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STANDARDS PAGE REFERENCES
M1 ARITHMETIC AND NUMBER CONCEPTS/NUMBER AND OPERATION CONCEPTS
The student produces evidence that demonstrates understanding of number and operation concepts, that is, the student:
M1a Uses addition, subtraction, multiplication, division, exponentiation, and root- 19, 28-29, 55, 58-61, 90, 101-102, 130-131, 138, 144, 164-165, 168, 171-173,
M1b Understands and uses operations such as opposite, reciprocal, raising to a
power, taking a root, and taking a logarithm.
M1c Has facility with the mechanics of operation as well as understanding of their typical meaning and uses in applications.
M1d Understands and uses number systems: natural, integer, rational, and real.
M1e Represents numbers in decimal or fraction form and in scientific notation, and graphs numbers on the number line and number pairs in the coordinate plane.
M1f Compares numbers using order relations, differences, ratios, proportions, percents, and proportional change.
M1g Carries out proportional reasoning in cases involving part-whole relationships and in cases involving expansions and contractions.
M1h Understands dimensionless numbers, such as proportions, percents, and multiplicative factors, as well as numbers with specific units of measure, such
numbers with length, time, and rate units.
19, 27, 60, 64, 133-136, 189, 199-201, 203, 206-209, 213-223, 226-240, 257-
259, 263, 284-285, 292-297, 304, 346-347
64, 102, 137-156, 444
15, 18-19, 20-23, 27-52, 59, 61, 63, 70, 76-77, 80, 88-89, 95, 114, 133-134,
136, 158-159, 168, 214, 223, 397-399, 421
M1i Carries out counting procedures such as those involving gets (unions and intersections) and arrangements (permutations and combinations).
M1 j Uses concepts such as prime, relatively prime, factor, divisor, multiple, and
divisibility in solving problems involving integers.
M1k Uses a scientific calculator effectively and efficiently in carrying out complex
483
55, 59-61, 130-131, 146-147, 223
55, 60, 133, 135, 146-149, 150-152, 160, 164-166, 223, 479
146-149, 151, 479, 509
146-147, 151, 154
104-105, 108, 144, 161-162, 164-165, 168, 281-285
M1l Recognizes and represents basic number patterns, such as patterns involving
Multiples, squares, or cubes.
161-162, 164-165, 168, 281, 285, 308, 348
M2 GEOMETRY AND MEASUREMENT CONCEPTS
The student produces evidence that demonstrates understanding of geometry and measurement concepts; that is, the student:
M2a Models situations geometrically to formulate and solve problems 15, 18, 21-22, 45, 58-59, 62, 73-75, 79, 88, 90-91, 93
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STANDARDS
M2b Works with two- and three-dimensional figures and their properties,
including polygons and circles, cubes and pyramids, and cylinders,
cones, and spheres.
M2c Uses congruence and similarity in describing relationships between
figures.
M2d Visualizes objects, paths, and regions in space, including intersections
and cross sections of three dimensional figures, and describes these
using geometric language.
M2e Knows, uses, and derives formulas for perimeter, circumference, area,
surface area, and volume of many types of figures.
M2f Uses the Pythagorean Theorem in many types of situations, and works
through more than one proof of this theorem.
M2g Works with similar triangles, and extends the ideas to include simple
uses of the three basic trigonometric functions.
M2h Analyzes figures in terms of their symmetries using, for example,
concepts of reflection, rotation, and translation.
M2i Compares slope (rise over run) and angle of elevation as measures of
steepness.
M2 j Investigates geometric patterns, including sequences of growing
shapes.
M2k Works with geometric measures of length, area, volume, and angle; and
non-geometric measures such as weight and time.
M2l Uses quotient measures, such as speed and density, that give “per unit”
amounts; and uses product measures, such as person-hours.
M2m Understanding the structure of standard measurement systems, both S1
and customary, including unit conversions and dimensional analysis.
M2n Solves problems involving scale, such as in maps and diagrams
M2o Represents geometric curves and graphs of functions in standard
coordinate systems.
