Download Math Problem Solving Grade 7

Roselle Park Middle School
Mathematics Department
Course of Study
Math Problem Solving
Grade 7
MATH PROBLEM SOLVING GRADE 7
In order to understand how these objectives are to be achieved, a sequence of topics is
listed for each unit. Space is provided on each page to allow for notes and
recommendations. The New Jersey Core Curriculum Content Standards and the New
Jersey Core Course Proficiencies are infused throughout the units. The objective of the
sixth grade math problem solving is to aid students in further exploring problem solving
skills related to standardized testing.
This guide applies to all students and meets the Affirmative Action guidelines.
Written by: Kimberly Guercio
Patricia Mawer
July 2008
Edited by:
Frances Kenny
Director of Math, Science &
Talented and Gifted Education
1
ROSELLE PARK PUBLIC SCHOOLS
MATHEMATICS PHILOSOPHY
Our children need to be well prepared for lives and careers in a technological
world and in a global economy. They need to be able to solve problem and reason
effectively. They need to use complex information and advanced tools. They need to
know and understand how to use and apply mathematics. These high standards will
benefit both our children and our society.
The Roselle Park High School Mathematics Curriculum will develop students’
understanding of concepts and help them to acquire essential skills. Their philosophy is
based upon the fact that all students possess the ability to be rational thinkers,
independent problem solvers, and efficient users of technology. Each student can achieve
success and pride while developing these skills. A comprehensive program has been
developed in a spiral and sequential format so those students will learn the many aspects
of mathematics and its applications. Emphasis will be placed on being actively involved
in learning mathematics, writing and talking about math, using critical thinking skills in
problem solving, using calculators, computers, and other mathematical tools of learning,
and achieving at a high level.
Consideration will be given to the individual student’s needs, interests, and
abilities. All students must develop and sharpen their skills, deepen their understanding
of mathematical concepts and processes, and hone their problem-solving, reasoning, and
communication abilities while using mathematics to make sense of, and solve,
compelling problem. For this to occur, rigorous mathematical content must be organized,
taught, and assessed in a problem-solving environment. The students will be challenged
to use math in meaningful ways, so that they come to realize how useful mathematics will
be in their lives. Moreover, the curriculum will also encourage the development of
positive attitudes and interests in mathematics, which will last a lifetime.
2
Roselle Park Public Schools Educational Goals
GOALS
1.
Communicate mathematically through written, oral, symbolic, and visual forms of
expression.
2.
Understand the interrelationships of mathematical ideas and the roles that
mathematics plays in other disciplines and in life.
3.
Use calculators, computers, manipulatives, and other mathematical tools to
enhance mathematical thinking and understanding.
4.
Develop the ability to pose and solve mathematical problems in mathematics,
other disciplines, and everyday experiences.
5.
Develop reasoning ability and become self-reliant, independent mathematical
thinkers.
6.
Demonstrate high levels of mathematical thought through experiences which
extend beyond traditional computation, algebra, and geometry.
7.
Develop an understanding of patterns, relationships, and functions, and use them
to represent and explain real world phenomena.
3
MATHEMATICS DEPARTMENT
COURSE PROFICIENCIES
Math 7
I. Descriptions:
The objective of the seventh grade math problem solving class is to aid students in
further exploring problem solving skills related to standardized testing. The
curriculum lays the foundations for the studies of algebra, geometry, and
probability. Basic operations with whole numbers, fractions, decimals, and
percents are reinforced and built upon. Students will also use explorations,
manipulatives, and technology to further understand concepts such as solving
equations and inequalities, graphing, geometry, and probability. Students will
develop fluency with operations involving integers. A basic goal is to improve
problem-solving strategies while maintaining real-world relevance. The pace of
the course and the depth of topics covered will vary in accordance to the level of
the class.
Students are identified in Grade 7 through tests and teacher recommendation.
II. Unit Topics:
Tools for Algebra and Geometry
 Test Taking Strategies
 Number Sense, Patterns, and Algebraic Thinking
 Decimal Operations
 Data Statistics
 Number Patterns and Fractions
 Fractions Operations
 Integers
 Equations, Inequalities, and Functions
 Ratios and Proportions
 Percents
 Probability
 Geometric Figures
 Measurement and Area
 Surface Area and Volume
4
III
Objectives:
Grade 7 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.
All students will be able to:
Express ratios as a fraction
Determine whether two ratios are equivalent
Find a ratio that is equivalent to a given ratio
Calculate the value of a variable as presented within a ratio
Write a proportion to model a given situation and then solve the proportion
Convert fractions to equivalent decimals and percents
Understand the concept of a percent greater than 100 and less than 1
Solve percent problems using the percent equation
Write and solve percent equations to model real life applications that include but
are not limited to interest, sales tax, discount, commission, and percent of
increase or decrease
Create a graphical model of a situation that will total 100 percent
Geometry and Measurement
All students will develop spatial sense and the ability to use geometric properties,
relationships, and measurements to model, describe and analyze phenomena.
Recognize the properties that make two figures similar
Use the properties of similarity to find the value of sides and angles in a pair of
similar figure
Prove two figures are similar
Create a mapping given a figure by applying various transformations including
rotation, translation, dilation and reflection
Graph figures on a coordinate plane
Create an image of a given figure using transformations and name the coordinates
of the image
Identify the sequence of transformations needed to map one figure into another
Determine the scale factor and find a specified measure on a scale drawing
Create a diagram that is a scale drawing of and actual location
Calculate the area of a triangle
Calculate the area of a trapezoid
Determine the perimeter and area of an irregular figure
Determine the complement and supplement of a given angle
5
Identify the relationship between vertical angles and use that relationship to find
the value of various angles.
Draw the next stage in a given fractal
Solve problems requiring calculations that involve different units of measure
within a measurement system
Utilize the reference sheet provide by the state of New Jersey to solve problems
Patterns and Algebra
All students will represent and analyze relationships among variable quantities and solve
problems involving functions, and algebraic concepts and processes.
Represent patterns on tables and graphs
Describe in words the behavior of a function
Graph equations in two variables
Analyze functional relationships
Create formulas for patterns in the form of Next =
Analyze growth patterns of a function including both exponential and geometric
growth
Graph integers on a number line
Determine the absolute value of an integer and explain how this is related to its
location on the number line
Perform operations with integers included addition, subtraction, multiplication
and division through the use of a number line, vectors and mental computation
Solve multi-step equations involving integers
Simplify all forms of algebraic expressions
Use the order of operations, including exponents and parenthesis to simplify
expression
Demonstrate the distributive property
Use the distributive property when simplifying expressions and solving equations
Data Analysis, Probability, and Discrete Mathematics
All students will develop an understanding of the concepts and techniques of data
analysis, probability, and discrete mathematics, and will use them to model situations,
solve problems, and analyze and draw appropriate inferences from data.
Select appropriate representation for given data
Interpret and answer questions about box and whisker plots
Display data on a scatter plot and identify correlations and outliers
Draw inference from a given graph
Model situation involving a simulation, using such things as a table of sums, to
differentiate between theoretical and experimental probability
6
Apply the multiplication principle to determine the number of possible outcomes
given a situation
Use permutation with and without replacement
Explore counting problems involving Venn Diagrams with three attributes
Apply techniques of systematic listing, counting and reasoning in a variety of
contexts
Mathematical Process
All students will use mathematical processes of problem solving, communication,
reasoning, representation and technology to solve problems and communicate
mathematical idea as described in the appropriate grade level New Jersey Core
Curriculum Content Standards.
IV
Types of Evaluations:
1.
2.
3.
4.
5.
6.
7.
8.
V
Tests
Quizzes
Class work/Notebooks
Class participation
Homework
Open ended questions
Rubric based assessment
Benchmark student assessments
Standards of Evaluation:
1.
2.
3.
4.
5.
6.
7.
8.
Tests
Quizzes
Class notes/Notebooks
Class participation
Homework
Open ended questions
Rubric based assessment
Benchmark student assessment
7
VI
Expectations:
1. Students will be responsible for textbooks and other supplies necessary to
complete a class work.
2. Students will maintain notes required by the teacher.
3. Students will be expected to list and follow all directions necessary to
complete assignments.
4. Students will be responsible for acceptable performance such as class
attendance, make up work, and testing.
5. Students will be responsible for efficient use of calculators, computers,
manipulatives, and other mathematical tools.
6. Students will review daily homework and concepts.
7. Students will organize review for tests including test-taking and testpreparation strategies.
8. Students will work effectively to complete group/individual assignments.
9. Students will review /take a mid-term and final exam.
8
STATE STANDARDS
MATHEMATICS
STANDARDS AND PROGRESS INDICATORS
GRADE 7
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.
Strands and Cumulative Progress Indicators
Building upon knowledge and skills gained in preceding grades, by the end of Grade 7,
students will:
A. Number Sense
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
2. Demonstrate a sense of the relative magnitudes of numbers.
3. Understand and use ratios, proportions, and percents (including percents greater
than 100 and less than 1) in a variety of situations.
4. Compare and order numbers of all named types.
5. Use whole numbers, fractions, decimals, and percents to represent equivalent
forms of the same number.
6. Understand that all fractions can be represented as repeating or terminating
decimals.
9
B. Numerical Operations
1. Use and explain procedures for performing calculations with integers and all
number types named above with:

