Enterprise City Schools
Enterprise City Schools K-6

Mathematics - AL: Grade Three

Mathematics

The National Council of Teachers of Mathematics Curriculum and Evaluation Standards provide educators with goals for school mathematics and guidelines for achieving these goals. The fifty-four standards are presented as a vision for school mathematics based on societal goals, student goals, research on teaching and learning, and professional guidelines. The Stanford Achievement Test, Ninth Edition (SAT-9) contains two subtests for Mathematics levels Primary 1 through Advanced 2. At the SESAT and Task levels, only one subtest of Mathematics is included. The Alabama Course of Study for Mathematics contains " . . . standards that describe what students should know and be able to do by the end of each grade level and course. Care has been taken to incorporate objectives from the Stanford Achievement Test, Ninth Edition (Stanford 9) and standards from the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM)."

The Alabama Course of Study for Mathematics " . . . content standards are organized by strands that represent continuous threads unifying all grade levels and courses. These strands are:
    * Number Sense, Number Systems, Number Theory;
    * Geometry, Spatial Sense, Measurement;
    * Patterns, Functions, Algebra; and
    * Probability, Statistics, Discrete Mathematics."

The Alabama Course of Study for Mathematics " . . . presents the fundamental content for each grade level and course. However, it is based upon the premise that all students are entitled to a mathematics program that builds and expands upon that content. School systems are encouraged to expand the content standards when necessary to address the needs of their students."

"The broad range of mathematical topics addressed in this document, the problem-solving focus of the mathematics program, and the development of mathematical concepts in a hands-on environment demand that technology use be an integral part of the K-12 program. Calculators are appropriate for exploratory purposes in Grades K-3 and should be used for problem solving in Grades 4-8. Calculators should be used on a regular basis in all courses and assessments in Grades 9-12. Computer use should be integrated with content topics as appropriate."

"Alabama's K-12 Mathematics program is designed so that when the content is combined with appropriate instruction, students will be able to make connections within the field of mathematics, across the curricula, and in real-life applications. Furthermore, all students should have opportunities to experience the beauty of mathematics, to appreciate the power of mathematics, and to gauge the importance of mathematics in their lives. Through thoughtful implementation of the Alabama Course of Study: Mathematics by teachers, Alabama students will gain the mathematical power necessary to be productive citizens in the twenty-first century."

The Alabama Course of Study for Mathematics content standards are organized by strands:

* Number Sense, Number Systems, Number Theory

"Number Sense, Number Systems, Number Theory includes content related to the understanding of number meanings, relationships among numbers, relative magnitude of numbers, effects of operations on numbers, and appropriate measures. This strand emphasizes counting skills, place value, number concepts and operations, and symbol sense. The content focuses on numbers used to quantify, name, measure, and identify location and a specific object in a collection. Relationships among various kinds of numbers including integers, fractions, decimals, percents, roots, exponents, logarithms, and numbers in scientific notation are included. Also included are the equivalent forms of these numbers.

Content related to number systems includes whole numbers, rational numbers, real numbers, and, complex numbers. Operations and relationships among operations within and across these number systems are included. Order relations among numbers from the same or different systems and properties of numbers within each system are also included.

Number theory content consists of concepts such as divisibility rules and prime, composite, square, even, and odd numbers, and the connections between the prime structure of a number and the number of its factors."

* Geometry, Spatial Sense, Measurement

"Geometry, Spatial Sense, Measurement focuses on the interpretation and understanding of two- and three-dimensional figures and their characteristics, the interrelationships of figures, and the effects of changes in figures. Also included are the identification, description, comparison, construction, classification, and analyzation of geometric figures as well as the determination of direction, orientation, and perspectives of figures in space. Additional content includes geometric vocabulary, geometric patterns, symmetry, transformations, angle properties of polygons, and similarity. The measurement-related content includes the understanding of length, capacity, weight, mass, area, volume, time, temperature, angle measures, and rates of change."

* Patterns, Functions, Algebra

"Patterns, Functions, Algebra content focuses on regularities in events, shapes, designs, and sets of numbers leading to the exploration of irregular pattern behavior. Content also includes the recognition, creation, and extension of numerical and geometric patterns while generalizing descriptions of these patterns. Description and representation of relationships with tables, graphs, verbal descriptions, and equations are also included. Translation among tables, equations, and graphs of functions as well as the analyzation of the effects of parameter changes on functions are included. Analyzation of functional relationships and the explanation of how a change in one quantity results in a change in another are included also. Domain, range, and maximum and minimum values are included. Additional algebra content includes the representation of variable quantities with expressions, equations, inequalities, and matrices. Topics such as solving linear equations and inequalities, modeling situations graphically, and operating on expressions are included."

