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.
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Algebra I Homework, Lesson Plans and Worksheets
Topics and Objectives (Module 1) |
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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 ( ) |
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Topics and Objectives (Module 2) |
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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) |
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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 ( ) |
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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 ( ) |
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Topics and Objectives (Module 4) |
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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) |
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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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Solutions for Algebra 1 Common Core 1st
Randall i. charles,basia hall, dan kennedy, get access to all of the answers and step-by-step video explanations to this book and 5,000+ more. try numerade free., foundations for algebra.
Solving Inequalities
An introduction to functions.
Linear Functions
Systems of Equations and Inequalities
Exponents and Exponential Functions
Polynomials and factoring, quadratic functions and equations, radical expressions and equations, rational expressions and functions, data analysis and probability.
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Introduction to Common Core Algebra - 1
Algebra 1 is the first of the five high-school courses (Algebra 1, Geometry, Algebra 2, Precalculus, and Calculus) and is typically taken in grade 9. However, some students take it in grade 7 or 8 so as to enable them to take Calculus or another college-level course in their senior high-school year.
The contents of Algebra 1 are divided among the following four domains:
- Expressions, Equations, and Inequalities
Now, while the standards covered under the Numbers and Statistics domains are more of an extension of the corresponding grade 8 ones, those under the Equations and Functions domains introduce the student to many big mathematical ideas. Let’s take a look at some of the big ideas from these two domains and how the standards approach them.
Expressions, Equations and Inequalities
The standards in this domain recap a lot of the Algebra that is learned through middle school. However, in addition to procedural fluency, the focus here is on explaining the reasoning.
For example, the standard process of solving a linear inequality in two variables, say $$2x + 4y < 12$$ involves dividing the XY-plane into two regions using its boundary line $$2x + 4y = 12$$
Then, the region which represents the solution is identified by considering test points in both regions. However, this process is rather mechanical and the reasoning behind isn’t usually explained. So, to help the student understand this intuitively, the standards recommend building on their existing knowledge of linear equations.
To do this, we would isolate the y in $$2x + 4y < 12$$ on its LHS, and rewrite it as $$y < 3 - \frac{1}{2}x$$
Now, the boundary line is $$y = 3 - \frac{1}{2}x$$ and this helps the student understand that, for a given x-value:
- if y is less than $$3 - \frac{1}{2}x$$ then (x, y) must lie below the boundary line.
- if y equals $$3 - \frac{1}{2}x$$ then (x, y) must lie on the boundary line.
- if y is greater than $$3 - \frac{1}{2}x$$ then (x, y) must lie above the boundary line.
To make this even clearer, the boundary line and a vertical line, say x = 4, and can be graphed as follows:
Here, when x = 4, $$3 - \frac{1}{2}x$$ equals $$3 - \frac{1}{2}(4)$$ or $$1$$
Hence, the line x = 4 intersects the boundary line at (4, 1) as shown above. Now, of the other points on the line x = 4:
- the ones whose y-coordinate is less than 1 lie below the boundary line.
- the ones whose y-coordinate is greater than 1 lie above the boundary line.
Similarly, for any point (x, y) to represent a solution to $$y < 3 - \frac{1}{2}x$$ it must lie below the boundary line $$y= 3 - \frac{1}{2}x$$
Thus, we show that the region below the boundary line is the solution to the given inequality.
This domain forms the bulk of the Algebra 1 course. The standards included here formalize the student’s middle-school-understanding of functions by introducing them to the function notation and the ideas of the domain and range. This is a super-important domain on which a large chunk of more advanced high-school Math is based.
To facilitate the development of an intuitive and deep conceptual understanding of the big ideas involved here, the standards recommend the use of a variety of visual-aids as follows:
Representation : The standards recommend giving the student ample exposure to switching among different representations of a function. For example, to get a visual sense of the relationship between the input and output of a function, it is important to start with:
- its algebraic representation, say f(x) = x 2 , move on to
- a tabular representation listing out a few of its input-output pairs, and finally to
- a graphical representation by plotting and joining the input-output pairs on a graph.
