GLEN RIDGE PUBLIC SCHOOLS
Curriculum
Guide
Course Title: MATH
7
Subject: Mathematics
Grade Level: 7
Department/School: Mathematics/
Duration: Full
year
Number of Credits: NA
Prerequisite: NA
Elective or Required: Required
Author: Jennifer Methe
Date Submitted: Summer 2007
Course Description
Math 7
Math 7 students develop fundamental
mathematical ideas and methods that provide the foundation for pre-algebra and
geometry concepts. Through hands-on
discovery with manipulatives and by reasoning about applied problems, students
develop a true understanding of concepts and procedures. This course emphasizes problem solving
strategies and the use of mental math and estimation. Topics include integers, fractions, decimals,
percents, ratios, proportions, measurement of two and three dimensional
figures, geometric properties, expressions, equations, number properties,
patterns, graphs, and data analysis.
GLEN RIDGE PUBLIC SCHOOLS
MATHEMATICS
Mathematics
and Computer Science are an integral part of our lives. Students must be actively involved in their
mathematics education with problem solving being an essential part of the
curriculum. The mathematics and computer
science curricula should emphasize thinking skills through a balance of
computation, intuition, common sense, logic, analysis and technology. Students will be engaged and challenged in a
student-centered learning environment that is developmentally appropriate. Students will communicate mathematical ideas
effectively by applying hands-on manipulatives, basic computational skills,
mathematical models, and technology in order to solve practical problems.
New Jersey
The Mathematics Standards
consist of five statements, which describe what is essential to excellent
mathematics education, and present a view of mathematics teaching and learning
that integrates the processes of mathematical activity, the content of
mathematics, and the learning environment in the classroom. The following standards were adopted by the
New Jersey State Board of Education.
This course will cover the
following Core Curriculum Standards:
Descriptive Statement: Numbers and arithmetic operations are what most of the
general public think about when they think of mathematics; and, even though
other areas like geometry, algebra, and data analysis have become increasingly
important in recent years, numbers and operations remain at the heart of
mathematical teaching and learning. Facility with numbers, the ability to
choose the appropriate types of numbers and the appropriate operations for a
given situation, and the ability to perform those operations as well as to
estimate their results, are all skills that are essential for modern day life.
Number Sense
Numerical Operations
Estimation
Descriptive Statement: Spatial sense is an intuitive feel for shape and space.
Geometry and measurement both involve describing the shapes we see all around
us in art, nature, and the things we make. Spatial sense, geometric
modeling, and measurement can help us to describe and interpret our physical
environment and to solve problems.
Geometric Properties
Transforming Shapes
Coordinate Geometry
Units of Measurement
Measuring Geometric Objects
Descriptive Statement: Algebra is a symbolic language used to
express mathematical relationships. Students need to understand how
quantities are related to one another, and how algebra can be used to concisely
express and analyze those relationships. Modern technology provides tools
for supplementing the traditional focus on algebraic procedures, such as
solving equations, with a more visual perspective, with graphs of equations displayed
on a screen. Students can then focus on understanding the relationship
between the equation and the graph, and on what the graph represents in a
real-life situation.
Patterns
Functions and Relationships
Modeling
Procedures
Descriptive
Statement: Data
analysis, probability, and discrete mathematics are important interrelated
areas of applied mathematics. Each provides students with powerful
mathematical perspectives on everyday phenomena and with important examples of
how mathematics is used in the modern world. Two important areas of
discrete mathematics are addressed in this standard;
a third area, iteration and recursion, is addressed in Standard 4.3 (Patterns
and Algebra).
Data Analysis
Probability
Discrete Mathematics
– Systematic Listing and Counting
Discrete Mathematics
– Vertex-edge Graphs and Algorithms
Descriptive Statement: The mathematical processes described here highlight ways of
acquiring and using the content knowledge and skills delineated in the first
four mathematics standards.
