MATHEMATICS
STANDARDS AND PROGRESS INDICATORS
STANDARD 4.1 ALL STUDENTS WILL DEVELOP THE ABILITY TO POSE AND SOLVE MATHEMATICAL PROBLEMS IN MATHEMATICS, OTHER DISCIPLINES, AND EVERYDAY EXPERIENCES.
Descriptive Statement: Problem posing and problem solving involve examining situations that arise in mathematics and other disciplines and in common experiences, describing these situations mathematically, formulating appropriate mathematical questions, and using a variety of strategies to find solutions. By developing their problem-solving skills, students will come to realize the potential usefulness of mathematics in their lives.
Cumulative Progress Indicators
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.
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.
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.
Descriptive Statement: Communication
of mathematical ideas will help students clarify and solidify their understanding
of mathematics. By sharing their mathematical understandings in written
and oral form with their classmates, teachers, and parents, students develop
confidence in themselves as mathematics reamers and enable teachers to
better monitor their progress.
Cumulative Progress Indicators
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 DISCIPLINE AND IN LIFE.
Descriptive Statement: Making connections enables
students to see relationships between different topics, and to draw on
those relationships in future study. This applies within mathematics,
so that students can translate readily between fractions and decimals,
or between algebra and geometry; to other content areas, so that students
understand how mathematics is used in the sciences, the social sciences,
and the arts; and to the everyday world, so that students can connect school
mathematics to daily life.
Cumulative Progress Indicators
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.
Descriptive Statement: Mathematical reasoning is the critical skill that enables a student to make use of all other mathematical skills. With the development of mathematical reasoning, students recognize that mathematics makes sense and can be understood. They learn how to evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize how those solutions can be applied. Mathematical reasoners are able to reflect on solutions to problems and determine whether or not they make sense. They appreciate the pervasive use and power of reasoning as a part of mathematics.
Cumulative Progress Indicators
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.
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, MANIPULATIVE,, AND OTHER MATHEMATICAL TOOLS TO ENHANCE MATHEMATICAL THINKING, UNDERSTANDING, AND POWER.
Descriptive Statement: Calculators, computers, manipulative, and other mathematical tools need to be used by students in both instructional and assessment activities. These tools should be used, not to replace mental math and paper-and-pencil computational skills, but to enhance understanding of mathematics and the power to use mathematics. Historically, people have developed and used manipulative (such as fingers, base ten blocks, geoboards, and algebra tiles) and mathematical devices (such as protractors, coordinate systems, and calculators) to help them understand and develop mathematics. Students should explore both new and familiar concepts with calculators and computers, but should also become proficient in using technology as it is used by adults, that is, for assistance in solving real-world problems.
Cumulative Progress Indicators
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 4.8 ALL STUDENTS WILL UNDERSTAND, SELECT, AND APPLY VARIOUS METHODS OF PERFORMING NUMERICAL OPERATIONS.
Descriptive Statement: Numerical operations are an essential part of the mathematics curriculum. Students must be able to select and apply various computational methods, including mental math, estimation, paper-and-pencil techniques, and the use of calculators. Students must understand how to add, subtract, multiply, and divide whole numbers, fractions, and others kinds of numbers. With calculators that perform these operations quickly and accurately, however, the instructional emphasis now should be on understanding the meanings and uses of the operations, and on estimation and mental skills, rather than solely on developing paper-and-pencil skills.
Cumulative Progress Indicators
8. Extend their understanding and use of arithmetic
operations to fractions, decimals, integers, and rational numbers.
10. Develop, apply, and explain procedures for computation
and estimation with whole numbers, fractions, decimals, integers, and rational
numbers.
STANDARD 4.9 ALL STUDENTS WILL DEVELOP AN UNDERSTANDING OF AND WILL USE MEASUREMENT TO DESCRIBE AND ANALYZE PHENOMENA,
Descriptive Statement: Measurement helps describe our
world using numbers. We use numbers to describe simple things like
length, weight, and temperature, but also complex things such as pressure,
speed, and brightness. An understanding of how we attach numbers
to those phenomena, familiarity with common measurement units like inches,
liters, and miles per hour, and a practical knowledge of measurement tools
and techniques are critical for students' understanding of the world around
them.
Cumulative Progress Indicators
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.
9. Determine the degree of accuracy needed in a given
situation and choose units accordingly.
13. Convert measurement units from one form
to another, and carry out calculations that involve various units of measurement.
14. Understand and apply measurement in their
own lives and in other subject areas.
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.
Descriptive Statement: Algebra is a language used to express mathematical relationships. Students need to understand how quantities are related to one another, and how algebra can be used to concisely express and analyze those relationships. Modem technology provides tools for supplementing the traditional focus on algebraic techniques, such as solving equations, with a more visual perspective, with graphs of equations displayed on a screen. Students can then focus on understanding the relationship between the equation and the graph, and on what the graph represents in a real-life situation.
Cumulative Progress Indicators
5..Understand and use variables, expressions, equations,
and inequalities.
