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Roselle Park School District

Mathematics Department

Course of Study

Math Grade 7 Honors

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MATH GRADE 7 HONORS

PRE-ALGEBRA

The purpose of this guide is to provide the instructor with a scope and sequence and the

course objectives. 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.

This guide applies to all students and meets the Affirmative Action guidelines.

Written by: Anne Marciano

Revised Summer 2007

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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.

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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.

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MATHEMATICS DEPARTMENT

COURSE PROFICIENCIES

Pre-Algebra

I. Descriptions:

The objective of the seventh grade honors pre-algebra math is to aid students in

making the transition from elementary mathematics to more advanced high school

math courses. The curriculum lays the foundations for the studies of algebra,

geometry, and statistics. 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 basic trigonometry.

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 through tests and teacher recommendation.

II. Unit Topics:

Variables, Expressions, and Integers

Solving Equations

Multi-Step Equations and Inequalities

Factors, Fractions, and Exponents

Rational Numbers and Equations

Ratio, Proportion, and Probability

Percents

Linear Functions

Real Numbers and Right Triangles

Measurement, Area, and Volume

Data Analysis and Probability

Polynomials and nonlinear Functions

Angle Relationships and Transformations

NJ Ask Skills

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III Objectives:

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.

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

Write numbers in scientific notation

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 are of a triangle

Calculate the are of a trapezoid

Determine the perimeter and area of an irregular figure

Determine the complement and supplement of a given angle

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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

Solve inequalities

Utilize the rules of exponents to simplify expressions and find products and

quotients

Simplify expressions involving negative exponents

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

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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

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 ina variety of

contexts

IV Types of Evaluations:

1. Tests

2. Quizzes

3. Class work/Notebooks

4. Class participation

5. Homework

6. Open ended questions

7. Rubric based assessment

V Standards of Evaluation:

1. Tests

2. Quizzes

3. Class notes/Notebooks

4. Class participation

5. Homework

6. Open ended questions

7. Rubric based assessment

VII 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 test-

preparation strategies.

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8. Students will work effectively to complete group/individual assignments.

9. Students will review /take a mid-term and final exam.

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.

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STATE STANDARDS

MATHEMATICS

STANDARDS AND PROGRESS INDICATORS

GRADE 8

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 the

course, 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 8 pertain to these

sets of numbers as well):

Rational numbers

Percents

Exponents

Roots

Absolute values

Numbers represented in scientific notation

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.

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6. Recognize that repeating decimals correspond to fractions and determine their

fractional equivalents.

5/7 = 0. 714285714285… = 0.714285

7. Construct meanings for common irrational numbers, such as π(pi) and the square

root of 2.

B. Numerical Operations

1. 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

2. Use exponentiation to find whole number powers of numbers.

3. Find square and cube roots of numbers and understand the inverse nature of

powers and roots.

4. Solve problems involving proportions and percents.

5. Understand and apply the standard algebraic order of operations, including

appropriate use of parentheses.

C. Estimation

1. Estimate square and cube roots of numbers.

2. Use equivalent representations of numbers such as fractions, decimals, and

percents to facilitate estimation.

3. Recognize the limitations of estimation and assess the amount of error resulting

from estimation.





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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.




A. Geometric Properties

1. 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

2. Understand and apply the Pythagorean theorem.

3. Understand and apply properties of polygons.

4. 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

5. Understand and apply the concept of similarity.

Using proportions to find missing measures

Scale drawings

Models of 3D objects

6. Use logic and reasoning to make and support conjectures about geometric objects.








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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

2. 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)

C. Coordinate Geometry

1. Use coordinates in four quadrants to represent geometric concepts.

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. Use approximate equivalents between standard and metric systems to estimate

measurements (e.g., 5 kilometers is about 3 miles).

3. Recognize that the degree of precision needed in calculations depends on how the

results will be used and the instruments used to generate the measurements.

4. Select and use appropriate units and tools to measure quantities to the degree of

precision needed in a particular problem-solving situation.

5. Recognize that all measurements of continuous quantities are approximations.













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6. Solve problems that involve compound measurement units, such as speed (miles

per hour), air pressure (pounds per square inch), and population density (persons

per square mile).