This sort of approach helps the student appreciate the interconnectedness of different forms of representation, and understand their advantages and disadvantages. It also helps them see how a graphical representation can be useful for a qualitative comparison between two functions covering parameters like their rates of changes, increasing/decreasing intervals, etc.
Key Features of the Graph : Most textbooks treat the key features of the graph of a function, e.g. its shape, intercepts, maximum/minimum values, etc., in isolation. As a result, the student is often unable to link the algebraic and geometric interpretations of a given function. For example, consider the graph of the function f(x) = x 2 - 6x +6 as follows:
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To understand why this graph is U-shaped , we can rewrite its function rule in the vertex form, i.e. f(x) = (x - 3) 2 - 3. This makes it easy to recognize that:
- The point (3, -3) is the lowest on the graph because that’s where the value of (x-3) 2 is minimum , i.e., 0.
- The line x = 3 divides the graph into identical halves as the values of (x-3) 2 are equal for x-values equidistant from 3 (for e.g., x = 1 and x = 5). Hence, the values of f(x) = (x-3) 2 - 3 are also equal for such x-values, and as a result, the graph is U-shaped.
Transformations : This is a problem-area for a lot of students as they try to commit a few formulas to memory, and then use them to solve problems. As a result, they are thrown off-guard by small changes in the way the question is worded and/or by a difference in the context. To avoid this, there is a comprehensive set of standards that are geared towards understanding the algebraic rationale behind the graphical relationships of functions like f(x) + k, kf(x), and f(kx) with f(x).
The Cuemath curriculum provides learning experiences of important concepts through concrete and pictorial representations and connects mathematics with the lives of students. Cuemath conducts Live Online Math classes . This makes the students love math and see its relevance in their day to day lives.
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Unit 11 – The Circular Functions
Rotations and Angle Terminology
LESSON/HOMEWORK
LESSON VIDEO
EDITABLE LESSON
EDITABLE KEY
Radian Angle Measurement
The Unit Circle
The Definition of the Sine and Cosine Functions
More Work with the Sine and Cosine Functions
Basic Graphs of Sine and Cosine
Vertical Shifting of Sinusoidal Graphs
The Frequency and Period of a Sinusoidal Graph
Sinusoidal Modeling
The Tangent Function
The Reciprocal Functions
Unit Review
Unit 11 Review – The Circular (Trig) Functions
UNIT REVIEW
EDITABLE REVIEW
Unit 11 Assessment Form A
EDITABLE ASSESSMENT
Unit 11 Assessment Form B
Unit 11 Assessment Form C
Unit 11 Assessment Form D
Unit 11 Exit Tickets
Unit 11 Mid-Unit Quiz (through Lesson 5) – Form A
Unit 11 Mid-Unit Quiz (through Lesson 5) – Form B
Unit 11 Mid-Unit Quiz (through Lesson 5) – Form C
Unit 11 Mid-Unit Quiz (through Lesson 5) – Form D
U11.AO.01 – Lesson 8.5.More Work Graphing Sine and Cosine
EDITABLE RESOURCE
U11.AO.02 – Sinusoidal Modeling of Daylight Data
U11.AO.03 Sinusoidal Modeling Teacher Directions
U11.AO.04 – Solving Trigonometric Equations Graphically
U11.AO.05 – Sinusoidal Modeling Additional Practice
U11.AO.06 – Practice Calculating Values of Various Trig Functions
U11.AO.07 – Practice with Radian Angle Measurement
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Unit 1 - The Building Blocks of Algebra. Table of Contents for Common Core Algebra I. Unit 2 - Linear Expressions, Equations, and Inequalities. Unit 3 - Functions. Unit 4 - Linear Functions and Arithmetic Sequences. Unit 5 - Systems of Linear Equations and Inequalities. Unit 6 - Exponents, Exponents, Exponents and More Exponents.
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. ... Chapter 1:Foundations for Algebra. Section 1-1: Variables and Expressions. Section 1-2: Order of Operations and Evaluating Expressions. Section 1-3: Real Numbers and the Number Line ...
