CORD GEOMETRY: Mathematics in Context

Correlation:

California State Curriculum Standards

ofMathematics

for Grades 9-10

To

CORD GEOMETRY: Mathematics in Context

CORD Geometry: Mathematics In Context

Student Edition...... 0-538-68127-6

Teacher's Annotated Edition...... 0-538-68128-4

Teacher's Resource Book...... 0-538-68170-5

Supplementary Worksheets...... 0-538-68685-5

Solutions Manual...... 0-538-68314-7

Video...... 0-538-68316-3

Computer Test Generator (IBM, MAC)...... 0-538-68315-5

STANDARDS / PAGE REFERENCES
NUMBER SENSE
1.Students compute with and simplify rational expressions and those containing exponents.
1.1add, subtract, multiply, divide and simplify expressions containing radicals and fractional exponents / pp. 6.32-6.42, 6.46-6.48
1.2use and interpret negative exponents and their properties, including expressions in scientific notation / Covered in CORD Bridges to Algebra and Geometry and CORD Algebra 1.
ALGEBRA AND FUNCTIONS
1.Students classify and identify attributes of basic families of functions (linear, quadratic, power, exponential, absolute value, simple polynomial, rational and radical).
1.1determine which type of function best models a situation, write an equation and use this equation to answer questions about the situation / pp. 7.27-7.33, 7.48, 7.58
1.2describe and sketch the graph of a linear, quadratic, power, exponential, absolute value, simple polynomial, rational, or radical function including its end behavior labeling key points / pp. 7.19-7.33, 7.49-7.51, 7.54-7.63
1.3given a graph of a function, identify which type of function, if any, it models and interpret the meaning of key points on the graph / pp. 7.19-7.63
1.4demonstrate and explain the effect that transformations have on both the equation and graph of a function / Covered in CORD Bridges to Algebra and Geometry and CORD Algebra 1.
2.Students demonstrate understanding of the concept of a function, identify its attributes, and determine the results of operations performed on functions.
2.1identify a function given as a table of values, an equation, or a graph, identify and explain its key characteristics (domain, range, intercepts, whether it is one-to-one), and translate among these representations / pp. 7.27-7.33
2.2determine the natural domain of a function and find the value of a function for a given element in its domain / pp. 7.27-7.33
2.3determine the inverse of a one-to-one function, the composition of two or more functions, and the composition of a function with itself when the function is given as an equation, a graph, or a set of ordered pairs, and discuss the relationships among these representations / Although the importance of this objective is recognized, inclusion would lengthen the text or require other topics be covered in less depth.
3.Students use a variety of techniques to solve and graph quadratic functions and interpret the results in the context of a problem situation.
3.1use patterns in the variables, exponents and coefficients to expand and factor quadratic expressions in one and two variables, relating these to the area and dimensions of rectangles, and recognizing the equivalence of expanded and factored forms / p. 8-7 and also covered in CORD Bridges to Algebra and Geometry and CORD Algebra 1.
3.2understand the relationships among the coefficients, factors, roots and x- and
y-intercepts of a quadratic function and use these to solve factorable quadratic equations / Covered in CORD Algebra 1.
3.3derive and use the quadratic formula to solve any quadratic equation in one variable including those with irrational or complex solutions / Covered in CORD Algebra 1.
3.4find and interpret the maximum or minimum value of a quadratic function / Although the importance of this objective is recognized, inclusion would lengthen the text or require other topics be covered in less depth.
