Common Core Algebra I Math (Worksheets, Homework, Lesson Plans)
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Looking for video lessons that will help you in your Common Core Algebra I math classwork or homework? Looking for Common Core Math Worksheets and Lesson Plans that will help you prepare lessons for Algebra I students?
The following lesson plans and worksheets are from the New York State Education Department Common Core-aligned educational resources. Eureka/EngageNY Math Algebra I Worksheets.
These Lesson Plans and Worksheets are divided into five modules.
Algebra I Homework, Lesson Plans and Worksheets
| Topics and Objectives (Module 1) |
|---|
| Introduction to Functions Studied This Year - Graphing Stories : Graphs of Piecewise Linear Functions ( ) :Graphs of Quadratic Functions ( ) : Graphs of Exponential Functions ( ) : Analyzing Graphs - Water Usage During a Typical Day at School ( ) : Two Graphing Stories ( ) |
| The Structure of Expressions : Algebraic Expressions - The Distributive Property ( ) : Algebraic Expressions - The Commutative and Associative Properties ( ) : Adding and Subtracting Polynomials ( ) : Multiplying Polynomials ( ) |
| Solving Equations and Inequalities : True and False Equations ( ) : Solution Sets for Equations and Inequalities ( ) : Solving Equations ( ) : Some Potential Dangers when Solving Equations ( ) : Solving Inequalities ( ) : Solution Sets of Two or More Equations (or Inequalities) Joined by “And” or “Or” ( ) : Solving and Graphing Inequalities Joined by “And” or “Or” ( ) : Equations Involving Factored Expressions ( ) : Equations Involving a Variable Expression in the Denominator ( ) : Rearranging Formulas ( , : Solution Sets to Equations and Inequalities with Two Variables ( ) ( ) , : Solution Sets to Simultaneous Equations ( ) ( ) : Applications of Systems of Equations and Inequalities ) |
| Creating Equations to Solve Problems : Solving Problems in Two Ways - Rules and Algebra ( ) , :Recursive Challenge Problem - The Double and Add 5 Game ( ) : Federal Income Tax ( ) |
| |
| Topics and Objectives (Module 2) |
|---|
| Shapes and Centers of Distributions : Distributions and Their Shapes ( ) : Describing the Center of a Distribution ( ) : Estimating Centers and Interpreting the Mean as a Balance Point ( ) |
| Describing Variability and Comparing Distributions : Summarizing Deviations from the Mean ( ) : Measuring Variability for Symmetrical Distributions ( ) : Interpreting the Standard Deviation ( ) : Measuring Variability for Skewed Distributions (Interquartile Range) ( ) : Comparing Distributions ( ) |
| Categorical Data on Two Variables : Summarizing Bivariate Categorical Data ( ) : Summarizing Bivariate Categorical Data with Relative Frequencies ( ) : Conditional Relative Frequencies and Association ( ) |
| Numerical Data on Two Variables , : Relationships between Two Numerical Variables ( ) : Modeling Relationships with a Line ( ) : Interpreting Residuals from a Line ( ) : More on Modeling Relationships with a Line ( ) , : Analyzing Residuals ( ) : Interpreting Correlation ( ) : Analyzing Data Collected on Two Variables |
| Topics and Objectives (Module 3) |
|---|
| Linear and Exponential Sequences : Integer Sequences - Should You Believe in Patterns? ( ) : Recursive Formulas for Sequences ( ) : Arithmetic and Geometric Sequences ( ) : Why Do Banks Pay YOU to Provide Their Services? ( ) : The Power of Exponential Growth ( ) : Exponential Growth - U.S. Population and World Population ( ) : Exponential Decay ( ) |
| : Why Stay with Whole Numbers? ( ) , :Representing, Naming, and Evaluating Functions ( ) : The Graph of a Function ( ) : The Graph of the Equation y=f(x) ( ) : Interpreting the Graph of a Function ( ) : Linear and Exponential Models - Comparing Growth Rates ( ) |
| |
| Transformations of Functions : Piecewise Functions ( ) : Graphs Can Solve Equations Too ( ) , , , : Four Interesting Transformations of Functions ( ) |
| Using Functions and Graphs to Solve Problems : Comparing Linear and Exponential Models Again ( ) : Modeling an Invasive Species Population ( ) : Newton's Law of Cooling ( ) : Piecewise and Step Functions in Context ( ) |