*Discrete Mathematics, Probability, Statistics

"Discrete Mathematics, Probability, Statistics content includes concepts of chance and the understanding of the relationship between the numerical expression of a probability and the events that precipitate these numbers. Probability concepts are extended to include concepts of independent and dependent events and their relationship to compound and conditional probability as well as the study of probability distributions such as the normal distribution.

Content related to the construction, reading, and interpretation of tables, charts, and graphs; to the interpretation of graphic information; to the determination of measures of central tendency, dispersion, and correlation; to the determination of the line of best fit for date points; and to the analyzation of effects of data transformations on measures of central tendency and dispersion are included also.

This strand also includes discrete mathematics topics such as counting principles, combinations, and permutations, linear programming, and algorithms. Additional topics include finite graphs, matrices, sequences, and recurrence relations."

Problem Solving is a process of inquiry and application. It is the means by which an individual uses previously acquired knowledge, skills, and understanding to satisfy the demands of an unfamiliar situation.

Communication includes learning the signs, symbols, and terms of mathematics. Furthermore, being able to communicate mathematically implies being able to read, write, and discuss ideas.

Connections includes the linking of conceptual and procedural knowledge, relating various representations of concepts or procedures, relating different topics in mathematics, and relating mathematics to other curriculum areas and to daily life.

Reasoning involves making a conjecture by generalizing from a pattern of observations made in particular cases (inductive reasoning) and then testing the conjecture by constructing either a logical verification or a counterexample (deductive reasoning). Describing objects or processes accurately including their properties, similarities, differences, and relationships is a part of mathematical reasoning.

Through the interweaving of mathematical concepts and processes, appropriate instruction, and independent exploration and study, students will realize the power of mathematics and will attain the goal of mathematical power."

AL: Grade Three

The Primary 3 level of the Stanford Achievement Test, Ninth Edition (SAT-9) assesses students in either the spring of Grade 3 or the fall of Grade 4.

According the Reviewer's Edition of the assessment, there are two sections of Mathematics:
    * Mathematics: Procedures
    * Mathematics: Problem Solving
"At all levels, the emphasis in Stanford 9 mathematics is on assessing skills and concepts within the contexts that require those skills and concepts outside of the classroom. This assessment of student proficiency in a modern mathematics curriculum encourages students to value mathematics and supports sound instructional practice in the mathematics classroom." The Alabama Course of Study for Mathematics provides goals for third grade students.

The "K-4 mathematics program consists of curriculum that includes developmentally appropriate activities that allow exploration of a wide variety of mathematical ideas in such a way that students develop an enjoyment of and curiosity about mathematics. Thus, students at this stage of development are empowered with confidence to interpret their world mathematically.

The learning environment of a K-4 classroom fosters students' exploration, development, discussion, and application of ideas. A problem-rich, non-rigid environment with a wealth of materials and interrelated experiences enables students to value mathematics, to think mathematically, and to appreciate the role of mathematics in their world. The exclusive use of textbooks is minimized while real-life situations requiring numerical thinking are emphasized.

A developmentally appropriate curriculum provides considerable time for students to construct mathematical understandings for themselves, to develop reasoning skills, and to develop communication skills. Active participation in both small and whole groups presents opportunities for students to share orally and to compare methods of finding solutions. This interaction with classmates helps students construct knowledge, learn other ways to think about ideas, and trust their own mathematical thinking. Encouraging students to think independently in response to real-life problems awakens them to a lifetime enjoyment of mathematics.

The content of the K-4 program is sequential and builds on prior experiences or grade levels. Students learn to use numbers to express quantities and relationships while mastering basic facts. Using a variety of materials, they learn to interpret the world around them through geometric explorations. They are involved in collecting, organizing, displaying, and interpreting data. In addition, students develop the ability to understand relationships through exploration of patterns. It is not intended that these topics be taught in insolation but as an integrated whole.

'How well children come to understand mathematical ideas is far more important than how many skills they acquire.' (NCTM Standards, p. 16)"