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

Impact of a dilation on the perimeter and area of a 2-dimensional figure

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).

3. Develop and apply strategies and formulas for finding the surface area and

volume of a three-dimensional figure.

Volume - prism, cone, pyramid

Surface area - prism (triangular or rectangular base), pyramid (triangular

or rectangular base)

Impact of a dilation on the surface area and volume of a three-dimensional

figure

4. Use formulas to find the volume and surface area of a sphere.

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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.




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

Arithmetic sequences (i.e., sequences generated by repeated addition of a

fixed number, positive or negative)

Geometric sequences (i.e., sequences generated by repeated multiplication

by a fixed positive ratio, greater than 1 or less than 1)

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

Rates of change (informal notion of slope)

2. Recognize and describe the difference between linear and exponential growth,

using tables, graphs, and equations.

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.




















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Using concrete materials (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)

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, graphically, and using formal algebraic

methods.

Multi-step, integer coefficients only (although answers may not be

integers)

Using paper-and-pencil, calculators, graphing calculators, spreadsheets,

and other technology

3. Solve simple linear inequalities.

4. Create, evaluate, and simplify algebraic expressions involving variables.

Order of operations, including appropriate use of parentheses

Distributive property

Substitution of a number for a variable

Translation of a verbal phrase or sentence into an algebraic expression,

equation, or inequality, and vice versa

5. Understand and apply the properties of operations, numbers, equations, and

inequalities.

Additive inverse

Multiplicative inverse

Addition and multiplication properties of equality

Addition and multiplication properties of inequalities
























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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.




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

Finding the median and mean (weighted average) using frequency data.

Effect of additional data on measures of central tendency

2. Make inferences and formulate and evaluate arguments based on displays and

analysis of data.

3. Estimate lines of best fit and use them to interpolate within the range of the data.

4. Use surveys and sampling techniques to generate data and draw conclusions about

large groups.

B. Probability

1. Interpret probabilities as ratios, percents, and decimals.

2. Determine probabilities of compound events.

3. Explore the probabilities of conditional events (e.g., if there are seven marbles in

a bag, three red and four green, what is the probability that two marbles picked

from the bag, without replacement, are both red).














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4. Model situations involving probability with simulations (using spinners, dice,

calculators and computers) and theoretical models.

Frequency, relative frequency

5. Estimate probabilities and make predictions based on experimental and theoretical

probabilities.

6. Play and analyze probability-based games, and discuss the concepts of fairness

and expected value.

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)

Factorial notation

Concept of combinations (e.g., number of possible delegations of 3 out of

23 students)

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 and algorithmic thinking to represent and find solutions to

practical problems.

Finding the shortest network connecting specified sites

Finding a minimal route that includes every street (e.g., for trash pick-up)

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

Limitations of computers (e.g., the number of routes for a delivery truck

visiting n sites is n!, so finding the shortest circuit by examining all circuits




















19

would overwhelm the capacity of any computer, now or in the future, even if

n is less than 100)

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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.




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.

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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)

Graphical representations (e.g., a line graph)

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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.

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SCOPE AND SEQUENCE

September

Unit I: Variables, Expressions and Integer

NJ Ask Lessons 1, 7, 9, 25

September/October

Unit II: Solving Equations

NJ Ask Lessons 40, 41,42,43,44, 45

October

Unit III: Multi-Step Equations and Inequalities

NJ Ask Lessons 22, 23, 24, 28

November

Unit IV: Factors, Fractions, and Exponents

Unit V: Rational Numbers and Equations

NJ Ask Lessons 2, 3, 4, 8, 10, 11

December

Unit VI: Ratio and Proportion

NJ Ask Lessons 5, 13

January

Unit VII: Percents


January/February

Unit VIII: Measurement, Area, and Volume

NJ Ask Lessons 16, 17, 18, 19, 20

February

Unit IX: Angle Relationships and Transformations

NJ Ask Lessons 12, 14, 15

March

Unit X: Data Analysis and Probability

NJ Ask Lessons 30, 31, 32, 33, 34, 35, 36, 37, 38, 39

April

Unit XI: Linear Functions


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May

Unit XII: Real Numbers and Right Triangles

May/June

Unit XIII: Polynomials and Nonlinear Functions

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UNIT I VARIABLES, EXPRESSIONS, AND INTEGERS

Duration: September

A. Major Objectives:

1. Write and evaluate variable expressions.

2. Perform operations with integers.

3. Plot points in a coordinate plane.

B. Sequence of Topics

1. Evaluate numerical expressions (4.3) (pp 5-9, 63-8, 78-82)

2. Use the order of operations, including exponents and parenthesis to

simplify expressions (4.3) (pp 10-20)