4.Students demonstrate an understanding of arithmetic, geometric and other sequences and series.
4.1identify, describe, extend and find the nth term of arithmetic, geometric and other sequences / pp. 2.5-2.7
4.2find the sum of finite arithmetic sequences / Although the importance of this objective is recognized, inclusion would lengthen the text or require other topics be covered in less depth.
4.3relate arithmetic and geometric sequences to linear and exponential functions, and express them in explicit and recursive form / Although the importance of this objective is recognized, inclusion would lengthen the text or require other topics be covered in less depth.
5.Students demonstrate facility with algebraic manipulations, perform algebraic computations easily and routinely, and rewrite expressions and equations to gain information and find solutions.
5.1use symbols to represent unknown quantities, and express relationships,
re-expressing them through algebraic manipulation as needed, and correctly interpret the results / pp. 1.14, 1.16, 1.27, 1.41, 2.27-2.28, 237, 3.45-3.47, 4.23, 4.25, 5.9, 5.36, 6.4, 6.6-6.7, 6.21, 6.27, 6.33, 8.19, 9.16, 9.32, 9.38
5.2write and solve linear and quadratic equations and inequalities, and absolute value inequalities in one variable, verify the solutions, and interpret the results graphically, relating the solutions and graphs to the situations modeled / pp. 7.27-7.33
5.3add, subtract, multiply, divide, reduce and simplify polynomial, rational and radical expressions and solve equations involving these quantities / Covered in CORD Bridges to Algebra and Geometry and CORD Algebra 1.
5.4relate the graph of a polynomial of degree three or higher to its factored symbolic form / Although the importance of this objective is recognized, inclusion would lengthen the text or require other topics be covered in less depth.
5.5Write and solve systems of linear and quadratic equations (including linear-quadratic and quadratic-quadratic systems), and inequalities, verify solutions, and interpret the results in terms of the graph and the situation modeled by the equations / Covered in CORD Bridges to Algebra and Geometry and CORD Algebra 1.
6.Students identify and demonstrate understanding about cyclic phenomena and situations that give rise to quadratic equations in two variables.
6.1identify situations and phenomena that are cyclic in nature (e.g., number of hours of daylight each day for 10 years, the height of a seat above the ground as a Ferris wheel turns), identify the length of the cycle, and use the values in one cycle to determine values everywhere / Although the importance of this objective is recognized, inclusion would lengthen the text or require other topics be covered in less depth.
6.2relate central angles of a circle centered at (0,0) on a coordinate grid (initial side on the positive x-axis, angles measured counterclockwise) with the sine, cosine and tangent of their reference triangles and explain why these can be considered periodic functions / Although the importance of this objective is recognized, inclusion would lengthen the text or require other topics be covered in less depth.
6.3construct a table of values for, find the center, the intercepts and other key features of, and graph equations of, circles, parabolas, ellipses and hyperbolas / pp. 9.4-9.10, 9.48-9.49
MEASURE AND GEOMETRY
1.Students select and use appropriate units, tools, geometric properties and degrees of accuracy to solve problems involving geometric and non-geometric measures.
1.1select and use appropriate units, precision and accuracy in measurements and computations done with them / pp. 1.12-1.25, 1.44-1.45, 1.48-1.50, 3.48-3.50, 4.36-4.38, 5.41-5.44, 6.44-6.46, 6.48-6.49, 7.48-7.49, 7.51-7.53, 8.37-8.41, 9.48-9.51, 10.54-10.55, 10.59-10.61, 11.68-11.72