M2p Analyzes geometric figures and proves simple things about them using
deductive methods.
M2q Explores geometry using computer programs such as CAD software.
sketchpad programs for LOGO.
3
PAGE REFERENCES
11, 25-29, 32, 43, 47-48, 57, 65, 75, 79-81, 83-84, 173
19, 24, 26-27, 53, 117
7-29, 33-46, 50-51, 56-97
374, 406-407, 518
84, 98-99, 107-108, 349
19, 21, 24-27, 29, 53, 87, 103-111, 117-118, 120-121
74-75, 100, 447
53, 519
15, 19-22, 25, 29, 46-47, 52-54, 59-61, 63, 76-77, 80, 84, 88-89, 91, 94-95,
98-103, 109, 112, 116, 158, 397-399, 421
386, 397-399, 420, 424, 429
15, 19-22, 52-53, 59-61, 63, 76-77, 80, 84, 88-89, 91, 94-95, 98-103, 110-
112, 114, 116, 158, 397-399, 406-407, 412, 421, 445
17, 20-22, 24, 48, 50, 52-53, 55, 81, 90, 95, 114, 416
105-108, 410-412, 426-427, 429, 431-438, 440-442, 449, 461, 464-465, 471
489
17, 57, 349
45, 76, 446

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STANDARDS
The student produces evidence that demonstrates understanding of function and algebra
Concepts; that is the student:
M3 FUNCTION AND ALGEBRA CONCEPTS
M3a Models given situations with formulas and functions, and interprets given formulas
and functions in terms of situations.
M3b Describes, generalizes, and uses basic types of functions; linear, exponential.
power, rational, square and square and square root, and cube and cube root.
M3c Utilizes the concepts of slope, evaluation, and inverse in working with functions
M3d Works with rates of many kinds, expressed numerically, symbolically, and
62, 101, 131, 149, 152, 15i8-159, 161-162, 164-165, 168, 174,
343, 356, 362-363, 377-380, 421, 461, 489, 504
94-144, 164-166, 168, 356-367, 461, 483
421
PAGE REFERENCES
140, 386, 397-399, 420, 424, 429, 437, 535
graphically.
M3e Represents constant rates as the slope of a straight line graph, and interprets slope
as the amount of one quantity (y) per unit amount of another (x).
M3f Understands and uses linear functions as a mathematical representation of
proportional relationships.
M3g Uses arithmetic sequences and geometric sequences and their sums, and sees these
as the discrete forms of linear and exponential functions, respectively.
M3h Defines, uses, and manipulates expressions involving variables, parameters,
Constants, and unknowns in work with formulas, functions, equations, and
inequalities.
M3I Represents functional relationships in formulas, tables, and graphs, and translates
between pairs of these.
M3j Solves equations symbolically, graphically, and numerically, especially linear,
quadratic, and exponential equations; and knows how to use the quadratic formula
for solving quadratic equations.
M3k Makes predictions by interpolating or extrapolating from given data or a given
graph.
M3l Understands the basic algebraic structure of number systems.
M2m Uses equations to represent curves such as lines, circles, and parabolas
421
60, 377
388, 342-343, 370, 385, 387, 424
28-29, 144, 149-152, 158-161, 164-165, 167-168, 277, 282, 340-
341, 356, 405, 454, 504-505
100-101, 104, 139-144, 146-150, 152-156, 160-162, 395, 421
152, 159, 161, 331, 377, 410-411, 416-419, 426-427, 461, 480,
505, 520
92, 132, 169, 155, 220, 354, 385-386, 391, 417, 480-482, 484,
509.
55, 70, 133, 135, 146-152, 160, 164-166, 223, 479
101, 395, 403, 405-406, 410-412, 418, 454, 456, 515
105, 107, 344, 350, 358-359, 364, 396-398, 410-412, 416-418,
432, 437, 442, 449-450, 471-474, 482, 489
149, 330, 340, 361, 364, 366, 389, 395-396, 431, 450, 489
M3n Uses technology such as graphics calculators to represent and analyze functions
and their graphs.
