The student solves quadratic equations using (concrete) models, tables, graphs, and algebraic methods. 7. Quadratic Equations * Quadratic Equations http://www.purplemath.com/modules/solvquad.htm Q&A Q&A (B) The student relates the solutions of quadratic equations to the roots of their functions. 7. Quadratic Equations * Type of Roots http://www.andrews.edu/~calkins/math/webte xts/numb12.htm#DISC Q&A A(d)3: Quadratic and other nonlinear functions: The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situation. Q&A (A) The students uses (patterns to generate) the laws of exponents and applies them in problem-solving situations. 3. Exponents and Radicals * Dividing Rational Numbers Rules of Exponents Roots and Radicals http://regentsprep.org/Regents/math /math-topic.cfm?TopicCode=exp Q&A Objective 6 The student will demonstrate an understanding of geometric relationships and spatial relationships. G(b)4: Geometric structures: The student uses a variety of representations to describe geometric relationships and solve problems. Q&A (A) The student selects an appropriate representation ({concrete,} pictorial, graphical, verbal, or symbolic) in order to solve problems. Mathematical Modeling Q&A G(c)1: Geometric patterns: The student identifies, analyzes, and describes patterns that emerge from two- and three-dimensional geometric figures. Q&A (A) The student uses numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles. Polygons and their Properties Similarity Proving Angle Conjectures Q&A Q&A (B) The student uses the properties of transformations and their compositions to make connections between mathematics and the real world in applications such as tessellations or fractals. Tessellations http://www.tessellations.org/ Q&A Q&A (C) The student identifies and applies patterns from right triangles to solve problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples. Pythagorean Theorem and It's Uses Triangles http://www.clarku.edu/~djoyce/trig/right.html Q&A G(e)3: Congruence and the geometry of size: The student applies the concept of congruence to justify properties of figures and solve problems. Q&A (A) The student uses congruence transformations to make conjectures and justify properties of geometric figures. Transformations http://www.mathsnet.net/transform/index.html Q&A Objective 7 The student will demonstrate an understanding of two- and three- dimensional representations of geometric relationships and shapes. G(d)1: Dimensionality and the geometry of location. The student analyzes the relationship between three-dimensional objects and relates two-dimensional representations and uses these representations to solve problems. Q&A (B) The student uses nets to represent (and construct) three-dimensional objects. http://www.mathsnet.net/geometry/solid/nets.html Q&A Q&A (C) The student uses top, front, side and corner views of three-dimensional objects to create accurate and complete representations and solve problems. http://illuminations.nctm.org/LessonDetail.aspx?ID=L406 Q&A G(d)2: Dimensionality and the geometry of location. The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly. Q&A (A) The student uses one- and two-dimensional coordinate systems to represent points, lines, line segments, and figures. 5. Linear Equations * Ordered Pairs Graphing Linear Relations http://www.rwc.uc.edu/koehler/biophys/1b.html Q&A Q&A (B) The student uses slope and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and (special segments of) triangles and other polygons. 5. Linear Equations * Parallel Lines Midpoint and Slope Slope of Lines Equations of Lines Lines and Angles Polygons and Their Properties http://regentsprep.org/regents/math/math-topic.cfm?TopicCode=parallel Q&A Q&A (C) The student (develops and) uses formulas, including distance and midpoint. Midpoint and Slope Distance Calculations http://regentsprep.org/regents/math/math-topic.cfm?TopicCode=midpoint Q&A G(e)2: Congruence and the geometry of size. The student analyzes properties and describes relationships in geometric figures. Q&A (D) The student analyzes characteristics of three-dimensional figures and their component parts. Volume Volume Formulas http://www.icoachmath.com/SiteMap/Three-dimensionalFigures.html Q&A Objective 8 The student will demonstrate an understanding of the concepts and uses of measurement and similarity. G(e)1: Congruence and the geometry of size. The student extends measurement concepts to find area, perimeter, and volume in problem situations. Q&A (A) The student finds areas of regular polygons and composite figures. Rectangles and Parallelograms Triangles, Trapezoids and Kites Areas of Regular Polygons