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Unit 1: Algebra foundations
About this unit.
Why did humans invent algebra in the first place? Let's look at the history and beauty of algebra, and review some fundamental ideas and tools we'll use throughout the course.
Overview and history of algebra
- Origins of algebra (Opens a modal)
- Abstract-ness (Opens a modal)
- The beauty of algebra (Opens a modal)
- Creativity break: Why is creativity important in algebra? (Opens a modal)
- Intro to the coordinate plane (Opens a modal)
- Why all the letters in algebra? (Opens a modal)
Introduction to variables
- What is a variable? (Opens a modal)
- Why aren't we using the multiplication sign? (Opens a modal)
- Creativity break: Why is creativity important in STEM jobs? (Opens a modal)
- Evaluating an expression with one variable (Opens a modal)
- Evaluating expressions with one variable (Opens a modal)
- Evaluating expressions with one variable Get 5 of 7 questions to level up!
Substitution and evaluating expressions
- Evaluating expressions with two variables (Opens a modal)
- Evaluating expressions with two variables: fractions & decimals (Opens a modal)
- Evaluating expressions with multiple variables Get 3 of 4 questions to level up!
- Evaluating expressions with multiple variables: fractions & decimals Get 3 of 4 questions to level up!
Combining like terms
- Intro to combining like terms (Opens a modal)
- Combining like terms with negative coefficients & distribution (Opens a modal)
- Combining like terms with negative coefficients (Opens a modal)
- Combining like terms with rational coefficients (Opens a modal)
- Combining like terms with negative coefficients Get 5 of 7 questions to level up!
- Combining like terms with negative coefficients & distribution Get 3 of 4 questions to level up!
- Combining like terms with rational coefficients Get 3 of 4 questions to level up!
Introduction to equivalent expressions
- Equivalent expressions (Opens a modal)
- Equivalent expressions Get 5 of 7 questions to level up!
Division by zero
- Why dividing by zero is undefined (Opens a modal)
- The problem with dividing zero by zero (Opens a modal)
- Undefined & indeterminate expressions (Opens a modal)
- Algebra foundations: FAQ (Opens a modal)
Common Core Algebra I Math (Worksheets, Homework, Lesson Plans)
Related Topics: Common Core Math Resources, Lesson Plans & Worksheets for all grades Common Core Math Video Lessons, Math Worksheets and Games for Algebra Common Core Math Video Lessons, Math Worksheets and Games for all grades
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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Quadratic Growth (Lesson 7.1)
Unit 1: generalizing patterns, day 1: intro to unit 1, day 2: equations that describe patterns, day 3: describing arithmetic patterns, day 4: making use of structure, day 5: review 1.1-1.3, day 6: quiz 1.1 to 1.3, day 7: writing explicit rules for patterns, day 8: patterns and equivalent expressions, day 9: describing geometric patterns, day 10: connecting patterns across multiple representations, day 11: review 1.4-1.7, day 12: quiz 1.4 to 1.7, day 13: unit 1 review, day 14: unit 1 test, unit 2: linear relationships, day 1: proportional reasoning, day 2: proportional relationships in the coordinate plane, day 3: slope of a line, day 4: linear equations, day 5: review 2.1-2.4, day 6: quiz 2.1 to 2.4, day 7: graphing lines, day 8: linear reasoning, day 9: horizontal and vertical lines, day 10: standard form of a line, day 11: review 2.5-2.8, day 12: quiz 2.5 to 2.8, day 13: unit 2 review, day 14: unit 2 test, unit 3: solving linear equations and inequalities, day 1: intro to unit 3, day 2: exploring equivalence, day 3: representing and solving linear problems, day 4: solving linear equations by balancing, day 5: reasoning with linear equations, day 6: solving equations using inverse operations, day 7: review 3.1-3.5, day 8: quiz 3.1 to 3.5, day 9: representing scenarios with inequalities, day 10: solutions to 1-variable inequalities, day 11: reasoning with inequalities, day 12: writing and solving inequalities, day 13: review 3.6-3.9, day 14: quiz 3.6 to 3.9, day 15: unit 3 review, day 16: unit 3 test, unit 4: systems of linear equations and inequalities, day 1: intro to unit 4, day 2: interpreting linear systems in context, day 3: interpreting solutions to a linear system graphically, day 4: substitution, day 5: review 4.1- 4.3, day 6: quiz 4.1 to 4.3, day 7: solving