Pencil-and-paper

Mental math

Calculator
2. Use exponentiation to find whole number powers of numbers.
3. Understand and apply the standard algebraic order of operations, including
appropriate use of parentheses.
C. Estimation
1. Use equivalent representations of numbers such as fractions, decimals, and
percents to facilitate estimation.
10
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.
Strands and Cumulative Progress Indicators
Building upon knowledge and skills gained in preceding grades, by the end of Grade 7,
students will:
A. Geometric Properties
1. Understand and apply properties of polygons.

Quadrilaterals, including squares, rectangles, parallelograms, trapezoids,
rhombi

Regular polygons

2. Understand and apply the concept of similarity.

Using proportions to find missing measures

Scale drawings

Models of 3D objects
3. Use logic and reasoning to make and support conjectures about geometric objects.
B. Transforming Shapes
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
C. Coordinate Geometry
1. Use coordinates in four quadrants to represent geometric concepts.
11
2. Use a coordinate grid to model and quantify transformations (e.g., translate right 4
units).
D. Units of Measurement
1. Solve problems requiring calculations that involve different units of measurement
within a measurement system (e.g., 4'3" plus 7'10" equals 12'1").
2. Select and use appropriate units and tools to measure quantities to the degree of
precision needed in a particular problem-solving situation.
3. Recognize that all measurements of continuous quantities are approximations.
E. Measuring Geometric Objects
1. Develop and apply strategies for finding perimeter and area.

Geometric figures made by combining triangles, rectangles and circles or
parts of circles

Estimation of area using grids of various sizes
2. Recognize that the volume of a pyramid or cone is one-third of the volume of the
prism or cylinder with the same base and height (e.g., use rice to compare
volumes of figures with same base and height).
12
STANDARD 4.3 (Patterns and algebra) All students will represent and analyze
relationships among variable quantities and solve problems involving patterns, functions,
and algebraic concepts and processes.
Strands and Cumulative Progress Indicators
Building upon knowledge and skills gained in preceding grades, by the end of Grade 7,
students will:
A. Patterns
1. Recognize, describe, extend, and create patterns involving whole numbers,
rational numbers, and integers.

