STANDARD 4.1 ALL STUDENTS WILL DEVELOP THE ABILITY TO POSE AND SOLVE MATHEMATICAL PROBLEMS IN MATHEMATICS, OTHER DISCIPLINES, AND EVERYDAY EXPERIENCES.

Cumulative Progress Indicators

Building upon knowledge and skills gained in the preceding grades, and demonstrating continued
progress in Indicators 4, 5, 6, 7, and 8 above, by the end of Grade 8, students:

*  Use discovery-oriented, inquiry-based, and problem-centered approaches to investigate and understand mathematical content appropriate to the middle grades.
*  Recognize, formulate, and solve problems arising from mathematical situations, everyday experiences, and applications to other disciplines.
*  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.
*  Recognize that there may be multiple ways to solve a problem, weigh their relative merits, and select and use appropriate problem-solving strategies.
*  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.

   Cumulative Progress Indicators

Building upon knowledge and skills gained in the preceding grades, and demonstrating continued
progress in Indicators 1, 2, 3, 4, and 5 above, by the end of Grade 8, students:

* Identify and explain key mathematical concepts and model situations using geometric and algebraic methods.
*  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.
*  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.

Cumulative Progress Indicators

Building upon knowledge and skills gained in the preceding grades, and demonstrating continued
progress in Indicators 1, 2, 3, and 4 above, by the end of Grade 8, students:

*  Recognize and apply unifying concepts and processes which are woven throughout mathematics.
*  Use the process of mathematical modeling in mathematics and other disciplines, and demonstrate understanding of its methodology, strengths, and limitations.
*  Apply mathematics in their daily lives and in career-based contexts.
*  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.

Cumulative Progress Indicators

Building upon knowledge and skills gained in the preceding grades, and demonstrating continued
progress in Indicators 2, 3, and 5 above, by the end of Grade 8, students:

*  Make conjectures based on observation and information, and test mathematical conjectures and arguments.
*  Justify, in clear and organized form, answers and solution processes in a variety of problems.
*  Follow and construct logical arguments, and judge their validity.
*  Recognize and use deductive and inductive reasoning in all areas of mathematics.
*  Utilize mathematical reasoning skills in other disciplines and in their lives.
*  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.

Cumulative Progress Indicators

Building upon knowledge and skills gained in the preceding grades, and demonstrating continued
progress in Indicators 1, 2, 3, 4, and 5 above, by the end of Grade 8, students:

* Use a variety of technologies to evaluate and validate problem solutions, and to investigate the properties of functions and their graphs.
* Use computer spreadsheets and graphing programs to organize and display quantitative information and to investigate properties of functions.

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.

Cumulative Progress Indicators

Building upon knowledge and skills gained in the preceding grades, by the end of Grade 8,
students:

*   Relate two-dimensional and three-dimensional geometry using shadows, perspectives, projections and maps.

*   Identify, describe, compare, and classify plane and solid geometric figures.
*   Understand the properties of lines and planes, including parallel and perpendicular lines and planes, and intersecting lines and planes and their angles of incidence.
*   Develop, understand, and apply a variety of strategies for determining perimeter, area, surface area, angle measure, and volume.
*   Investigate, explore, and describe geometry in nature and real-world applications, using models, manipulative, and appropriate technology.

STANDARD 4.8 ALL STUDENTS WILL UNDERSTAND, SELECT, AND APPLY VARIOUS METHODS OF PERFORMING NUMERICAL OPERATIONS.

Cumulative Progress Indicators

Building upon knowledge and skills gained in the preceding grades, and demonstrating continued
progress in Indicator 6 above, by the end of Grade 8, students:
*  Extend their understanding and use of arithmetic operations to fractions, decimals, integers, and rational numbers.
*  Develop, apply, and explain procedures for computation and estimation with whole numbers, fractions, decimals, integers, and rational numbers.
*  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.

Cumulative Progress Indicators

Building upon knowledge and skills gained in the preceding grades, by the end of Grade 8,
students:

*  Use estimated and actual measurements to describe and compare phenomena.
* Read and interpret various scales, including those based on number lines and maps.
* Determine the degree of accuracy needed in a given situation and choose units accordingly.
* Understand that all measurements of continuous quantities are approximate.
*  Explore situations involving quantities which cannot be measured directly or conveniently.
*  Convert measurement units from one form to another, and carry out calculations that involve various units of measurement.
*  Understand and apply measurement in their own lives and in other subject areas.
*  Apply their knowledge of measurement to the construction of a variety of two- and three-dimensional figures.

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.
Cumulative Progress Indicators

Building upon knowledge and skills gained in the preceding grades, by the end of Grade 8,
students:
* Represent and describe mathematical relationships with tables, rules, simple equations, and graphs.
* Understand and describe the relationships among various representations of patterns
and functions.
* Use patterns, relationships, and functions to model situations and to solve problems in mathematics and in other subject areas.
*  Analyze functional relationships to explain how a change in one quantity results in a change in another.
*  Understand and describe the general behavior of functions.
*  Use patterns, relationships, and linear functions to model situations in mathematics and in other areas.

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.

Cumulative Progress Indicators

Building upon knowledge and skills gained in the preceding grades, by the end of Grade 8,
students:

*  Generate, collect, organize, and analyze data and represent this data in tables, charts, and graphs.
*  Select and use appropriate graphical representations and measures of central tendency (mean, mode and median) for sets of data.
*  Make inferences and formulate and evaluate arguments based on data analysis and data displays.