| |
| Topics and Objectives (Module 4) |
|---|
| Quadratic Expressions, Equations, Functions, and Their Connection to Rectangles , : Multiplying and Factoring Polynomial Expressions ( ) , : Advanced Factoring Strategies for Quadratic Expressions ( ) : The Zero-Product Property ( ) : Solving Basic One-Variable Quadratic Equations ( ) : Creating and Solving Quadratic Equations in One Variable ( ) : Exploring the Symmetry in Graphs of Quadratic Functions ( ) : Graphing Quadratic Functions from Factored Form, f(x)=a(x-m)(x-n) ( ) : Interpreting Quadratic Functions from Graphs and Tables ( ) |
| Using Different Forms for Quadratic Functions , : Completing the Square ( ) : Solving Equations by Completing the Square ( ) : Deriving the Quadratic Formula ( ) : Using the Quadratic Formula ( ) : Graphing Quadratic Equations From the Vertex Form, y=a(x-h) +k ( ) : Graphing Quadratic Functions From the Standard Form, f(x)=ax +bx+c ( ) |
| Function Transformations and Modeling : Graphing Cubic, Square Root, and Cube Root Functions : Translating Functions ( ) : Stretching and Shrinking Graphs of Functions ( ) : Transformations of the Quadratic Parent Function, f(x)=x ( ) : Comparing Quadratic, Square Root, and Cube Root Functions Represented in Different Ways ( ) , : Modeling with Quadratic Functions ( ) |
| Topics and Objectives (Module 5) |
|---|
| Elements of Modeling : Analyzing a Graph ( ) : Analyzing a Data Set ( ) : Analyzing a Verbal Description ( ) |
| Completing the Modeling Cycle : Modeling a Context from a Graph ( ) : Modeling from a Sequence ( ) , : Modeling a Context from Data ( ) ( ) , : Modeling a Context from a Verbal Description ( ) ( ) |
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- Polynomials
Welcome to the Algebra 1 Polynomials Unit!
This unit is a brief introduction to the world of Polynomials. We will add, subtract, multiply, and even start factoring polynomials.
Click on the lesson below that interests you, or follow the lessons in order for a complete study of the unit.
Polynomials Unit
- Introduction to Polynomials (Definitions)
- Adding Polynomials
- Subtracting Polynomials
- Multiplying Polynomials
- Using the FOIL Method to Multiply Binomials
- Squaring a Binomial - Using a Special Rule
- Difference of Two Squares - "Special Binomials" Using a Special Rule
- Factoring Polynomials Using the Greatest Common Factor (GCF)
- Factoring Polynomials by Grouping
- Factoring Trinomials
- Factoring Trinomials with A Lead Coefficient Greater Than One
Need Additional Help?
As you study this unit, if you find that you need more help, please visit the Algebra Class E-courses . You will find many examples on video, and a lot of practice problems with step-by-step answer keys.
Introduction to Polynomials
So, what is a Polynomial ? This is definitely not a word that we hear everyday.
A Polynomial is a finite sum of terms . This includes subtraction as well, since subtraction can be written in terms of addition. Let's take a look at a couple of examples and this will make more sense.
Examples of Polynomials
2x 2 + 3x - 5
2x 2 y 2 + 3xy - 5xy 2
5x + 3y +6x +2y
As you can see from the examples above, we are simply adding (or subtracting) two or more terms together.
Polynomials can also be classified according to the number of terms. Let's take a look!
REMEMBER : Terms are separated by a plus sign or a minus sign.
Let's take a look at one more definition! The degree of a polynomial with one variable is the highest power to which the variable is raised. Take a look!
Degree of Polynomials
Polynomials in one variable should be written in order of decreasing powers. If this is the case, the first term is called the lead coefficient. The exponent of this first term defines the degree of the polynomial.
Now, for one last definition, which is actually a review! If two or more terms have exactly the same variables , then they are called like terms.
Okay... now you are ready to dive into the polynomials unit! If you are new to Polynomials, I would suggest starting with adding polynomials.
Good luck - you can do it!