Descriptions using tables, verbal and symbolic rules, graphs, simple
equations or expressions

Finite and infinite sequences

Generating sequences by using calculators to repeatedly apply a formula
B. Functions and Relationships
1. Graph functions, and understand and describe their general behavior.

Equations involving two variables
C. Modeling
1. Analyze functional relationships to explain how a change in one quantity can
result in a change in another, using pictures, graphs, charts, and equations.
2. Use patterns, relations, symbolic algebra, and linear functions to model situations.

Using manipulatives, tables, graphs, verbal rules, algebraic
expressions/equations/inequalities

Growth situations, such as population growth and compound interest,
using recursive (e.g., NOW-NEXT) formulas (cf. science standard 5.5 and
social studies standard 6.6)
13
D. Procedures
1. Use graphing techniques on a number line.

Absolute value

Arithmetic operations represented by vectors (arrows) (e.g., "-3 + 6" is
"left 3, right 6")
2. Solve simple linear equations informally and graphically.

Multi-step, integer coefficients only (although answers may not be
integers)

Using paper-and-pencil, calculators, graphing calculators, spreadsheets,
and other technology
3. Create, evaluate, and simplify algebraic expressions involving variables.

Order of operations, including appropriate use of parentheses

Substitution of a number for a variable
4. Understand and apply the properties of operations, numbers, equations, and
inequalities.

Additive inverse

Multiplicative inverse
14
STANDARD 4.4 (Data analysis, probability, and discrete mathematics) All students will
develop an understanding of the concepts and techniques of data analysis, probability,
and discrete mathematics, and will use them to model situations, solve problems, and
analyze and draw appropriate inferences from data.
Strands and Cumulative Progress Indicators
Building upon knowledge and skills gained in preceding grades, by the end of Grade 7,
students will:
A. Data Analysis (or Statistics)
1. Select and use appropriate representations for sets of data, and measures of central
tendency (mean, median, and mode).

Type of display most appropriate for given data

Box-and-whisker plot, upper quartile, lower quartile

Scatter plot

Calculators and computer used to record and process information
2. Make inferences and formulate and evaluate arguments based on displays and
analysis of data.
B. Probability
1. Interpret probabilities as ratios, percents, and decimals.
2. Model situations involving probability with simulations (using spinners, dice,
calculators and computers) and theoretical models.

Frequency, relative frequency
3. Estimate probabilities and make predictions based on experimental and theoretical
probabilities.
4. Play and analyze probability-based games, and discuss the concepts of fairness
and expected value.
15
C. Discrete Mathematics—Systematic Listing and Counting
1. Apply the multiplication principle of counting.

Permutations: ordered situations with replacement (e.g., number of
possible license plates) vs. ordered situations without replacement (e.g.,
number of possible slates of 3 class officers from a 23 student class)
2. Explore counting problems involving Venn diagrams with three attributes (e.g.,
there are 15, 20, and 25 students respectively in the chess club, the debating team,
and the engineering society; how many different students belong to the three clubs
if there are 6 students in chess and debating, 7 students in chess and engineering,
8 students in debating and engineering, and 2 students in all three?).
3. Apply techniques of systematic listing, counting, and reasoning in a variety of
different contexts.
D. Discrete Mathematics—Vertex-Edge Graphs and Algorithms
1. Use vertex-edge graphs to represent and find solutions to practical problems.

Finding the shortest network connecting specified sites

Finding the shortest route on a map from one site to another

Finding the shortest circuit on a map that makes a tour of specified sites
16
STANDARD 4.5 (Mathematical processes) All students will use mathematical processes
of problem solving, communication, connections, reasoning, representations, and
technology to solve problems and communicate mathematical ideas.
Strands and Cumulative Progress Indicators
Building upon knowledge and skills gained in preceding grades, by the end of Grade 7,
students will:
A. Problem Solving
1. Learn mathematics through problem solving, inquiry, and discovery.
2. Solve problems that arise in mathematics and in other contexts (cf. workplace
readiness standard 8.3).

Open-ended problems

Non-routine problems

Problems with multiple solutions

Problems that can be solved in several ways
3. Select and apply a variety of appropriate problem-solving strategies (e.g., "try a
simpler problem" or "make a diagram") to solve problems.
4. Pose problems of various types and levels of difficulty.
5. Monitor their progress and reflect on the process of their problem solving activity.
B. Communication
1. Use communication to organize and clarify their mathematical thinking.

Reading and writing

Discussion, listening, and questioning
2. Communicate their mathematical thinking coherently and clearly to peers,
teachers, and others, both orally and in writing.
3. Analyze and evaluate the mathematical thinking and strategies of others.
4. Use the language of mathematics to express mathematical ideas precisely.
17
C. Connections
1. Recognize recurring themes across mathematical domains (e.g., patterns in
number, algebra, and geometry).
2. Use connections among mathematical ideas to explain concepts (e.g., two linear
equations have a unique solution because the lines they represent intersect at a
single point).
3. Recognize that mathematics is used in a variety of contexts outside of
mathematics.
4. Apply mathematics in practical situations and in other disciplines.
5. Trace the development of mathematical concepts over time and across cultures
(cf. world languages and social studies standards).
6. Understand how mathematical ideas interconnect and build on one another to
produce a coherent whole.
D. Reasoning
1. Recognize that mathematical facts, procedures, and claims must be justified.
2. Use reasoning to support their mathematical conclusions and problem solutions.
3. Select and use various types of reasoning and methods of proof.
4. Rely on reasoning, rather than answer keys, teachers, or peers, to check the
correctness of their problem solutions.
5. Make and investigate mathematical conjectures.

Counterexamples as a means of disproving conjectures

Verifying conjectures using informal reasoning or proofs.
6. Evaluate examples of mathematical reasoning and determine whether they are
valid.
E. Representations
1. Create and use representations to organize, record, and communicate
mathematical ideas.