2. Represent situations and number patterns with concrete
materials, tables, graphs, verbal rules, and standard algebraic notation.
7. Use graphing techniques on a number line
to model both absolute value and arithmetic operations.
8. Analyze tables and graphs to identify properties
and relationships.
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.
11. Explore linear equations through the use of calculators,
computers, and other technology.
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,
Descriptive Statement: Discrete mathematics is the branch of mathematics that deals with arrangements of distinct objects. It includes a wide variety of topics and techniques that arise in everyday life, such as how to find the best route from one city to another, where the objects are cities arranged on a map. It also includes how to count the number of different combinations of toppings for pizzas, how best to schedule a list of tasks to be done, and how computers store and retrieve arrangements of information on a screen. Discrete mathematics is the mathematics used by decision-makers in our society, from workers in government to those in health care, transportation, and telecommunications. Its various applications help students see the relevance of mathematics in the real world.
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.
8. Experiment with iterative and recursive processes,
with the aid of calculators and computers.
9. Explore methods for storing, processing,
and communicating information.
STANDARD 4.16 ALL STUDENTS WILL DEMONSTRATE HIGH LEVELS
OF MATHEMATICAL THOUGHT THROUGH EXPERIENCES WHICH EXTEND BEYOND TRADITIONAL
COMPUTATION, ALGEBRA, AND GEOMETRY.
Descriptive Statement: High expectations for all students
form a critical part of the learning environment. The belief of teachers,
administrators, and parents that a student can and will succeed in mathematics
often makes it possible for that student to succeed. Beyond that,
this standard calls for a commitment that all students will be continuously
challenged and enabled to go as far mathematically as they can.
SCIENCE
STANDARDS AND PROGRESS INDICATORS
STANDARD 5.1 ALL STUDENTS WILL LEARN TO IDENTIFY SYSTEMS OF INTERACTING COMPONENTS AND UNDERSTAND HOW THEIR INTERACTIONS COMBINE TO PRODUCE THE OVERALL BEHAVIOR OF THE SYSTEM.
Descriptive Statement: The natural world and the world built by humans both provide examples of systems where interacting parts work together as a whole. This standard asks students to analyze, understand, and design systems of integrating parts.
Cumulative Progress Indicators
4. Describe components of a system and how they
influence one another.
5. Recognize that most systems are components
of larger systems and that the output of one component can become the input
to other components.
6. Disassemble and reassemble the components
of a system, analyzing how they interact with each other.
STANDARD 5.2 ALL STUDENTS WILL DEVELOP PROBLEM-SOLVING, DECISION-MAKING, AND INQUIRY SKILLS REFLECTED BY FORMULATING USABLE QUESTIONS AND HYPOTHESES, PLANNING EXPERIMENTS, CONDUCTING SYSTEMATIC OBSERVATIONS, INTERPRETING AND ANALYZING DATA, DRAWING CONCLUSIONS, AND COMMUNICATING RESULTS.
Descriptive Statement: Students best learn science by doing science. Science is not merely a collection of facts and theories but a process, a way of thinking about and investigating the world in which we live. This standard addresses those skills that are used by scientists as they discover and explain the physical universe - skills that are an essential and ongoing part of learning science.
Cumulative Progress Indicators
6. Identify problems that can be solved by conducting
experiments.
7. Design and conduct experiments incorporating
the use of a control.
8. Collect and organize data to support the
results of an experiment.
9. Communicate experimental findings using words,
charts, graphs, pictures, and diagrams.
10. Evaluate the strengths and weaknesses of
claims, arguments, and data.
11. Assess the risks and benefits associated
with alternative actions.
STANDARD 5.4 ALL STUDENTS WILL DEVELOP AN UNDERSTANDING OF TECHNOLOGY AS AN APPLICATION OF SCIENTIFIC PRINCIPLES.
Descriptive Statement: Understanding the unique interdependence of science and technology is an important goal of science education. This standard is an attempt to show students how the application of scientific knowledge can be used to improve the human condition and how technological development affects the quality of life.
Cumulative Progress Indicators
4. Find and report on examples of how technology helps people.
8. Explain how engineers and others apply scientific
knowledge to solve practical problems.
9. Compare the advantages and disadvantages
of alternative solutions to practical problems.
STANDARD 5.5 ALL STUDENTS WILL INTEGRATE MATHEMATICS
AS A TOOL FOR
PROBLEM-SOLVING IN SCIENCE, AND AS A MEANS OF EXPRESSING
AND/OR MODELING SCIENTIFIC THEORIES.
Descriptive Statement: Galileo is credited with asserting
that "Mathematics is the language with which God wrote the Universe." Science
cannot be practiced or learned without appreciation of the role of mathematics
in discovering and expressing natural laws. This standard recognizes
the need for students to fully integrate mathematics skills with their
learning of science.
Cumulative Progress Indicators
1. Judge whether estimates, measurements, and
computations of quantities are reasonable.
2. Use a variety of measuring instruments, emphasizing
appropriate units.