M3o Uses functions to analyze patterns and represent their structure.
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STANDARDS
M4 STATISTICS AND PROBABILITY CONCEPTS
The student demonstrates understanding of statistics and probability concepts; that is, the student:
M4a Organizes, analyzes, and displays single-variable data, choosing appropriate
frequency distributions, circle graphs, line plots, histograms, and summary
statistics.
PAGE REFERENCES
23, 202, 204, 206-207, 211, 213, 387, 391, 393, 399
M4b
M4c
Organizes, analyzes, and displays two-variable data using scatter plots, estimated
regression lines, and computer generated regression lines and correlation
Uses sampling techniques to draw inferences about large populations.
M4d Understands that making an inference about a population from a sample always
Involves uncertainty and that the role of statistics is to estimate the size of that
uncertainty.
94, 261-262, 279, 394, 409, 421, 423, 432, 442, 471-475, 479-
480, 484, 489-491
199-223, 226-227, 230-237, 252-253, 263-264, 310-313
200-210, 214, 230, 236-237, 261, 280
M4e Formulates hypotheses to answer a question and uses data to test hypotheses.
M4f Interprets representations of data, compares distributions of data, and critiques
conclusions and the use of statistics, both in school materials and in public
documents.
M4g Explores questions of experimental design, use of control groups, and reliability.
297, 300-310
138, 158-162, 208, 212-213, 223, 225-227, 235-236, 246, 250-
251, 256, 263, 273-275, 295-298, 301, 307
184-196, 306
184, 199, 201, 206-209, 228 M4h Creates and uses models of probabilistic situations and understands the role of
assumptions in this process.
M4i Uses concepts such as equally likely, sample space, outcome, and event in
analyzing situations involving chance.
M4j Constructs appropriate sample spaces, and applies the addition and multiplication
principles for probabilities.
M4k Uses the concept of a probability distribution to discuss whether an event is rare or
reasonably likely.
201-204, 209, 216-223, 235-237
209, 251-253
206, 208, 235-237, 292-293
M4l Chooses an appropriate probability model and uses it to arrive at a theoretical
M4m Uses relative frequencies based on empirical data to arrive at an experimental
probability for a chance event.
M4n Designs simulations including Monte Carlo simulations to estimate probabilities.
M4o Works with the normal distribution in some of its basic applications
207-209, 228, 251
201-204
23, 230, 321, 529, 534
529-531, 534
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STANDARDS PAGE REFERENCES
M5 PROBLEM SOLVING AND MATHEMATICAL REASONING
The student demonstrates problem solving by using mathematical concepts and skills to solve non-routine problems that do not lay out specific and detailed steps to follow, and solves problems that make demands on all three aspects of the solution processformulation, implementation, and conclusion.
Formulation
M5a The student participates in the formulation of problems; that is, given the
statement of a problem situation, the student:
 fills out the formulation of a definite problem that is to be solved;
 extracts pertinent information from the situation as a basis for working on the problem;
 asks and answers a series of appropriate questions in pursuit of a solution and
does so with minimal “scaffolding” in the form of detailed guiding questions.
130, 170, 588-589
130, 170, 588-589
130, 170, 588-589
Implementation
M5b The student makes the basic choices involved in planning and carrying out a
solution; that is, the student:
 chooses and employs effective problem solving strategies in dealing with
non-routine and multi-step problems;
 selects appropriate mathematical concepts and techniques from different areas
of mathematics and applies them to the solution of the problem;
 applies mathematical concepts to new situations within mathematics and uses
mathematics to model real world situations involving basic applications of
mathematics in the physical and biological sciences, the social sciences, and business.
Conclusion
M5c The student provides closure to the solution process through summary statements
And general conclusions; that is, the student:
 concludes a solution process with a useful summary of results;
 evaluates the degree to which the results obtained represent a good response to the initial problem;
 formulates generalizations of the results obtained;
 carries out extensions of the given problem to related problems.