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Common Core Algebra I.Unit 7.Lesson 1.Introduction to Polynomials.by eMathInstruction
emathinstruction
Sep 19, 2016
In this lesson, we look at the similarities between the base 10 number system and polynomials and use these similarities in order to combine polynomials using addition and subtraction.
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Common Core State Standards Initiative
High School: Algebra
Standards in this domain:, ccss.math.content.hsa.introduction introduction, expressions..
An expression is a record of a computation with numbers, symbols that represent numbers, arithmetic operations, exponentiation, and, at more advanced levels, the operation of evaluating a function. Conventions about the use of parentheses and the order of operations assure that each expression is unambiguous. Creating an expression that describes a computation involving a general quantity requires the ability to express the computation in general terms, abstracting from specific instances.
Reading an expression with comprehension involves analysis of its underlying structure. This may suggest a different but equivalent way of writing the expression that exhibits some different aspect of its meaning. For example, p + 0.05 p can be interpreted as the addition of a 5% tax to a price p . Rewriting p + 0.05 p as 1.05 p shows that adding a tax is the same as multiplying the price by a constant factor.
Algebraic manipulations are governed by the properties of operations and exponents, and the conventions of algebraic notation. At times, an expression is the result of applying operations to simpler expressions. For example, p + 0.05 p is the sum of the simpler expressions p and 0.05 p . Viewing an expression as the result of operation on simpler expressions can sometimes clarify its underlying structure.
A spreadsheet or a computer algebra system (CAS) can be used to experiment with algebraic expressions, perform complicated algebraic manipulations, and understand how algebraic manipulations behave.
Equations and inequalities.
An equation is a statement of equality between two expressions, often viewed as a question asking for which values of the variables the expressions on either side are in fact equal. These values are the solutions to the equation. An identity, in contrast, is true for all values of the variables; identities are often developed by rewriting an expression in an equivalent form.
The solutions of an equation in one variable form a set of numbers; the solutions of an equation in two variables form a set of ordered pairs of numbers, which can be plotted in the coordinate plane. Two or more equations and/or inequalities form a system. A solution for such a system must satisfy every equation and inequality in the system.
An equation can often be solved by successively deducing from it one or more simpler equations. For example, one can add the same constant to both sides without changing the solutions, but squaring both sides might lead to extraneous solutions. Strategic competence in solving includes looking ahead for productive manipulations and anticipating the nature and number of solutions.
Some equations have no solutions in a given number system, but have a solution in a larger system. For example, the solution of x + 1 = 0 is an integer, not a whole number; the solution of 2 x + 1 = 0 is a rational number, not an integer; the solutions of x 2 - 2 = 0 are real numbers, not rational numbers; and the solutions of x 2 + 2 = 0 are complex numbers, not real numbers.
The same solution techniques used to solve equations can be used to rearrange formulas. For example, the formula for the area of a trapezoid, A = (( b 1 + b 2 )/2) h , can be solved for h using the same deductive process. Inequalities can be solved by reasoning about the properties of inequality. Many, but not all, of the properties of equality continue to hold for inequalities and can be useful in solving them.
Connections to Functions and Modeling. Expressions can define functions, and equivalent expressions define the same function. Asking when two functions have the same value for the same input leads to an equation; graphing the two functions allows for finding approximate solutions of the equation. Converting a verbal description to an equation, inequality, or system of these is an essential skill in modeling.
Algebra Overview
- Seeing Structure in Expressions
- Interpret the structure of expressions
- Write expressions in equivalent forms to solve problems
Arithmetic with Polynomials and Rational Functions
- Perform arithmetic operations on polynomials
- Understand the relationship between zeros and factors of polynomials
- Use polynomial identities to solve problems
- Rewrite rational functions
Creating Equations
- Create equations that describe numbers or relationships
Reasoning with Equations and Inequalities
- Understand solving equations as a process of reasoning and explain the reasoning
- Solve equations and inequalities in one variable
- Solve systems of equations
- Represent and solve equations and inequalities graphically
Mathematical Practices
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
Arithmetic with Polynomials & Rational Expressions
Creating equations ✭, reasoning with equations & inequalities.