3. Graph integers on a number line (4.3) (pp 22-6)

4. Determine the absolute value of an integer and explain how this is

related to its location on the number line (4.3) (pp 22-6)

5. Add integers on a number line. (4.3) (p 28)

6. Add integers (4.3) (pp 29-33)

7. Subtract integers (4.3) (pp 34-8)

8. Multiple and divide integers (4.3) (pp 42-6)

9. Identify and plots points on a coordinate plane (4.3) (pp 47-51)

10. Use the four step plan to problem solve (4.5) (pp14-5)

11. Problem Solving: Reading the Problem (4.5) (58-9)

11. NJ Ask Coach (4.2, 4.3, 4.5) (pp. 22-4, 50-5, 64-7, 175-181)

C. Core Materials

Pre-Algebra

Larson, Boswell, Kanold, and Stiff

McDougal Littell, 2005

D. Supplemental Materials:

1. Practice Workbook

2. Notetaking Guide

3. Special Activities Book

4. Resource Book

5. Warm-up Transparencies

6. Homework Quiz Transparencies

7. Worked Out Solutions Guide

8. Assessment Book

9. Manipulatives

10. eWorkbook Plus @CLASSZONE.COM

11. eTutorial Plus @CLASSZONE.COM

12. NJ Ask Coach Grade 7

mailto:[email protected]

26

E. Suggested Assignments, Projects, Field Trips, Speakers:

1. Complete exercises in textbook for each lesson.

2. Complete practice worksheets.

3. Use calculator/computer to complete classroom and computer

problems when necessary.

4. Complete and review chapter prior to test/quizzes using text and

teacher made materials.

5. Daily Do Nows

6. Extra Practice and Practice Tests on Classzone.

7. Complete practice in NJ Ask Coach Book.

F. Suggested Assessments:

1. Tests

2. Quizzes

3. Class Participation

4. Notebook/Class work

5. Homework

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UNIT II SOLVING EQUATIONS

Duration: September/October


1. Use addition, multiplication, and the distributive property

2. Simplify variable expressions

3. Solve equations using addition, subtraction, multiplication and

division.


1. Use properties of addition and multiplication. (4.3) (pp 63-7)

2. Use the distributive property to simplify expressions. (4.3) (pp 71-5)

3. Simplify variable expressions. (4.3) (pp78-82)

4. Solve one step equations using addition and subtraction. (4.3)

(pp. 91-5)

5. Solve one step equations using multiplication and division.

(4.3) (pp 97-101)

6. Solve equations involving decimals. (4.3) (pp 102-7)

7. NJ Ask Coach (4.5) (pp 276-98)

C. Core Materials

Pre-Algebra





2. Notetaking Guide


4. Resource Book




8. Assessment Book

9. Manipulatives





28








5. Daily Do Nows




1. Tests

2. Quizzes



5. Homework

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UNIT III MULTI-STEP EQUATIONS AND INEQUALITIES

Duration: October


1. Write and solve two-step equations

2. Use the distributive property to solve equations

3. Write and solve inequalities

4. Graph inequalities on a number line


1. Write and solve two-step equations including those with fractions.

(4.1, 4.3, 4.5) (pp 120-4)

2. Solve equations that include grouping symbols. (4.1, 4.3) (pp 125-9)

3. Solve equations with variables on both sides. (4.3) (pp 131-5)

4. Solve and graph inequalities using addition and subtraction. (4.3, 4.5)

(pp 138-142)

5. Solve and graph inequalities using multiplication and division.

( 4.3, 4.5) (pp 144- 8)

6. Solve and graph multi-step inequalities. (4.3, 4.5) (pp149-153)

7. NJ Ask (pp162-171,172-4, 195-210)

C. Core Materials

Pre-Algebra





2. Notetaking Guide


4. Resource Book




8. Assessment Book

9. Manipulatives





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5. Daily Do Nows




1. Tests

2. Quizzes



5. Homework

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UNIT IV FACTORS, FRACTIONS AND EXPONENTS

Duration: November

(Note: Some of the sections in this chapter have been eliminated as they are skills

previously mastered. The concept of fractions as well as performing operations with

them is a skill that should have been mastered previously. If that is not the case

then there may be a need to review the initial sections of this chapter. The focus of

this chapter should be the addition of the variable to both the numerator and

denominator of the fraction and all operations pertaining to those variables.)