Concrete representations (e.g., base-ten blocks or algebra tiles)

Pictorial representations (e.g., diagrams, charts, or tables)

Symbolic representations (e.g., a formula)
18

Graphical representations (e.g., a line graph)
2. Select, apply, and translate among mathematical representations to solve
problems.
3. Use representations to model and interpret physical, social, and mathematical
phenomena.
F. Technology
1. Use technology to gather, analyze, and communicate mathematical information.
2. Use computer spreadsheets, software, and graphing utilities to organize and
display quantitative information.
3. Use graphing calculators and computer software to investigate properties of
functions and their graphs.
4. Use calculators as problem-solving tools (e.g., to explore patterns, to validate
solutions).
5. Use computer software to make and verify conjectures about geometric objects.
6. Use computer-based laboratory technology for mathematical applications in the
sciences.
19
Scope and Sequence
September
Pretest
Test Taking Strategies
Calculator Instruction
October
Number Sense, Patterns, and Algebraic Thinking
Decimal Operations
November
Data and Statistics
December
Number Patterns and Fractions
Fraction Operations
January
Integers
Equations, Inequalities, and Functions
February
Equations, Inequalities, and Functions
Ratios and Proportions
March
Percents
Probability
Geometric Figures
April
Measurement and Area
Surface Area and Volume
May
Integer Operations
June
Variables
Equations
20
UNIT I
A.
TEST TAKING STRATEGIES
Duration: September
Major Objectives:
1.
2.
3.
4.
5.
B.
Sequence of Topics:
1.
2.
3.
4.
5.
6.
7.
C.
To learn and utilize the skills necessary to answer multiple choice
questions.
To learn and utilize the skills necessary to answer extended
response questions.
To learn and utilize the skills necessary to answer short response
questions.
To review basic mathematical facts, including decimal operations.
To explore basic calculator skills.
Answering the question asked (4.5) (p. 2)
Eliminating answers (4.5) (p. 6)
Writing a short answer response (4.5) (p. 3)
Writing extended responses (4.5) (p. 4)
Working backwards (4.5) (p. 7)
Review operations with decimals (4.1) (p. 22, 35, 38)
Explore basic calculator skills.
Core Material:
Test-Taking Strategies
Pearson Prentice Hall 2007
Measuring Up 7
Brooks, Carlin, McLaughlin, Perry, Vogt
People’s Education 2006
D.
Supplemental Materials:
1.
2.
3.
4.
5.
6.
7.
8.
Teacher made transparencies
Teacher made worksheets
Power Point Presentations
Study Island
Success Maker
Calculators
Internet
NJASK Coach WriteMath
21
E.
Suggested Assignments, Projects, Field Trips, Speakers:
1.
2.
3.
4.
5.
F.
Complete exercises in book for each lesson
Complete practice worksheets
Use calculator/computer to complete classroom and homework
problems
Complete/review chapter prior to test/quizzes using text and
teacher made materials.
NJASK Do Now
Suggested Assessments:
1.
2.
3.
4.
5.
6.
Test
Quizzes
Class Participation
Notebook/Classwork
Homework
Benchmark Tests
22
UNIT II
A.
NUMBER SENSE, PATTERNS, AND ALGEBRAIC THINKING
Duration: October
Major Objectives:
1.
2.
To describe patterns and use them to solve problems.
To apply the order of operations to evaluate variable expressions
involving powers and exponents and to solve equations.
B.
Sequence of Topics:
1.
Describe patterns using whole number operations. (4.3)
2.
Evaluate variable expressions. (4.3)
3.
Write repeated multiplication using exponents. (4.1)
4.
Use the order of operations to evaluate expressions involving two
or more operations. (4.1)
5.
Use mental math to solve equations. (4.3)
6.
Use formulas to find perimeter and area. (4.2)
7.
Use a 4-step plan to solve problems. (4.5)
C.
Core Material:
New Jersey ASK Coach
Kaplan
Triumph Learning 2005
Measuring Up
Peoples Education 2006
D.
Supplemental Materials:
1.
2.
3.
4.
5.
6.
7.
E.
Educational Design- Pre GEPA
Instructivision Inc.– Pre GEPA Success
Peoples Publishing- Measuring Up on the NJ GEPA
Teacher made transparencies
Teacher made worksheets
Study Island
Success Maker
Suggested Assignments, Projects, Field Trips, Speakers:
1.
2.
3.
Complete exercises in NJASK Coach / Measuring Up for each
lesson
Complete sample test questions at the end of each unit
Use calculator/computer to complete classroom and homework
problems
23
4.
5.
F.
Complete/review chapter prior to test/quizzes using text and
teacher made materials
NJASK Do Now
Suggested Assessments:
1.
2.
3.
4.
5.
6.
7.
Test
Quizzes
Class participation
Notebook/classwork
Homework
Study Island
Success Maker
24
UNIT III
A.
DECIMAL OPERATIONS
Duration: October
Major Objectives:
1.
2.
B.
Sequence of Topics:
1.
2.
3.
4.
5.
6.
7.
C.
To perform operations with decimals, including comparing and
rounding decimals.
To solve real-world problems involving scientific notation and
metric measurements.
Compare, order, and round decimals. (4.1)
Add and subtract decimals. (4.1)
Multiply decimals. (4.1)
Divide decimals. (4.1)
Read and write numbers using scientific notation. (4.1)
Measure and estimate using metric units. (4.2)