Problem Solving Reasoning
Communication Representations
Connections Technology
Scope and Sequence
|
Standard 4.1 (Number and
Numerical Operations) All students
will develop number sense and will perform standard numerical operations and
estimations on all types of numbers in a variety of ways. |
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4.1 |
|
7 |
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8 |
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By the end of Grade 7,
students will: |
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By the end of Grade 8,
students will: |
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|
A. |
Number Sense |
|
|
|
|
A.1 |
Extend understanding of the
number system by constructing meanings for the following (unless otherwise
noted, all indicators for grade 7 pertain to these sets of numbers as well):
rational numbers, percents, whole numbers with exponents. |
M |
Extend understanding of the
number system by constructing meanings for the following (unless otherwise
noted, all indicators for grade 8 pertain to these sets of numbers as well):
rational numbers, percents, exponents, roots, absolute values, numbers
represented in scientific notation. |
M |
|
A.2 |
Demonstrate a sense of the
relative magnitudes of numbers. |
M |
Demonstrate a sense of the
relative magnitude of numbers. |
M |
|
A.3 |
Understand and use ratios,
proportions, and percents (including percents greater than 100 and less than
1) in a variety of situations. |
M |
Understand and use ratios,
proportions, and percents (including percents greater than 100 and less than
1) in a variety of situations. |
M |
|
A.4 |
Compare and order numbers
of all named types. |
M |
Compare and order numbers
of all named types. |
M |
|
A.5 |
Use whole numbers,
fractions, decimals, and percents to represent equivalent forms of the same
number. |
M |
Use whole numbers,
fractions, decimals, and percents to represent equivalent forms of the same
number. |
M |
|
A.6 |
Understand that all
fractions can be represented as repeating or terminating decimals. |
M |
Recognize that repeating
decimals correspond to fractions and determine their fractional equivalents:
5/7 = 0.714285714285… = 0.714285 |
M |
|
A.7 |
|
|
Construct meanings for
common irrational numbers, such as (pi) and the square root of 2. |
M |
|
B. |
Numerical Operations |
|
|
|
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B.1 |
Use and explain procedures
for performing calculations with integers and all number types named above
with: pencil-and-paper, mental math, calculator. |
M |
Use and explain procedures
for performing calculations involving addition, subtraction, multiplication,
division, and exponentiation with integers and all number types named above
with: pencil-and-paper, mental math, calculator. |
M |
|
B.2 |
Use exponentiation to find
whole number powers of numbers. |
M |
Use exponentiation to find
whole number powers of numbers. |
M |
|
B.3 |
Understand and apply the
standard algebraic order of operations, including appropriate use of
parentheses. |
M |
Find square and cube roots
of numbers and understand the inverse nature of powers and roots. |
M |
|
B.4 |
|
|
Solve problems involving
proportions and percents. |
M |
|
B.5 |
|
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Understand and apply the
standard algebraic order of operations, including appropriate use of
parentheses. |
M |
|
C |
Estimation |
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C.1 |
Use equivalent
representations of numbers such as fractions, decimals, and percents to
facilitate estimation. |
M |
Estimate square and cube
roots of numbers. |
M |
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C.2 |
|
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Use equivalent
representations of numbers such as fractions, decimals, and percents to
facilitate estimation. |
M |
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C.3 |
|
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Recognize the limitations
of estimation and assess the amount of error resulting from estimation. |
M |
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Standard 4.2 (Geometry
and Measurement) All students will
develop spatial sense and the ability to use geometric properties,
relationships, and measurement to model, describe and analyze phenomena. |
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4.2 |
|
7 |
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8 |
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By
the end of grade 7, students will: |
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By
the end of grade 8, students will: |
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|
A. |
Geometric Properties |
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A.1 |
Understand and apply
properties of polygons: quadrilaterals, including squares, rectangles,
parallelograms, trapezoids, rhombi; regular polygons. |
M |
Understand and apply concepts
involving lines, angles, and planes:
complementary and supplementary angles; vertical angles; bisectors and
perpendicular bisectors; parallel, perpendicular, and intersecting planes;
intersection of plane with cube, cylinder, cone, and sphere. |
M |
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|
A.2 |
Understand and apply the
concept of similarity: using proportions to find missing measures, scale
drawings, models of 3D objects. |
M |
Understand and apply the
Pythagorean theorem. |
M |
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|
A.3 |
Use logic and reasoning to
make and support conjectures about geometric objects. |
M |
Understand and apply
properties of polygons: quadrilaterals, including squares, rectangles,
parallelograms, trapezoids, rhombi; regular polygons; sum of measures of
interior angles of a polygon; which polygons can be used alone to generate a tessellation
and why. |
M |
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A.4 |
|
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Understand and apply the
concept of similarity: using proportions to find missing measures, scale
drawings, models of 3D objects. |
M |
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|
A.5 |
|
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Use logic and reasoning to
make and support conjectures about geometric objects. |
M |
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B. |
Transforming Shapes |
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B.1 |
Understand and apply
transformations: finding the image, given the pre-image, and vice-versa;
sequence of transformations needed to map one figure onto another;
reflections, rotations, and translations result in images congruent to the
pre-image; dilations (stretching/shrinking) result in images similar to the
pre-image. |
M |
Understand and apply
transformations: finding the image, given the pre-image, and vice-versa;
sequence of transformations needed to map one figure onto another;
reflections, rotations, and translations result in images congruent to the
pre-image; dilations (stretching/shrinking) result in images similar to the
pre-image. |
M |
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B.2 |
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Use iterative procedures to
generate geometric patterns: fractals (e.g., the Koch Snowflake);
self-similarity; construction of initial stages; patterns in successive
stages (e.g., number of triangles in each stage of Sierpinski's Triangle). |
M |
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