Mathematics Curriculum Grade 9

Algebra 1 Foundations Series Buena Regional High School

Created for New Jersey school districts through a project of the New Jersey Department of Education, Office of Academic Standards, in partnership with the N.J Association for Supervision and Curriculum Development and the N.J. Principals and Supervisors Association.

Mathematics Curriculum

Grade 9

Buena Regional School District Buena, NJ



Board of Education

Debra Bell, President

James Abba, Vice-President Mark Beamer Jr.

John Cressey Syd D’Angelo

Valentina DiPrimio Lynda Gazzara

Al Gazzara Barbara Meyrick

Matt Walker Edward Zebedies

Superintendent

John Destefano

Supervisor

Brian Kern

Curriculum Committee

Curriculum Approval Date

2015



Curriculum Design Template

Content Area: Mathematics

Course Title: Algebra 1 – Foundations Series Grade Level: 9

Chapter 1

Pacing Guide

Approx 25 days

Chapter 2

Pacing Guide

Approx 20 days

Chapter 3

Pacing Guide

Approx 20 days

Chapter 7

Pacing Guide

Approx 25 days

Chapter 8

Pacing Guide

Approx 25 days

Chapter 4

Pacing Guide

Approx 20 days

Chapter 5

Pacing Guide

Approx 21 days

Chapter 6

Pacing Guide

Approx 22 days

Date Created:



Algebra 1 – Foundations Series

Prentice Hall

Pacing Guide

CHAPTER 1: FOUNDATIONS FOR ALGEBRA (approx. 25 teaching days)

1-1 Variables and Expressions

1-2 Order of Operations and Evaluating Expressions

1-3 Real Numbers and the Number Line

1-4 Properties of Real Numbers

1-5 Adding and Subtracting Real Numbers

1-6 Multiplying and Dividing Real Numbers

1-7 Distributive Property

1-8 Introduction to Functions

1-9 Patterns, Equations, and Graphs

CHAPTER 2: SOLVING EQUATIONS (approx. 20 teaching days)

2-1 Solving One-Step Equations

2-2 Solving Two-Step Equations

2-3 Solving Multi-Step Equations

2-4 Equations with Variables on Both Sides

CHAPTER 3: SOLVING INEQUALITIES (approx. 20 teaching days)

3-1 Inequalities and Their Graphs

3-2 Solving inequalities using Addition and Subtraction

3-3 Solving inequalities using Multiplication and Division

3-4 Solving Multi-Step Inequalities

3-6 Compound Inequalities

3-7 Absolute Value Equations and Inequalities

CHAPTER 7: EXPONENTS AND EXPONENTIAL FUNCTIONS (approx. 20

teaching days)

7-1 Zero and Negative Exponents

7-2 Scientific Notation

7-3 Multiplication Properties with the Same Base

7-4 More Multiplication Properties of Exponents

7-5 Division Properties of Exponents

7-6 Exponential Functions



CHAPTER 8: POLYNOMIALS AND FACTORING (approx. 20 teaching days)

8-1 Adding and Subtracting Polynomials

8-2 Multiplying and Factoring

8-3 Multiplying Binomials

8-4 Multiplying Special Cases

8-5 Factoring x2+bx+c

8-6 Factoring ax2+bx+c

8-7 Factoring Special Cases

8-8 Factoring by Grouping

CHAPTER 4: GRAPHS AND FUNCTIONS (approx. 20 teaching days)

4-1 Using Graphs to Relate Two Quantities

4-2 Patterns and Linear Functions

4-3 Patterns and Nonlinear Functions

4-4 Graphing a Function Rule

4-5 Writing a Function Rule

4-6 Formalizing Relations and Functions

CHAPTER 5: LINEAR EQUATIONS AND THEIR GRAPHS (approx. 21 teaching

days)

5-1 Rate of Change and Slope

5-2 Direct Variation

5-3 Slope-Intercept Form

5-4 Point-Slope Form

5-5 Standard Form

5-6 Parallel and Perpendicular Lines

5-7 Scatter Plots and Trend Lines

5-8 Graphing Absolute Value Functions

CHAPTER 6: SYSTEMS OF EQUATIONS AND INEQUALITIES (approx. 20

teaching days)

6-1 Solving systems by Graphing

6-2 Solving systems using Substitution

6-3 Solving systems using Elimination

6-5 Linear Inequalities

6-6 Systems of Linear Inequalities



Chapter 1 Overview


Unit Title: Foundations for Algebra (Chapter 1)

Target Course/Grade Level: Algebra 1 – Foundations Series/ Grade 9

Unit Summary:

Students will learn rules for graphing and for performing mathematical operations to ensure that

the values obtained will be consistent.

Primary interdisciplinary connections: Science

21st century themes:

• Reflect critically on learning experiences and processes

• Demonstrate the creative, critical thinking, collaboration and problem solving skills needed to

function successfully as both global citizens and workers in diverse ethnic and organizational

cultures.