Convert between metric units. (4.2)
Core Material:
New Jersey ASK Coach
Kaplan
Triumph Learning 2005
Measuring Up
Peoples Education 2006
D.
Supplemental Materials:
1.
2.
3.
4.
5.
6.
7.
E.
Educational Design- Pre GEPA
Instructivision Inc.– Pre GEPA Success
Peoples Publishing- Measuring Up on the NJ GEPA
Teacher made transparencies
Teacher made worksheets
Study Island
Success Maker
Suggested Assignments, Projects, Field Trips, Speakers:
1.
Complete exercises in NJASK Coach / Measuring Up for each
lesson
25
2.
3.
4.
5.
F.
Complete sample test questions at the end of each unit
Use calculator/computer to complete classroom and homework
problems
Complete/review chapter prior to test/quizzes using text and
teacher made materials
NJASK Do Now
Suggested Assessments:
1.
2.
3.
4.
5.
6.
7.
Test
Quizzes
Class participation
Notebook/classwork
Homework
Study Island
Success Maker
26
UNIT IV
A.
DATA AND STATISTICS
Duration: November
Major Objectives:
1.
2.
B.
Sequence of Topics:
1.
2.
3.
4.
5.
6.
7.
C.
To study the mean, median, and mode of a data set.
Use bar graphs, line graphs, stem-and-leaf plots, box-and-whisker
plots, and histograms to display and analyze the distribution of the
values in a data set.
Describe data using mean, median, and mode. (4.4)
Make and interpret bar graphs and line graphs. (4.4)
Display data using stem-and-leaf plots. (4.4)
Display data using box-and-whisker plots (4.4)
Make and interpret histograms (4.4)
Choose an appropriate display for a data set. (4.4)
NJASK Preparation, Coach book. (4.1)
Core Material:
New Jersey ASK Coach
Kaplan
Triumph Learning 2005
Measuring Up
Peoples Education 2006
D.
Supplemental Materials:
1.
2.
3.
4.
5.
6.
7.
Educational Design- Pre GEPA
Instructivision Inc.– Pre GEPA Success
Peoples Publishing- Measuring Up on the NJ GEPA
Teacher made transparencies
Teacher made worksheets
Study Island
Success Maker
27
E.
Suggested Assignments, Projects, Field Trips, Speakers:
1.
2.
3.
4.
5.
F.
Complete exercises in NJASK Coach / Measuring Up for each
lesson
Complete sample test questions at the end of each unit
Use calculator/computer to complete classroom and homework
problems
Complete/review chapter prior to test/quizzes using text and
teacher made materials
NJASK Do Now
Suggested Assessments:
1.
2.
3.
4.
5.
6.
7.
Test
Quizzes
Class participation
Notebook/classwork
Homework
Study Island
Success Maker
28
UNIT V
A.
NUMBER PATTERNS AND FRACTIONS
Duration: December
Major Objectives:
1.
2.
B.
Sequence of Topics:
1.
2.
3.
4.
5.
6.
7.
8.
C.
To find the greatest common factor and least common multiple of
two or more numbers.
To compare fractions and mixed numbers, and to write
fractions as decimals and vice versa.
Write a number as a product of primes. (4.1) (pp. 165-169)
Find the greatest common factor of two or more numbers. (4.1)
(pp. 170-174)
Write equivalent fractions. (4.1) (pp. 176-180)
Find the least common multiple of two or more numbers. (4.1)
(pp. 182-186)
Compare and order fractions. (4.1) (pp. 189-192)
Compare and order fractions and mixed numbers. (4.1)
(pp. 194-198)
Write fractions as decimals and decimals as fractions. (4.1)
(pp. 199-204)
NJASK Preparation, Coach book. (4.2) (pp. 82-111)
Core Material:
New Jersey ASK Coach
Kaplan
Triumph Learning 2005
Measuring Up
Peoples Education 2006
D.
Supplemental Materials:
1.
2.
3.
4.
5.
6.
7.
Educational Design- Pre GEPA
Instructivision Inc.– Pre GEPA Success
Peoples Publishing- Measuring Up on the NJ GEPA
Teacher made transparencies
Teacher made worksheets
Study Island
Success Make
29
E.
Suggested Assignments, Projects, Field Trips, Speakers:
1.
2.
3.
4.
5.
F.
Complete exercises in NJASK Coach / Measuring Up for each
lesson
Complete sample test questions at the end of each unit
Use calculator/computer to complete classroom and homework
problems
Complete/review chapter prior to test/quizzes using text and
teacher made materials
NJASK Do Now
Suggested Assessments:
1.
2.
3.
4.
5.
6.
7.
Test
Quizzes
Class participation
Notebook/classwork
Homework
Study Island
Success Maker
30
UNIT VI
A.
FRACTION OPERATIONS
Duration: December
Major Objectives:
1.
2.
B.
Sequence of Topics:
1.
2.
3.
4.
5.
6.
C.
To add and subtract fractions and mixed numbers.
To multiply and divide fractions and mixed numbers, and to
learn about customary units.
Add and subtract fractions. (4.1)
Add and subtract mixed numbers. (4.1)
Multiply fractions and mixed numbers. (4.1)
Divide fractions and mixed numbers. (4.1)
Measure and estimate using customary units. (4.1)
Convert between customary units. (4.1)
Core Material:
New Jersey ASK Coach
Kaplan
Triumph Learning 2005
Measuring Up
Peoples Education 2006
D.
Supplemental Materials:
1.
2.
3.
4.
5.
6.
7.
E.
Educational Design- Pre GEPA
Instructivision Inc.– Pre GEPA Success
Peoples Publishing- Measuring Up on the NJ GEPA
Teacher made transparencies
Teacher made worksheets
Study Island
Success Maker
Suggested Assignments, Projects, Field Trips, Speakers:
1.
2.
3.
Complete exercises in NJASK Coach / Measuring Up for each
lesson
Complete sample test questions at the end of each unit
Use calculator/computer to complete classroom and homework