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!
Now, 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 detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice ...
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.
This unit begins by ensuring that students understand that solutions to equations are points that make the equation true, while solutions to systems make all equations (or inequalities) true. Graphical and substitution methods for solving systems are reviewed before the development of the Elimination Method.
This algebra course follows Common Core Standards. For our old algebra site, click HERE. Welcome to our Flipped - Mastery Classroom Website. We are so glad that you are taking responsibility for your education in Algebra I. SEMESTER 1. UNIT 1: Analyze Graphs and Expressions. UNIT 2: Create and Solve Equations/Ineq. UNIT 3: Systems of Equations.
2 1 2 1 x x y y y mx b y y 1 m(x x 1) x (x 1,y 1) (x 2,y 2) TYPES OF SLOPE Positive Negative Zero Underfined + - 0 m m 1 Parallel Slopes Perpendicular Slopes m || m LINEAR INEQUALITIES y mx b y mx by mx b y mx b T YPES O F N UMBER , 2, 6, e Standard Form: y ax2 bx c Vertex Form :
Understanding High School Math 2015 Common Core Algebra 1 Student Edition Grades 8/9 0th Edition homework has never been easier than with Chegg Study. ... Unlike static PDF High School Math 2015 Common Core Algebra 1 Student Edition Grades 8/9 0th Edition solution manuals or printed answer keys, our experts show you how to solve each problem ...
Solutions for Algebra 1 Common Core 1st Randall I. Charles,Basia Hall, Dan Kennedy Get access to all of the answers and step-by-step video explanations to this book and 5,000+ more. Try Numerade free. Join Free Today. Chapters. 1 Foundations for Algebra . 9 sections 649 questions +104 more. 2 Solving . 10 sections ...
We develop general methods for solving linear equations using properties of equality and inverse operations. Thorough review is given to review of equation solving from Common Core 8th Grade Math. Solutions to equations and inequalities are defined in terms of making statements true. This theme is emphasized throughout the unit.
Step-by-step solution. Step 1 of 3. Write the following system of linear-quadratic equations; Step 2 of 3. Graph both the equations on the same coordinate system. Step 3 of 3. The points where the graphs of the two functions intersect are the solutions of the linear-quadratic system. Observe that the graph of the linear function intersects the ...
In this lesson, students use properties of exponents and the distributive property to multiply polynomials, including cubing a binomial. Links between base-1...
Common Core Math High School: Algebra: Seeing Structure in Expressions. HSA.SSE.A Interpret the structure of expressions. ... Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. Finite geometric series. Finite geometric series formula.
Introduction to Common Core Algebra - 1. Jun 9, 216 min read. Algebra 1 is the first of the five high-school courses (Algebra 1, Geometry, Algebra 2, Precalculus, and Calculus) and is typically taken in grade 9. However, some students take it in grade 7 or 8 so as to enable them to take Calculus or another college-level course in their senior ...
In this lesson students work with basic proportional reasoning problems and develop proportional relationships that they then graph. For the worksheet used i...
In this lesson students first learn how to graph a simple quadratic by hand and then graph a more complex one using calculator technology. Through this, stud...
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 ...
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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 ...
FREE Lessons, Homework Sets, and Videos eMATHinstruction makes teaching math a whole lot easier and learning math a whole lot more fun. We provide ... Common Core Algebra I; Common Core Geometry; Common Core Algebra II; Algebra 2 + Trigonometry; For Teachers. Select a course to view FREE lessons, homework sets, and lesson videos. Free Spanish ...
Unit 6 - Exponents, Exponents, Exponents and More Exponents. This unit begins with a fundamental treatment of exponent rules and the development of negative and zero exponents. We then develop the concepts of exponential growth and decay from a fraction perspective. Finally, percent work allows us to develop growth models based on constant ...
Assessment. Unit 11 Mid-Unit Quiz (through Lesson 5) - Form B. ASSESSMENT. ANSWER KEY. EDITABLE ASSESSMENT. EDITABLE KEY.