Unit Rationale:

To creatively think and problem solve

Learning Targets

Standards:

• O: Operations on Numbers and Expressions

• N: Non-Linear Relationships

Content Statements:

• O1: Number Sense and Operations

• N2: Non-Linear Equations

CPI # Cumulative Progress Indicator (CPI)

O1.a Reasoning with real numbers

O1.B1 Using Variables in different ways

O1.c Using numerical exponential expressions

O2.a Using algebraic exponential expressions

N2.a Solving linear equations

Unit Essential Questions

• How can students represent quantities, patterns,

and relationships?

• How are properties related to Algebra?

Unit Enduring Understandings

• Being able to compute fluently means making

smart choices about which tools to use and when

to use them.

Unit Learning Targets



Students will …

• Students will learn to write and evaluate expressions with unknown values

• Properties are used to simplify expressions.

Evidence of Learning

Summative Assessment

• Individual Concept Maps

• Student Created Graphic Organizer

• Unit Test-Problem Solving

• Test and Quizzes

• Publisher – Standardized Test

Equipment needed:

• Textbook

• Handouts

• Material Listed in Lesson Plan

• Smart Board

Teacher Resources:

• Learning Focused Manual



Chapter 2 Overview


Unit Title: Solving Equations (Chapter 2)

Target Course/Grade Level: Algebra 1– Foundations Series / Grade 9

Unit Summary:

Students will learn that real-world situations are problems that can be modeled with equations,

solved, and then analyzed.






cultures

Unit Rationale:

Real world situations can be modeled through algebraic equations

Learning Targets

Standards:

• O: Operations on Numbers and Expressions

• L: Linear Relationships

Content Statements;

• O1. Number Sense and Operations

• L2. Linear Equations and Inequalities.


O1.b Using ratios, rates, and proportions

L2.a Solving linear equations and inequalities


• Can equations that appear to be different be

equivalent?

• How can you solve equations?

• What kinds of relationships can proportions

represent?


• Rules of arithmetic and algebra can be used together

with notions of equivalence to transform equations

and inequalities so solutions can be found.


Students will ...

• Calculate unit rate

• Use proportions to solve problems involving



percents, measurements in similar figures, and

indirect measurement

• Find equivalent equations using inverse

operations and simplification

• Solve equations using addition, subtraction,

multiplication, and division

• Use the Multiplication Property of Equality

and the Cross Products Property to solve

proportions


Summative Assessment:

• Unit Exam – solving equations

• Students will work in groups and solve

problems that relate to the student’s world

• Written explanation to explain what they

are doing – step by step process

• Publisher – Activities, Games, and Puzzles

Equipment needed:

• Handouts

• Graphic Organizers

• Smart Board

• Publisher – Home Video Tutor

Teacher Resources:




Chapter 3 Overview


Unit Title: Solving Inequalities (Chapter 3)


Unit Summary:

Students will learn how to solve inequalities and absolute value equations involving many of the same procedures as solving equations, but their solutions may result in intervals of accepted

values.






cultures.

Unit Rationale:

Real world situations can be modeled through algebraic inequalities.

Learning Targets

Standards: Linear Relationship

Content Statements:

• L2. Linear Equations and Inequalities

CPI# Cumulative Progress Indicator (CPI)

L.2.a Solving Linear equations and inequalities

L.2.b Solving equations involving absolute value

L.2.e Modeling with single variable linear equations or one-or two- variable equations


• How do you represent relationships between

quantities that are not equal?

• Can inequalities that appear to be different

be equivalent?

• How can you solve inequalities?


• Rules of arithmetic and algebra can be used together

with notions of equivalence to transform equations and

inequalities so solutions can be found.


Students will ...

• Learn to write and graph inequalities

• Use properties to generate equivalent



inequalities



• Group Work

• Unit Exam

• Drill and Practice

• Written explanation of the steps or

sequence

• Publisher- Find the Errors worksheet

• Publisher – Chapter Project

Equipment needed

• Smart Board

• Textbook

• Graphic Organizer

• Publisher – Homework Video Tutor

Teacher Resources:




Chapter 7 Overview


Unit Title: Exponents and Exponential Functions (Chapter 7)


Unit Summary:

Students will learn that problems using scientific notation and other exponential expressions

illustrate exponentiation rules.





function successfully as both global citizens and workers in diverse ethnic and organizational cultures.

Unit Rationale:

Exponentiation rules are utilized in simplifying expressions and writing exponential functions

Learning Targets

Standards:

O: Operations on Numbers and Expressions

N: Non-Linear Relationships

Content Statements:

O1. Number Sense and Operations

O2. Algebraic Expressions

N2. Non-Linear Equations


O1.c Using numerical exponential expressions

O2.a Using algebraic exponential expressions

O2.b Operating with polynomial expressions

N2.B1 Solving simple exponential equations


• How can you represent very large and very small

numbers?

• How can you simplify expressions involving

exponents?


• Expand students’ understandings and skills related

to exponential expressions




Students will ...

• Learn to write numbers in Scientific Notation

• Define and use zero and negative exponents

• Learn the rules for multiplying powers

• Learn the rules for dividing powers


Summative Assessment :

• Quizzes and Tests

• Group work where students bring in work from another curriculum that shows an increase or

decrease

• Explain real world uses and explanation

• Publisher – Find the Errors worksheet

Equipment needed:

• Handouts


• Smart Board


Teacher Resources:




Chapter 8 Overview


Unit Title: Polynomials and Factoring (Chapter 8)


Unit Summary:

Students will learn factoring, the inverse process for multiplying polynomials, is used to break

down trinomials into their factors.




