| Standard 4.1:
All Students Will Develop The
Ability To Pose And Solve Mathematical Problems In
Mathematics, Other Disciplines, And Everyday
Experiences |
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10. Use discovery-oriented,
inquiry-based, and problem-centered approaches to
investigate and understand mathematical content
appropriate to the middle grades. |
|
11. Recognize, formulate, and solve
problems arising from mathematical situations,
everyday experiences, and applications to other
disciplines. |
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12. Construct and use concrete,
pictorial, symbolic, and graphical models to
represent problem situations and effectively apply
processes of mathematical modeling in mathematics and
other areas. |
|
13. Recognize that there may be multiple
ways to solve a problem, weigh their relative merits,
and select and use appropriate problem-solving
strategies. |
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14. Persevere in developing alternative
problem-solving strategies if initially selected
approaches do not work. |
| Standard 4.2:
All Students Will Communicate
Mathematically Through Written, Oral, Symbolic, And
Visual Forms Of Expression |
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6. Identify and explain key mathematical
concepts and model situations using geometric and
algebraic methods. |
|
7. Use mathematical language and symbols
to represent problem situations, and recognize the
economy and power of mathematical symbolism and its
role in the development of mathematics. |
|
8. Analyze, evaluate, and explain
mathematical arguments and conclusions presented by
others. |
| Standard 4.3:
All Students Will Connect
Mathematics To Other Learning By Understanding The
Interrelationships Of Mathematical Ideas And The
Roles That Mathematics And Mathematical Modeling Play
In Other Disciplines And In Life |
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8. Recognize and apply unifying concepts
and processes which are woven throughout mathematics. |
|
9. Use the process of mathematical
modeling in mathematics and other disciplines, and
demonstrate understanding of its methodology,
strengths, and limitations. |
|
10. Apply mathematics in their daily
lives and in career-based contexts. |
|
11. Recognize situations in other
disciplines in which mathematical models may be
applicable, and apply appropriate models,
mathematical reasoning, and problem solving to those
situations. |
| Standard 4.4:
All Students Will Develop
Reasoning Ability And Will Become Self-Reliant,
Independent Mathematical Thinkers |
|
6. Make conjectures based on observation
and information, and test mathematical conjectures
and arguments. |
|
7. Justify, in clear and organized form,
answers and solution processes in a variety of
problems. |
|
8. Follow and construct
logical arguments, and judge their validity.
|
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9. Recognize and use deductive and
inductive reasoning in all areas of mathematics. |
|
10. Utilize mathematical reasoning skills
in other disciplines and in their lives. |
|
11. Use reasoning rather than relying on
an answer-key to check the correctness of solutions
to problems. |
| Standard 4.5:
All Students Will Regularly And
Routinely Use Calculators, Computers, Manipulatives,
And Other Mathematical Tools To Enhance Mathematical
Thinking, Understanding, And Power |
|
6. Use a variety of technologies to
evaluate and validate problem solutions, and to
investigate the properties of functions and their
graphs. |
|
7. Use computer spreadsheets and graphing
programs to organize and display quantitative
information and to investigate properties of
functions. |
| Standard 4.6:
All Students Will Develop Number
Sense And An Ability To Represent Numbers In A
Variety Of Forms And Use Numbers In Diverse
Situations |
|
10. Understand money notations, count and
compute money, and recognize the decimal nature of
United States currency. |
|
11. Extend their understanding of the
number system by constructing meanings for integers,
rational numbers, percents, exponents, roots,
absolute values, and numbers represented in
scientific notation. |
|
12. Develop number sense necessary for
estimation. |
|
13. Expand the sense of magnitudes of
different number types to include integers, rational
numbers, and roots. |
|
14. Understand and apply ratios,
proportions, and percents in a variety of situations. |
|
15. Develop and use order relations for
integers and rational numbers. |
|
16. Recognize and describe patterns in
both finite and infinite number sequences involving
whole numbers, rational numbers, and integers. |
|
17. Develop and apply number theory
concepts, such as primes, factors, and multiples, in
real-world and mathematical problem situations. |
|
18. Investigate the relationships among
fractions, decimals, and percents, and use all of
them appropriately. |
|
19. Identify, derive, and compare
properties of numbers. |
| Standard 4.7:
All Students Will Develop Spatial
Sense And An Ability To Use Geometric Properties And
Relationships To Solve Problems In Mathematics And In
Everyday Life |
|
11. Relate two-dimensional and
three-dimensional geometry using shadows,
perspectives, projections and maps. |
|
12. Understand and apply the concepts of
symmetry, similarity and congruence. |
|
13. Identify, describe, compare, and
classify plane and solid geometric figures. |
|
14. Understand the properties of lines
and planes, including parallel and perpendicular
lines and planes, and intersecting lines and planes
and their angles of incidence. |
|
15. Explore the relationships among
geometric transformations (translations, reflections,
rotations, and dilations), tessellations (tilings),
and congruence and similarity. |
|
16. Develop, understand, and apply a
variety of strategies for determining perimeter,
area, surface area, angle measure, and volume. |
|
17. Understand and apply the Pythagorean
Theorem. |
|
18. Explore patterns produced by
processes of geometric change, relating iteration,
approximation, and fractals. |
|
19. Investigate, explore, and describe
geometry in nature and real-world applications, using
models, manipulatives, and appropriate technology. |
| Standard 4.8:
All Students Will Understand,
Select, And Apply Various Methods Of Performing
Numerical Operations |
|
8. Extend their understanding and use of
arithmetic operations to fractions, decimals,
integers, and rational numbers. |
|
9. Extend their understanding of basic
arithmetic operations on whole numbers to include
powers and roots. |
|
10. Develop, apply, and explain
procedures for computation and estimation with whole
numbers, fractions, decimals, integers, and rational
numbers. |
|
11. Develop, apply, and explain methods
for solving problems involving proportions and
percents. |
|
12. Understand and apply the standard
algebraic order of operations. |
| Standard 4.9: All
