ࡱ> } dkbjbj55 4__db     t@BBBBBB)˨HB- B  o F  @ @ t(@~U&^,0j+`& >, $(BB : : Scope and Sequence 2009-2010 Texarkana Independent School District I = Introduced P = Practiced M= Mastered  111.32Algebra I (One Credit). Grade 9. High School Grading Period 1 2 3 4 5 6 (1)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: describe 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 selection IP PM (B) gather 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 I P P P PM (C)describe 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) IP P P P P PM (D)represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities IP P P P P PM (E)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. I P P P PM (2)The student uses the properties and attributes of functions. The student is expected to: (A)identify 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) I P P PM (B)identify 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. I P P P PM (C)interpret situations in terms of given graphs or create 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. I P P P PM (D)collect and organize data, make and interpret scatterplots (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 calculator I P P PM (3) 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)use symbols to represent unknowns and variables Including organizing data that demonstrates a positive linear correlation, a negative linear correlation, and no correlation with and without a graphing calculator IP P P P P PM (B)look 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 differences IP P P P P PM (4) 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)find 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) IP P P P P PM (B)use the commutative, associative, and distributive properties to simplify algebraic expressions IP P P P PM (C)use the commutative, associative, and distributive properties to simplify algebraic expressions I P P P PM (5) The student understands that linear functions can be represented in different ways and translates among their various representations. The student is expected to: (A)determine 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. I P P P PM (B)determine the domain and range for linear functions in given situations Including: Earning a salary and/or commission Speed Temperature, etc I P P P PM (C)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. I P P P PM (6) 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)develop 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) I P P P PM (B)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 I P P P PM (C)investigate, 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 I P P P PM (D)graph 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. IP P P P PM (E)determine 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. I P P P PM (F)interpret 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 form I P P PM (G)relate 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 calculator IP P P PM (7) 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)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. IP P P P P M (B)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 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 IP P P P P PM (C)interpret 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 calculator IP P P P P PM (8) 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)analyze situations and formulate systems of linear equations in two unknowns to solve problems Including setting up a system given a real world situation. IPM (B)solve 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) IPM (C)interpret 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 calculators IPM (9) 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. Following are performance descriptions. (A)determine the domain and range for quadratic functions in given situations Including graphs, tables, verbal descriptions, and equations. IPM (B)investigate, describe, and predict the effects of changes in a on the graph of y = ax2 + c Including: Equations in which is a number less than 0 and greater than 0. Using a graphing calculator. IPM (C) investigate, 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 calculator IPM (D) analyze 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 applications IPM (10) 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) solve 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 tiles IPM (B) make 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) IPM (11) 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) use patterns to generate the laws of exponents and apply them in problem-solving situations Including: Using the terminology dependent and independent events Reviewing fraction, decimal, and % conversions Teaching calculator concepts (i.e. decimal to fraction) IP P PM analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methods Including: Teaching difference between theoretical and experimental probability Reviewing fraction, decimal, and % conversions calculator use IPM analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods IPM  111.24Mathematics, Grade 8.Middle School123456(8.1) Number, operation, and quantitative reasoning. The student understands that different forms of numbers are appropriate in different situations. The student is expected to:select and use appropriate forms of rational numbers to solve real-life problems including those in proportional relationships. Examples include: Using multiple forms of fractions, decimals, percents, positive and negative integers within a single problem. IP  P  P P P PM(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:estimate 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 I  PMGeometry and spatial reasoning. The student uses transformational geometry to develop spatial sense. The student is expected to: generate similar shapes 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 1 IPM(B) graph dilations, reflections, and translations on a coordinate plane. IPMGeometry and spatial reasoning. The student uses geometry to model and describe the physical world. The student is expected to: 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 IPMuse 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 dimension Various representations of limits of measures IPM use pictures or models to demonstrate the Pythagorean Theorem; Including: When inscribed in a circle or polygon and/or real life pictorial examples Vocabulary: (i.e. hypotenuse, leg, radius, diameter) I PMlocate 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) IPM(8.8) Measurement. The student uses procedures to determine measures of three-dimensional figures. The student is expected to:find lateral and total surface area of prisms, pyramids, and cylinders using [concrete] models and nets (two-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) Recognizing symbol (H") means approximately equal to I P Mconnect 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) I P Mestimate measurements and use formulas to solve application problems involving lateral and total surface area and volume. Including: Measurements in metric and standard units for cubes, cylinders, cone, 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) I P M(8.9) Measurement. The student uses indirect measurement to solve problems. The student is expected to:use 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)  I PMuse proportional relationships in similar two-dimensional figures or similar three-dimensional figures to find missing measurements. Including: Setting up proportions or using 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) IP PM(8.10) Measurement. The student describes how changes in dimensions affect linear, area, and volume measures. The student is expected to: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 Finding missing dimensions or area or perimeter Using the same scale factor determine the proportional effects upon a figure Vocabulary: (i.e. perimeter, area, scale factors, dilation /dilated, enlargement, reduction, similar, dimension, proportional) Generalizing the effects on perimeter, area and volume if the length, width, and height are changed by the same scale factor I P M(B) describe the resulting effect on volume when dimensions of a solid are changed proportionally.IPM(8.11) Probability and statistics. The student applies concepts of theoretical and experimental probability to make predictions. The student is expected to:find 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 results. I P M(B) use 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 results. I P M(8.12) Probability and statistics. The student uses statistical procedures to describe data. The student is expected to:select 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 range  IP PM(C) 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. Including: Frequency tables Vocabulary (i.e. intervals, scale) IP PM(8.13) Probability and statistics. The student evaluates predictions and conclusions based on statistical data. The student is expected to:recognize misuses of graphical or numerical information and evaluate 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.  I P M(8.14) Underlying processes and mathematical tools. The student applies Grade 8 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics; IP P P P P PM(B) use a problem-solving model that incorporates under-standing the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness;  IP P P P P PM(C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem. IP P P P P PM(8.15) Underlying processes and mathematical tools. The student communicates about Grade 8 mathematics through informal and mathematical language, representations, and models. The student is expected to:(A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models. IP P P P P PM(8.16) Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to:make conjectures from patterns or sets of examples and non-examples; Including: Defining a concept introduced at 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-examples IP P P P P PM(B) validate his/her conclusions using mathematical properties and relationships. 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