MATH STANDARDS

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There are six mathematics content standards, which encompass the curriculum standards created by the National Council of Teachers of Mathematics: Number Sense and Number Systems; Computation and Estimation; Measurement, Statistics and Probability; Patterns, Relations, and Algebra; and Geometry.

Number Sense and Number Systems refer to an intuitive understanding of numbers in the following ways: "[1] understanding the meanings of numbers; [2] having an awareness of multiple relationships among numbers; [3] recognizing the relative magnitude of numbers; [4] knowing the relative effect of operating on numbers; and [5] possessing referents for measures of common objects and situations in the environment." (NCTM Addenda Series, Grades 5-8)

Through problem-solving situations, all students will construct their own understanding, so that by the end of grade 8 they will:

·         Have an intuitive understanding of rational numbers.

·         Justify the appropriateness of a method of approximation or calculation and verify the reasonableness of a result.

·         Represent and use numbers (integers, fractions, decimals, exponents, and scientific notation).

·         Represent and apply ratios, proportions, and percents.

·         Demonstrate how basic arithmetic operations are related to one another.

·         Demonstrate the composition and decomposition of numbers (primes, factors, and multiples).

·         Investigate and represent number relations, using various types of graphs.

Computation and Estimation refer to computational and non-computational procedures that deal with numbers that students select and use. They include invented methods and technologies that are applied when conducting real world and other investigations.

Through problem-solving situations, all students will construct their own understanding, so that by the end of grade 8 they will:

·         Develop proficiency with addition, subtraction, multiplication, and division of rational numbers.

·         Create, analyze, and communicate procedures for computation and strategies for estimation.

·         Develop and communicate an understanding for solving proportions.

·         Use estimation to defend the reasonableness of solutions.

·         Use scientific calculators and computers in appropriate computational situations.

MEASUREMENT refers to selecting and understanding appropriate attributes, units, and tools needed to estimate, make, and use measurements.

Through problem-solving situations, all students will construct their own understanding, so that by the end of grade 8 they will:

·         Develop formulas or procedures to solve problems involving perimeter, area, capacity, angle measurement, and weight and mass.

·         Extend and apply the process of measurement.

·         Select and use appropriate units and tools to measure.

·         Develop concepts of rate (miles per hour, feet per second) and other derived and indirect measurements.

·         Demonstrate a proficiency in measurement and "measurement sense".

·         Have an intuitive understanding of systems of measurement.

STATISTICS and PROBABILITY refer to collecting, organizing, displaying, and analyzing information, and making and interpreting predications based on uncertainty.

Through problem-solving situations, all students will construct their own understanding, so that by the end of grade 8 they will:

·         Construct and interpret tables, graphs, and charts.

·         Analyze data to formulate reasonable predications and convincing arguments based on the analysis of data.

·         Recognize and use the measures of central tendency (mean, median, mode, range).

·         Use probability and statistics to make informed decisions in real-life situations.

·         Design and carry out experiments or simulations to determine probability.

·         Communicate conclusions based on analysis of data.

·         Use a scientific calculator to explore statistics.

PATTERNS, RELATIONS, and ALGEBRA refer to studying patterns to make conjectures about relationships, exploring relationships, and developing generalizations.

Through problem-solving situations, all students will construct their own understanding, so that by the end of grade 8 they will:

·         Identify, analyze, extend, and create patterns in different formats.

·         Describe and represent relations through different formats (tables, graphs, verbal rules, open sentences, equations, and geometry).

·         Identify and justify an appropriate representation for a given situation.

·         Use patterns and functions to represent and solve problems.

·         Use concepts of variable, expression, and equation.

·         Analyze tables, graphs, rules, equations, and identify relationships.

·         Solve linear equations.

·         Investigate inequalities

GEOMETRY  refers to exploring geometric properties and developing spatial sense.

Through problem-solving situations, all students will construct their own understanding, so that by the end of grade 8 they will:

·         Identify, describe, classify, and compare two- and three-dimensional geometric figures.

·         Explore the transformations of geometric figures (translation, rotation, and reflection).

