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6.1/7.1/8.1 The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

Instructional Considerations

Current TEKS New 8th grade TEKS 2013-14 2014-15 Current TEKS New HS TEKS

8.14A identify the mathematics and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics.

6.1A/7.1A/8.1A apply mathematics to problems arising in everyday life, society, and the workplace

8.14B use a problem-solving strategy that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution of reasonableness

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

6.1B/7.1B/8.1B use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution

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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

6.1C/7.1C/8.1C select tools, including real objects, manipulatives, paper/pencil, and technology, as appropriate and techniques, including mental math, estimation, and number sense, as appropriate to solve problems

8.15A communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models

6.1D/74.1D/8.1D communicate mathematical ideas, reasoning, and their implications using multiple representation, including symbols, diagrams, graphs, and language as appropriate

8.15B evaluate the effectiveness of different representations to communicate ideas

6.1E/7.1E/8.1E create and use representations to organize, record and communicate mathematical ideas

8.16A make conjectures from patterns or sets of examples and non-examples

6.1F/7.1F/8.1F analyze mathematical relationships to connect and communicate mathematical ideas

8.16B validate his/her conclusions using mathematical properties and relationships

6.1G/7.1G/8.1G display, explain and justify mathematical ideas and arguments using precise mathematical language in written or oral communications



8.2 The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to:



8.2A extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers

None

8.1C approximate (mentally and with calculators) the value of irrational numbers as they arise from problem situations (such as

)

8.2B approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line

A.11A use patterns to generate the laws of exponents and apply them in problem-solving situations

A.11A simplify numerical radical expressions involving square roots

A.11B simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents

8.1D express numbers in scientific notation, including negative exponents, in appropriate problem situations

8.2C convert between standard decimal notation and scientific notation

None

8.1E compare and order real numbers with a calculator

8.1A compare and order rational numbers in various forms including integers, percent’s, and positive and negative fractions and decimals

8.2D order a set of real numbers arising from mathematical and real-world contexts

None



8.3 The student applies mathematical process standards to use proportional relationships to describe dilations. The student is expected to:



8.3A generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation

G.11A use and extend similarity properties and transformations to explore and justify conjectures about geometric figures

G.7A apply the definition of similarity in terms of a dilation to identify similar figures and their proportional sides and the congruent corresponding angles

8.6B graph dilations, reflections, and translations on a coordinate plane

8.3B compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane

8.3C use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation

G.10A use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane

G.11A use and extend similarity properties and transformations to explore and justify conjectures about geometric figures.

G.3A describe and perform transformations of figures in a plane using coordinate notation



8.4 The student applies mathematical process standards to explain proportional and non-proportional relationships involving slope. The student is expected to:



8.4A use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 – y1) / (x2 – x1), is the same for any two points (x1, y1) and (x2, y2) on the same line

A.6A develop the concept of slope as a rate of change and determine slopes from graphs, tables, and algebraic representations

A.3A determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various

forms, including y=mx+b , Ax+By=C , and y− y=m( x−x1)

8.4B graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship

A.6B interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs

A.3B calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context in mathematical and real-world problems.




8.4C use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems.


A.3B calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context in mathematical and real-world problems.

A.6D graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept

A.3C graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problem

8.5 The student applies mathematical process standards to use proportional and non-proportional relationships to develop foundational concepts of functions. The student is expected to:



8.4 generate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description)

8.5A represent linear proportional situations with tables, graphs, and equations in the form of y = kx

A.6G relate direct variation to linear functions and solve problems involving proportional change

A.2D write and solve equations involving direct variation

8.5B represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0

A.6D graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept

A.2B write linear equations in 2 variables in various forms,

includingy=mx+b ,Ax+By=C

,y− y=m( x−x1) , given one point and the slope, and two given points



A.5A determine whether or not given situations can be represented by linear functions

8.5C contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation

P.3C use regression to determine the appropriateness of a linear function to model real life data (including technology to determine the correlation coefficient)

A.4A calculate, using technology, the correlation coefficient between 2 quantitative variables and interpret the quantity as a measure of the strength of linear association

8.12B draw conclusions and make predictions by analyzing trends in scatterplots

8.5D use a trend line that approximates the linear relationship between bivariate sets of data to make predictions

8.5A predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations

8.5E solve problems involving direct variation

A.6G relate direct variation to linear functions and solve problems involving proportional change

A.2D write and solve equations involving direct variation

A.1D represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities

8.5G identify functions using sets of ordered pairs, tables, mappings, and graphs

None



8.4 generate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description)

A.5C use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions

8.5I write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations


A.2C write linear equations in two variables given a table of values, a graph, and a verbal description

8.3A compare and contrast proportional and non-proportional linear relationships

8.5F distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form of y=kx or y=mx+b, where b does not equal 0


A.2C write linear equations in two variables given a table of values, a graph, and a verbal description

8.5H identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems

None



8.6 The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas. The student is expected to:



8.8B connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects

8.6A describe the volume formula V = Bh of a cylinder in terms of its base area and its height

8.6B model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas

G.8D find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composite of these figures in problem situations

G.11D apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

8.7C use pictures or models to demonstrate the Pythagorean Theorem

8.6C use models and diagrams to explain the Pythagorean theorem

G.5D identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.

