Texarkana Independent School District
|Scope and Sequence |
|2009-2010 |
|Texarkana Independent School District |
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|I = Introduced P = Practiced M= Mastered |
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| | 111.32 Algebra I (One Credit). | |
| |Grade 9. High School | |
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| |Grading Period | |
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| |(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 | |
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| |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 | |
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| |(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 | |
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| |(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) | |
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| |(D) represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities | |
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| |(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. | |
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| |(2) The student uses the properties and attributes of functions. The student is expected to: | |
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| |(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) | |
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| |(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. | |
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| |(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. | |
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| |(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 | |
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| |(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| |
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| |(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 | |
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| |(B) look for patterns and represent generalizations algebraically | |
| |Including expressions in the form of, but not limited to: | |
| |•an, an±b, a/n, n/a, a/n ± b, n/a ± b, a ±n, n – a | |
| |•geometric sequence | |
| |•arithmetic sequence | |
| |•common ratios and differences | |
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| |(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: | |
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| |(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) | |
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| |(B) use the commutative, associative, and distributive properties to simplify algebraic expressions | |
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| |(C) use the commutative, associative, and distributive properties to simplify algebraic expressions | |
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| |(5) | |
| |The student understands that linear functions can be represented in different ways and translates among their various representations. The student is | |
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| |(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. | |
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| |(B) determine the domain and range for linear functions in given situations | |
| |Including: | |
| |•Earning a salary and/or commission | |
| |•Speed | |
| |•Temperature, etc… | |
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| |(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. | |
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| |(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: | |
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| |(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) | |
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| |(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 | |
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| |(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 | |
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| |(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. | |
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| |(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. | |
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| |(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 | |
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| |(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 | |
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| |(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: | |
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| |(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. | |
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| |(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 | |
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| |(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 | |
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| |(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: | |
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| |(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. | |
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| |(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) | |
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| |(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 | |
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| |(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. | |
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| |(A) determine the domain and range for quadratic functions in given situations | |
| |Including graphs, tables, verbal descriptions, and equations. | |
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| |(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. | |
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| |(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 | |
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| |(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 | |
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| |(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: | |
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| |(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 | |
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| |(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) | |
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| |(11) | |
| |The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations. The student is expected | |
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| |(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) | |
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| |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 | |
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| |© analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods | |
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| |IPM | |
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|111.24 Mathematics, | |
|Grade 8. Middle School | |
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|(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: | | | | | | |
|(B) graph dilations, reflections, and translations on a coordinate plane. | | | | | | |
| | |IPM | | | | |
|Geometry and spatial reasoning. The student uses | | | | | | |
|geometry to model and describe the physical world. The student is expected to: | | | | | | |
|use 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 | |IPM | | | | |
|•Various representations of limits of measures | | | | | | |
| use pictures or models to demonstrate the Pythagorean Theorem; | | | | | | |
|Including: | | | | | | |
|•When inscribed in a circle or polygon and/or real life pictorial examples |I |PM | | | | |
|•Vocabulary: (i.e. hypotenuse, leg, radius, diameter) | | | | | | |
|locate and name points on a coordinate plane using ordered pairs of rational numbers. | | | | | | |
|Including: | | | | | | |
|•Using all four quadrants | |IPM | | | | |
|•Vocabulary (i.e. x-axis, y-axis, x-coordinate, y-coordinate, quadrants, origin) | | | | | | |
|(8.8) Measurement. The student uses procedures to determine measures of three-dimensional | | | | | | |
|figures. The student is expected to: | | | | | | |
|connect models of prisms, cylinders, pyramids, spheres, and cones to formulas for volume of these | | | | | | |
|objects; | | | | | | |
|Including: | | | |I |P |M |
|•Matching nets and models to appropriate formulas to problem solve | | | | | | |
|•Real-life models (i.e. sphere-basketball) | | | | | | |
|estimate 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, | | | |I |P |M |
|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) | | | | | | |
|(8.9) Measurement. The student uses indirect measurement to solve problems. The student is | | | | | | |
|expected to: | | | | | | |
|use 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 |IP |PM | | | | |
|rotated | | | | | | |
|•Vocabulary: (i.e. similar, corresponding, scale factor, dimensions, rotation, proportional and | | | | | | |
|two- and three- dimensional figures) | | | | | | |
|(8.10) Measurement. The student describes how changes in dimensions affect linear, area, and | | | | | | |
|volume measures. The student is expected to: | | | | | | |
|(B) describe the resulting effect on volume when dimensions of a solid are changed | | | |I |P |M |
|proportionally. | | | | | | |
|(8.11) Probability and statistics. The student applies concepts of theoretical and experimental | | | | | | |
|probability to make predictions. The student is expected to: | | | | | | |
|(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 | | | |I |P |M |
|•Analyzing data from a table or graph | | | | | | |
|Using experimental results and comparing those results with the theoretical results. | | | | | | |
|(8.12) Probability and statistics. The student uses statistical procedures to describe data. The | | | | | | |
|student is expected to: | | | | | | |
|(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. | |IP |PM | | | |
|Including: | | | | | | |
|•Frequency tables | | | | | | |
|Vocabulary (i.e. intervals, scale) | | | | | | |
|(8.13) Probability and statistics. The student evaluates predictions and conclusions based on | | | | | | |
|statistical data. The student is expected to: | | | | | | |
|(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: | | | | | | |
|(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: | | | | | | |
|(8.16) Underlying processes and mathematical tools. The student uses logical reasoning to make | | | | | | |
|conjectures and verify conclusions. The student is expected to: | | | | | | |
|(B) validate his/her conclusions using mathematical properties and relationships. | | | | | | |
| |IP |P |P |P |P |PM |
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