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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| | 111.35 Pre-Calculus (One-Half to One Credit). | |

| |  High School  | |

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| |Grading Period | |

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| |(c.1) The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations| |

| |of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigonometric, and piecewise-defined functions. The | |

| |student is expected to: | |

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| |(A)  describe parent functions symbolically and graphically, including f(x) = xn, f(x) = ln x, f(x) = loga x, f(x) =?/x , f(x) = ex, f(x) = |x|, f(x) = ax, | |

| |f(x) = sin x, f(x) = arcsin x, etc. | |

| |Including f(x) = xn, f(x) = 1n x, f(x) = loga x, f(x) = 1/x, f(x) = ex, f(x) = |x|, f(x) = ax, f(x) = sin x , f(x) = arcsin x, etc. | |

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| |(B)  determine the domain and range of functions using graphs, tables, and symbols | |

| |Including parent functions such as f(x) = xn, f(x) = 1n x, f(x) = loga x, f(x) = 1/x, f(x) = ex, f(x) = |x|, f(x) = ax, f(x) = sin x , f(x) = arcsin x, etc.| |

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| |(C)  describe symmetry of graphs of even and odd functions | |

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| |(D)  recognize and use connections among significant values of a function (zeros, maximum values, minimum values, etc.), points on the graph of a function, | |

| |and the symbolic representation of a function | |

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| |(E)  investigate the concepts of continuity, end behavior, asymptotes, and limits and connect these characteristics to functions represented graphically and| |

| |numerically | |

| |Including | |

| |•Using the zoom and trace features of graphing calculators, to discover that a linear equation can be written for most curves around a point (a, f (a)) if | |

| |zoomed in close enough. | |

| |•Limit notation for right and left hand limits. | |

| |•Estimating limits from graphs, and from tables of values | |

| |•Calculating limits using algebra | |

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| |(c.2) The student interprets the meaning of the symbolic representations of functions and operations on functions to solve meaningful problems. The student | |

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| |(A)  apply basic transformations, including a ? f(x), f(x) + d, f(x - c), f(b ? x), and compositions with absolute value functions, including |f(x)|, and | |

| |f(|x|), to the parent functions | |

| |Including a • f(x), f(x) + d, f(x - c), f(b • x), and compositions with absolute value functions, including |f(x)|, and f(|x|), to the parent functions. | |

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| |(B)  perform operations including composition on functions, find inverses, and describe these procedures and results verbally, numerically, symbolically, | |

| |and graphically | |

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| |(C)  investigate identities graphically and verify them symbolically, including logarithmic properties, trigonometric identities, and exponential properties| |

| |Including logarithmic properties, trigonometric identities, and exponential properties. | |

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| |(c.3) The student uses functions and their properties, tools and technology, to model and solve meaningful problems. The student is expected to: | |

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| |(A)  investigate properties of trigonometric and polynomial functions | |

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| |(B)  use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data | |

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| |(C)  use regression to determine the appropriateness of a linear function to model real-life data (including using technology to determine the correlation | |

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| |(D)  use properties of functions to analyze and solve problems and make predictions | |

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| |(E)  solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas and incorporate radian| |

| |measure where needed | |

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| |(c.4) The student uses sequences and series as well as tools and technology to represent, analyze, and solve real-life problems. The student is expected to:| |

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| |(A)  represent patterns using arithmetic and geometric sequences and series | |

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| |(B)  use arithmetic, geometric, and other sequences and series to solve real-life problems | |

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| |(C)  describe limits of sequences and apply their properties to investigate convergent and divergent series | |

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| |(D)  apply sequences and series to solve problems including sums and binomial expansion | |

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| |(c.5) The student uses conic sections, their properties, and parametric representations, as well as tools and technology, to model physical situations. The | |

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| |(A)  use conic sections to model motion, such as the graph of velocity vs. position of a pendulum and motions of planets such as the graph of | |

| |velocity vs. position of a pendulum and motions of planets. | |

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| |use properties of conic sections to describe physical phenomena such as the reflective properties of light and sound | |

| |such as the reflective properties of light and sound. | |

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| |(C)  convert between parametric and rectangular forms of functions and equations to graph them | |

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| |(D)  use parametric functions to simulate problems involving motion | |

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| |(c.6) The student uses vectors to model physical situations. The student is expected to: | |

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| |(A)  use the concept of vectors to model situations defined by magnitude and direction | |

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| |(B)  analyze and solve vector problems generated by real-life situations | |