1.2know, use, derive formulas for and solve problems involving perimeter, circumference, area, volume, lateral area and surface area of common geometric figures / pp. 5.7, 5.9, 6.12, 6.14, 8.4-8.36, 8.44-8.53, 10.18-10.53, 10.59-10.72
1.3know, use, derive formulas for and solve problems involving weight, monetary and time systems selecting appropriate units and degrees of accuracy / pp. 1.15, 2.8, 2.55-2.56, 3.10, 6.8-6.9, 6.51, 6.55, 7.56, 7.58, 8.16, 8.30, 10.32, 10.64-10.65
1.4describe how changes in the dimensions of an object affect the perimeter, area and volume (e.g., tripling the radius of a sphere multiplies its volume by 27) / pp. 6.12, 6.14, 10.25, 10.27, 10.29, 10.32-10.33, 10.40
2.Students identify, formulate and confirm conjectures, find missing measures, and solve problems involving angles, right triangles, other polygons and circles.
2.1find and use measures of sides, interior and exterior angles of triangles and polygons to classify figures (e.g., isosceles, obtuse, convex, regular) and solve problems (e.g., determine the number of degrees in a central angle of a regular polygon) / pp. 3.30-3.34, 3.50-3.51, 5.5-5.15, 5.39-5.40
2.2describe the relationships between vertical angles, angles that are supplementary and complementary, and angles formed when parallel lines are cut by a transversal express and use these to find missing angle measures in such systems / pp. 3.12-3.25, 3.56
2.3apply the properties of angles, arcs, chords, radii, tangents and secants to solve problems involving circles / pp. 9.11-9.61
2.4use the Pythagorean Theorem, its converse, properties of special right triangles (e.g., sides in the ratio 3-4-5, angles of 30-60-90 degrees), and right triangle trigonometry to find missing information about triangles / pp. 6.32-6.43, 6.46-6.48, 11.51-11.63, 11.70-11.72
2.5compare, contrast, classify and solve problems involving quadrilaterals (e.g., square, rhombus, rectangle, parallelogram, trapezoid, kite, cyclic) on the basis of their definitions and properties (e.g., opposite sides, consecutive angles, diagonals) / pp. 5.16-5.38, 5.41-5.44, 5.49, 5.51, 5.53
3.Students deepen their understanding of the interrelationships among two- and three-dimensional geometric objects and visualize and describe objects, paths and regions in space.
3.1perform standard straight edge and compass constructions (e.g., construct angle bisectors, angle bisectors, parallel lines, divide a line segment into proportional parts), and justify the process used / pp. 1.36-1.43, 1.46-1.48
3.2use transformations in the coordinate plane or in space (translations, rotations and reflections) (e.g., identify the type of transformation underlying symmetry in figures, show how one object in a pair of congruent objects can be translated, reflected and/or rotated to “sit on top of” its counterpart) / pp. 11.4-11.50, 11.64-11.70, 11.73-11.81
3.3identify the structural parts (e.g., angles, shape of sides, orientation of sides, circumference) and characteristics (e.g., symmetry, shape of cross-sections) of
three-dimensional objects and use these to classify the objects and answer questions about them (e.g., a penny can be seen as a cylinder with small height so its volume is V=[pi]r^2h) / pp. 10.4-10.72
3.4identify and describe objects formed by rotating a simple plane figure (e.g., semicircle, triangle, rectangle) about an axis and describe the perpendicular cross section of the solid formed / pp. 9.41-9.44, 10.48
3.5use geometric language to describe how the conic sections are derived as cross sections of a cone / Although the importance of this objective is recognized, inclusion would lengthen the text or require other topics be covered in less depth.