linear systems using elimination, day 8: determining number of solutions algebraically, day 9: graphing linear inequalities in two variables, day 10: writing and solving systems of linear inequalities, day 11: review 4.4- 4.7, day 12: quiz 4.4 to 4.7, day 13: unit 4 review, day 14: unit 4 test, unit 5: functions, day 1: using and interpreting function notation, day 2: concept of a function, day 3: functions in multiple representations, day 4: interpreting graphs of functions, day 5: review 5.1-5.4, day 6: quiz 5.1 to 5.4, day 7: from sequences to functions, day 8: linear functions, day 9: piecewise functions, day 10: average rate of change, day 11: review 5.5-5.8, day 12: quiz 5.5 to 5.8, day 13: unit 5 review, day 14: unit 5 test, unit 6: working with nonlinear functions, day 1: nonlinear growth, day 2: step functions, day 3: absolute value functions, day 4: solving an absolute value function, day 5: review 6.1-6.4, day 6: quiz 6.1 to 6.4, day 7: exponent rules, day 8: power functions, day 9: square root and root functions, day 10: radicals and rational exponents, day 11: solving equations, day 12: review 6.5-6.9, day 13: quiz 6.5 to 6.9, day 14: unit 6 review, day 15: unit 6 test, unit 7: quadratic functions, day 1: quadratic growth, day 2: the parent function, day 3: transforming quadratic functions, day 4: features of quadratic functions, day 5: forms of quadratic functions, day 6: review 7.1-7.5, day 7: quiz 7.1 to 7.5, day 8: writing quadratics in factored form, day 9: solving quadratics using the zero product property, day 10: solving quadratics using symmetry, day 11: review 7.6-7.8, day 12: quiz 7.6 to 7.8, day 13: quadratic models, day 14: unit 7 review, day 15: unit 7 test, unit 8: exponential functions, day 1: geometric sequences: from recursive to explicit, day 2: exponential functions, day 3: graphs of the parent exponential functions, day 4: transformations of exponential functions, day 5: review 8.1-8.4, day 6: quiz 8.1 to 8.4, day 7: working with exponential functions, day 8: interpreting models for exponential growth and decay, day 9: constructing exponential models, day 10: rational exponents in context, day 11: review 8.5-8.8, day 12: quiz 8.5 to 8.8, day 13: unit 8 review, day 14: unit 8 test, learning targets.
Understand that quadratic functions have a linear rate of change, or a constant second difference over equal intervals of the domain.
Identify patterns or scenarios that can be represented by quadratic functions.
Distinguish quadratic growth from linear and exponential growth.
| Tasks/Activity | Time |
|---|---|
| Activity | 20 minutes |
| Debrief Activity with Margin Notes | 15 minutes |
| QuickNotes | 5 minutes |
| Check Your Understanding | 10 minutes |
Activity: Starburst Growth
Lesson handouts, media locked.
Our Teaching Philosophy:
Experience first, formalize later (effl), experience first.
Algebra 1 Unit 7 Overview and Learning Targets: Word | pdf
Students start Unit 7 with a sequence task about Starburst candies. The Starburst are in a rectangular array and the number of rows and columns changes from one figure to the next. This leads to 2-dimensional growth which is associated with quadratic growth.
In question 3, students complete a table with the number of Starbursts in each figure. It is important that students show their calculation so they can make use of structure when writing a general rule. For example, for Figure 10, students would write 10(12)=120.
In parts b and c, students compare the growth of the Starbursts to the patterns they encountered in Unit 1 and review the vocabulary of arithmetic and geometric sequences.
Monitoring Questions
- What shape is made by the Starbursts? Why is this important?
- Why is counting one-by-one not the best strategy for determining the number of Starbursts?
- How does the number of rows relate to the Figure number?
- How does the number of columns relate to the Figure number?
- How can you tell if this sequence is arithmetic or not?
- How can you tell if this sequence is geometric or not?
Formalize Later
Today’s debrief is focused on different ways of identifying quadratic growth. Visually, growth happens in 2-dimensions. Equations for quadratic patterns can be written as the product of linear factors. Multiplying these factors will result in an x 2 x^2 x 2 term. Consecutive terms have a constant second difference. Students should be able to use multiple strategies to determine if a pattern or equation demonstrates quadratic growth.