http://www.algebralab.org/lessons/lesson.aspx?file=Geo metry_AreaPerimeterRegularPolygons.xml Q&A Q&A (B) The student finds areas of sectors and arc lengths of circles using proportional reasoning. Arc Lengths http://www.themathpage.com/aTrig/arc-length.htm Q&A Q&A (C) The student (develops, extends and) uses the Pythagorean Theorem. Pythagorean Theorem The Theorem of Pythagoras http://regentsprep.org/regents/Math/math-topic.cfm?TopicCode=fpyth Q&A Q&A (D) The student finds surface area and volumes of prisms, pyramids, spheres, cones and cylinders in problem situations. Volume Volume Formulas Surface Area http://regentsprep.org/Regents/Math/math-topic.cfm?TopicCode=fsolid Q&A G(f)1: Similarity and the geometry of shape. The student applies the concepts of similarity to justify properties of figures and solve problems. Q&A (A) The student uses similarity properties and transformations to (explore and) justify conjectures about geometric figures. Similarity Transformations http://regentsprep.org/Regents/Math/math-topic.cfm?TopicCode=similar Q&A Q&A (B) The student uses ratios to solve problems involving similar figures. Ratios and Proportions Similarity http://regentsprep.org/regents/Math/math-topic.cfm?TopicCode=ratio Q&A Q&A (C) In a variety of ways, the student (develops,) applies, and justifies triangle similarity relationships, such as right triangle ratios, (trigonometric ratios,) and Pythagorean triples. Special Right Triangles Similarity http://aah.ryan-usa.com/node69.html Q&A Q&A (D) The student describes the effect on perimeter, area, and volume when length, width, or height of a three-dimensional solid is changed and applies this idea in solving problems. Rectangles and Parallelograms Volume Formulas Perimeter Q&A Objective 9 The student will demonstrate an understanding of percents, proportional relationships, probability, and statistics in application problems. 8.3: Patterns, relationships, and algebraic thinking. The student identifies proportional relationships in problem situations and solves problems. Q&A (B) The student is expected to estimate and find solutions to application problems involving percents and proportional relationships, such as similarity and rates. Ratios and Proportions Percent Similarity http://aaamath.com/B/rat62ax2.htm Q&A 8.11: Probability and statistics. The student applies the concepts of theoretical and experimental probability to make predictions. Q&A (A) The student is expected to find the probabilities of compound events (dependent and independent). Possible Outcomes http://regentsprep.org/Regents/math /math-topic.cfm?TopicCode=events Q&A Q&A (B) The student is expected to use theoretical probabilities and experimental results to make predictions and decisions. Estimate Probability Q&A 8.12: Probability and statistics. The student uses statistical procedures to describe data. Q&A (A) The student is expected to select the appropriate measure of central tendency to describe a set of data for a particular purpose. Data Calculations http://ceds.vu.edu.au/studentlearning/Cour seSpecific/PsychStatsTopics/CentralTenden cy/CentralTendencyIntro.htm Q&A Q&A (C) The student is expected to construct circle graphs, bar graphs and histograms, with and without technology. Graphs http://www.mathwithmrherte.com/circle_graphs.htm Q&A 8.13: Probability and statistics. The student evaluates predictions and conclusions based on statistical data. Q&A (A) The student is expected to recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis. Data Display Analysis Q&A Objective 10 The student will demonstrate an understanding of the mathematical processes and tools used in problem solving. 8.14: Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines and activities in and outside of school. Q&A (A) The student is expected to identify and apply mathematics in to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. http://www.nzmaths.co.nz/PS/Info/PSStrat egies.aspx\ Q&A Q&A (B) The student is expected to use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. http://library.thinkquest.org/25459/learnin g/problem/#strategy Q&A Q&A (C) The student is expected to 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. http://www.nzmaths.co.nz/PS/Info/PSStrat egies.aspx\ Q&A 8.15: Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models. Q&A (A) The student is expected to communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. Q&A 8.16: Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. Q&A (A) The student is expected to make conjectures from patterns or sets of examples and nonexamples Q&A Q&A (B) The student is expected to validate his/her conclusions using mathematical properties and relationships. Q&A