ࡱ> oqhijklmn` vbjbj ;& jjjj22283488"888m:: :$hi=-:@m:==jj88o9DDD=rjR88D=DD2P"&8z8 7BN2m?Nt#O00g@g&g&:;D=<<2:::ODj:::====1jjjjjj  EIGHTH GRADEALGEBRA I and NINTH GRADE TAKSGEOMETRY and TENTH GRADE TAKS8.1Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations. The student is expected to:8.1Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate for different situations. The student is expected to: 8.1A Compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals. Including numbers represented as fractions and decimals. 8.1B Select and use appropriate forms of rational numbers to solve real-life problems. Including those involving proportional relationships.8.1B Select and use appropriate forms of rational numbers to solve real-life problems. 8.1C Approximate (mentally and with calculators) the value of irrational numbers as they arise from problem situations (such as, "2). Including using geometric problems using the square root of a number Including the square root of any number less than 14.8.1DExpress numbers in scientific notation, including negative exponents, in appropriate problem situation. Including: Converting numbers back to standard form Scientific notation using positive or negative exponents8.2Number, operation, and quantitative reasoning. The student selects and uses appropriate operations to solve problems and justify solutions. The student is expected to:8.2A Select appropriate operations to solve problems involving rational numbers and justify the selections. Including formulating equations with appropriate order of operations (addition, subtraction, multiplication, division, square, and square root) with positive and negative integers, fractions, decimals, and percents.8.2B Use appropriate operations to solve problems involving rational numbers in problem situations. Including problems with multi-operations (addition, subtraction, multiplication, division, square and square root) and mixed forms of rational numbers (positive and negative integers, fractions, decimals, and percents).8.2CEvaluate a solution for reasonableness. Including application problems for money, measurement, and percent.8.2DUse multiplication by a constant factor (unit rate) to represent proportional relationships. Including: Using multiple forms of fractions, decimals, percents, positive and negative integers within a single problem. (Example: 1 gallon = 4 quarts (g=4q)) Referring to the measurement side of the TAKS chart Including percents, fractions, and decimals.8.3 Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. The student is expected to:A.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. The student is expected to:A.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. The student is expected to:8.5 Patterns, relationships, and algebraic thinking. The student uses graphs, tables, and algebraic representations to make predictions and solve problems. The student is expected to:8.3 Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. The student is expected to: 8.3 Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. The student is expected to:8.5Geometric patterns. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to:A.1ADescribe independent and dependent quantities in functional relationships. Including: Linear and quadratic functions Explaining a functional relationship by using one variable to describe another variable. Selecting the independent or dependent quantity in an equation or verbal description and justifying the selectionA.1ADescribe independent and dependent quantities in functional relationships. Including: Linear and quadratic functions Explaining a functional relationship by using one variable to describe another variable. Selecting the independent or dependent quantity in an equation or verbal description and justifying the selectionA.1BGather and record data and use data sets to determine functional relationships between quantities. Including: Students collecting data that models linear and quadratic functions Writing equations from a table of data Generating a list of data from a functional relationship Using a graphing calculator (specifically using the table function in the calculator). An option would be to teach linear regression using the calculator.A.1BGather and record data and use data sets to determine functional relationships between quantities. Including: Students collecting data that models linear and quadratic functions. Writing equations from a table of data Generating a list of data from a functional relationship Using a graphing calculator.8.5BFind and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change) Including: Expressions in which the constant rate of change is expressed as a fraction or a decimal nth term table Finding the nth term Using the nth term to find a specific term The formula for the arithmetic sequence (answers should be in distributive format) The first term + common difference (n 1) Vocabulary (i.e. substitute, algebraic expression, rule, expression, nth term, prediction, pattern, correlation, term, sequence) Numbers position in a sequenceA.1CDescribe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations. Including: Areas of circles and squares Perimeters of squares, equilateral triangles, and circumference Constant rate of change (i.e. slope) Literal equations (a = lw solve for l) G.5AUse numeric and geometric patterns to develop algebraic expressions representing geometric properties Including describing functional relationships in writing equations or inequalities as they pertain to: Areas of circles and polygons Perimeters of polygons and circumference of circlesA.1CDescribe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations. Including: Areas of circles and squares Perimeters of squares, equilateral triangles, and circumference Constant rate of change8.3BEstimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates. Including: Ratios that may not be in lowest terms represented in a table, graph, equation, verbal description and geometric representations. Setting up a proportion problem from a verbal description Using data in a table Dilations (Enlargements and reductions) of geometric figures Measurements using standard and metric units Unit conversions A.1DRepresent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities. Including quadratic relationships and linear relationships (constant rate of change) with and without a graphing calculator. A.1DRepresent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities. Including quadratic relationships (areas of circles and squares) and linear relationships (perimeters of squares, equilateral triangles, circumference, and constant rate of change) with and without a graphing calculator.8.3BEstimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates. Including linear relationships (constant rate of change, and similar figures) with and without a graphing calculator.8.3BEstimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates. Including linear relationships (perimeters of squares, equilateral triangles, circumference, constant rate of change, and similar figures) with and without a graphing calculator.8.5APredict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations. Including: Multiple representations of a table, graph, equation, sequence or verbal description within a single context of a problem Present and future incremental predictions Vocabulary: (i.e. Interval, scale, nth term, coordinate plane, position, sequence, trend, correlation, relationships, variables, positive, negative, algebraic equations, evaluate, rule prediction, between, pattern, exceed, arithmetic sequence, term) Positive, negative and no correlation or trend Answer choices in the form of an inclusive/exclusive relationship (Example: Between 5 and 12) (Example: >, <, d", e") Graphs to include: " Line Graph " Bar Graph " Multiple Bar Graph " Pie Chart " Histogram " Scatter plot " Box and Whiskers " Pictograph " Circle Graph " Line Plots " Stem and leafA.1E Interpret and make decisions, predictions, and critical judgments from functional relationships. Including linear relationships (constant rate of change) quadratic relationships communicated with concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities. A.1E Interpret and make decisions, predictions, and critical judgments from functional relationships. Including linear relationships (perimeters of squares and equilateral triangles, circumference, constant rate of change, and similar figures) and quadratic relationships (area of circle and square) communicated with concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities.8.3 Patterns, relationships, and algebraic thinking. The student identifies proportional or non-proportional linear relationships in problem situations and solves problems. The student is expected to:A.2Foundations for functions. The student uses the properties and attributes of functions. The student is expected to:G.4 Geometric structure. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to:8.4Patterns, relationships, and algebraic thinking. The student makes connections among various representations of a numerical relationship. The student is expected to:A.2Foundations for functions. The student uses the properties and attributes of functions. The student is expected to:8.12Probability and statistics. The student uses statistical procedures to describe data. The student is expected to:8.3ACompare and contrast proportional and non-proportional linear relationships. Including Ratios that may not be in lowest terms represented in a table, graph, equation, verbal description and geometric representations. Setting up a proportion problem from a verbal description Using data in a table Dilations (Enlargements and reductions) of geometric figures Measurements using standard and metric units Unit conversions A.2AIdentify and sketch the general forms of linear (y = x) and quadratic (y = x2) parent functions. Including : Investigations with and without a graphing calculator Specifically using the terminology parent functions Including parent functions that have been altered (for example a parabola turned upside down still belongs to the parent function y=x2) A.2AIdentify and sketch the general forms of linear (y = x) and quadratic (y = x2) parent functions. Including investigations with and without a graphing calculator. This SE was not tested in 2003 or 2004 at this grade.A.2BIdentify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete. Including: Values displayed in a table Values displayed by an equation Values displayed in a graph. Values displayed by an inequality. Values from a verbal description of everyday experiences such as temperature, money, height, etc. A.2BIdentify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete. Including: A range of values displayed in a table A range of values displayed in a graph A range of values displayed by an inequality A range of values from a verbal description of everyday experiences such as temperature, money, height, etc. 8.4AThe student is expected to generate a different representation of data given another representation of data (such as table, graph, equation, or verbal description). Including: Multiple representations of a table, graph, equation, sequence or verbal description within a single context of a problem Present and future incremental predictions Vocabulary: (i.e. Interval, scale, nth term, coordinate plane, position, sequence, trend, correlation, relationships, variables, positive, and negative Graphs to include: Line Graph Bar Graph Multiple Bar Graph Histogram Scatter plot Pictograph Circle Graph Line Plots Stem and leaf Venn DiagramA.2CInterpret situations in terms of given graphs or creates situations that fit given graphs. Including interpreting real-world situations in terms of graphs and also describing a real-world situation that fits a graph. G.4A The student is expected to select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems. Including: Interpreting real-world geometric situations in terms of graphs, tables, and literal equations Describing real-world geometric situations that fit appropriate representations A.2CInterpret situations in terms of given graphs or creates situations that fit given graphs. Including interpreting real-world situations in terms of graphs and also describing a real-world situation that fits a graph. 8.12BDraw conclusions and make predictions by analyzing trends in scatter plots. Including: Describe the scatterplot in words (increasing/decreasing) Scatter plots that show no trend Positive, negative and no correlations or trends A.2D Collect and organize data, make and interpret scatter plots (including recognizing positive, negative, or no correlation for data approximating linear situations) and model, predict, and make decisions and critical judgments in problem situations. Including organizing data that demonstrates a positive linear correlation, a negative linear correlation, and no correlation with and without a graphing calculatorA.2D Collect and organize data, make and interpret scatter plots including recognizing positive, negative, or no correlation for data approximating linear situations) and model, predict, and make decisions and critical judgments in problem situations. Including organizing data that demonstrates a positive linear correlation, a negative linear correlation, and no correlation with and without a graphing calculatorA.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. The student is expected to:A.