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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| | 111.33 Algebra II Pre-AP (One-Half to One Credit). | |
| |Grade 10. High School | |
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| |Grading Period | |
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| |(1) The student uses properties and attributes of functions and applies functions to problem situations. The student is expected to: | |
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| |(A) identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations | |
| |Including: | |
| |•Linear and quadratic function | |
| |•Explaining a functional relationship by using one variable to describe another variable. | |
| |• Selecting the independent or dependent quantity in an equation and justifying the selection | |
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| |(B) collect and organize data, make and interpret scatterplots, fit the graph of a function to the data, interpret the results, and proceed to model, | |
| |predict, and make decisions and critical judgments | |
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| |(2) 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) use tools including factoring and properties of exponents to simplify expressions and to transform and solve equations Including investigations with | |
| |and without a graphing calculator. | |
| |Solving equations 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 graphing calculator to determine zeros of equations | |
| |Properties of Exponents including: | |
| |•Powers of Zero (a0 = 1) | |
| |•Negative exponents (a-b = 1/ab ) | |
| |•Multiplying common bases ( ax * ay = ax +y ) | |
| |•Dividing common bases ( ax/ay = ax-y ) | |
| |• Power to power (( ax )y = axy ) | |
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| |(B) use complex numbers to describe the solutions of quadratic equations | |
| |Including: | |
| |• Numbers of the form a + bi | |
| |• Real numbers in the form of a + 0i | |
| |• Interpretations from graph | |
| |• Analysis of discriminant | |
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| |(3) The student formulates systems of equations and inequalities from problem situations, uses a variety of methods to solve them, and analyzes the | |
| |solutions in terms of the situations. The student is expected to: | |
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| |(A) analyze situations and formulate systems of equations in two o | |
| |more unknowns or in equalities in two unknowns to solve | |
| |problems | |
| |Including similarity, a constant rate of change, area, perimeter, | |
| |circumference, and proportions. | |
| |Including setting up a system of two or three equations given a real world situation | |
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| |(B) use algebraic methods, graphs, tables, or matrices, to solve | |
| |systems of equations or inequalities | |
| |Including algebraic patterns such as imaginary numbers, | |
| |geometric patterns, such as fractals, and other iterations. | |
| |Including setting up and solving systems of two and three equations with and without a graphing calculator. | |
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| |(C) interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts Including: | |
| |•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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| |(4) The student connects algebraic and geometric representations of functions. The student is expected to: | |
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| |(A) identify and sketch graphs of parent functions, including linear (f(x) = x), quadratic (f(x) = x2), exponential (f(x) = ax), and logarithmic (f(x) = | |
| |logax) functions, absolute value of x (f(x) = |x|), square root of x, and reciprocal of x (f(x) = 1/x) 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 calculator Including: | |
| |• f(x) = a3 | |
| |• [pic] | |
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| |(B) extend parent functions with parameters such as a in f(x) = a/x and describe the effects of the parameter changes on the graph of parent functions | |
| |Including: | |
| |• Stretches and shrinks | |
| |• Translations | |
| |• Reflections | |
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| |(C) describe and analyze the relationship between a function and its inverse Including | |
| |examples of functions such as linear and quadratic relationships, and non-examples such as y² = x.[pic] | |
| |Including: | |
| |•Ordered pairs (list, chart, map) | |
| |•Algebraic representation | |
| |•Graph of reflection over y = x | |
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| |(5) The student knows the relationship between the geometric and algebraic descriptions of conic sections. The student is expected to: | |
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| |(A) describe a conic section as the intersection of a plane and a cone | |
| |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 | |
| |Including: | |
| |•Parabolas | |
| |•Circles | |
| |•Ellipses | |
| |•Hyperbolas | |
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| |(B) sketch graphs of conic sections, to relate simple parameter changes in the equation to corresponding changes in the graph Including identifications | |
| |for: | |
| |•Parabolas-focus, vertex, directrix | |
| |•Circles-center, radius | |
| |•Ellipse-foci, major and minor axis (a and b), center, (optional eccentricity) | |
| |•Hyperbolas (optional)-vertices, foci, asymptotes, eccentricity, conjugate and transverse axis (a and b) | |