1. Simplifying and comparing fractions

2. Simplifying expression using rules for exponents

3. Explore the use of negative exponents

4. Write numbers using scientific notation


1. Write fractions in simplest form when they include variables in

the numerator and or the denominator. (4.1, 4.3) (pp. 182-6)

2. Find the least common multiple of two or more variable terms.

(4.1, 4.3) (pp 187-191)

3. Multiply and divide terms with the same base using the rules of

exponents. (4.1, 4.3) (pp 194-8)

4. Write and simplify expression using negative exponents. (4.3)

(199-203)

5. Write numbers using scientific notation. (4.1, 4.2) (pp 204-8)

6. NJ Ask (pp 56-63, 68-71, 72-4)

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UNIT V RATIONAL NUMBERS AND EXPONENTS

Duration: November

(Note: Some of the components of this chapter may be a review for certain classes.

The concept of fractions should have been mastered previously. The new concepts

regarding fractions involve computations involving positive and negative fractions

as well as solving equations and inequalities involving positive and negative

fractions. Although the sequence of topics includes every section, the teacher should

use his or her professional judgment as to the pace and the amount of work

completed in each section.)


1. Identify rational numbers

2. Write fractions as decimals and decimals as fractions

3. Performing operations with fractions and mixed numbers

4. Solve equations and inequalities with rational numbers


1. Convert fractions to decimals, identify rational numbers,

and write repeating decimals as fractions. (4.1) (pp 219-224)

2. Add and subtract fractions with like denominators. (4.1, 4.3)

(pp 225-9)

3. Add and subtract fractions with unlike denominators. (4.1, 4.3)

(pp. 230-5)

4. Multiply fractions. (4.1, 4.3, 4.5) (pp 237-241)

5. Divide fractions. (4.1, 4.3, 4.5) (pp 243-6)

6. Solve multi-step equations involving positive and negative fractions.

(4.1, 4.3, 4.5) (pp 247-51)

7. Solve equations by clearing out the fraction or decimal using the LCD.

(4.1, 4.3) (pp 253-7)

8. NJ Ask (pp 25-7, 28-33, 34-9)

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UNIT VI RATIO AND PROPORTION

Duration: December

(Note: The topics covered in section 6.7 and 6.8 have been moved to a later unit)


1. Find ratio and unit rates

2. Write and solve proportions

3. Identify similar and congruent figures

4. Use similar figures to find unknown sides of a figure

5. Find the probability of events.


1. Write ratios to represent a given situation and find unit

rates. (4.1, 4.5) (pp 269-273)

2. Write and solve proportions. (4.1, 4.5) (pp 275-9)

3. Determine if two ratios are equivalent and solve proportions

using cross products. (4.1, 4.5) (pp 280-283)

4. Identify congruent and similar figures. (4,1, 4.2, 4.5) (pp 288-292)

5. Use properties of similarity to find the value of sides and angles

in a pair of similar figures and to prove figures similar. (4.1, 4.2)

(pp 293-7)

6. Determine the scale factor and find a specified measure on a scale

drawing. (4.1, 4.2) (pp 299-304)

7. NJ Ask (pp 40-3, 90-5)

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UNIT VII PERCNTS

Duration: January


1. Find the percent of a number

2. Solve percent problems

3. Find the percent of change in a quantity

4. Solve real word problems using percents including but not limited

to markups, discounts, sales tax, and tips.

5. Calculate interest earned and account balance


1. Use a fraction to find the percent of a number. (4.1) (pp 329-333)

2. Use proportions to solve percent problems. (4.1, 4.5) (pp 335- 9)

3. Convert fractions and decimals to percents, including those greater

than 100 and less than 1 and use them to solve percent problems.