problems
31
4.
5.
F.
Complete/review chapter prior to test/quizzes using text and
teacher made materials
NJASK Do Now
Suggested Assessments:
1.
2.
3.
4.
5.
6.
7.
Test
Quizzes
Class participation
Notebook/classwork
Homework
Study Island
Success Maker
32
UNIT VII
A.
INTEGERS
Duration: January
Major Objectives:
1.
2.
B.
Sequence of Topics:
1.
2.
3.
4.
5.
6.
7.
8.
7.
C.
To compare and order integers and perform integer addition,
subtractions, multiplication, and division.
To define rational numbers and graph points in the coordinate
plane.
Compare and order integers. (4.1)
Add integers. (4.1)
Subtract integers. (4.1)
Multiply integers. (4.1)
Divide integers (4.1)
Perform operations on rational numbers. (4.1)
Evaluate expression using the distributive property. (4.3)
Identify and plot points in a coordinate plane. (4.2)
NJASK Preparation, Coach book. (4.3)
Core Material:
New Jersey ASK Coach
Kaplan
Triumph Learning 2005
Measuring Up
Peoples Education 2006
D.
Supplemental Materials:
1.
2.
3.
4.
5.
6.
7.
E.
Educational Design- Pre GEPA
Instructivision Inc.– Pre GEPA Success
Peoples Publishing- Measuring Up on the NJ GEPA
Teacher made transparencies
Teacher made worksheets
Study Island
Success Maker
Suggested Assignments, Projects, Field Trips, Speakers:
33
1.
2.
3.
4.
5.
F.
Complete exercises in NJASK Coach / Measuring Up for each
lesson
Complete sample test questions at the end of each unit
Use calculator/computer to complete classroom and homework
problems
Complete/review chapter prior to test/quizzes using text and
teacher made materials
NJASK Do Now
Suggested Assessments:
1.
2.
3.
4.
5.
6.
7.
Test
Quizzes
Class participation
Notebook/classwork
Homework
Study Island
Success Maker
34
UNIT VIII
A.
EQUATIONS, INEQUALITIES, AND FUNCTIONS
Duration: January / February
Major Objectives:
1.
2.
B.
Sequence of Topics:
1.
2.
3.
4.
5.
6.
7.
8.
C.
To write and simplify expressions, and solve equations and
inequalities.
To use equations, table, and graphs to represent functions.
Write variable expressions and equations. (4.3)
Simplify variable expressions. (4.3)
Solve addition and subtraction equations. (4.3)
Solve multiplication and division equations. (4.3))
Solve two-step equations. (4.3)
Write and solve inequalities. (4.3)
Write and evaluate function rules. (4.3)
Graph functions in a coordinate plane. (4.3)
Core Material:
New Jersey ASK Coach
Kaplan
Triumph Learning 2005
Measuring Up
Peoples Education 2006
D.
Supplemental Materials:
1.
2.
3.
4.
5.
6.
7.
E.
Educational Design- Pre GEPA
Instructivision Inc.– Pre GEPA Success
Peoples Publishing- Measuring Up on the NJ GEPA
Teacher made transparencies
Teacher made worksheets
Study Island
Success Maker
Suggested Assignments, Projects, Field Trips, Speakers:
1.
Complete exercises in NJASK Coach / Measuring Up for each
lesson
35
2.
3.
F.
Complete sample test questions at the end of each unit
Use calculator/computer to complete classroom and homework
problems
4.
Complete/review chapter prior to test/quizzes using text and
teacher made materials
5.
NJASK Do Now
Suggested Assessments:
1.
2.
3.
4.
5.
6.
7.
Test
Quizzes
Class participation
Notebook/classwork
Homework
Study Island
Success Maker
36
UNIT IX
A.
RATIOS AND PROPORTIONS
Duration: February
Major Objectives:
1.
2.
B.
Sequence of Topics:
1.
2.
3.
4.
5.
6.
C.
Apply ratios, rates, and unit rates to solve proportions and to scale
drawings.
To explore the relationship between rate and the slope of a line
Write and compare ratios. (4.1)
Use rates to compare two quantities with different units. (4.1)
Find the slope of a line. (4.3)
Solve proportions using equivalent ratios and algebra (4.3)
Solve proportions using cross products. (4.3)
Use proportions with models. (4.5)
Core Material:
New Jersey ASK Coach
Kaplan
Triumph Learning 2005
Measuring Up
Peoples Education 2006
D.
Supplemental Materials:
1.
2.
3.
4.
5.
6.
7.
E.
Educational Design- Pre GEPA
Instructivision Inc.– Pre GEPA Success
Peoples Publishing- Measuring Up on the NJ GEPA
Teacher made transparencies
Teacher made worksheets
Study Island
Success Maker
Suggested Assignments, Projects, Field Trips, Speakers:
1.
2.
3.
Complete exercises in NJASK Coach / Measuring Up for each
lesson
Complete sample test questions at the end of each unit
Use calculator/computer to complete classroom and homework
problems
37
4.
5.
F.
Complete/review chapter prior to test/quizzes using text and
teacher made materials
NJASK Do Now
Suggested Assessments:
1.
2.
3.
4.
5.
6.
7.
Test
Quizzes
Class participation
Notebook/classwork
Homework
Study Island
Success Maker
38
UNIT X
A.
PERCENTS
Duration: March
Major Objectives:
1.
2.
B.
C.
Examine the relationships among fractions, decimals, and percents
when writing fractions and decimals as percents.
Solve percent problems, including discounts, markups, sales tax,
tips, and simple interest.
Sequence of Topics:
1.
2.
Use a fraction to find the percent of a number. (4.1)
Use proportions to solve percent problems. (4.1
3.
4.
5.
6.
7.
8.
9.
10.
Write percents as decimals and decimals as percents. (4.1)
Solve proportions using equivalent ratios and algebra. (4.3)