| |Including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles. | |
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| |(C) identify symmetries from graphs of conic sections 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 | |
| |Including horizontal and vertical symmetry | |
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| |(D) identify the conic section from a given equation Including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are | |
| |Pythagorean triples. | |
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| |(E) use the method of completing the square | |
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| |(6) The student understands that quadratic functions can be represented in different ways and translates among their various representations. The student | |
| |is expected to: | |
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| |(A) determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to | |
| |quadratic equations and inequalities Including algebraic expressions in which the equation is in slope-intercept form, point-slope form, and | |
| |standard form with and without a graphing calculator. | |
| |Including from: | |
| |•Graphs | |
| |•Quadratic equations | |
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| |(B) relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions Including algebraic | |
| |expressions in which the equation is in slope-intercept form, point-slope form, and standard form with and without a graphing calculator. | |
| |Including: | |
| |•Determine graph from equation | |
| |•Write equation given a word problem | |
| |•Write equation given a chart | |
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| |(C) determine a quadratic function from its roots or a graph Including algebraic expressions in which the equation is in slope-intercept form, point-slope | |
| |form, and standard form with and without a graphing calculator. | |
| |Including: | |
| |•Sum and product of roots | |
| |•Multiply the binomials to obtain standard form of equation | |
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| |(7) The student interprets and describes the effects of changes in the parameters of quadratic functions in applied and mathematical situations. The | |
| |student is expected to: | |
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| |(A) use characteristics of the quadratic parent function to sketch the related graphs and connect between the y = ax2 + bx + c and the y = a(x - h)2 + k | |
| |symbolic representations of quadratic functions 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 | |
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| |(B) use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x - h)2 + k form of a | |
| |function in applied and purely mathematical situations Including: | |
| |•Using information from concrete models to write linear equations, plot graphs, and solve equations | |
| |•Use graphs to solve linear equations and inequalities | |
| |•Algebraic expressions in which the equation is in slope-intercept form, point-slope form, and standard form | |
| |•Using a graphing calculator | |
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| |(8) The student formulates equations and inequalities based on quadratic 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 quadratic functions and formulate quadratic equations or inequalities to solve problems 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 | |
| |Including: | |
| |•Transforming from standard to vertex form by completing the square | |
| |•Expanding vertex form to obtain standard form | |
| |Including: | |
| |•Graphs | |
| |•Tables | |
| |•Equations drawn from word problems | |
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| |(B) analyze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula | |
| |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 calculator | |
| |Including: | |
| |•Stretch and shrink (a) | |
| |•Shift left/right (h) | |
| |•Shift up/down (k) | |
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| |(C) compare and translate between algebraic and graphical solutions of quadratic 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 calculators | |
| |Including determining roots (zeros, solutions, and x-intercepts) from an equation or graph. | |
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| |(D) solve quadratic equations and inequalities using graphs, tables, and algebraic methods | |
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| |(9) The student formulates equations and inequalities based on square root 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) use the parent function to investigate, describe, and predict the effects of parameter changes on the graphs of square root functions and describe | |
| |limitations on the domains and ranges Including: | |
| |•Using rational exponents to represent radicals | |
| |•Stretch/shrink | |
| |•Translations | |
| |•Reflections | |
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| |(B) relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions Including: | |
| |•Determining graphs from equations | |
| |•Write equations given a word problem | |
| |•Write equations given a chart | |
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| |(C) determine the reasonable domain and range values of square root functions, as well as interpret and determine the reasonableness of solutions to square| |
| |root equations and inequalities Including investigation of extraneous solutions as | |
| |well as imaginary numbers. | |
