TAKS Grade 10 Math

Grade 10 Mathematics Correlation Between the Texas Essential Knowledge and Skills for Mathematics and the eTAP Lessons Functions \| Properties of Functions \| Linear Functions \| Linear Equations and Inequalities \| Quadratic and Other Nonlinear Functions \| Geometric Relationships \| Geometric Shapes \| Measurement and Similarity \| Percents, Proportional Relationships, Probability \| Problem Solving Your browser does not support inline frames or is currently configured not to display inline frames.
Pre-Test	Texas Essential Knowledge Skills		eTAP Lessons	Post-Test
			Outside Link
	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.		Q&A
			http://whyslopes.com/etc/ThreeSkillsForAlgebra/PS-2006-11-17-dependent-or-independent-variable.html
	(B)	The student [gathers and records data, or] uses data sets, to determine functional (systematic) relationships between quantities.	Methods of Collecting, Representing, & Displaying Data
			http://en.wikipedia.org/wiki/Function_(mathematics)
	(C)	The student describes functional relationships for given problem situations and writes equations or inequalities to answer questions arising from the situations.
			http://regentsprep.org/Regents/math/mode ling/Funclink.htm
	(D)	The student represents relationships among quantities using [concrete] models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities.
			http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=tree
	(E)	The student interprets and makes inferences from functional relationships.
			http://www.eduplace.com/math/mathsteps/3/e/index.html
	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.
	(A)	The student identifies [and sketches] the general forms of linear ( y = x) and quadratic ( y = x² ) parent functions.	Graphing Linear Equations Solving Quadratic Equations by Graphing
			http://www.purplemath.com/modules/grphquad.htm http://www.purplemath.com/modules/graphlin.htm
	(B)	For a variety of situations, the student identifies the mathematical domains and ranges and determines reasonable domain and range values for given situations.	Number Relations
			http://www.purplemath.com/modules/ fcns.htm
	(C)	The student interprets situations in terms of given graphs [or creates situations that fit given graphs].	Graphs
			http://mathforum.org/alejandre/sprea dsheet.html
	(D)	In solving problems, the student [collects and] organizes data, [makes and] interprets scatter plots, and models, predicts, and makes decisions and critical judgments.	Methods of Collecting, Representing, & Displaying Data
			http://mathforum.org/alejandre/sprea dsheet.html
	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.
	(A)	The student uses symbols to represent unknowns and variables.	Numerical and Literal Numbers

	(B)	Given situations, the student looks for patterns and represents generalizations algebraically.
			http://www.math.com/school/subj ect2/lessons/S2U1L1DP.html
	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.
	(A)	The student finds specific function values, simplifies polynomial expressions, transforms and solves equations, and factors as necessary in problem situations.	Monomials and Polynomials Equations Factoring
			http://www.bymath.com/studyguide/al g/sec/alg3.html http://www.321know.com/equ.htm http://www.jamesbrennan.org/algebra/p olynomials/factoring_polynomials.htm
	(B)	The student uses the commutative, associative, and distributive properties to simplify algebraic expressions.	Distributive and Additive Identity, Multiplicative Identity Property and Properties of Equality Commutative and Associative Property
			http://www.purplemath.com/modul es/numbprop.htm
	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.
	(A)	The student determines whether or not given situations can be represented by linear functions.	Functions
			http://id.mind.net/~zona/mmts/functionInstitute/l inearFunctions/linearFunctions.html
	(C)	The student translates among and uses algebraic, tabular, graphical, or verbal descriptions of linear functions.	Functions and Graphs

	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.
	(A)	The student develops the concept of slope as rate of change and determines slopes from graphs, tables, and algebraic representations.	Slope of a Line
			http://www.purplemath.com/modu les/slope.htm
	(B)	The student interprets the meaning of slope and intercepts in situations using data, symbolic representations, or graphs.	Graphing Linear Equations I.
			http://www.purplemath.com/mod ules/slopyint.htm
	(C)	The student investigates, describes, and predicts the effects of changes in m and b on the graph of y = mx + b.	Slope Intercept Form
			http://www.ltcconline.net/greenl/java/ BasicAlgebra/LineGraph/LineGraph.htm
	(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.	Graphing Linear Equations I.
			http://www.purplemath.com/m odules/strtlneq.htm http://www.curriculum.org/tcf/tea chers/projects/algebra/LinearEquation08.adp
	(E)	The student determines the intercepts of linear functions from graphs, tables, and algebraic representations.	Slope Intercept Form of Equations
			http://standards.nctm.org/document/eexa mples/chap7/7.5/index.htm
	(F)	The student interprets and predicts the effects of changing slope and y-intercept in applied situations.	Slope of a Line Slope Intercept Form of Equations
			http://standards.nctm.org/document/eexa mples/chap7/7.5/index.htm
	(G)	The student relates direct variation to linear functions and solves problems involving proportional change.	Direct Variation
			http://www.explorelearning.com/index.cfm ?method=cResource.dspView&ResourceID=130
	Objective 4. The student will formulate and use linear equations and inequalities. 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 solutions in terms of the situation.
	(A)	The student analyzes situations involving linear functions and formulates linear equations or inequalities to solve problems.	Equations Inequalities
			http://www.cut-the-knot.org/arithm etic/WProblem.shtml
	(B)	The student investigates methods for solving linear equations and inequalities using [concrete] models, graphs, and the properties of equality, selects a method, and solves the equations and inequalities.2	Equations Inequalities
			http://www.purplemath.com/mo dules/solvelin.htm
	(C)	For given contexts, the student interprets and determines the reasonableness of solutions to linear equations and inequalities.