Use equations to solve percent problems. (4.3)
Use percents to interpret and make circle graphs. (4.4)
Find a percent of change in a quantity. (4.5)
Find discounts, markups, sales tax, and tips. (4.5)
Calculate simple interest. (4.5)
NJASK Preparation, Coach book. (4.4)
Core Material:
New Jersey ASK Coach
Kaplan
Triumph Learning 2005
Measuring Up
Peoples Education 2006
D.
Supplemental Materials:
1.
2.
3.
4.
5.
6.
7.
Educational Design- Pre GEPA
Instructivision Inc.– Pre GEPA Success
Peoples Publishing- Measuring Up on the NJ GEPA
Teacher made transparencies
Teacher made worksheets
Study Island
Success Maker
39
E.
Suggested Assignments, Projects, Field Trips, Speakers:
1.
2.
3.
4.
5.
F.
Complete exercises in NJASK Coach / Measuring Up for each
lesson
Complete sample test questions at the end of each unit
Use calculator/computer to complete classroom and homework
problems
Complete/review chapter prior to test/quizzes using text and
teacher made materials
NJASK Do Now
Suggested Assessments:
1.
2.
3.
4.
5.
6.
7.
Test
Quizzes
Class participation
Notebook/classwork
Homework
Study Island
Success Maker
40
UNIT XI
A.
PROBABILITY
Duration: March
Major Objectives:
1.
2.
B.
Sequence of Topics:
1.
2.
3.
4.
5.
6.
7.
C.
To count the possible outcomes of an experiment using tree
diagrams and the counting principle, and study permutations and
combinations.
Examine methods for calculating the probability of events,
including dependent and independent events.
Find probabilities. (4.4)
Use a tree diagram to find all possible outcomes. (4.4)
Use the counting principle to count outcomes. (4.4)
Use permutations and combinations (4.4)
Find the probability that either of two events occurs. (4.4)
Find the probability of compound events. (4.4)
NJASK Preparation, Coach book. (4.5)
Core Material:
New Jersey ASK Coach
Kaplan
Triumph Learning 2005
Measuring Up
Peoples Education 2006
D.
Supplemental Materials:
1.
2.
3.
4.
5.
6.
7.
E.
Educational Design- Pre GEPA
Instructivision Inc.– Pre GEPA Success
Peoples Publishing- Measuring Up on the NJ GEPA
Teacher made transparencies
Teacher made worksheets
Study Island
Success Maker
Suggested Assignments, Projects, Field Trips, Speakers:
1.
Complete exercises in NJASK Coach / Measuring Up for each
lesson
41
2.
3.
4.
5.
F.
Complete sample test questions at the end of each unit
Use calculator/computer to complete classroom and homework
problems
Complete/review chapter prior to test/quizzes using text and
teacher made materials
NJASK Do Now
Suggested Assessments:
1.
2.
3.
4.
5.
6.
7.
Test
Quizzes
Class participation
Notebook/classwork
Homework
Study Island
Success Maker
42
UNIT XII
A.
GEOMETRIC FIGURES
Duration: March
Major Objectives:
1.
2.
B.
Sequence of Topics:
1.
2.
3.
4.
5.
6.
7.
8.
C.
To explore angles, triangles, and polygons, and investigate
congruent and similar polygons.
To study three types of transformations: translations, reflections,
and rotations.
Classify angles by their measures. (4.2)
Identify special pairs of angles and types of lines. (4.2)
Classify triangles. (4.2)
Classify quadrilaterals and other polygons. (4.2)
Use properties of similar and congruent polygons. (4.2)
Use similar triangles to find lengths. (4.2)
Identify transformations and symmetry in figures. (4.2)
Graph transformations in a coordinate plane. (4.2)
Core Material:
New Jersey ASK Coach
Kaplan
Triumph Learning 2005
Measuring Up
Peoples Education 2006
D.
Supplemental Materials:
1.
2.
3.
4.
5.
6.
7.
E.
Educational Design- Pre GEPA
Instructivision Inc.– Pre GEPA Success
Peoples Publishing- Measuring Up on the NJ GEPA
Teacher made transparencies
Teacher made worksheets
Study Island
Success Maker
Suggested Assignments, Projects, Field Trips, Speakers:
1.
2.
Complete exercises in NJASK Coach / Measuring Up for each
lesson
Complete sample test questions at the end of each unit
43
3.
4.
5.
F.
Use calculator/computer to complete classroom and homework
problems
Complete/review chapter prior to test/quizzes using text and
teacher made materials
NJASK Do Now
Suggested Assessments:
1.
2.
3.
4.
5.
6.
7.
Test
Quizzes
Class participation
Notebook/classwork
Homework
Study Island
Success Maker
44
UNIT XIII
A.
MEASUREMENT AND AREA
Duration: April
Major Objectives:
1.
2.
B.
Sequence of Topics:
1.
2.
3.
4.
5.
6.
7.
C.
To use the Pythagorean Theorem.
To apply the area formulas for parallelograms, triangles,
trapezoids, and circles to solve real-world problems.
Evaluate expression involving square roots. (4.1)
Approximate square roots of numbers. (4.1)
Find the length of a side of a right triangle. (4.2)
Find the area of parallelograms. (4.2)
Find the areas of triangles and trapezoids. (4.2)
Find the circumferences of circles. (4.2)
Find the areas of circles. (4.2)
Core Material:
New Jersey ASK Coach
Kaplan
Triumph Learning 2005
Measuring Up
Peoples Education 2006
D.
Supplemental Materials:
1.
2.
3.
4.
5.
6.
7.
E.
Educational Design- Pre GEPA
Instructivision Inc.– Pre GEPA Success
Peoples Publishing- Measuring Up on the NJ GEPA
Teacher made transparencies
Teacher made worksheets
Study Island
Success Maker