Students Will Develop An Understanding Of And Will
Use Measurement To Describe And Analyze Phenomena. |
|
7. Use estimated and actual measurements
to describe and compare phenomena. |
|
8. Read and interpret various scales,
including those based on number lines and maps. |
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9. Determine the degree of accuracy
needed in a given situation and choose units
accordingly. |
|
10. Understand that all measurements of
continuous quantities are approximate. |
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11. Develop formulas and procedures for
solving problems related to measurement. |
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12. Explore situations involving
quantities which cannot be measured directly or
conveniently. |
|
13. Convert measurement units from one
form to another, and carry out calculations that
involve various units of measurement. |
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14. Understand and apply measurement in
their own lives and in other subject areas. |
|
15 Understand and explain the impact of
the change of an object's linear dimensions on its
perimeter, area, or volume. |
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16. Apply their knowledge of measurement
to the construction of a variety of two- and
three-dimensional figures. |
| Standard 4.10:
All Students Will Use A Variety
Of Estimation Strategies And Recognize Situations In
Which Estimation Is Appropriate |
|
8. Develop, apply, and explain a variety
of different estimation strategies in problem
situations involving quantities and measurement. |
|
9. Use equivalent representations of
numbers such as fractions, decimals, and percents to
facilitate estimation. |
| Standard 4.11:
All Students Will Develop An
Understanding Of Patterns, Relationships, And
Functions And Will Use Them To Represent And Explain
Real-World Phenomena |
|
7. Represent and describe mathematical
relationships with tables, rules, simple equations,
and graphs. |
|
8. Understand and describe the
relationships among various representations of
patterns and functions. |
|
9. Use patterns, relationships, and
functions to model situations and to solve problems
in mathematics and in other subject areas. |
|
10. Analyze functional relationships to
explain how a change in one quantity results in a
change in another. |
|
11. Understand and describe the general
behavior of functions. |
|
12. Use patterns, relationships, and
linear functions to model situations in mathematics
and in other areas. |
|
13. Develop, analyze, and explain
arithmetic sequences. |
| Standard 4.12:
All Students Will Develop An
Understanding Of Statistics And Probability And Will
Use Them To Describe Sets Of Data, Model Situations,
And Support Appropriate Inferences And Arguments |
|
9. Generate, collect, organize, and
analyze data and represent this data in tables,
charts, and graphs. |
|
10. Select and use appropriate graphical
representations and measures of central tendency
(mean, mode and median) for sets of data. |
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11. Make inferences and formulate and
evaluate arguments based on data analysis and data
displays. |
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12. Use lines of best fit to interpolate
and predict from data. |
|
13. Determine the probability of a
compound event. |
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14. Model situations involving
probability, such as genetics, using both simulations
and theoretical models. |
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15. Use models of probability to predict
events based on actual data. |
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16. Interpret probabilities as ratios and
percents. |
| Standard 4.13:
All Students Will Develop An Understanding Of
Algebraic Concepts And Processes And Will Use Them To
Represent And Analyze Relationships Among Variable
Quantities And To Solve Problems |
|
5. Understand and use variables,
expressions, equations, and inequalities. |
|
6. Represent situations and number
patterns with concrete materials, tables, graphs,
verbal rules, and standard algebraic notation. |
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7. Use graphing techniques on a number
line to model both absolute value and arithmetic
operations. |
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8. Analyze tables and graphs to identify
properties and relationships. |
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9. Understand and use the rectangular
coordinate system. |
|
10. Solve simple linear equations using
concrete, informal, and graphical methods, as well as
appropriate paper-and-pencil techniques. |
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11. Explore linear equations through the
use of calculators, computers, and other technology. |
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12. Investigate inequalities and
nonlinear equations informally. |
|
13. Draw freehand sketches of, and
interpret, graphs which model real phenomena. |
| Standard 4.14:
All Students Will Apply The
Concepts And Methods Of Discrete Mathematics To Model
And Explore A Variety Of Practical Situations. |
|
6. Use systematic listing, counting, and
reasoning in a variety of different contexts. |
|
7. Recognize common discrete mathematical
models, explore their properties, and design them for
specific situations. |
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8. Experiment with iterative and
recursive processes, with the aid of calculators and
computers. |
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9. Explore methods for storing,
processing, and communicating information. |
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10. Devise, describe, and test algorithms
for solving optimization and search problems. |
| Standard 4.15:
All Students Will Develop An
Understanding Of The Conceptual Building Blocks Of
Calculus And Will Use Them To Model And Analyze
Natural Phenomena |
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4. Recognize and express the difference
between linear and exponential growth. |
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5. Develop an understanding of infinite
sequences that arise in natural situations. |
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6. Investigate, represent, and use
non-terminating decimals. |
|
7. Represent, analyze, and predict
relations between quantities, especially quantities
changing over time. |
|
8. Approximate quantities with increasing
degrees of accuracy. |
|
9. Understand and use the concept of
significant digits. |
|
10. Develop informal ways of
approximating the surface area and volume of familiar
objects, and discuss whether the approximations make
sense. |
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11. Express mathematically and explain
the impact of the change of an object's linear
dimensions on its surface area and volume. |