- Standards for Mathematical Practice
- How to read the grade level standards
- Introduction
- Counting & Cardinality
- Operations & Algebraic Thinking
- Number & Operations in Base Ten
- Measurement & Data
- Number & Operations—Fractions¹
- Number & Operations in Base Ten¹
- Number & Operations—Fractions
- Ratios & Proportional Relationships
- The Number System
- Expressions & Equations
- Statistics & Probability
- The Real Number System
- Quantities*
- The Complex Number System
- Vector & Matrix Quantities
- Arithmetic with Polynomials & Rational Expressions
- Creating Equations*
- Reasoning with Equations & Inequalities
- Interpreting Functions
- Building Functions
- Linear, Quadratic, & Exponential Models*
- Trigonometric Functions
- High School: Modeling
- Similarity, Right Triangles, & Trigonometry
- Expressing Geometric Properties with Equations
- Geometric Measurement & Dimension
- Modeling with Geometry
- Interpreting Categorical & Quantitative Data
- Making Inferences & Justifying Conclusions
- Conditional Probability & the Rules of Probability
- Using Probability to Make Decisions
- Courses & Transitions
- Mathematics Glossary
- Mathematics Appendix A
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N-Gen Math Algebra I
The full experience and value of eMATHinstruction courses are achieved when units and lessons are followed in order. Students learn skills in earlier units that they will then build upon later in the course. Lessons can be used in isolation but are most effective when used in conjunction with the other lessons in this course. All Lesson/Homework files, Spanish translations of those files, and videos are available for free. Other resources, such as answer keys and more, are accessible with a paid membership .
Each month August through May we release new resources for this course that are accessible with a Teacher Plus membership. We release new resources in unit order throughout the school year. You can see a list of our new releases by visiting our blog and selecting the most recent newsletter.
If you have an Algebra I membership, please note that you also have access to the paid resources for Common Core Algebra I .
Standards Alignment – Powered by EdGate
- Table of Contents for N-Gen Math Algebra I and Standards Alignment
- Unit 1 - The Building Blocks of Algebra
- Unit 2 - Linear Equations and Inequalities
- Unit 3 - Functions
- Unit 4 - Linear Functions
- Unit 5 - Linear Systems
- Unit 6 - Exponential Algebra and Functions
- Unit 7 - Polynomials
- Unit 8 - Quadratic Functions
- Unit 9 - Roots and Irrational Numbers
- Unit 10 - Functions and Their Transformations
- Unit 11 - Statistics
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EMATHINSTRUCTION COMMON CORE ALGEBRA 1 HOMEWORK ANSWERS
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FACTORING POLYNOMIALS COMMON CORE ALGEBRA I HOMEWORK 2. 3. NCY I entify the greatest common facto or each of the following sets of monomials. (a) 6x2 and 24x3 (d) 2x3, 6x2, and 12x (b) 5x and 10x2 (e) 1 t2, 48t, and 80 (c) 2x4 and 10x2 (f) 8t5, 12t3, and 16t Which of the following is the greatest common factor of the terms 36x y and 24xy7 ? (l ...
These lessons introduce polynomials as analogous to the integers and multiple parallel are drawn to the integers throughout the unit. Fluency skills are emphasized throughout the unit. These skills include adding, multiplying, and factoring polynomials. Applications problems are given in terms of primarily area models.
Find step-by-step solutions and answers to Algebra 1 Common Core - 9780133185485, as well as thousands of textbooks so you can move forward with confidence. ... Section 1-8: An Introduction to Equations. Section 1-9: Patterns, Equations, and Graphs. Page 68: Chapter Review. Page 73: ... Polynomials and Factoring. Section 8-1: Adding and ...
Lesson 16: Graphing Quadratic Equations From the Vertex Form, y=a (x-h) 2 +k ( Vide0) Lesson 17: Graphing Quadratic Functions From the Standard Form, f (x)=ax 2 +bx+c ( Video Lesson) Function Transformations and Modeling. Topic C Overview. Lesson 18: Graphing Cubic, Square Root, and Cube Root Functions.
In this lesson we learn about the standard form of a polynomial, how polynomials are similar to integers, and how to add and subtract polynomials. You can a...