(4.1, 4.5) (pp 340-4)

4. Use an algebraic equation to solve percent problems. (4.1, 4.5)

(pp 345-351)

5. Find the percent of change of an equation. (4.1, 4.5) (pp 352-6)

6. Write and solve percent equations to model real life application that

include but are not limited to interest, sales tax, discount,

and commission. (4.1, 4.5) (pp 357-366)

7. NJ Ask (4.1, 4.5) (pp 44-9, 156-161)

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UNIT VIII MEASUREMENT, AREA, AND VOLUME

Duration: January/February

(Note: Two chapters have been moved to follow the chapters on geometry. Much of

the beginning of this unit is review and should be completed quickly. The focus of

section 10.5, 10.6 and 10.7 should be to utilize the reference sheet that is used on

state testing to find surface area and volume.)


1. Classify triangles and polygons

2. Find areas of triangles, parallelograms and trapezoids

3. Find the circumferences and areas of circles

4. Find surface areas and volumes of solids


1. Classify triangles and calculate the missing angle measures. (4.2)

(pp 511-5)

2. Classify polygons and quadrilaterals. (4.2) (pp 516-520)

3. Calculate the perimeter and area of triangles, squares, and rectangles.

(4.2) (pp 60-70, 74)

4. Calculate the areas of parallelograms, trapezoids and

irregular figures. (4.2) (pp 521-5)

5. Find the circumferences and areas of circles. (4.2) (pp 528-533)

6. Use the NJ reference sheet to find the surface areas of prisms and

cylinders. (4.2, 4.5) (pp 538-543)

7. Use the NJ reference sheet to find the surface areas of pyramids and

cones. (4.2, 4.5) (pp 544-9)

8. Use the NJ reference sheet to find the volume of solids. (4.2)

(pp 552-6, 558-563)

9. Building and sketching solids using dot paper. (4.2) (pp 550-1)

10. NJ Ask (pp 112-7, 118-123, 124-8, 129-140, 141-7)

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UNIT IX ANGLE RELATIONSHIPS AND TRANSFORMATIONS

Duration: February


1. Classify special angle pairs

2. Identify angles formed by a transversal intersecting two lines

3. Finding measures of interior and exterior angles of polygons

4. Transform figures in a coordinate plane

5. Describe line symmetry and rotational symmetry


1. Identify special pairs of angles and use those relationships

to find the value of various angles. (4.2) (pp 709-713)

2. Identify angles created when two parallel lines are cut by

a transversal and use those relationships to find the value of

various angles. (4.2, 4.5) (pp 716-720)

3. Find the measure of interior and exterior angles of polygons. (4.2)

(pp 722-7)

4. Translate figures in a coordinate plane and identify a sequence of

transformations to map one figure into another. (4.2) (pp 729-733)

5. Reflect figures and identify lines of symmetry. (4.2) (pp 734- 8)

6. Rotate figures and identify rotational symmetry. (4.2) (pp741-6)

7. Dilate figures in a coordinate plane. Identify the scale factor and the

coordinates of the image and pre-image. (4.2) (pp 747-751)

8. NJ Ask (pp 82-89, 96-105, 106-111)

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UNIT X DATA ANALYSIS AND PROBABILITY

Duration: March

(Note: Much of the beginning of this unit is review and should be covered as

quickly as possible.)


1. Create histograms stem-and-leaf plots and box-and-whisker plots

2. Choose appropriate displays for data

3. Collect and interpret data

4. Calculate the probability for simple and compound events,

disjoint and overlapping events, and dependent and independent

events

5. Find permutations and combinations


1. Utilize given data to create a display including stem-and-leaf

plot, histogram, and box-and-whisker plot. (4.4, 4.5) (pp 581-592)

2. Analyze graphs to interpret the information displayed and choose an

appropriate display for given data. (4.4, 4.5) (pp 596-600, 609-613)

3. Identify methods of collecting data as well as the terminology

particular methods. (4.4) (pp 601-5)

4. Find the probability of an event and use the counting principle to find

find probabilities. (4.1, 4.4, 4.5) (pp 306-317)

5. Use permutations combinations to determine possible outcomes.

(4.4, 4.5) (pp 615-625)