68-69, 93-94, 113, 129, 190-191, 254, 291, 393, 453, 455, 470-474,
588-89
588-589
4-5, 124-127, 180-183, 316-319, 382-385, 400, 496-499, 554-557
170,588-589
588-589
170, 588-589
170, 588-589
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STANDARDS
M6 MATHEMATICAL SKILLS AND TOOLS
The student demonstrates fluency with basic and important skills by using these skills accurately and automatically, and demonstrates practical competence and persistence with other skills by using them effectively to accomplish a task, perhaps referring to notes, or books, perhaps working to reconstruct a method; that is, the student:
M6a Carries out numerical calculations and symbol manipulations effectively, using
mental computations, pencil and paper, or other technological aids, as appropriate.
M6b Uses a variety of methods to estimate the values, in appropriate units, of quantities
met in applications, and rounds numbers used in applications to an appropriate
degree of accuracy.
M6c Evaluates and analyzes formulas and functions of many kinds, using both pencil
and paper and more advance technology.
PAGE REFERENCES
19, 59-60, 62-63, 90, 101-102, 108-110, 129, 136, 138-139, 143-
144, 148-151, 158-159, 173, 207, 282-285, 356, 368-369, 421, 524
16, 21, 191, 214, 221, 236, 238, 240, 250, 263-264, 275-277, 279,
289, 293, 296, 298, 305, 387, 390, 421
84, 90, 101-102, 108-111, 130-131, 149, 152, 158-159, 161-162,
164-163, 174, 281-285, 339, 343-344, 357-358, 361, 364, 370, 374-
375, 408-409, 426-427, 438-439
87, 103, 106-108, 111, 115-121, 405 M6d Uses basic geometric terminology accurately, and deduces information about basic
geometric figures in solving problems.
M6e makes and uses rough sketches, schematic diagrams, or precise scale diagrams to
enhance a solution.
23-24, 45-47, 52, 55, 69, 75, 79, 88, 90-91, 524-526
M6f
M6g
scatter plots, regression lines, and histograms.
M6h
M6 i
Uses the number line and Cartesian coordinates in the plane and in space.
Creates and interprets graphs of many kinds, such as function graphs, circle graphs,
Sets up and solves equations symbolically (when possible) and graphically.
Knows how to use algorithms in mathematics, such as the Euclidean Algorithm
M6j Uses technology to create graphs or spreadsheets that contribute to the
understanding of a problem.
M6k Writes a simple computer program to carry out a computation or simulation to be
repeated many times.
M6l Uses tools such as rulers, tapes, compasses, and protractors in solving problems.
151, 435, 447-448, 548
23, 94, 105, 108, 344, 347, 363, 366, 370, 373, 375, 386-389, 393,
398, 404, 416-417, 449, 458, 464 –467, 505, 546-547
243, 340-342, 344, 356, 358, 412, 417, 419, 426-427, 439, 475
128-135
132, 150, 164, 168, 339, 350, 359, 421, 430, 437-439, 449-450,
454, 461, 469, 484-486, 505, 513, 521
23, 231, 534
18, 47, 53, 61, 93, 99-100, 104-105, 108, 150, 403-404
374, 445, 518 M6m Knows standard methods to solve basic problems and uses these methods in
approaching more complex problems.
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STANDARDS
M7 MATHEMATICAL COMMUNICATION
PAGE REFERENCES
The student uses the language of mathematics, its symbols, notation, graphs, and expressions, to communicate through reading, writing, speaking, and listening, and communicates about mathematics by describing mathematical ideas and concepts and explaining reasoning and results; that is the student:
M7a Is familiar with basic mathematical terminology, standard notation and use of
symbols, common conventions for graphing, and general features of effective
mathematical communication styles.
M7b Uses mathematical representations with appropriate accuracy, including numerical
tables, formulas, functions, equations, charts, graphs, and diagrams.
M7c Organizes work and presents mathematical procedures and results clearly,
systematically, succinctly, and correctly.