One way to identify quadratic equations is by rewriting them in standard form, so the highest exponent is easily seen. We prefer doing this with an area model, as it helps students see the distributive property visually. If your students are not familiar with this model, take time to explain it to them. We prefer this method over the “FOIL” method because the multiplication of all the terms is more easily seen and the like terms are easily identifiable on the diagonal.
Math Medic Help
Applying the Quadratic Formula (Part 1)
Select all the equations that have 2 solutions.
\((x + 3)^2 = 9\)
\((x - 5)^2 = \text- 5\)
\((x + 2)^2-6 = 0\)
\((x - 9)^2+25 = 0\)
\((x + 10)^2 = 1\)
\((x - 8)^2 = 0\)
\(5=(x+1)(x+1)\)
For access, consult one of our IM Certified Partners .
A frog jumps in the air. The height, in inches, of the frog is modeled by the function \(h(t) = 60t-75t^2\) , where \(t\) is the time after it jumped, measured in seconds.
Solve \(60t - 75t^2 = 0\) . What do the solutions tell us about the jumping frog?
A tennis ball is hit straight up in the air, and its height, in feet above the ground, is modeled by the equation \(f(t) = 4 + 12t - 16t^2\) , where \(t\) is measured in seconds since the ball was thrown.
- Find the solutions to the equation \(0 = 4 + 12t - 16t^2\) .
- What do the solutions tell us about the tennis ball?
Rewrite each quadratic expression in standard form.
- \((x+1)(7x+2)\)
- \((8x+1)(x-5)\)
- \((2x+1)(2x-1)\)
- \((4+x)(3x-2)\)
Find the missing expression in parentheses so that each pair of quadratic expressions is equivalent. Show that your expression meets this requirement.
- \((4x-1)(\underline{\hspace{1in}})\) and \(16x^2 -8x +1\)
- \((9x + 2)(\underline{\hspace{1in}})\) and \(9x^2 -16x -4\)
- \((\underline{\hspace{1in}})(\text-x + 5)\) and \(\text-7x^2 +36x-5\)
The number of downloads of a song during a week is a function, \(f\) , of the number of weeks, \(w\) , since the song was released. The equation \(f(w) = 100,\!000 \boldcdot \left(\frac{9}{10}\right)^w\) defines this function.
- What does the number 100,000 tell you about the downloads? What about the \(\frac{9}{10}\) ?
- Is \(f(\text-1)\) meaningful in this situation? Explain your reasoning.
Consider the equation \(4x^2 - 4x -15 = 0\) .
- Identify the values of \(a\) , \(b\) , and \(c\) that you would substitute into the quadratic formula to solve the equation.
Evaluate each expression using the values of \(a\) , \(b\) , and \(c\) .
\(\text- b\)
\(b^2 - 4ac\)
\(\sqrt{b^2 - 4ac}\)
\(\text- b \pm \sqrt{b^2 - 4ac}\)
\(\dfrac{\text- b \pm \sqrt{b^2 - 4ac}}{2a}\)
- The solutions to the equation are \(x=\text-\frac 32\) and \(x=\frac52\) . Do these match the values of the last expression you evaluated in the previous question?
- Describe the graph of \(y=\text-x^2\) . (Does it open upward or downward? Where is its \(y\) -intercept? What about its \(x\) -intercepts?)
Without graphing, describe how adding \(16x\) to \(\text-x^2\) would change each feature of the graph of \(y = \text-x^2\) . (If you get stuck, consider writing the expression in factored form.)