Suggested Assignments, Projects, Field Trips, Speakers:
1.
2.
3.
Complete exercises in NJASK Coach / Measuring Up for each
lesson
Complete sample test questions at the end of each unit
Use calculator/computer to complete classroom and homework
problems
45
4.
5.
F.
Complete/review chapter prior to test/quizzes using text and
teacher made materials
NJASK Do Now
Suggested Assessments:
1.
2.
3.
4.
5.
6.
7.
Test
Quizzes
Class participation
Notebook/classwork
Homework
Study Island
Success Maker
46
UNIT XIV
A.
SURFACE AREA AND VOLUME
Duration: April
Major Objectives:
1.
2.
B.
Sequence of Topics:
1.
2.
3.
4.
5.
6.
C.
To classify and sketch prisms, pyramids, cylinders, and cones, and
their nets.
To explore and use the formulas for the surface area and volume of
rectangular prisms and cylinders.
Classify solids and identify their parts. (4.2)
Sketch solids. (4.2)
Find surface areas of rectangular prisms. (4.2)
Find surface areas of cylinders. (4.2)
Find volumes of rectangular prisms. (4.2)
Find volumes of cylinders. (4.2)
Core Material:
New Jersey ASK Coach
Kaplan
Triumph Learning 2005
Measuring Up
Peoples Education 2006
D.
Supplemental Materials:
1.
2.
3.
4.
5.
6.
7.
E.
Educational Design- Pre GEPA
Instructivision Inc.– Pre GEPA Success
Peoples Publishing- Measuring Up on the NJ GEPA
Teacher made transparencies
Teacher made worksheets
Study Island
Success Maker
Suggested Assignments, Projects, Field Trips, Speakers:
1.
2.
3.
4.
Complete exercises in NJASK Coach / Measuring Up for each
lesson
Complete sample test questions at the end of each unit
Use calculator/computer to complete classroom and homework
problems
Complete/review chapter prior to test/quizzes using text and
teacher made materials
47
5.
F.
NJASK Do Now
Suggested Assessments:
1.
2.
3.
4.
5.
6.
7.
Test
Quizzes
Class participation
Notebook/classwork
Homework
Study Island
Success Maker
48
UNIT XV
A.
REVIEW INTEGER OPERATIONS (beginning 8th Grade Topic)
Duration: May
Major Objectives:
1.
2.
3.
B.
Sequence of Topics:
1.
2.
3.
4.
5.
6.
7.
8.
7.
C.
To compare and order integers and perform integer addition,
subtractions, multiplication, and division.
To define rational numbers and graph points in the coordinate
plane.
To expand on topics learned earlier in the year to ensure students
are well prepared for the beginning of 8th grade.
Compare and order integers. (4.1)
Add integers. (4.1)
Subtract integers. (4.1)
Multiply integers. (4.1)
Divide integers (4.1)
Perform operations on rational numbers. (4.1)
Evaluate expression using the distributive property. (4.3)
Identify and plot points in a coordinate plane. (4.2)
NJASK Preparation, Coach book. (4.3)
Core Material:
New Jersey ASK Coach
Kaplan
Triumph Learning 2005
Measuring Up
Peoples Education 2006
D.
Supplemental Materials:
1.
2.
3.
4.
5.
6.
7.
E.
Educational Design- Pre GEPA
Instructivision Inc.– Pre GEPA Success
Peoples Publishing- Measuring Up on the NJ GEPA
Teacher made transparencies
Teacher made worksheets
Study Island
Success Maker
Suggested Assignments, Projects, Field Trips, Speakers:
49
1.
2.
3.
4.
5.
F.
Complete exercises in NJASK Coach / Measuring Up for each
lesson
Complete sample test questions at the end of each unit
Use calculator/computer to complete classroom and homework
problems
Complete/review chapter prior to test/quizzes using text and
teacher made materials
NJASK Do Now
Suggested Assessments:
1.
2.
3.
4.
5.
6.
7.
Test
Quizzes
Class participation
Notebook/classwork
Homework
Study Island
Success Maker
50
UNIT XVI
Topic)
REVIEW VARIABLES AND EQUATIONS (beginning 8th Grade
Duration: June
A.
Major Objectives:
1.
2.
3.
B.
Sequence of Topics:
1.
2.
3.
4.
5.
6.
7.
8.
9.
C.
To write and simplify expressions, and solve equations and
inequalities.
To use equations, table, and graphs to represent functions.
To expand on topics learned earlier in the year to ensure students
are well prepared for the beginning of 8th grade.
Write variable expressions and equations. (4.3)
Simplify variable expressions. (4.3)
Solve addition and subtraction equations. (4.3)
Solve multiplication and division equations. (4.3))
Solve two-step equations. (4.3)
Write and solve inequalities. (4.3)
Write and evaluate function rules. (4.3)
Graph functions in a coordinate plane. (4.3)
NJASK Preparation, Coach book. (4.3)
Core Material:
New Jersey ASK Coach
Kaplan
Triumph Learning 2005
Measuring Up
Peoples Education 2006
D.
Supplemental Materials:
1.
2.
3.
4.
5.
6.
7.
E.
Educational Design- Pre GEPA
Instructivision Inc.– Pre GEPA Success
Peoples Publishing- Measuring Up on the NJ GEPA
Teacher made transparencies
Teacher made worksheets
Study Island
Success Maker
Suggested Assignments, Projects, Field Trips, Speakers:
1.
Complete exercises in NJASK Coach / Measuring Up for each
lesson
51
2.
3.
4.
5.
F.
Complete sample test questions at the end of each unit
Use calculator/computer to complete classroom and homework
problems
Complete/review chapter prior to test/quizzes using text and
teacher made materials
NJASK Do Now
Suggested Assessments:
1.
2.
3.
4.
5.
6.
7.
Test
Quizzes
Class participation
Notebook/classwork
Homework
Study Island
Success Maker
52