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Mathematics Standards and Benchmarks
Mathematics Standard 1:
Uses a variety of strategies in the problem-solving process
Level III (Grade 6-8)
- Understands how to break a complex problem into simpler parts or use a similar problem type to solve a problem
- Uses a variety of strategies to understand problem-solving situations and processes (e.g., considers different strategies and approaches to a problem, restates problem from various perspectives)
- Formulates a problem, determines information required to solve the problem, chooses methods for obtaining this information, and sets limits for acceptable solutions
- Represents problem situations in and translates among oral, written, concrete, pictorial, and graphical forms
- Generalizes from a pattern of observations made in particular cases, makes conjectures, and provides supporting arguments for these conjectures (i.e., uses inductive reasoning)
- Constructs informal logical arguments to justify reasoning processes and methods of solutions to problems (i.e., uses informal deductive methods)
- Understands the role of written symbols in representing mathematical ideas and the use of precise language in conjunction with the special symbols of mathematics
- Uses a variety of reasoning processes (e.g., reasoning from a counter example, using proportionality) to model and to solve problems
Level IV (Grade 9-12)
- Uses a variety of strategies (e.g., identify a pattern, use equivalent representations) to understand new mathematical content and to develop more efficient solution methods or problem extensions
- Constructs algorithms for multi-step and non-routine problems
- Constructs logical verifications or counter examples to test conjectures and to justify algorithms and solutions to problems (i.e., uses deductive reasoning)
- Uses formal mathematical language and notation to represent ideas, to demonstrate relationships within and among representation systems, and to formulate generalizations
- Understands the components of mathematical modeling (i.e., problem formulation, mathematical model, solution within the model, interpretation of solution within the model, validation in original real-world problem situation)
Mathematics Standard 6:
Understands and applies basic and advanced concepts of statistics and data analysis
Level III (Grade 6-8)
- Reads and interprets data in charts, tables, plots (e.g., stem-and-leaf, box-and-whiskers, scatter), and graphs (e.g., bar, circle, line)
- Uses data and statistical measures for a variety of purposes (e.g., formulating hypotheses, making predictions, testing conjectures)
- Understands faulty arguments, common errors, and misleading presentations of data
Level IV (Grade 9-12)
- Understands the concept of correlation (e.g., the difference between a "true" correlation and a "believable" correlation; when two variables are correlated)
- Understands how the reader's bias, measurement error, and display distortion can affect the interpretation of data
- Understands how concepts of representativeness, randomness, and bias in sampling can affect experimental outcomes and statistical interpretations
- Understands that making an inference about a population from a sample always involves uncertainty and the role of statistics is to estimate the size of that uncertainty
Mathematics Standard 7:
Understands and applies basic and advanced concepts of probability
Level III (Grade 6-8)
- Determines probability using mathematical/theoretical models (e.g., table or tree diagram, area model, list, counting procedures, sample space)
- Understands how predictions are based on data and probabilities (e.g., the difference between predictions based on theoretical probability and experimental probability)
- Understands that the measure of certainty in a given situation depends on a number of factors (e.g., amount of data collected, what is known about the situation, how current data are)
- Understands the relationship between the numerical expression of a probability (e.g., fraction, percentage, odds) and the events that produce these numbers
Level IV (Grade 9-12)
- Understands the concepts of independent and dependent events and how they are related to compound events and conditional probability
- Understands the properties of the normal curve (i.e., the graph used to approximate the distribution of data for many real-world phenomena) and how the normal curve can be used to answer questions about sets of data
Mathematics Standard 9:
Understands the general nature and uses of mathematics
Level III (Grade 6-8)
- Understands that mathematicians often represent real things using abstract ideas like numbers or lines; they then work with these abstractions to learn about the things they represent
Level IV (Grade 9-12)
- Understands that mathematics is the study of any pattern or relationship, but natural science is the study of those patterns that are relevant to the observable world
- Understands that theories in mathematics are greatly influenced by practical issues; real-world problems sometimes result in new mathematical theories and pure mathematical theories sometimes have highly practical applications
- Understands that mathematics provides a precise system to describe objects, events, and relationships and to construct logical arguments
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Selected Standards and Benchmarks
used by permission:
Copyright
2003 McRel
Mid-continent Research for
Education and Learning
2550 S. Parker Road, Suite 500
Aurora, CO 80014
Telephone: (303) 337-0990
www.mcrel.org/standards-benchmarks
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