M7d Communicates logical arguments clearly, showing why a result makes sense and why
The reasoning is valid.
M7e Presents mathematical ideas effectively both orally and in writing.
20, 24, 30-31, 34, 38, 40-41, 45, 69, 95-97, 161, 171, 194, 294,
298, 335, 404, 430, 433, 478
7, 38-39, 44-45, 67-69, 141, 196-201, 214-218, 224, 230-231,
235-236, 239, 248-249, 273, 286, 366
14, 18, 38-39, 84, 150, 161, 169, 181, 205, 223, 235, 302, 333,
343, 520, 568
8-11, 69, 80-81, 85, 264, 591
7-11, 21-22, 24-25, 27, 29, 32, 35, 42, 70-71, 80-82, 87-89, 91,
93-94
10, 84, 115, 205, 302, 577 M7f Explains mathematical concepts clearly enough to be of assistance to those who
may be having difficulty with them.
M7g Writes narrative accounts of the history and process of work on a mathematical
problem or extended project
M7h Writes succinct accounts of the mathematical results obtained in a mathematical
problem or extended project, with diagrams, graphs, tables, and formulas integrated
into the text.
35-36, 181, 223, 295, 301-302, 347, 355-356, 508, 577
38-39, 84, 150, 161, 169, 223, 235, 302, 343
M7I Keeps narrative accounts of process separate from succinct accounts of results, and
realizes that doing so can enhance the effectiveness of each.
14, 161, 181, 205, 520, 568
M8 PUTTING MATHEMATICS TO WORK
The student conducts at least one large scale investigation or project each year drawn from the following kinds and, over the course of high school, conducts investigations or projects drawn from at least three of the kinds. A single investigation or project may draw on more than one kind.
M8a Data study, in which the student:
 carries out a study of data relevant to current civic, economic, scientific, health, or social issues;
236, 386-387
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STANDARDS
 uses methods of statistical inference to generalize from the data;
 prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.
268, 301
287, 301
PAGE REFERENCES
M8b Mathematical model of a physical system or phenomenon, in which the student:
 carries out a study of a physical system or phenomenon by constructing a
mathematical model based on functions to make generalizations about the structure of the
365, 374, 463-464, 484, 491, 588-589, 592-594
system;
 uses structural analysis (a direct analysis of the structure of the system) rather than numerical or statistical analysis (an analysis of data about the system);
 prepares a report that explains the purpose of the project, the organizational plan , and conclusions, and uses an appropriate balance of different ways of presenting information
365, 588-589, 592-594
588-589, 592-594
M8c Design of a physical structure, in which the student:
 creates a design for a physical structure;
 uses general mathematical ideas and techniques to discuss specifications for building the structure;
 prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.
113
113
319-332, 373, 593-594
M8d Management and planning analysis, in which the student:
 carries out a study of a business or public policy situation involving issues such as optimization, cost-benefit projections, and risks;
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STANDARDS
 uses decision rules and strategies both to analyze options and balance trade-offs; and brings in mathematical ideas that serve to generalize the analysis across different conditions;
 prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.
M8c Pure mathematics investigation, in which the student:
 carries out a mathematical investigation of a phenomenon or concept in pure mathematics; p;pp;’p’o
 uses methods of mathematical reasoning and justification to make generalizations about the phenomenon;
 prepares a report that explains the purpose of the project, the organizational plan, and conclusions, and uses an appropriate balance of different ways of presenting information.
M8f History of a mathematical idea, in which the student:
 carries out a historical study tracing the development of a mathematical concept and the people who contributed to it;
 includes a discussion of the actual mathematical content and its place in the curriculum of the present day.
 prepares a report that explains the purpose of the project, the organizational plan and conclusions, and uses an appropriate balance of different ways of presenting information.
324-339, 332-335, 353
PAGE REFERENCES
345
13, 82, 140, 142, 145-149, 153-155, 157, 163-164, 193, 295, 299, 443
128-129, 133, 137-144, 146-163, 298-299, 469, 507, 557, 587, 590
254, 286-287
10