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. The student is expected to:A.3AUse symbols to represent unknowns and variables. Including similarity, constant rate of change, area, perimeter, circumference, and proportions. Write an expression to represent the solution to a problem.A.3AUse symbols to represent unknowns and variables. Including similarity, constant rate of change, area, perimeter, circumference, and proportions.A.3BLook for patterns and represent generalizations algebraically. Including expressions in the form of, but not limited to: an, anb, a/n, n/a, a/n b, n/a b, a n, n a geometric sequence arithmetic sequence common ratios and differencesA.3BLook for patterns and represent generalizations algebraically. Including expressions in the form of, but not limited to: an, anb, a/n, n/a, a/n b, n/a b, a n, n a geometric sequence arithmetic sequence common ratios and differencesA.4Foundations 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. The student is expected to: A.4Foundations 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. The student is expected to: A.4AFind specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations. Including: Areas of rectangles and squares. Factoring binomials and trinomials. Apply the commutative, associative, and distributive properties to solve equations. Substitute a value for a variable. Use a graphing calculator to find specific function values (e.g. zeros of quadratic functions)A.4AFind specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations. Including: Areas of rectangles and squares Factoring binomials and trinomials Apply the commutative, associative, and distributive properties to solve equations Substitute a value for a variable Using a graphing calculatorA.4BUse the commutative, associative, and distributive properties to simplify algebraic expressions.A.4BUse the commutative, associative, and distributive properties to simplify algebraic expressions.A.4CConnect equation notation with function notation, such as y = x + 1 and f(x) = x + 1. Including examples of functions such as linear and quadratic relationships, and non-examples such as y2 = x.A.5Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations. The student is expected to:A.5Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations. The student is expected to:A.5ADetermine whether or not given situations can be represented by linear functions. Including: Verbal descriptions that describe a constant rate of change and a rate of change that is not constant A table of values with a constant rate of change and a table of values in which the rate of change is not constant. A.5ADetermine whether or not given situations can be represented by linear functions. Including: Verbal descriptions that describe a constant rate of change and a rate of change that is not constant A table of values with a constant rate of change and a table of values in which the rate of change is not constant.A.5BDetermine the domain and range for linear functions in given situations. Including: Earning a salary and/or commission Speed Temperature, etcA.5C Use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions. Including: Real-world verbal descriptions of a constant rate of change such as earning an hourly wage or a constant speed. Connecting the graph of a line to a description of a real-world experience. Connecting an algebraic expression to a description of a real-world experience. Using a graphing calculator. A.5C Use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions. Including: Real-world verbal descriptions of a constant rate of change such as earning an hourly wage or a constant speed Connecting the graph of a line to a description of a real-world experience Connecting an algebraic expression to a description of a real-world experience Using a graphing calculator A.6Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected to:A.6Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected to:A.6ADevelop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations. Including algebraic equations in which the equation is in slope-intercept form, point-slope form, and standard form with and without a graphing calculator. Such as: Formulas with a linear relationship (i.e. d = r t) Slope formula Sketch of a line on a coordinate plane (given a table)A.6ADevelop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations. Including algebraic expressions in which the equation is in slope-intercept form, point-slope form, and standard form with and without a graphing calculator.A.6B Interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs. Including algebraic equations in slope-intercept form, point-slope form, and standard form with and without a graphing calculator. Such as: Symbolic representations including use of tables and real world applications Representation of slope as integers, fractions, decimals and mixed numbers A.6B Interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs. Including algebraic expressions in which the equation is in slope-intercept form, point-slope form, and standard form with and without a graphing calculator. A.6CInvestigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b; Including algebraic equations in which the equation is in slope-intercept form, point-slope form, and standard form with and without a graphing calculator. Such as: Transformation Changing Slope and/or y intercept Doubling/halving slope Parallel and perpendicular slope relationshipsA.6CInvestigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b; Including algebraic equations in which the equation is in slope-intercept form, point-slope form, and standard form with and without a graphing calculator. A.6DGraph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept. Including algebraic equations in slope-intercept form, point-slope form, and standard form with and without a graphing calculator. A.6DGraph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept. Including algebraic expressions in which the equation is in slope-intercept form, point-slope form, and standard form with and without a graphing calculator.A.6EDetermine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations. Including algebraic equations in slope-intercept form, point-slope form, and standard form with and without a graphing calculator. A.6EDetermine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations. Including algebraic expressions in which the equation is in slope-intercept form, point-slope form, and standard form with and without a graphing calculator.A.6FInterpret and predict the effects of changing slope and y-intercept in applied situations. Including Real-world situations tht model a constant change such as a salary, commission, a ride in a taxi, renting a car, speed, buying gasoline, etc. Algebraic equations in slope-intercept form, point-slope form, and standard formA.6FInterpret and predict the effects of changing slope and y-intercept in applied situations. Including Real-world situations that model a constant change such as a salary, commission, a ride in a taxi, renting a car, speed, buying gasoline, etc. Algebraic equations in slope-intercept form, point-slope form, and standard formA.6GRelate direct variation to linear functions and solve problems involving proportional change. Including: Real-world situations that model a constant change such as a salary, commission, a ride in a taxi, renting a car, speed, buying gasoline, etc. Algebraic equations in slope-intercept form, point-slope form, and stand form Using a graphing calculatorA.6GRelate direct variation to linear functions and solve problems involving proportional change. Including: Real-world situations that model a constant change such as a salary, commission, a ride in a taxi, renting a car, speed, buying gasoline, etc. Algebraic equations in slope-intercept form, point-slope form, and stand form Using a graphing calculatorA.7Linear 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. The student is expected to:A.7Linear 