	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 solutions in terms of the situation.
	(A)	The student analyzes situations and formulates systems of linear equations to solve problems.	Simultaneous Linear Equations
			http://www.purplemath.com/mo dules/systprob.htm
	(B)	The student solves systems of linear equations using [concrete] models, graphs, tables, and algebraic methods.	Simultaneous Linear Equations
			http://www.algebralab.org/studyaids /studyaid.aspx?file=Algebra1_7-1.xml
	(C)	For given contexts, the student interprets and determines the reasonableness of solutions to systems of linear equations.

	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.
	(B)	The student investigates, describes, and predicts the effects of changes in a on the graph of y = ax².
			http://www.personal.kent.edu/~rmuha mma/Algorithms/MyAlgorithms/parabola.htm
	(C)	The student investigates, describes, and predicts the effects of changes in c on the graph of y = x² + c.	Solving Quadratic Equations by Graphing
			http://www.mathwarehouse.com/geo metry/parabola/
	(D)	For problem situations, the student analyzes graphs of quadratic functions and draws conclusions.	Quadratic Functions
			http://members.shaw.ca/ron.blond/QF A.CSF.APPLET/index.html
	A(d)(2) Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods.
	(A)	The student solves quadratic equations using [concrete] models, tables, graphs, and algebraic methods.	Quadratics
			http://www.purplemath.com/modules/ solvquad.htm
	(B)	The student relates the solutions of quadratic equations to the roots of their functions.	Sum and Product of Roots
			http://www.sosmath.com/algebra/qu adraticeq/root/root.html
	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 situations.
	(A)	The student uses [patterns to generate] the laws of exponents and applies them in problem-solving situations.	Rules of Exponents
			http://www.purplemath.com/mod ules/exponent.htm
	Objective 6. The student will demonstrate an understanding of geometric relationships and spatial reasoning. (8.6) Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense. The student is expected to
	(A)	generate similar shapes using dilations including enlargements and reductions; and	Transformations
			http://nlvm.usu.edu/en/nav/frames_asi d_295_g_3_t_3.html?open=activities
	(B)	graph dilations, reflections, and translations on a coordinate plane.	Tessellations
			http://mathforum.org/sum95/suzanne/ symsusan.html
	(8.7) Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to
	(D)	locate and name points on a coordinate plane using ordered pairs of rational numbers.	Ordered Pairs
			http://www.mathwarehouse.com/ordered-pairs/interactive-ordereded-pairs.html
	Objective 7. The student will demonstrate an understanding of two- and three-dimensional representations of geometric relationships and shapes. (8.7) Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to
	(A)	draw solids from different perspectives;

	(B)	use geometric concepts and properties to solve problems in fields such as art and architecture; and

	(C)	use pictures or models to demonstrate the Pythagorean Theorem.	Pythagorean Theorem Pythagorean Theorem and Its Use
			http://www.ies.co.jp/math/java/geo/pythagoras.html
	Objective 8. The student will demonstrate an understanding of the concepts and uses of measurement and similarity. (8.8) Measurement. The student uses procedures to determine measures of solids. The student is expected to
	(A)	find surface area of prisms and cylinders using [concrete] models and nets (two dimensional models);	Three Dimensional Shapes and Surface Area
			http://www.mathguide.com/lessons/Surface Area.html
	(B)	connect models to formulas for volume of prisms, cylinders, pyramids, and cones; and	Volume Formulas More Volumes and Areas
			http://en.wikipedia.org/wiki/Volume
	(C)	estimate answers and use formulas to solve application problems involving surface area and volume.	Three Dimensional Shapes and Surface Area

	(8.9) Measurement. The student uses indirect measurement to solve problems. The student is expected to
	(A)	use the Pythagorean Theorem to solve real-life problems; and	Pythagorean Theorem Pythagorean Theorem and Its Use
			http://www.ies.co.jp/math/java/geo/pyth agoras.html
	(B)	use proportional relationships in similar shapes to find missing measurements.	Similarity
			http://www.beaconlearningcenter.com/We bLessons/SamsSimilarShapes/default.htm
	(8.10) Measurement. The student describes how changes in dimensions affect linear, area, and volume measures. The student is expected to
	(A)	describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally; and	Proportions with Area and Volume

	(B)	describe the resulting effect on volume when dimensions of a solid are changed proportionally.	Proportions with Area and Volume

	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. The student is expected to
	(B)	estimate and find solutions to application problems involving percents and proportional relationships, such as similarity and rates.	Similar Triangles Ratios and Proportions Percent

	(8.11) Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to
	(A)	find the probabilities of compound events (dependent and independent); and	Possible Outcomes of Compound Events
			http://wind.caspercollege.edu/~pwildman /stat/chap3lesson/chap3sec3and4.html
	(B)	use theoretical probabilities and experimental results to make predictions and decisions.	Estimate the Probability of Future Events
			http://www.zweigmedia.com/ThirdEdSite/ tutorialsf2/frames6_3.html
	(8.12) Probability and statistics. The student uses statistical procedures to describe data. The student is expected to
	(A)	select the appropriate measure of central tendency to describe a set of data for a particular purpose; and	Data Calculations
			http://www.explorelearning.com/index.cfm?m ethod=cResource.dspView&ResourceID=262
	(C)	construct circle graphs, bar graphs, and histograms, with and without technology.	Graphs
			http://www.ifm.eng.cam.ac.uk/dstools/r epresent/graphs.html
	(8.13) Probability and statistics. The student evaluates predictions and conclusions based on statistical data. The student is expected to
	(B)	recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis.

	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. The student is expected to
	(A)	identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;

	(B)	use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; and

	(C)	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.

	(8.15) Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models. The student is expected to
	(A)	communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.

	(8.16) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to
	(A)	make conjectures from patterns or sets of examples and nonexamples; and

	(B)	validate his/her conclusions using mathematical properties and relationships.