3. Use mathematical skills and concepts in ordering,
counting, identifying, measuring, and describing.
4. Use tables and graphs to represent and interpret
data.
5. Recognize and comprehend the orders of magnitude
associated with large and small physical quantities.
6. Express experimental data in several equivalent
forms such as integers, fractions, decimals, and percents.
7. Infer mathematical relationships among variables
using graphs, tables, and charts.
8. Express the output units of the calculation
in terms of the input units.
9. Select appropriate measuring instruments
based on the degree of precision needed.
STANDARD 5.8 ALL STUDENTS WILL GAIN AN UNDERSTANDING
OF THE STRUCTURE AND BEHAVIOR OF MATTER.
Descriptive Statement: Exploring the nature of matter and energy is essential to an understanding of the physical universe. This standard leads students from their experiences with the states and properties of matter, to the development of models of the atom and the underlying principles of chemistry.
Cumulative Progress Indicators
4. Identify characteristic properties of matter,
and use one or more of those properties to separate a mixture of substances.
5. Show how substances can react with each other
to form new substances having characteristic properties different from
those of the original substances.
6. Know that all matter is made up of atoms
that may join together to form molecules, and that the state of matter
is determined by the arrangement and motion of the atoms or molecules.
7. Explain how atoms are rearranged when substances
react, but that the total number of atoms and the total mass of the newly
formed substances remains the same as that of the original substances.
STANDARD 5.9 ALL STUDENTS WILL GAIN AN UNDERSTANDING OF NATURAL LAWS AS THEY APPLY TO MOTION, FORCES, AND ENERGY TRANSFORMATIONS.
Descriptive Statement: Basic principles of physics emerge in this standard, where the study of force and motion leads students to the concept of energy. All forms of energy are introduced and investigated, and principles of transformation and laws of conservation are developed.
Cumulative Progress Indicators
3. Recognize that some forces are invisible and
can act at a distance.
4. Investigate sources of heat and show how
heat can be transferred from one place to another.
5. Investigate sources of light and show how
light behaves when it strikes different objects.
11. Describe the various forms of energy, including
heat, light, sound, chemical, nuclear,
mechanical, and electrical energy, and that
energy can be transformed from one form to another.
12. Explain how heat flows through materials
or across space from warmer objects to cooler ones until both objects are
at the same temperature.
13. Explain that the sun is a major source of
the earth's energy and that energy is emitted in various forms, including
visible light, infrared and ultraviolet radiation.
14. Show how light is reflected, refracted,
or absorbed when it interacts with matter and how colors appear as a result
of this interaction.
15. Show how vibrations in materials can generate
waves which can transfer energy from
one place to another.
STANDARD 5.10 ALL STUDENTS WILL GAIN AN UNDERSTANDING OF THE STRUCTURE, DYNAMICS, AND GEOPHYSICAL SYSTEMS OF THE EARTH.
Descriptive Statement: The study of science should include a study of the planet Earth and its relationship to the rest of the universe. This standard describes what students should know about the composition of the earth and the forces that shape it, while Standard 5.11 describes what students should know about astronomy and space science.
Cumulative Progress Indicators
1. Recognize and demonstrate the use of different
kinds of maps.
3. Identify major sources and uses of water,
discussing the forms in which it appears.
4. Collect and record weather data to identify
existing weather conditions, and recognize how those conditions affect
our daily lives.
9. Monitor local weather conditions and changes
in the atmosphere that lead to weather systems.
STANDARD 5.11 ALL STUDENTS WILL GAIN AN UNDERSTANDING OF THE ORIGIN, EVOLUTION, AND STRUCTURE OF THE UNIVERSE.
Descriptive Statement: The study of science should include a study of the planet earth and its relationship to the rest of the universe. This standard describes what students should know about astronomy and space science, while Standard 5. 10 describes what students should know about the composition of the earth and the forces that shape it.
Cumulative Progress Indicators
5. Explain how naturally occurring events on
earth are related to the positions of the sun and earth
STANDARD 5.12 ALL STUDENTS WILL DEVELOP AN UNDERSTANDING
OF THE ENVIRONMENT AS A SYSTEM OF INTERDEPENDENT COMPONENTS AFFECTED BY
HUMAN ACTIVITY AND NATURAL PHENOMENA.
Descriptive Statement: Creating an awareness of the need to protect and preserve natural resources is a goal of science education. This standard calls for students to develop knowledge of environmental issues. including management of natural resources, production and use of energy, waste management, and the interdependence of ecosystems.
Cumulative Progress Indicators
1. Investigate the interdependence of living
things and their environment.
2. Explain how meeting human requirements affects
the environment.
3. Recognize that natural resources are not
always renewable.
4. Evaluate the impact of personal and societal
activities on the local and global environment.
5. Compare and contrast practices that affect
the use and management of natural resources.
6. Recognize that individuals and groups may
have differing points of view on environmental issues.
7. Analyze the components of various ecosystems
and the effects of those components on organisms.
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