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| |(D) determine solutions of square root equations using graphs, tables, and algebraic methods Including graphical | |
| |representations on the calculator | |
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| |(E) determine solutions of square root inequalities using graphs and tables | |
| |Including graphical representations on the calculator | |
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| |(F) analyze situations modeled by square root functions, formulate equations or inequalities, select a method, and solve problems Including investigation | |
| |of extraneous solutions. | |
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| |(G) connect inverses of square root functions with quadratic functions | |
| |Including confirming: | |
| |•Graphically | |
| |•Algebraically | |
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| |(10) The student formulates equations and inequalities based on rational 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) use quotients of polynomials to describe the graphs of rational functions, predict the effects of parameter changes, describe limitations on the | |
| |domains and ranges, and examine asymptotic behavior Including analysis of a | |
| |predetermined graph | |
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| |(B) analyze various representations of rational functions with respect to problem situations Including: | |
| |•Graphs | |
| |•Tables | |
| |•Equations | |
| |•Verbal description | |
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| |(C) determine the reasonable domain and range values of rational functions, as well as interpret and determine the reasonableness of solutions to rational | |
| |equations and inequalities Including: | |
| |•Use of graphing calculator | |
| |•Solving denominator = to zero to determine vertical asymptotes (domain) | |
| |•Calculate horizontal asymptotes (range) | |
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| |(D) determine the solutions of rational equations using graphs, tables, and algebraic methods Including: | |
| |•Calculator applications | |
| |•Solving equations | |
| |•Finding zeros within a table | |
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| |(E) determine solutions of rational inequalities using graphs and tables | |
| |Including: | |
| |•Calculator applications (shading) | |
| |•Check values from table | |
| |•Check algebraically (optional) | |
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| |(F) analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or quadratic function, and solve the | |
| |problem Including: | |
| |•Graphs | |
| |•Tables | |
| |•Equations drawn from word problems | |
| |Examples include: | |
| |A motorboat goes 36 miles upstream on a river whose current is running at 3 miles per hour. What is the speed of the boat (assuming that it maintains a | |
| |constant speed relative to the water)? | |
| |Equation the student should derive and solve: [pic] Total trip (round trip) is 5 hours d + d = t | |
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| |(G) use functions to model and make predictions in problem situations involving direct and inverse variation Including: | |
| |•Finding constant of variation | |
| |•Using constant to solve for unknown | |
| |Examples include: | |
| |The cost per person to rent a chartered bus varies inversely as the number of people who ride the bus. If 40 people pay $9.50 each to ride the chartered | |
| |bus, what is the cost per person if only 25 people go? | |
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| |(11) The student formulates equations and inequalities based on exponential and logarithmic 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) develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses | |
| |Including converting equations from exponential form to logarithmic form and vice versa. | |
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| |(B) use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions,| |
| |describe limitations on the domains and ranges, and examine asymptotic behavior Including: | |
| |•Stretches/shrinks | |
| |•Translations | |
| |•Reflections | |
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| |(C) determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of | |
| |solutions to exponential and logarithmic equations and inequalities Including: | |
| |•Graphical representation | |
| |•Equation representation | |
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| |(D) determine solutions of exponential and logarithmic equations using graphs, tables, and algebraic methods | |
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| |(E) determine solutions of exponential and logarithmic inequalities using graphs and tables Including: | |
| |•Finding roots on the calculator | |
| |•Finding zeros in a table | |
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| |(F) analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem Including problem of these types: | |
| |•Exponential growth and decay | |
| |•Half-life | |
| |•Compound interest | |
| |•Other examples | |
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| |ADDITIONAL TEKS | |
|Mathematics, |Grading Period |
|Grade 8. Middle School | |
| |1 |2 |3 |4 |5 |6 |
|(8.3) The student identifies proportional or non-proportional linear relationships in problem | | | | | | |
|situations and solves problems. The student is expected to: | | | | | | |
|(8.6) Geometry and spatial reasoning. The student uses transformational geometry to develop | | | | | | |