6. Find the probability of disjoint or overlapping events using a

calculations or Venn Diagrams. (4.4, 4.5) (pp 626-632)

7. Identify an event as independent or dependent and calculate the

probability of the event occurring. (4.4, 4.5) (pp 634-9)

8. NJ Ask (pp 218-222, 223-6, 233-7, 238-242, 243-5, 246-251, 252-5,

262-8)

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UNIT XI LINEAR FUNCTIONS

Duration: April

(Note: The following three units are introductory units for skills that will be

mastered in Algebra I. Although it is recommended that all sections be covered

during the year, if pacing becomes difficult teachers should complete the lessons

that are not labeled as supplemental first. If time allows the class should complete

the supplemental lessons)


1. Represent relations and functions in various ways

2. Determine the slope of a given line and calculate the slope

of a line given specific information

3. Write and graph linear equations in two variables

4. Graph and solve systems of equations

5. Graph linear inequalities in two variables


1. Graph functions on a coordinate plane and identify the domain

and range. (4.3, 4.5) (pp 385-9)

2. Graph equations in two variables. (4.3, 4.5) (pp 391-6)

3. Graph linear equations using intercepts. (4.3, 4.5) (pp 398-402)

4. Find the slope of a line given a graph, a description, or two points on

the line. (4.3) (pp 404-9)

5. Graph linear equations in slope-intercept form. (4.3, 4.5) (pp 412-7)

6. Write the equation of a line given specific information. (supplemental)

(4.3) (pp 419-424)

7. Use function notation to represent linear relationships and write the

equation for a given function. (supplemental) (4.3) (pp 426-430)

8. Graph systems of linear equation in order to find their common

solution. (4.3, 4.5) (pp 431-5)

9. Graph linear inequalities. (supplemental) (4.3) (pp 436-441)

10. NJ Ask (pp 182-7, 188-195)

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UNIT XII REAL NUMBERS AND RIGHT TRIANGLES

Duration: May


1. Explore square roots

2. Use the Pythagorean Theorem to solve problems

3. Compare real numbers

4. Use the distance, midpoint and slope formulas

5. Apply the sine, cosine and tangent ratio


1. Approximate the square roots of numbers and solve equations

containing square roots. (4.1, 4.3) (pp 453-7)

2. Use the properties of square roots to simplify square roots.

(supplemental) (4.1, 4.3) (pp 458-461)

3. Use the Pythagorean Theorem to solve problems. (4.1, 4.3, 4.5)

(pp 465-9)

4. Compare and order real numbers. (4.1) (pp 470-4)

5. Use the distance, midpoint and slope formulas to solve problems.

(supplemental) (4.1, 4.3) (pp 476-481)

6. Use the properties of special right triangles to solve problems.

(supplemental) (4.1, 4.2) (pp 483-7)

7. Use the tangent ratio to find the side lengths of a right triangle.

(supplemental) (4.1, 4.2, 4.3) (pp 489-493)

8. Use the sine and cosine ratio to find the side lengths of a right triangle

as well as solve problems. (supplemental) (4.1, 4.2, 4.3, 4.5)

(pp 494-8)

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UNIT XIII POLYNOMIALS AND NONLINEAR FUNCTIONS

Duration: May/June


1. Classify polynomials

2. Add, subtract, and multiply polynomials

3. Use the rules of exponents to simplify polynomial expressions

4. Graph nonlinear functions

5. Represent arithmetic and geometric sequences


1. Write polynomials in standard form and classify them by their degree.

(supplemental) (4.3) (pp 651-5)

2. Add and subtract polynomials. (supplemental) (4.3) (pp 657-661)

3. Multiply and divide polynomials. (supplemental) (4.3) (pp 662-6)

4. Use FOIL to multiply binomials. (supplemental) (4.3) (pp 668-672)

5. Simplify expressions using the rules of exponents. (supplemental)

(4.3) (pp 674-7)

6. Graph quadratic functions. (supplemental) (4.2, 4.3, 4.5)

(pp 679-683)

7. Graph exponential functions. (supplemental) (4.2, 4.3, 4.5)

(pp 686-691)

8. Extend and graph sequences. (4.1, 4.3, 4.5) (pp 692-7)

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