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. The student is expected to:A.7A Analyze situations involving linear functions and formulate linear equations or inequalities to solve problems. Including: Real-world problems involving a constant rate of change where the value of the y-intercept is zero or not zero. Algebraic equations in slope-intercept form, point-slope form, and standard form.A.7A Analyze situations involving linear functions and formulate linear equations or inequalities to solve problems. Including: Real-world problems involving a constant rate of change with a constant and a constant rate of change without a constant Algebraic expressions in which the equation is in slope-intercept form, point-slope form, and standard form.A.7BInvestigate 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. Including: Using information from concrete models to write linear equations and inequalities, plot graphs, and solve equations and inequalities Use graphs to solve linear equations and inequalities Algebraic equations and inequalities in slope-intercept form, point-slope form, and standard form Using a graphing calculator A.7BInvestigate 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. Including: Using information from concrete models to write linear equations and inequalities, plot graphs, and solve equations and inequalities Use graphs to solve linear equations and inequalities Algebraic equations and inequalities in slope-intercept form, point-slope form, and standard form Using a graphing calculator A.7CInterpret and determine the reasonableness of solutions to linear equations and inequalities. Including: Linear relationships in tables, equations, inequalities, and verbal descriptions Algebraic equations and inequalities in slope-intercept form, point-slope form, and standard form Using a graphing calculatorA.7CInterpret and determine the reasonableness of solutions to linear equations and inequalities. Including: Linear relationships in tables, equations, inequalities, and verbal descriptions Equations in the form of y = mx and y = mx+b Algebraic expressions in which the equation is in slope-intercept form, point-slope form, and standard form Using a graphing calculatorA.8Linear 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. The student is expected to:G.7 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. The student is expected to:A.8Linear 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. The student is expected to:A.8AAnalyze situations and formulate systems of linear equations in two unknowns to solve problems. Including setting up a system given a real world situation.A.8AAnalyze situations and formulate systems of linear equations in two unknowns to solve problem. Including: Algebraic expressions in which the equation is in slope-intercept form, point-slope form, and standard form Using the addition method to solve a system in which there is no solution, one solution, and infinite solutions Using the substitution method to solve a system in which there is no solution, one solution, and infinite solutions.A.8BSolve systems of linear equations using concrete models, graphs, tables, and algebraic methods. Including: Using the addition method (aka elimination method or combinations method) to solve a system in which there is no solution, one solution, and infinite solutions Using the substitution method to solve a system in which there is no solution, one solution, and infinite solutions Using a graphing calculator to find the intersection of the system (i.e. the solution) G.7BUse slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons.A.8B Solve systems of linear equations using concrete models, graphs, tables, and algebraic methods. Including: Algebraic expressions in which the equation is in slope-intercept form, point-slope form, and standard form. Using the addition method to solve a system in which there is no solution, one solution, and infinite solutions. Using the substitution method to solve a system in which there is no solution, one solution, and infinite solutions. Using a graphing calculatorA.8CInterpret and determine the reasonableness of solutions to systems of linear equations. Including: Algebraic equations in slope-intercept form, point- slope form, and standard form. Using the addition method to solve a system in which there is no solution, one solution, and infinite solutions. Using the substitution method to solve a system in which there is no solution, one solution, and infinite solutions. Using graphing calculatorsA.8CInterpret and determine the reasonableness of solutions to systems of linear equations. Including: Algebraic expressions in which the equation is in slope-intercept form, point-slope form, and standard form Using the addition method to solve a system in which there is no solution, one solution, and infinite solutions. Using the substitution method to solve a system in which there is no solution, one solution, and infinite solutions Using graphing calculatorsA.9Quadratic 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. The student is expected to:A.9Quadratic 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. The student is expected to:A.9ADetermine the domain and range for quadratic functions in given situations: Including graphs, tables, verbal descriptions, and equations.A.9BInvestigate, describe, and predict the effects of changes in a on the graph of y = ax2 + c. Including: Equations in which a is a number less than 0 and greater than 0. Using a graphing calculator.A.9BInvestigate, describe, and predict the effects of changes in a on the graph of y = ax2 + c. Including: Equations in which a is a number less than 0 and greater than 0. Using a graphing calculator.A.9CInvestigate, describe, and predict the effects of changes in c on the graph of y = ax2 + c. Including: Equations in which c is a number less than 0 Equations in which c is a number greater than 0 Using a graphing calculatorA.9CInvestigate, describe, and predict the effects of changes in c on the graph of y = ax2 + c. Including: Equations in which c is a number less than 0 and greater than 0 Using a graphing calculatorA.9DAnalyze graphs of quadratic functions and draw conclusions. Including: Naming the vertex Naming the zeros (roots, solutions, and x-intercepts) Determine whether a is positive or negative Finding the domain and range Applying quadratics to real world applicationsA.9DAnalyze graphs of quadratic functions and draw conclusions. Including: Naming the vertex Naming the zeros Estimate a in y = ax2 + c. Finding the domain and rangeA.10Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods. The student is expected to:A.10Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods. The student is expected to:A.10ASolve quadratic equations using concrete models, tables, graphs, and algebraic methods. Including: Factoring Graphing calculators to find zeros (roots, solutions, and x-intercepts) Other methods such as algebra tilesA.10ASolve quadratic equations using concrete models, tables, graphs, and algebraic methods. Including: Algebra tiles. Factoring Graphing calculatorsA.10BMake connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function. Including: Using a graphing calculator Factoring Real world problems such as area of a rectangle Other methods such as algebra tiles Use terminology (i.e. solutions, roots, zeros, and x-intercepts)A.10BMake connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function. Including: Using a graphing calculator Factoring Algebra tiles Real world problems such as area of a rectangle A.11Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations. The student is expected to:A.11Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations. The student is expected to:A.11AUse patterns to generate the laws of exponents and apply them in problem-solving situations.A.11AUse patterns to generate the laws of exponents and apply them in problem-solving situations.A.11BAnalyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methods.A.11CHYPERLINK "http://www.themathlab.com/Algebra"Analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods. 8.6Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense. The student is expected to:8.6Geometry and spatial reasoning. The student uses transformational geometry to develop spatial sense. The student is expected to:G.5 Geometric patterns. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to:G.11Similarity and the geometry of shape. The student applies the concepts of similarity to justify properties of figures and solve problems. The student is expected to:8.6AGenerate similar figures using dilations including enlargements and reductions. Including: Figures graphed on a coordinate grid Figures with dimensions labeled in the diagram Vocabulary: (i.e. similar, dilation, enlargement, reduction, coordinate plane, vertex, dimension, proportional, corresponding side, scale factor) Multiply to solve for dilations by using the scale factor Enlargements scale factor greater than 1 Reductions scale factor less than 18.6AGenerate similar figures using dilations including enlargements and reductions. Including: Figures graphed on a coordinate grid Figures with dimensions labeled in the diagram. Problems in which vertices are given and require the student to plot the figure.G.5A Use numeric and geometric patterns to develop algebraic expressions representing geometric properties. Including: Finding the sum of the interior angles of polygons Deriving volume formulas Discovering the area formulas for a regular polygon Discovering the relationship among the sides of 45-45-90 and 30-60-90 triangles G.11B Use ratios to solve problems involving similar figures. Including: Comparing the areas, perimeters and volumes of similar polygons and solids Dilations 8.6AGenerate similar figures using dilations including enlargements and reductions. Including: Figures graphed on a coordinate grid Figures with dimensions labeled in the diagram Problems in which vertices are given and require the student to plot the figure8.6BGraph dilations, reflections, and translations on a coordinate plane. Including: All four quadrants Reflections across the x or y axes Dilations include enlargements or reductions Vocabulary: (i.e. similar, dilation, enlargement, reduction, coordinate plane, vertex, dimension, translation, reflection proportional, corresponding side, scale factor)8.6BGraph dilations, reflections, and translations on a coordinate plane. Including terminology: mapped x , y , z 8.6BGraph dilations, reflections, and translations on a coordinate plane.8.7Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to:8.7Geometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to:G.6 Dimensionality and the geometry of location. The student analyzes the relationship between three-dimensional geometric figures and related two-dimensional representations and uses these representations to solve problems. The student is expected to:G.7 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. The student is expected to:8.7A Draw three-dimensional figures from different perspectives. Include: Drawing three dimensional figures when given a specified view Drawing two dimensional views when a three dimensional figure is given 8.7A Draw three-dimensional figures from different perspectives. Include: nets review of classification of polygons and polyhedrons G.6C Use orthographic and isometric views of three-dimensional geometric figures to represent and construct three-dimensional geometric figures and solve problems. Including the use of unit blocks to explore concrete models. 8.7ADraw three-dimensional figures from different perspectives. 8.7BUse geometric concepts and properties to solve problems in fields such as art and architecture. Include: Using the given data to solve for perimeter, circumference, area, volume or a dimension Various representation of limits of measures8.7BUse geometric concepts and properties to solve problems in fields such as art and architecture. Include: Scale factors and measurement conversion Area and perimeter 8.7BUse geometric concepts and properties to solve problems in fields such as art and architecture8.7CUse pictures or models to demonstrate the Pythagorean Theorem. Including: When inscribed in a circle or polygon and/or real life pictorial examples (see sample questions) Vocabulary: (i.e. hypotenuse, leg, radius, diameter)8.7CUse pictures or models to demonstrate the Pythagorean Theorem. Include: The introduction in the use of TAKS formula chart Teaching how to find the square roots on the calculator8.7CUse pictures or models to demonstrate the Pythagorean Theorem.8.7DLocate and name points on a coordinate plane using ordered pairs of rational numbers. Including: Using all four quadrants Vocabulary: (i.e. x-axis, y-axis, x-coordinate, y- coordinate, quadrants, origin) 8.7DLocate and name points on a coordinate plane using ordered pairs of rational numbers. G.7A Use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures. Including triangles and quadrilaterals. 8.7DLocate and name points on a coordinate plane using ordered pairs of rational numbers.8.8Measurement. The student uses procedures to determine measures of three-dimensional figures. The student is expected to:8.8Measurement. The student uses procedures to determine measures of three-dimensional figures. The student is expected to:G.8Congruence and the geometry of size. The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations. The student is expected to:8.8AFind lateral and total surface area of prisms, pyramids, and cylinders using concrete models and nets (2 dimensional models). No spheres, No cones Including: Unit conversions in two and three dimensions Using formula chart rulers and formulas Various representations of limits of measures of edges Vocabulary (i.e. surface area, prism, rectangular prism, triangular prism, cylinder, pyramid, lateral surface area, edge, face vertex, height, base, total surface area, net) Measurements in metric and standard units Recognizing symbol H" means approximately equal to8.8AFind lateral and total surface area of prisms, pyramids, and cylinders using concrete models and nets (2 dimensional models). Including: Using the original TAKS formula chart rulers consistently when measuring Reviewing how to read and use a ruler Measurements in metric and standard unitsG.8AFind area of regular polygons, circles, and composite figures.G.8DFind surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations.8.8AFind lateral and total surface area of prisms, pyramids, and cylinders using concrete models and nets (two-dimensional models).8.8B Connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects. Including: Matching nets and models to appropriate formulas to problem solve Real-life models (i.e. sphere-basketball) Including measurements in metric and standard units. 