|spatial sense. The student is expected to: | | | | | | |
|(B) graph dilations, reflections, and translations on a coordinate plane | | | | | | |
|(8.7) The student uses geometry to model and describe the physical world. The student is expected | | | | | | |
|to: | | | | | | |
|(B) 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 | | | | | | |
|Various representations of limits of measures | | | | | | |
|(C) 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) | | | | | | |
|(D) locate 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) | | | | | | |
|(8.8) The student uses procedures to determine measures of three-dimensional figures. The | | | | | | |
|student is expected to: | | | | | | |
|(B) 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) | | | | | | |
|(C) 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, | | | | | | |
|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) The student uses indirect measurement to solve problems. The student is expected to: | | | | | | |
|(B) use 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) | | | | | | |
|(8.10) 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 proportionally| | | | | | |
|(8.11) 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 | | | | | | |
|•Analyzing data from a table or graph | | | | | | |
|Using experimental results and comparing those results with the theoretical results. | | | | | | |
|(8.12) 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 | | | | | | |
|Including: | | | | | | |
|•Frequency tables | | | | | | |
|Vocabulary (i.e. intervals, scale) | | | | | | |
|(8.13) The student evaluates predictions and conclusions based on statistical data. The student is| | | | | | |
|expected to: | | | | | | |
|(8.14) 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 understanding the problem, making a plan, | | | | | | |
|carrying out the plan, and evaluating the solution for reasonableness | | | | | | |
|(C) select or develop an appropriate problem-solving strategy from a variety of different types, | | | | | | |
|including drawing a picture, looking for a pattern, systematic guessing and checking, acting it | | | | | | |
|out, making a table, working a simpler problem, or working backwards to solve a problem | | | | | | |
|(8.15) The student communicates about Grade 8 mathematics through informal and mathematical | | | | | | |
|language, representations, and models. The student is expected to: | | | | | | |
|(8.16) 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 | | | | | | |
|111.32 Algebra I (One Credit). | | | | | | |
|Grade 9. High School | | | | | | |
|(A.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: | | | | | | |
|(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. | | | | | | |
|(C) 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. | | | | | | |
|(D) represent relationships among quantities using concrete models, tables, graphs, diagrams, | | | | | | |
|verbal descriptions, equations, and inequalities | | | | | | |
|(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. | | | | | | |
|(A.2) The student uses the properties and attributes of functions. The student is expected to: | | | | | | |
|(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.| | | | | | |
|(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. | | | | | | |
|(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 | | | | | | |
|(A.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: | | | | | | |
|(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 | | | | | | |
|(A.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: | | | | | | |
|(B) use the commutative, associative, and distributive properties to simplify algebraic | | | | | | |
|expressions | | | | | | |
|(C) use the commutative, associative, and distributive properties to simplify algebraic | | | | | | |
|expressions | | | | | | |
|(A.5) The student understands that linear functions can be represented in different ways and | | | | | | |
|translates among their various representations. The student is expected to: | | | | | | |
|(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. | | | | | | |
|(A.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: | | | | | | |
|(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 | | | | | | |
|(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 | | | | | | |
|(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. | | | | | | |
|(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. | | | | | | |
|(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 | | | | | | |
|(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 | | | | | | |
|(A.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: | | | | | | |
|(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 | | | | | | |
|(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 | | | | | | |
|(A.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: | | | | | | |
|(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) | | | | | | |
|(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 | | | | | | |
|(A.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. | | | | | | |
|(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 | | | | | | |
|(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 | | | | | | |
|(A.10) The student understands there is more than one way to solve a quadratic equation and solves| | | | | | |
|it using appropriate methods. The student is expected to: | | | | | | |
|(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) | | | | | | |
|(A.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: | | | | | | |
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