·         Represent and solve problems, using geometric figures.

·         Construct models of two- and three-dimensional shapes.

PROCESS STANDARDS

The process by which students learn mathematics is just as important as the mathematics content they learn. For students to develop an understanding of and appreciation for mathematics, it is essential that they learn mathematics through solving problems, using mathematical reasoning, communicating mathematical ideas, and making mathematical connections.

These four mathematical process standards encompass the first four curriculum standards created by the National Council of Teachers of Mathematics.

MATHEMATICS as PROBLEM SOLVING is the central focus of mathematics education and should engage students in developmentally appropriate problem-solving situations. Problem solving is a method of inquiry and application and provides opportunities for all students. "Problem solving should be the central focus of all mathematics instruction and an integral part of all mathematical activity. Problem solving is not a distinct topic, but a process that should permeate the entire program and provide the context in which concepts and skills are learned." (NCTM Curriculum and Evaluation Standards)

Students will engage in problem solving to construct their own understanding so that by the end of grade 8 they will:

·         Use problem-solving approaches to investigate, understand, and develop conjectures about mathematical concepts.

·         Generalize solutions to apply strategies to new situations.

·         Use concrete, pictorial, and symbolic representations to develop and apply strategies to solve multi-step and non-routine problems.

·         Apply the process of mathematical modeling to real-world situations.

MATHEMATICS as COMMUNICATION helps students construct meaning between their concrete, informal, intuitive understandings and the abstract, symbolic language of mathematics. Mathematics communication refers to the ability to observe, represent, talk, listen, read, and write about mathematics. Students become actively engaged in doing mathematics when they explore, investigate, describe, and explain mathematical ideas. Students learn when they are given the opportunity to think about their ideas; talk with and listen to other students; and share ideas, strategies, and solutions. Reading and writing about mathematics helps students and teachers reflect on their work and clarify ideas and conjectures. Communication gives teachers valuable insight from which to make instructional decisions as well as provide students with opportunities to demonstrate their understanding and knowledge. "Mathematics can be thought of as a language because of its power to represent and communicate ideas concisely." (NCTM Curriculum and Evaluation Standards).

Students will engage in communication to construct their own understanding so that by the end of grade 8 they will:

·         Model situations in mathematics and other disciplines through communication.

·         Develop an understanding of mathematics concepts, including the role of mathematical notations and definition.

·         Use the skills of language and observations to interpret and evaluate mathematical ideas.

·         Use mathematical ideas, language, and symbols to converse with others and to make conjectures and convincing arguments.

MATHEMATICS as REASONING is the justification of solutions, thinking processes, and conjectures in a variety of ways. The ability to reason enables students to solve problems in their lives, to validate their thinking, and to enhance their mathematical confidence. Through the development of logical reasoning, students develop both intellectually and verbally. "Reasoning is fundamental to the knowing and doing of Mathematics." (NCTM Curriculum and Evaluation Standards)

Students will engage in reasoning to construct their own understanding so that by the end of grade 8 they will:

·         Identify and use deductive and inductive reasoning.

·         Judge the validity of their thinking.

·         Formulate and validate mathematical conjectures.

MATHEMATICS as CONNECTIONS address the need for students to make connections among various topics within mathematics as well as to make connections between mathematics and other disciplines. The ability to explore, recognize, develop, and expand the interconnectedness of topics within mathematics and other disciplines enhances students' understanding of the usefulness of mathematics and how it relates to everyday situations. "Connections help students broaden their perspective, to view mathematics as an integrated whole rather than an isolated set of topics, and to acknowledge whole rather than an isolated set of topics, and to acknowledge its relevance and usefulness both in and out of school." (NCTM Curriculum and Evaluation Standards)

Students will engage in making connections to construct their own understanding so that by the end of grade 8 they will:

·         See how topics and concepts in mathematics are integrated.

·         Explore problems and describe results by using multiple representations.

·         Build upon a mathematical idea to understand other mathematical ideas.

·         Use mathematics to solve problems and model situations in other disciplines.