3.6relate the concept of symmetry to curved shapes in the plane and to solid objects / pp. 11.9-11.10, 11.28
4.Students demonstrate understanding of an axiomatic system, and the nature of proof.
4.1identify and give examples of undefined terms, axioms, theorems, inductive and deductive reasoning / pp. 1.4-1.11, 2.4-2.54, 3.13
4.2construct and judge the validity of a logical argument including giving counterexamples and understanding quantifiers / pp. 2.27-2.41, 2.45, 3.11, 3.14-3.15, 3.21, 3.24, 3.37, 3.41, 3.50-3.51, 3.61, 4.13, 4.16-4.17, 4.19, 4.24, 4.27, 4.29-4.30, 5.22, 5.24, 5.26, 5.28, 5.34, 6.9, 6.20, 6.24, 6.33, 7.47, 8.25, 9.31, 9.35, 9.40, 10.47
4.3select and use deductive, indirect, algebraic, or transformational methods of proof in a variety of circumstances / pp. 2.4-2.41, 2.45, 3.11, 3.14, 3.24, 3.37, 3.41, 4.13, 4.16-4.19, 4.29-4.30, 5.13, 5.24, 5.26, 5.34, 6.9, 6.20, 6.33, 7.18, 7.22, 7.35, 7.47, 9.15-9.16
4.4prove the Pythagorean Theorem using algebraic and geometric arguments / pp. 6.32-6.33
4.5identify similar and congruent triangles and other polygons and their corresponding parts and prove basic theorems about them / pp. 4.4-4.48, 6.13-6.31, 6.48-6.49
4.6know and prove theorems about angles, triangles and polygons / pp. 2.35-2.41, 2.45, 3.13-3.34, 3.43-3.47, 4.4-4.51, 5.10-5.15, 5.23-5.44, 6.10-6.43
4.7know and prove theorems about the properties of angles, arcs, chords, radii, tangents and secants of circles
/ pp. 9.11-9.61
STATISTICS, DATA ANALYSIS AND PROBABILITY
1.Students make inferences and predictions based on the analysis of a set of data and transformations performed on it.
1.1explain the difference between the mean, mode and median with respect to the sensitivity of each measure to changes in the data set / Covered in CORD Bridges to Algebra and Geometry and CORD Algebra 1.
2.Students estimate relative frequency, compute probability and demonstrate understanding of ways to make predictions from samples, and experiments in situations involving uncertainty, including dependent and conditional events.
2.1use combinations and permutations to count the number of arrangements of a set of elements and distinguish between the two, and relate to the determination of theoretical probabilities / Covered in CORD Bridges to Algebra and Geometry and CORD Algebra 1.
2.2demonstrate understanding of a random variable and how it can be used to make predictions about a population from a sample / Covered in CORD Bridges to Algebra and Geometry and CORD Algebra 1.
2.3graph and interpret probability distributions including the binomial distributions, and use them to discuss whether an event is rare or reasonably likely / Although the importance of this objective is recognized, inclusion would lengthen the text or require other topics be covered in less depth.
PROBLEM SOLVING AND MATHEMATICAL REASONING
1.Students make decisions about how to approach problems.
1.1analyze problems by identifying relationship, discriminating relevant from irrelevant information, identifying missing information, sequencing and prioritizing information and observing patterns / pp. 1.44-1.50, 2.4-2.67, 3.48-3.53, 4.36-4.40, 5.39-5.44, 6.44-6.49, 7.48-7.53, 8.37-8.43, 9.48-9.54, 10.54-10.61, 11.64-11.72
1.2formulate reasonable mathematical conjectures based upon a general description of a situation and ask and answer appropriate questions in pursuit of a solution / pp. 1.23, 1.26, 1.28, 1.34, 1.44, 2.5-2.6, 2.37, 3.6, 3.13, 3.27-3.28, 3.31, 3.36, 4.31, 4.33, 4.40, 5.13, 5.27, 5.29, 5.35, 5.40, 6.12, 6.18-6.19, 6.32, 9.11, 9.42, 11.37-11.38, 11.47, 11.51
2.Students select and use appropriate concepts and techniques from different areas of mathematics to find solutions.
