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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| |Mathematical Models with Applications | |
| |(One-Half to One Credit). High School | |
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| |Grading Period | |
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| |(c.1) The student uses a variety of strategies and approaches to solve both routine and non-routine problems. The student is expected to: | |
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| |(A) compare and analyze various methods for solving a real-life problem | |
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| |(B) use multiple approaches (algebraic, graphical, and geometric methods) to solve problems from a variety of disciplines | |
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| |(C) select a method to solve a problem, defend the method, and justify the reasonableness of the results | |
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| |(c.2) The student uses graphical and numerical techniques to study patterns and analyze data. The student is expected to: | |
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| |(A) interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, scatterplots, line plots, stem and leaf plots,| |
| |and box and whisker plots to draw conclusions from the data | |
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| |(B) analyze numerical data using measures of central tendency, variability, and correlation in order to make inferences | |
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| |(C) analyze graphs from journals, newspapers, and other sources to determine the validity of stated arguments | |
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| |(D) use regression methods available through technology to describe various models for data such as linear, quadratic, exponential, etc., select the most | |
| |appropriate model, and use the model to interpret information | |
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| |(c.3) The student develops and implements a plan for collecting and analyzing data in order to make decisions. The student is expected to: | |
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| |(A) formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw reasonable | |
| |conclusions | |
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| |(B) communicate methods used, analyses conducted, and conclusions drawn for a data-analysis project by written report, visual display, oral report, or | |
| |multi-media presentation | |
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| |(C) determine the appropriateness of a model for making predictions from a given set of data | |
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| |(c.4) The student uses probability models to describe everyday situations involving chance. The student is expected to: | |
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| |(A) compare theoretical and empirical probability | |
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| |(B) use experiments to determine the reasonableness of a theoretical model such as binomial, geometric, etc | |
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| |(c.5) The student uses functional relationships to solve problems related to personal income. The student is expected to: | |
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| |(A) use rates, linear functions, and direct variation to solve problems involving personal finance and budgeting, including compensations and deductions | |
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| |(B) solve problems involving personal taxes | |
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| |(C) analyze data to make decisions about banking | |
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| |(c.6) The student uses algebraic formulas, graphs, and amortization models to solve problems involving credit. The student is expected to: | |
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| |(A) analyze methods of payment available in retail purchasing and compare relative advantages and disadvantages of each option | |
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| |(B) use amortization models to investigate home financing and compare buying and renting a home | |
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| |(C) use amortization models to investigate automobile financing and compare buying and leasing a vehicle | |
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| |(c.7) The student uses algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to: | |
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| |(A) analyze types of savings options involving simple and compound interest and compare relative advantages of these options | |
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| |(B) analyze and compare coverage options and rates in insurance | |
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| |(C) investigate and compare investment options including stocks, bonds, annuities, and retirement plans | |
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| |(c.8) The student uses algebraic and geometric models to describe situations and solve problems. The student is expected to: | |
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| |(A) use geometric models available through technology to model growth and decay in areas such as population, biology, and ecology | |
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| |(B) use trigonometric ratios and functions available through technology to calculate distances and model periodic motion | |
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| |(C) use direct and inverse variation to describe physical laws such as Hook's, Newton's, and Boyle's laws | |
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| |(c.9) The student uses algebraic and geometric models to represent patterns and structures. The student is expected to: | |
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| |(A) use geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and architecture | |
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| |(B) use geometric transformations, proportions, and periodic motion to describe mathematical patterns and structure in music | |
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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: | | | | | | |
|(8.11) 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 |I |P |P |PM | | |
|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 |I |P |P |PM | | |
|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, |I |P |P |M | | |
|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, |IP |P |M | | | |
|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 |I |P |P |M | | |
|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 |I |P |P |M | | |
|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 | |I |P |M | | |
|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, |IP |PM | | | | |
|verbal descriptions, equations, and inequalities | | | | | | |
|(E) interpret and make decisions, predictions, and critical judgments from functional | |I |P |PM | | |
|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|IP |M | | | | |
|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 |I |P |M | | | |
|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, |I |PM | | | | |
|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 |I |PM | | | | |
|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 |I |P |M | | | |
|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 +|I |P |M | | | |
|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 |I |P |M | | | |
|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|I |P |M | | | |
|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 |I |P |M | | | |
|•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 |I |P |M | | | |
|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, |I |P |M | | | |
|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, |I |P |PM | | | |
|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 | |I |PM | | | |
|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 | |I |PM | | | |
|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 |I |P |P |P |M | |
|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 | | |I |P |M | |
|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 | | |I |P |M | |
|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, | |I |P |P |M | |
|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 | | |I |P |PM | |
|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: | | | |IP |PM | |
|•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: | | |IP |P |M | |
|•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: | | |IP |P |M | |
|•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,| | | |I |PM | |
|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 | | |IP |M | | |
|are changed and apply this idea in solving problems | | | | | | |
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