8.8B Connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects. Include: Reviewing how to read EXIT level formula chart for Volume Reviewing how to find the Volume of solids Reviewing how to read and use a ruler Using the original TAKS formula chart rulers consistently when measuring; instead of handheld rulers G.8D Find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations.8.8B Connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects. 8.8CEstimate measurements and use formulas to solve application problems involving lateral and total surface area and volume. Including: Measurement in standard and metric units for cubes, cylinders, cones, spheres, and prisms. Rounding all dimensions to whole numbers. Using 3 for pi symbol. The capital B on the formula chart is the area of the base. Vocabulary (i.e. surface area , prism, rectangular prism, triangular prism, cylinder, pyramid, lateral surface area, edge, face, vertex, height, base, total surface area, net, volume). Real-life models (i.e. rectangular prism = a present or a shoe box) Including measurements in metric and standard units for cubes, cylinders, cone, spheres, and prisms.8.8CEstimate measurements and use formulas to solve application problems involving lateral and total surface area and volume. Connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects. Include: Reviewing the concepts of estimation, rounding and place value Reviewing how to read and use a ruler Using the TAKS formula chart ruler consistently, instead of a handheld ruler8.8CEstimate measurements and use formulas to solve application problems involving lateral and total surface area and volume. Connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these objects. 8.9Measurement. The student uses procedures to determine measure of three-dimensional figures. The student is expected to: 8.9Measurement. The student uses procedures to determine measure of three-dimensional figures. The student is expected to: G.5 Geometric patterns. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to:G.8 Congruence and the geometry of size. The student uses tools to determine measurements of geometric figures and extends measurements concepts to find perimeter, area, and volume in problem situations. The student is expected to:G.11 Similarity and the geometry of shape. The student applies the concepts of similarity to justify properties of figures and solve problems. The student is expected to:8.9AUse the Pythagorean Theorem to solve real-life problems Including: When inscribed in a circle or polygon and/or real life pictorial examples Vocabulary: (i.e. hypotenuse, leg, radius, diameter) Examples of Pythagorean triples are (3, 4, 5), (6, 8, 10), (5, 12, 13), (15, 8, 17),(12, 16, 20), (7, 24, 25) etc. 8.9AUse the Pythagorean Theorem to solve real-life problems Include: Using TAKS formula chart Teaching how to find square roots on the calculator G.5DIdentify and apply patterns from right triangles to solve meaningful problems including special right triangles (45-45-90 and30-60-90) and triangles whose sides are Pythagorean triples. Including trig ratios sine, cosine, tangentG.8C Derive, extend, and use the Pythagorean Theorem Including: Distance formula Unknown lengths in polygons and circlesG.11C Develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trig ratios, and Pythagorean triples using a variety of methods. Including: Triangle Prop Theorem Angle Bisector Proportionality Sine, Cosine, & Tangent8.9A Use the Pythagorean Theorem to solve real-life problems8.9BUse proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements. Including: Setting up proportions or using a scale factor Identifying the corresponding sides of similar figures when the figure is rotated and/or not rotated Vocabulary (i.e. similar, corresponding, scale factor, dimensions, rotation, proportional and two-and three-dimensional figures)8.9BUse proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements.8.9BUse proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements. 8.10Measurement: The student describes how changes in dimensions affect linear, area, and volume measures. The student is expected to:8.10Measurement: The student describes how changes in dimensions affect linear, area, and volume measures. The student is expected to:G.11Similarity and the geometry of shape. The student applies the concepts of similarity to justify properties of figures and solve problems. The student is expected to:8.10A Describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally. Including: Using a scale factor and/or dilations with whole numbers or fractions Rectangles Finding missing dimensions or area or perimeter Squares Using the same scale factor proportionately in a figure the effects Circles Vocabulary: (i.e. perimeter, area, scale factors, dilation/dilated, A review of the scale factor concepts enlargement, reduction, similar, dimension, proportional) Generalizing the effects on perimeter, area and volume if the length, Examples include: width, and height are changed by the same scale factor8.10A Describe the resulting effects on perimeter and area when dimensions of a shape are changed proportionally. Including: Rectangles Squares Circles A review of the scale factor concepts G.11D Describe the effects on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems.8.10A Describe the resulting effect on perimeter and area when dimensions of a shape are changed proportionally. 8.10B Describe the resulting effects on volume when dimensions of a solid are changed proportionally 8.10B Describe the resulting effects on volume when dimensions of a solid are changed proportionally. Including: Rectangular prisms CylindersG.11D Describe the effects on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems.8.10BDescribe the resulting effect on volume when dimensions of a solid are changed proportionally.8.11Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to:8.11Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to:8.11Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to:8.11AFind the probabilities of dependent and independent events. Including: Displaying the results as a fraction or a decimal or percent Working the problem from a verbal description Analyzing data from a table or graph Using experimental results and comparing those results with the theoretical results8.11AFind the probabilities of dependent and independent events. Including: Using the terminology dependent and independent events Reviewing fraction, decimal, and % conversions Teaching calculator concepts (i.e. decimal to fraction) 8.11AFind the probabilities of dependent and independent events.8.11BUse theoretical