2.1apply strategies and results from simpler problems to more complex situations and integrate concepts and techniques from different areas of mathematics / pp. 1.44-1.63, 2.47-2.67, 3.48-3.63, 4.36-4.48, 5.39-5.53, 6.44-6.59, 7.48-7.63, 8.37-8.53, 9.48-9.61, 10.54-10.72, 11.64-11.81
2.2employ forms of mathematical reasoning and proof appropriate to the solution of the problem at hand, including deductive and inductive reasoning, making and testing conjectures and using counterexamples and indirect proof / pp. 2.4-2.41, 2.45, 3.11, 3.14, 3.24, 3.37, 3.41, 4.13, 4.16-4.19, 4.29-4.30, 5.13, 5.24, 5.26, 5.34, 6.9, 6.20, 6.33, 7.18, 7.22, 7.35, 7.47, 9.15-9.16
2.3solve for unknown or undecided quantities using algebra, graphing, sound reasoning and other strategies / pp. 1.14, 1.27, 1.41, 1.51-1.65, 2.12, 2.27-2.42, 2.55-2.65, 3.5, 3.8, 3.43, 3.54-3.65, 4.25, 4.41-4.51, 5.9, 5.45-5.55, 6.21, 6.27, 6.50-6.51, 7.27-7.38, 7.54-7.65, 8.7, 8.28, 8.44-8.55, 9.38, 9.55-9.63, 10.62-10.75, 11.73-11.84
2.4make and test conjectures using both inductive and deductive reasoning / pp. 1.23, 1.26, 1.28, 1.34, 1.44, 2.5-2.6, 2.37, 3.6, 3.13, 3.27-3.28, 3.31, 3.36, 4.31, 4.33, 4.40, 5.13, 5.27, 5.29, 5.35, 5.40, 6.12, 6.18-6.19, 6.32, 9.11, 9.42, 11.37-11.38, 11.47, 11.51
2.5show mathematical reasoning in solutions in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams and models / pp. 1.44-1.65, 2.47-2.69, 3.48-3.65, 4.36-4.50, 5.39-5.55, 6.44-6.61, 7.48-7.65, 8.37-8.55, 9.48-9.63, 10.54-10.74, 11.64-11.83
2.6express the solution clearly and logically using appropriate mathematical notation and terms and clear language, and support solutions with evidence, in both oral and written work / pp. 1.9, 1.16, 1.24, 1.33, 1.42, 1.48, 1.64, 2.7, 2.14, 2.19, 2.24, 2.32, 2.39, 2.44, 2.54, 2.68, 3.9, 3.16-3.17, 3.23, 3.32, 3.40, 3.47, 3.64, 4.8, 4.15, 4.22, 4.28, 4.34, 4.49, 5.8, 5.14, 5.18, 5.24, 5.30, 5.37, 5.54, 6.8, 6.14, 6.23, 6.30, 6.36, 6.41, 6.60, 7.8-7.9, 7.16, 7.24, 7.31, 7.45, 7.64, 8.8, 8.14, 8.20, 8.24, 8.29, 8.34-8.35, 9.8, 9.15, 9.23, 9.30, 9.39, 9.45, 9.62, 10.8, 10.15, 10.23, 10.31, 10.39, 10.44, 10.51, 10.73, 11.9, 11.16, 11.23, 11.29, 11.34, 11.41, 11.48, 11.55, 11.60, 11.82
2.7indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy / pp. 1.12-1.25, 1.44-1.45, 1.48-1.50, 3.48-3.50, 4.36-4.38, 5.41-5.44, 6.44-6.46, 6.48-6.49, 7.48-7.49, 7.51-7.53, 8.37-8.41, 9.48-9.51, 10.54-10.55, 10.59-10.61, 11.68-11.72
3.Students move beyond a particular problem by making general conclusions, summary statements and posing new, related questions and comments.
3.1explain the logic inherent in a solution process, by making generalizations and showing that they are valid, and by revealing mathematical patterns inherent in a situation / pp. 2.4-2.9, 2.21-2.41, 2.47-2.54, 3.61, 4.16, 4.19, 4.25, 5.13, 6.20, 6.26, 6.33, 8.22, 8.28, 9.27, 10.48, 11.47
3.2differentiate clearly between giving examples that support a conjecture and giving a proof of the conjecture / pp. 1.23, 1.26, 1.28, 1.34, 1.44, 2.5-2.6, 2.37, 3.6, 3.13, 3.27-3.28, 3.31, 3.36, 4.31, 4.33, 4.40, 5.13, 5.27, 5.29, 5.35, 5.40, 6.12, 6.18-6.19, 6.32, 9.11, 9.42, 11.37-11.38, 11.47, 11.51
3.3support the conjecture and conclusion with logical statements and arguments in both oral and written work appropriate to both purpose and audience / pp. 1.23, 1.26, 1.28, 1.34, 1.44, 2.5-2.6, 2.37, 3.6, 3.13, 3.27-3.28, 3.31, 3.36, 4.31, 4.33, 4.40, 5.13, 5.27, 5.29, 5.35, 5.40, 6.12, 6.18-6.19, 6.32, 9.11, 9.42, 11.37-11.38, 11.47, 11.51
3.4formulate generalizations of the results obtained and extend them to other areas of mathematics and other circumstances, including expressing the solution as a general rule / pp. 1.44-1.63, 2.47-2.67, 3.48-3.63, 4.36-4.48, 5.39-5.53, 6.44-6.59, 7.48-7.63, 8.37-8.53, 9.48-9.61, 10.54-10.72, 11.64-11.81

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