In 2008, Kirk founded eMathInstruction and published Algebra 2 with Trigonometry. Common Core Algebra I is eMathInstruction's second offering and the first to have complete ... for helping out on the homework sets for early portions of the text. His help gave me the mental strength to ... Lesson #1 - Introduction to Polynomials Lesson #2 ...
jjjn name: date: introduction to polynomials common core algebra the way we write numbers in our systems is interesting because with only 10 digits, and we are
Adding and Subtracting Polynomials. Section 6-5: Multiplying Polynomials. Page 437: Exercises. Page 446: Chapter Test. ... with expert-verified solutions from Algebra 1 Common Core 1st Edition, you'll learn how to solve your toughest homework problems. Our resource for Algebra 1 Common Core includes answers to chapter exercises, as well as ...
Polynomials. Welcome to the Algebra 1 Polynomials Unit! This unit is a brief introduction to the world of Polynomials. We will add, subtract, multiply, and even start factoring polynomials. Click on the lesson below that interests you, or follow the lessons in order for a complete study of the unit.
This introduction to polynomials covers common terminology like terms, degree, standard form, monomial, binomial and trinomial. Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Created by 1. Hello Fren.
Step-by-step video answers explanations by expert educators for all Algebra 1 Common Core 1st by Randall I. Charles,Basia Hall, Dan Kennedy only on Numerade.com. For Educators; Login; ... An Introduction to Functions. 7 sections 300 questions RW +104 more. 5 Linear Functions ... Polynomials and Factoring. 8 sections 482 questions +104 more. 9 ...
Learn how to factor polynomials in this Common Core Algebra I video lesson. Watch examples and practice problems with clear explanations and step-by-step solutions.
A polynomial is a special algebraic expression with terms that consist of real number coefficients and variable factors with whole number exponents. Polynomials do not have variables in the denominator of any term. The degree of a term in a polynomial is defined to be the exponent of the variable, or if there is more than one variable in the ...
Watch Common Core Algebra I.Unit 7.Lesson 1.Introduction to Polynomials.by eMathInstruction, Math, All, Math Videos on TeacherTube. X. Find Lessons! Join Free! ... Common Core Algebra I.Unit 7.Lesson 1.Introduction to Polynomials.by eMathInstruction All / Math. emathinstruction. Sep 19, 2016. 6462 views.
The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. Khan Academy's Algebra 1 course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience!
Unit 8 - Quadratic Functions and Their Algebra. These lessons introduce quadratic polynomials from a basic perspective. We then build on the notion of shifting basic parabolas into their vertex form. Completing the square is used as a fundamental tool in finding the turning point of a parabola. Finally, the zero product law is introduced as a ...
GCF factoring introduction Get 3 of 4 questions to level up! ... Factoring higher-degree polynomials: Common factor (Opens a modal) Strategy in factoring quadratics (part 1 of 2) ... this course aligns to Pearson Education's Algebra 1 Common Core. It is not affiliated with, sponsored by, reviewed, approved or endorsed by Pearson Education or ...
Write an equation to model the relationship between these quantities given a fixed energy output. Transform a quadratic equation written in standard form to an equation in vertex form, ( x − p ) 2 = q , by completing the square. Example 1: Write the quadratic equation, y= − 2 x 2 − 16 x − 20 in vertex form.
CCSS.Math.Content.HSA.REI.A.1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. CCSS.Math.Content.HSA.REI.A.2.
Expressions known as polynomials are used widely in algebra. Applications of these expressions are essential to many careers, including economists, engineers, and scientists. In this chapter, we will find out what polynomials are and how to manipulate them through basic mathematical operations.
N-Gen Math Algebra I. The full experience and value of eMATHinstruction courses are achieved when units and lessons are followed in order. Students learn skills in earlier units that they will then build upon later in the course. Lessons can be used in isolation but are most effective when used in conjunction with the other lessons in this course.
Algebra 1 Common Core: Home List of Lessons Semester 1 > > > > > ... Common Core Standard: A-APR.A.1 Need a tutor? Click this link and get your first session free! ... To purchase the entire course of lesson packets, click here. Solutions. alg_1.5_practice_solutions_.pdf: File Size: 474 kb: File Type: pdf: Download File. Corrective Assignment ...
Common core algebra i.unit #7.lesson #1.introduction to polynomials by Arihant loney trigonometry sl irodov calculus burman maron coordinate Algebra common core homework answer answers unit relatively examples try keep simple