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for School Leadership Team I - Newark Pulic Schools

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    A Curriculum Guide forMathematics

    Grade 7

    Newark Public Schools

    Office of Mathematics

2004

2

    NEWARK PUBLIC SCHOOLS

    2004-05

    ADMINISTRATION

    District Superintendent..................................................................................Ms. Marion A. BoldenDistrict Deputy Superintendent......................................................................Ms. Anzella K. NelmsChief of Staff....................................................................................................Ms. Bessie H. White

    Chief Financial Officer.............................................................................................Mr. Ronald Lee

    Human Resource Services

    Assistant Superintendent.........................................................................Ms. Joanne C. Bergamottofor School Leadership Team I

    Assistant Superintendent...................................................................................Dr. J. Russell Garris

    for School Leadership Team II

    Assistant Superintendent.........................................................................Dr. Glenda Johnson-Greenfor School Leadership Team III

    Assistant Superintendent..........................................................................................Ms. Lydia Silva

    for School Leadership Team IV

    Assistant Superintendent.......................................................................................Dr. Don Marinarofor School Leadership Team V

    Assistant Superintendent..................................................................................Dr. Gayle W. GriffinDepartment of Teaching and Learning

    Associate Superintendent..................................................................................Ms. Alyson BarillariDepartment of Special Education

    Associate Superintendent................................................................................Mr. Benjamin O'NealDepartment of Special Programs

    3

    Department

    of

    Teaching and Learning

    Dr. Gayle W. GriffinAssistant SuperintendentOffice of Mathematics

    May L. Samuels

    Director

    GRADE 7 MATHEMATICS

    CURRICULUM

    GUIDE

    Table of Contents

    Mission Statement............................................................................................................................5

    4

Philosophy........................................................................................................................................6

    To the Teacher.................................................................................................................................7

    Course Description...........................................................................................................................9

    Course Proficiencies......................................................................................................................10

    Suggested Timeline........................................................................................................................13

    Suggested Pacing and Objectives (with New Jersey Core Content Standards).............................14Open Ended Problem Solving and Scoring...................................................................................21Reference:

    Instructional Technology (Web Sources)......................................................................................31NJCCCS and Cumulative Progress Indicators...............................................................................32Holistic Scoring Guide for Math Open-Ended Items....................................................................41National Council of Teachers of Mathematics Principles and Standards......................................42Glossary.........................................................................................................................................43

    5

    Mission Statement

    The Newark Public Schools recognizes that each child is a unique individual possessing talents, abilities, goals, and dreams. We further recognize that each child can be successful only when we acknowledge all aspects of that child’s life: addressing their needs; enhancing their intellect; developing their character; and uplifting their spirit. Finally, we recognize that individuals learn, grow, and achieve differently; and it is therefore critical that, as a district, we provide a diversity of programs based on student needs.

    As a district we recognize that education does not exist in a vacuum. In recognizing the rich diversity of our student population, we also acknowledge the richness of the diverse environment that surrounds us. The numerous cultural, educational, and economic institutions that are part of the greater Newark community play a critical role in the lives of our children. It is equally essential that these institutions become an integral part of our educational program.To this end, the Newark Public Schools is dedicated to providing a quality education, embodying a philosophy of critical and creative thinking and designed to equip each graduate with the knowledge and skills needed to be a productive citizen. Our educational program is informed by high academic standards, high expectations, and equal access to programs that provide and motivate a variety of interests and abilities for every student based on his or her needs. Accountability at every level is an integral part of our approach. As a result of the conscientious, committed, and coordinated efforts of teachers, administrators, parents, and the community, all

    children will learn.

    Adapted from: The Newark Public Schools Strategic Plan

    6

    Philosophy

    “Imagine a classroom, a school, or a school district where all students have access to high-quality, engaging mathematics instruction. There are ambitious expectations for all, with accommodation for those who need it. Knowledgeable teachers have adequate resources to support their work and are continually growing as professionals. The curriculum is mathematically rich, offering students opportunities to learn important mathematical concepts and procedures with understanding. Technology is an essential component of the environment. Students confidently engage in complex mathematical tasks chosen carefully by teachers. They draw on knowledge from a wide variety of mathematical topics, sometimes approaching the same problem from different mathematical perspectives or representing the mathematics in different ways until they find methods that enable them to make progress. Teachers help students make, refine, and explore conjectures on the basis of evidence and use a variety of reasoning and proof techniques to confirm or disprove those conjectures. Students are flexible and resourceful problem solvers. Alone or in groups and with access to technology, they work productively and reflectively, with the skilled guidance of their teachers. Orally and in writing, students communicate their ideas and results effectively. They value mathematics and engage actively in learning it.” *

    This model, envisioned in the NCTM Standards 2000, is the ideal which Newark Public Schools

    hopes to achieve in all mathematics classrooms. We believe the classroom described above is attainable through the cooperative efforts of all Newark Public Schools stakeholders.

     *A Vision for School Mathematics

    National Council of Teachers of Mathematics

    Standards 2000

    7

    To the Teacher

    The Connected Mathematics Program is a standards-based, problem-centered curriculum. The

    role of the teacher in a problem-centered curriculum differs from the traditional role, in which the teacher explains ideas thoroughly and demonstrates procedures so students can quickly and accurately duplicate these procedures. A problem-centered curriculum is best suited to an inquiry model of instruction. The teacher and students investigate a series of problems; through discussion of solution methods, embedded mathematics, and appropriate generalizations students grow in their ability to become reflective learners. Teachers have a crucial role to play in establishing the expectations for discussion in the classroom and for orchestrating discourse on a daily basis.