probabilities and experimental results to make predictions and decisions Including: Displaying the results as a fraction or a decimal or percent Working the problem from a verbal description Analyzing data from a table or graph Using experimental results and comparing those results with the theoretical results8.11BUse theoretical probabilities and experimental results to make predictions and decisions Including: Teaching difference between theoretical and experimental probability Reviewing fraction, decimal, and % conversions Calculator use8.11BUse theoretical probabilities and experimental results to make predictions and decisions8.11CSelect and use different models to simulate an event. Including: Displaying the results as a fraction or a decimal or percent Using experimental results from independent and dependent events and comparing those results with the theoretical results (Such as using spinners, dice, and/or marbles in a sack in a probability event)8.12Probability and statistics. The student uses statistical procedures to describe data. The student is expected to:8.12Probability and statistics. The student uses statistical procedures to describe data. The student is expected to:8.12Probability and statistics. The student uses statistical procedures to describe data. The student is expected to:8.12ASelect the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation. Including: Finding mean, median, mode and range to justify an answer The effects of changing data on mean, median, mode and range8.12ASelect the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation. Including: Mean Median Mode 8.12ASelect the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation. 8.12BSee SE Algebra I (2D) Draw conclusions and make predictions by analyzing trends in scatterplots. Including: Scatter plots that show no trend Positive, negative and no correlations or trends Describe the scatter plot in words (increasing/decreasing)8.12BSee SE Algebra I (2D8.12CSelect 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.8.12CSelect 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. 8.12CSelect 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. 8.13Probability and statistics. The student uses statistical procedures to describe data. The student is expected to:8.13Probability and statistics. The student uses statistical procedures to describe data. The student is expected to:8.13Probability and statistics. The student uses statistical procedures to describe data. The student is expected to:8.13AEvaluate methods of sampling to determine validity of an inference made from a set of data. Including biased sampling due to method of collecting the data. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.13BRecognize misuses of graphical or numerical information and evaluates predictions and conclusions based on data analysis Including analyzing all parts of a bar graph (title, vertical and horizontal scale) and table of values for possible misleading information.8.13BRecognize misuses of graphical or numerical information and evaluates predictions and conclusions based on data analysis 8.13BRecognize misuses of graphical or numerical information and evaluates predictions and conclusions based on data analysis 8.14Underlying processes and math tools. The student applies grade 8 math to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:8.14Underlying processes and math tools. The student applies grade 8 math to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:8.14Underlying processes and math tools. The student applies grade 8 math to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:8.14AIdentify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.14AIdentify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.14AIdentify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.14BUse a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.14BUse a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. This student expectation can be tested in every strand including one or more than one TEKS at a time. Including: Review of key vocabulary words (i.e. per, each, and of means to multiply) Review of problem solving strategies (i.e. draw a picture or a table)8.14BUse a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.14CSelect 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. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.14CSelect 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. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.14CSelect 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. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.14DSelect tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.15Underlying processes and math tools. The student communicates about Grade 8 math through informal and mathematical language, representations, and models. The student is expected to:8.15Underlying processes and math tools. The student communicates about Grade 8 math through informal and mathematical language, representations, and models. The student is expected to:8.15Underlying processes and math tools. The student communicates about Grade 8 math through informal and mathematical language, representations, and models. The student is expected to:8.15ACommunicate mathematical ideas using language, efficient tools, appropriate units and graphical, numerical, physical, or algebraic mathematical models. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.15ACommunicate mathematical ideas using language, efficient tools, appropriate units and graphical, numerical, physical, or algebraic mathematical models. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.15ACommunicate mathematical ideas using language, efficient tools, appropriate units and graphical, numerical, physical, or algebraic mathematical models. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.15BEvaluate the effectiveness of different representations to communicate ideas. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.16Underlying processes and math tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to:8.16Underlying processes and math tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to:8.16Underlying processes and math tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to:8.16AMake conjectures from patterns or sets of examples and non-examples. Including: Defining a concept introduced in a higher grade Showing a pattern, examples, and/or non-examples Expecting students to choose a correct response by analyzing the pattern, examples, or non-examples8.16AMake conjectures from patterns or sets of examples and non-examples. Including: Defining a concept introduced in a higher grade Showing a pattern, examples, and/or non-examples Expecting students to choose a correct response by analyzing the pattern, examples, or non-examples8.16AMake conjectures from patterns or sets of examples and non-examples. Including: Defining a concept introduced in a higher grade Showing a pattern, examples, and/or non-examples Expecting students to choose a correct response by analyzing the pattern, examples, or non-examples8.16BValidate his/her conclusions using mathematical properties and relationships. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.16BValidate his/her conclusions using mathematical properties and relationships. This student expectation can be tested in every strand including one or more than one TEKS at a time.8.16BValidate his/her conclusions using mathematical properties and relationships. This student expectation can be tested in every strand including one or more than one TEKS at a time.G.1The student understands the structure of, and relationships within, an axiomatic system. The student is expected to:G.1A Develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems. Including the use of direct proofs, manipulatives and technology to draw conclusions and discover relationships about geometric shapes and their properties.G.1B Recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes. Including: The discovery of Pi and its applications A historical discussion of Euclids elements and how they are used in the development of modern geometry A time line of geometrys developmentsG.1C Compare and contrast the structures and implications of Euclidean and non-Euclidean geometries. Including parallelism as exhibited in Euclids 5th postulate. Non-Euclidean geometries include: Spherical to show parallel lines do not exist as defined in Euclidean geometry Cylindrical to show parallel lines do exist as defined in Euclidean geometryG.2Geometric Structure. The student analyzes geometric relationships in order to make and verify conjectures. The student is expected to:G.2A Use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships. Including: The use of manipulatives and technology The construction of angle bisectors, perpendicular bisectors, parallel lines, congruent angles, congruent segments, perpendicular lines at a point on a line, perpendicular lines from a point to a line and segment bisectorsG.2BMake conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic. Including: Reflections Translations Rotations The use of direct proofs, manipulatives and technology to draw conclusions and discover relationships about geometric shapes and their properties.G.3Geometric structure. The student applies logical reasoning to justify and prove mathematical statements. The student is expected to:G.3A Determine the validity of a conditional statement, its converse, inverse, and contrapositive. Including consistent usage as it applies to geometric figures and relationships.G.3B Construct and justify statements about geometric figures and their properties; Including: The formulation of conclusions in the form of a conditional statement The use of manipulatives and technology to draw conclusions about geometric figures G.3C Use logical reasoning to prove statements are true and find counter examples to disprove statements that are false. Examples include: The statement All right angles are congruent is true. Is the converse also true? If not, provide a counterexample that disproves the statement.G.3D Use inductive reasoning to formulate a conjecture. Including: The student discovery of the sum of the interior angles of a polygon Finding the volume of cones and pyramids The student discovery of relationships among similar polygons and solids G.3EUse deductive reasoning to prove a statement. Including: Triangle congruence statements (angle-side-angle, side-side-side, angle-angle-side, side-angle-side and hypotenuse-leg) The relationships among the angles of parallel lines (i.e. alternate interior angles, same side interior angles, corresponding anglesG.5Geometric patterns. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to:G.5BUse 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.5CUse properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations.G.6Dimensionality and the geometry of location. The student analyzes the relationship between three-dimensional geometric figures and related two-dimensional representations and uses these representations to solve problems. The student is expected to:G.6ADescribe and draw the intersection of a given plane with various three-dimensional geometric figures. Including conics and other cross-sectional views of geometric solids.G.6BUse nets to represent and construct three-dimensional geometric figuresG.7Dimensionality and the geometry of location. The student understands that coordinate systems provide convenient and efficient ways of representing geometric figures and uses them accordingly. The student is expected to:G.7CDerive and use formulas involving length, slope, and midpoint Including: The relationship between Pythagorean theorem and the distance formula The application of the formulas to prove properties of figures such as rhombi, squares, rectangles, etc.G.8Congruency and the geometry of size. The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations. The student is expected to:G.8BFind areas of sectors and arc lengths of circles using proportional reasoning. Including: ArcLength = Central angle Circumference 360 Area of sector = Central angle Area of circle 360G.9Congruence and the geometry of size. The student analyzes properties and describes relationships in geometric figures. The student is expected to:G.9AFormulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models. Including: Finding the slopes of lines to determine their relationship (parallel, perpendicular or intersecting) Student discovery of Mid-segment theorem., Dual Parallels theorem, Dual Perpendiculars theorem and Triangle Proportionality theoremG.9BFormulate and test conjectures about the properties and attributes of polygons and their component parts based on explorations and concrete models. Including: Recognizing polygons (through decagons) Properties of regular polygons Properties of quadrilaterals, triangles, and special polygons (e.g. hexagons)G.9CFormulate and test conjectures about the properties and attributes of circles and the lines that intersect them based on explorations and concrete models. Including: Identifying tangents, secants, chords, diameters, radii, inscribed angles, central angles Student exploration of the properties of intersecting chords, secants and tangents. Exploration of the relationships among angles in circles Application of central angles to the reading of circle graphsG.9DAnalyze the characteristics of polyhedra and other three-dimensional figures and their component parts based on explorations and concrete models. Including: Prisms (with regular polygon bases to 10 sides) Pyramids Cones Cylinders SpheresG.10Congruence and the geometry of size. The student applies the concept of congruence to justify properties of figures and solve problems. The student is expected to:G.10AUse congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane. Including rotations, reflections, translations, and combinations of these.G.10BJustify and apply triangle congruence relationships. 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The student applies the concepts of similarity to justify properties of figures and solve problems. The student is expected to:G.11AUse and extend similarity properties and transformations to explore and justify conjectures about geometric figures. 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