- the \(x\) -intercepts
- the \(y\) -intercept
- the direction of opening of the U-shape graph
- $ 0.00 0 items
Unit 7 – Polynomials
Introduction to Polynomials
LESSON/HOMEWORK
LECCIÓN/TAREA
LESSON VIDEO
EDITABLE LESSON
EDITABLE KEY
SMART NOTEBOOK
Adding and Subtracting Polynomials
Multiplying Polynomials
More Work Multiplying Polynomials
Factoring Polynomials
Conjugate Binomials
Factoring Trinomials
Complete Factoring
Recognizing Structure to Factor
Factoring Challenging Trinomials
Unit Review
Unit 7 Review
UNIT REVIEW
REPASO DE LA UNIDAD
EDITABLE REVIEW
Unit 7 Assessment – Form A
EDITABLE ASSESSMENT
Unit 7 Assessment – Form B
Unit 7 Exit Tickets
Unit 7 Mid-Unit Quiz – Form A
U07.AO.01 – Optimizing the Volume of an Open Box
PDF DOCUMENT - SPANISH
EDITABLE RESOURCE
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Our resource for Algebra 1: Homework Practice Workbook 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 problems, you can take the guesswork out of studying and move forward with confidence. Find step-by-step solutions and answers ...
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!
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Warm-up. This Math Talk encourages students to to rely on the structure of equations, properties of operations, and what they know about solutions to equations to mentally solve problems. It also prompts students to recall that dividing a number by 0 leads to an undefined result, preparing them for the work later in the lesson.
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In this lesson, students use properties of exponents and the distributive property to multiply polynomials, including cubing a binomial. Links between base-1...
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.
The standards taught in each Math Medic Algebra 1 lesson can be found here. The unit overviews and learning targets for the Math Medic Algebra 1 course can be found here. Units. Unit 1: Generalizing Patterns. Unit 2: Linear Relationships. Unit 3: Solving Linear Equations and Inequalities. Unit 4: Systems of Linear Equations and Inequalities.
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 7-2: Multiplying Powers with the Same Base. Section 7-3: More Multiplication Properties of Exponents. Section 7-4: Division Properties of Exponents. Page 447: Mid-Chapter Quiz ...
Letters everywhere! In this lesson we solve classic linear equations where some or all of the constants are unknown. Parallels are drawn in each problem to l...
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Algebra 1 Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7. Alg1.7 Quadratic Equations. In this unit, students interpret, write, and solve quadratic equations. They learn that writing and solving quadratic equations is a way to precisely describe and answer questions about quadratic functions. It is especially useful for finding input values ...
Unit 4: Systems of Linear Equations and Inequalities. Day 1:Intro to Unit 4. Day 2:Interpreting Linear Systems in Context. Day 3:Interpreting Solutions to a Linear System Graphically. Day 4:Substitution. Day 5:Review 4.1- 4.3. Day 6:Quiz 4.1 to 4.3. Day 7:Solving Linear Systems Using Elimination. Day 8:Determining Number of Solutions Algebraically.
1 Transformers: Shifty y's; 2 Transformers: More Than Meets the y's; 3 Building the Perfect Square; 4 Square Deal; 5 Be There or Be Square; 6 Factor Fixin' 7 The x-Factor; 8 The Wow Factor; 9 Lining Up Quadratics; 10 I've Got a Fill-in; 11 All Things Being Equal; 12 Formula for Success; 13 Comparison Shopping; Self Assessments
Problem 7. Consider the equation . Identify the values of , , and that you would substitute into the quadratic formula to solve the equation. Evaluate each expression using the values of , , and . The solutions to the equation are and .
What is the second objective of Algebra 2 Unit 2 Lesson 7? To use the properties of real numbers to simplify and evaluate algebraic expressions. What is the third objective of Algebra 2 Unit 2 Lesson 7? To solve an equation or inequality, including absolute value and compound inequalities.
Unit 7 - Polynomials. 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.
View Algebra 2.7 Homework (1).pdf from MATH 0617 at Glendale High, Springfield. Unit 2 Lesson 7 Cumulative Practice Problems 1. Match each equation with an equivalent equation. Some of the answer
Home / Courses / N-Gen Math Algebra I / Unit 7 - Polynomials. Unit 7 - Polynomials. Lesson 1 Introduction to Polynomials. LESSON/HOMEWORK. LECCIÓN/TAREA. LESSON VIDEO. ANSWER KEY. EDITABLE LESSON. EDITABLE KEY. SMART NOTEBOOK. Lesson 2 Adding and Subtracting Polynomials. LESSON/HOMEWORK.
Algebra 2 Unit 7 Lesson 1. Get a hint. complex number. Click the card to flip 👆. a number in the form a + bi when 'a' is a real number and bi is a pure imaginary number. Click the card to flip 👆. 1 / 6.