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|Additional TEKS |

|Mathematics, |Grading Period |

|Grade 8.  Middle School | |

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|(8.3) The student identifies proportional or non-proportional linear relationships in problem | | | | | | |

|situations and solves problems. The student is expected to: | | | | | | |

|(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 |IPM | | | | | |

|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 |IPM | | | | | |

|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, |IPM | | | | | |

|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, |IPM | | | | | |

|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 |IPM | | | | | |

|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 |IPM | | | | | |

|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) describe functional relationships for given problem situations and write equations or |IPM | | | | | |

|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) | | | | | | |

|(D) represent relationships among quantities using concrete models, tables, graphs, diagrams, |IPM | | | | | |

|verbal descriptions, equations, and inequalities | | | | | | |

|(E) interpret and make decisions, predictions, and critical judgments from functional |IPM | | | | | |

|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|IPM | | | | | |

|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 |IPM | | | | | |

|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, |IPM | | | | | |

|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 |IPM | | | | | |

|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 |IPM | | | | | |

|expressions | | | | | | |

|(C) connect equation notation with function notation, such as |IPM | | | | | |

|y = x + 1 and f(x) = x + 1 | | | | | | |

|(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 |IPM | | | | | |

|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 |IPM | | | | | |

|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 +|IPM | | | | | |

|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 |IPM | | | | | |

|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|IPM | | | | | |

|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 |IPM | | | | | |

|•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 |IPM | | | | | |

|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, |IPM | | | | | |

|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) investigate methods for solving linear equations and inequalities using concrete models, |IPM | | | | | |

|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.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 |IPM | | | | | |

|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 |IPM | | | | | |

|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 |IPM | | | | | |

|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 |IPM | | | | | |

|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 |IPM | | | | | |

|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: | | | | | | |

|111.34 Geometry (One Credit).   | | | | | | |

|Grade 10. High School | | | | | | |

|(G.4) The student uses a variety of representations to describe geometric relationships and solve | | | | | | |

|problems. The student is expected to: | | | | | | |

|(G.5) The student uses a variety of representations to describe geometric relationships and solve | | | | | | |

|problems. The student is expected to: | | | | | | |

|(B) use numeric and geometric patterns to make generalizations about geometric properties, |IPM | | | | | |

|including properties of polygons, ratios in similar figures and solids, and angle relationships in| | | | | | |

|polygons and circles Including properties of | | | | | | |

|polygons, ratios in similar figures and solids, and angle relationships in polygons and circles | | | | | | |

|(C) use properties of transformations and their compositions to make connections between |IPM | | | | | |

|mathematics and the real world, such as tessalations | | | | | | |

|(D) identify and apply patterns from right triangles to solve meaningful problems, including |IPM | | | | | |

|special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples | | | | | | |

|Including trigonometric ratios sine, cosine, tangent | | | | | | |

|(G.6) 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: | | | | | | |

|(C) use orthographic and isometric views of three-dimensional geometric figures to represent and |IPM | | | | | |

|construct three-dimensional geometric figures and solve problems | | | | | | |

|Including the use of unit blocks to explore concrete models. | | | | | | |

|(G.7) The student understands that coordinate systems provide convenient and efficient ways of | | | | | | |

|representing geometric figures and uses them accordingly. The student is expected to: | | | | | | |

|(B) use slopes and equations of lines to investigate geometric relationships, including parallel |IPM | | | | | |

|lines, perpendicular lines, and special segments of triangles and other polygons | | | | | | |

|(C) derive and use formulas involving length, slope, and midpoint Including: |IPM | | | | | |

|•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.8) The student uses tools to determine measurement of geometric figures and extends measurement| | | | | | |

|concepts to find perimeter, area, and volume in problem situations. The student is expected to: | | | | | | |

|(B) find areas of sectors and arc lengths of circles using proportional reasoning |IPM | | | | | |

|Including: | | | | | | |

|• [pic] | | | | | | |

|• Area of sector ═ Central Angle | | | | | | |

|Area of circle 3600 | | | | | | |

|(C) derive, extend, and use the Pythagorean Theorem Including: |IPM | | | | | |

|•Distance formula | | | | | | |

|•Unknown lengths in polygons and circles | | | | | | |

|(D) find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites|IPM | | | | | |

|of these figures in problem situations | | | | | | |

|(G.9) The student analyzes properties and describes relationships in geometric figures. The | | | | | | |

|student is expected to: | | | | | | |

|(G.10) The student applies the concept of congruence to justify properties of figures and solve | | | | | | |

|problems. The student is expected to: | | | | | | |

|(G.11) The student applies the concepts of similarity to justify properties of figures and solve | | | | | | |

|problems. The student is expected to: | | | | | | |

|(B) use ratios to solve problems involving similar figures Including: |IPM | | | | | |

|•Comparing the areas, perimeters and volumes of similar polygons and solids | | | | | | |

|•Dilations | | | | | | |

|(C) develop, apply, and justify triangle similarity relationships, such as right triangle ratios,|IPM | | | | | |

|trigonometric ratios, and Pythagorean triples using a variety of methods | | | | | | |

|(D) describe the effect on perimeter, area, and volume when one or more dimensions of a figure |IPM | | | | | |

|are changed and apply this idea in solving problems | | | | | | |

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