G.9B apply the relationships in special right triangles 30-60-90 and 45-45-90 and the Pythagorean Theorem, including Pythagorean triples to solve problems



8.7 The student applies mathematical process standards to use geometry to solve problems. The student is expected to: Instructional Considerations


8.8C estimate measurements and use formulas to solve application problems involving lateral and total surface area and volume

8.7A solve problems involving the volume of cylinders, cones, and spheres

8.7B use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders

G.8D find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composite of these figures in problem situations

G.11D apply the formulas for the volume of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure

G.11C apply the formulas for the total and lateral surface area of three-dimensional figures, including prisms, pyramids, cones, cylinders, spheres, and composite figures, to solve problems using appropriate units of measure.

8.9A use the Pythagorean Theorem to solve real-life problems

G.7C derive and use formulas involving length, slope, and midpoint

8.7C use the Pythagorean Theorem and its converse to solve problems

8.7D determine the distance between two points on a coordinate plane using the Pythagorean Theorem

G.5D identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.

G.9B apply the relationships in special right triangles 30-60-90 and 45-45-90 and the Pythagorean Theorem, including Pythagorean triples to solve problems

8.8 The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to:





A.7A analyze situations involving linear functions and formulate linear equations or inequalities to solve problems

8.8A write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants

A.4A find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations

A.4B use the commutative, associative, and distributive properties to simplify algebraic expressions

A.7B investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities.

A.5A solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

A.5B solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides

8.8B write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants

8.8C model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants

8.8 The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to:





G.5B use 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

G.9A formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models

G.11C develop, apply, and justify triangle similarity relationships…

8.8D use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles

G.5B use 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

G.9A formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models

G.9B formulate and test conjectures about the properties and attributes of polygons and their component parts based on explorations and concrete models

G.9C formulate and test conjectures about the properties and attributes of circles and the lines that intersect them based on explorations and concrete models

G.10B justify and apply triangle congruence relationships

G.5A investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools

G.6A verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points its perpendicular bisector and apply these relationships to solve problems

8.9 The student applies mathematical process standards to use multiple representations to develop foundational concepts of simultaneous linear equations. The student is expected to:





A.8C interpret and determine the reasonableness of solutions to systems of linear equations

8.9 identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations

A.8B solve systems of linear equations using concrete models, graphs, tables, and algebraic methods

A.8C interpret and determine the reasonableness of solutions to systems of linear equations

A.3F graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist

A.3G estimate graphically the solutions to systems of two linear equations with two variables in real world problems



8.10 The student applies mathematical process standards to develop transformational geometry concepts. The student is expected to:



8.6B graph dilations, reflections, and translations on a coordinate plane

8.10A generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane

8.10B differentiate between transformations that preserve congruence and those that do not

8.10C explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes on a coordinate plane using an algebraic representation

G.10A use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane

G.11A use and extend similarity properties and transformations to explore and justify conjectures about geometric figures

G5C use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations

G.3A describe and perform transformations of figures in a plane using coordinate notation

G.3B determine the image or pre image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane

G.3C identify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane

8.10A describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally

8.10D model the effect on linear and area measurements of dilated two-dimensional shapes

G.11D describe the effect of perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems

G.10B determine and describe how changes in the linear dimensions of a shape affect it’s perimeter, area, surface area, or volume, including proportional and non-proportional dimensional change



8.11 The student applies mathematical process standards to use statistical procedures to describe data. The student is expected to:



8.12B draw conclusions and make predictions by analyzing trends in scatterplots

8.11A construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data

P.3B use functions such a logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data

P.3C use regression to determine the appropriate of a linear function to model real-life data (including using technology to determine the correlation coefficient)

A2.8A analyze data to select the appropriate model from among linear, quadratic, and exponential models

A2.8B use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data

8.11B determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points

None

8.11C simulate generating random samples of the same size from a population with known characteristics to develop the notion of a random sample being representative of the population from which it was selected

None



8.12 The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one’s life as a knowledgeable consumer and investor. The student is expected to:



8.12A solve real-world problems comparing how interest rate and loan length affect the cost of credit

None

8.12B calculate the total cost of repaying a loan, including credit cards and easy access loans, under various rates of interest and over different periods using an online calculator

None

8.12 C explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time

None

8.12 D calculate and compare simple interest and compound interest earnings

None

8.12E identify and explain the advantages and disadvantages of different payment methods

None



8.12F analyze situations to determine if they represent financially responsible decisions and identify the benefits of financial responsibility and the costs of financial irresponsibility

None

8.12G estimate the cost of a two-year and four-year college education, including family contribution, and devise a periodic savings plan for accumulating the money needed to contribute to the total cost of attendance for at least the first year of college

None

8th grade-Deleted Content

8.1B select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships 8.2A select appropriate operations to solve problems involving rational numbers and justify the selections 8.2B use appropriate operations to solve problems involving rational numbers in problem situations 8.2C evaluate a solution for reasonableness 8.5B find and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change) 8.6A generate similar figures using dilations including enlargements and reductions 8.7A draw three-dimensional figures from different perspectives 8.7B use geometric concepts and properties to solve problems in fields such as art and architecture 8.7D locate and name points on a coordinate plane using ordered pairs of rational numbers 8.8A find lateral and total surface area of prisms, pyramids, and cylinders using concrete models and nets (two-dimensional model) 8.9B use proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements 8.10B describe the resulting effect on volume when dimensions of a solid are changed proportionally 8.11A find the probabilities of dependent and independent events 8.11B use theoretical probabilities and experimental results to make predictions and decisions 8.11C select and use different models to simulate an event



8.12A use variability (range, including interquartile range (IQR)) and select the appropriate measure of central tendency to describe a set of data and justify the choice for a particular situation

8.12C select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, stem and leaf plots, circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, with and without the use of technology

8.13A evaluate methods of sampling to determine validity of an inference made from a set of data 8.13B recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis


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