• Demonstrate the creative, critical thinking, collaboration and problem solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational

cultures.

Unit Rationale:

Algebraic expressions help determine which technique of factoring will work best.

Learning Targets

Standards:

O: Operations on Numbers and Expressions

N: Non-linear Relationships

Content Statements:

O2. Algebraic Expressions

N1. Non-Linear Functions


O2.b Operating with polynomials expressions

O2.c Factoring polynomials expressions

N1.a Representing quadratic functions in multiple ways

N1.b Distinguishing between function types


• Can two algebraic expressions that appear to be

different be equivalent?

• How are the properties of real numbers related to

polynomials?


• Symbols can be used to represent an algebraic

expression in an unlimited number of equivalent

ways




Students will ...

• Add and subtract polynomial expressions

• Multiply polynomial expressions

• Factor polynomials

• Use the Commutative and Associative Properties to manipulate polynomial expressions

• Use the Distributive Property to multiply polynomials and factor polynomials



• Quizzes and Tests

• Describe in words the process


Equipment needed:


• Smart Board

• Teacher Resource Manual


Teacher Resources:




Chapter 4 Overview


Unit Title: An Introduction to Functions (Chapter 4)


Unit Summary:

Students will learn how a pattern of change can be described through a function, table, or graph.






cultures.

Unit Rationale

Real world data will used as models to demonstrate function rules, tables, or graphs

Learning Targets

Standards: Linear Relationships

Content Statements L1: Linear Functions


L1.a Representing linear functions in multiple ways

L1.b Analyzing linear function

L1. C Graphing linear functions involving absolute value

L1.d Using linear models


• How do you use graphs to model

situations?

• What differences exist between relations

and functions?

• What strategies can I use to determine if

a relation is a function?


• Associations of relationships are fundamental to

understanding functions


Students will ...

• Represent functions, using tables,

equations, and graphs



• Students will use function notation

• Students will represent arithmetic

sequences using function rules



• Tests and Quizzes


• Drill and Practice


• Publisher – Activities, Games and Puzzles

Equipment needed:

• Smart Board



Teacher Resources:




Chapter 5 Overview


Unit Title: Linear Functions (Chapter 5)


Unit Summary:

Lines can be represented algebraically and graphically






cultures.

Unit Rationale:

Students use algebraic methods to solve problems by exploring, modeling, and describing patterns

and relations involving numbers, shapes, data, and graphs. They communicate their reasoning

used to solve these problems.

Learning Targets

Standards: Linear Relationships

Content Statements: L1. Linear Functions

L2. Linear Equations and Inequalities


L1. A Representing linear functions in multiple ways

L.1.b. Analyzing linear function

L.1. c Graphing linear functions involving absolute value

L.1.d Using Linear models

L.2.c Graphing linear inequalities


• What does the slope of a line indicate about the

line?

• What information does the equation of a line

give you?

• How can you make predictions based on a


• Associations of relationships are fundamental to

understanding functions



scatter plot?


Students will ...

• Find slope using a formula

• Find slope using a graph

• Analyze various slopes and describe their meaning

• Find the line of best fit

• Analyze trend lines in scatter plots



• Tests and Quizzes

• Group work



Equipment needed:

• Smart board



Teacher Resources:




Chapter 6 Overview


Unit Title: Systems of Equations and Inequalities (Chapter 6)


Unit Summary:

Solving an equation is the process of rewriting the equation to make what it says about its

variables as simple as possible




• Demonstrate the creative, critical thinking, collaboration and problem solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational

cultures.

Unit Rationale:

Lines can be represented algebraically and graphically

Learning Targets

Standards: L: Linear Relationships

D: Data, Statistics, and Probability

Content Statements:

• L1: Linear Functions

• L2: Linear Equations and Inequalities

• D1: Data and Statistical Analysis


L2.a Solving linear equations and inequalities

L2.c Graphing linear inequalities

L2.d Solving systems of linear equations

L2.e Modeling with variable linear equations, one or two variable inequalities or systems of

equations

D1.a Interpreting linear trends in data

D1.b Comparing data using summary statistics

D1.c Evaluating data-based reports in the media


• How can you solve s system of equations or


• Some problems can be modeled by systems of



inequalities?

• Can systems of equations model real-world

situations?

linear equations

• Solutions to a linear inequality in two variables can be represented in the coordinate plane as the

set of all points on one side of a boundary line


Students will ...

• Learn to solve systems of equations or inequalities by graphing

• Learn to solve systems of equations or inequalities by substitution

• Learn to solve systems of equations or inequalities by elimination

• Write equations and inequalities to represent situations

• Examine constraints placed on real world situations



• Test and Quizzes



Equipment needed:

• Smart Board

• Textbook



Teacher Resources:


Mathematics Curriculum Grade 9

Documents

Transcript of Mathematics Curriculum Grade 9