    The Connected Mathematics materials are designed to help students and teachers build an effective pattern of instruction in the classroom. A community of mutually supportive learners works together to make sense of the mathematics through: the problems themselves; the justification the students are asked to provide on a regular basis; student opportunities to discuss and write about their ideas. To help teachers think about their teaching, the Connected

    Mathematics Program uses a three-phase instructional model, which contains a Launch of the

    lesson, an Exploration of the central problem, and a Summary of the new learning.

    The Launch of a lesson is typically done as a whole class; yet during this launch phase of instruction students are sometimes asked to think about a question individually before discussing their ideas as a whole class. The launch phase is also the time when the teacher introduces new ideas, clarifies definitions, reviews old concepts, and connects the problem to past experiences of the students. It is critical that, while giving students a clear picture of what is expected, the teacher is careful not to reveal too much and lower the challenge of the task to something routine, or limit the rich array of strategies that may evolve from an open launch of the problem. In the Explore phase, students may work individually, in pairs, in small groups, or occasionally as a whole class to solve the problem. As they work, they gather data, share ideas, look for patterns, make conjectures, and develop problem-solving strategies. The teacher's role during this phase is to move about the classroom, observing individual performance and encouraging on-task behavior. The teacher helps students persevere in their work by asking appropriate questions and providing confirmation or redirection where needed. For students who are interested in deeper investigation, the teacher may provide extra challenges related to the problem. These challenges are provided in the Teacher's Guide.

    Substantive whole-class discussion most often occurs during the Summarize phase when

    individuals and groups share their results. Led by the teacher's questions, the students investigate ideas and strategies and discuss their thoughts. Questioning by other students and the teacher challenges students' ideas, driving the development of important concepts. Working together, the students synthesize information, look for generalities, and extract the strategies and skills involved in solving the problem. Since the goal of the summarize phase is to make the mathematics in the problem more explicit, teachers often pose, toward the end of the summary, a quick problem or two to be done individually as a check of student progress.

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    Connected Mathematics is different from traditional programs. Because important concepts are embedded within problems rather than explicitly stated and demonstrated in the student text, the teacher plays a critical role in helping students develop appropriate understanding, strategies, and skills. It is the teachers' thoughtful reflections on student learning that will create a productive classroom environment. Teachers who have experienced success with Connected Mathematics have made two noteworthy suggestions:

    (i)The teacher should work through each investigation prior to the initiation of instruction.

    Teachers who invest time in doing the problems in at least two different ways will be

    better equipped to Launch the investigation, facilitate the Exploration and Summary of

    the problem, and know what mathematics assessment is appropriate.

    (ii)The teacher should engage in ongoing professional conversations about the mathematics

    in the Connected Mathematics Program they are using, sharing strategies for improving

    student achievement.

    The format of the student books is also much different from traditional mathematics texts. The student pages are uncluttered and have few non-essential features. Because students develop strategies and understanding by solving problems, the books do not contain worked-out examples that demonstrate solution methods. Since it is also important that students develop understanding of mathematical definitions and rules, the books contain few formal definitions and rules. These non-consumable student books should be kept in a three-ring binder during instruction and collected when instruction has been completed. It is essential that the teacher develops and maintains a notebook management system. "Getting to Know Connected

    Mathematics: An Implementation Guide” provides strategies to assist the teacher with the

    purposes and organizational format for student notebooks.

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    Course Description

    The grade seven curriculum helps students develop sound mathematical habits by learning important questions to ask themselves about any situation that can be represented and modeled mathematically. Bits and Pieces II continues to build understanding and recognize relationships of fractions, decimals and percents. Stretching and Shrinking allows students to solve real-world

    problems by using the precise mathematical definition for similarity: understanding scale factors, equivalent ratios, and similarity transformations. Comparing and Scaling develops the student's

    ability to make intellectual comparisons of quantitative information using ratios, fractions, decimals, rates, unit rates, and percents and to recognize when such reasoning is appropriate. Filling and Wrapping takes an experimental approach to explore three-dimensional

    measurement: surface areas and volumes of rectangular prisms and cylinders. Accentuate the

    Negative develops a disposition to seek ways of making sense of mathematical ideas and skills and deciding when and how those skills can be used. By modeling strategies (using the number line) and using manipulatives (colored chips), the addition, subtraction, multiplication, and division of negative and positive integers will more deeply integrated into students' own mathematical knowledge and resources. Data Around Us exposes students to the ideas of

    number sense through the awareness of magnitude, measurement, and numeration. Numerical information is used to make decisions by comparison or to derive new information by performing operations on given data. What Do You Expect? deepens students' understanding of

    experimental and theoretical probability. Using probability models (counting trees and area models) and probability concepts (expected value and independent and dependent events), students will make real-world decisions.

    Prerequisite

    None

    Course Requirements

    Students are expected to:

    meet district attendance policy

    participate in class discussions, cooperative learning exercises, and individual and group

    classwork assignments

    complete homework assignments

    keep an updated, accurate notebook

    demonstrate an acceptable level of proficiency in course objectives through teacher-

    developed quizzes and tests, alternative and project-based assessments, and district

    assessments

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