What is a solution to an equation? What does it look like? What is the growth pattern? What is the y intercept? CPM Materials modified by Mr.
|
|
- James Eaton
- 5 years ago
- Views:
Transcription
1 Common Core Standard: Preparation for 8.EE.8b in Lesson What is a solution to an equation? What does it look like? What is the growth pattern? What is the y intercept? CPM Materials modified by Mr. Deyo
2 Title: IM8 Ch How Can I Change It To y=mx+b Form? Date: Learning Target By the end of the period, I will solve twovariable linear equations for one variable and rewrite linear equations in y = mx + b form. I will demonstrate this by completing Four Square notes and by solving problems in a pair/group activity.
3 Home Work: Sec Desc. Date Due Review & Preview 2 Problems: 5 6, 5 7
4
5 Vocabulary 1) growth factor 2) y intercept 3) solve (for a variable) 4) linear equation
6
7 5.1.1 How Can I Change It To y = mx + b Form? So far in this course, you have used your Equation Mat and/or symbols to find solutions for all types of linear equations with one variable. Today you will learn how to apply these skills to solving linear equations with two variables. As you work today, keep these questions in mind: By the end of this lesson, you should be able to answer the following target questions: What is a solution to an equation? What does it look like? What is the growth pattern? What is the y intercept?
8 5 1 You now have a lot of experience working with equations that compare two quantities. For example, while working with the height of a tree, you found the relationship y = 4x + 5, which compared x (the number of years after it was planted) with y (its height in feet). Use the equation for this tree to answer the questions below. What was its starting height? How can you tell from the equation? What was its growth rate? (That is, how many feet did the tree grow per year?) Justify your answer.
9 tiledata=bhcc3%205 2b cla2x boy aajqvqhajrmq1abpvtqaas5ssaasetv aar9svaarituabqfsjauwlppauwcqwauwnrfauw4qwauxjp9auxqpvaux5qmauxprra uyvqnauygrthf5 2b o9o9 IM 8 Ch How Can I Change It to y=mx+b Form.notebook 5 2a&c CHANGING FORMS You can find the growth rate and starting value for y = 4x + 5 quickly, because the equation is in y = mx + b form. But what if the equation is in a different form? Explore this situation below using 5 2b tiles (CPM). a) The line 6x + 2y = 10 is written in standard form. Can you tell what the growth of the line is? Its y intercept? Predict these values. growth = y intercept = b) The equation 6x + 2y = 10 is shown on the Equation Mat on the next page. Set up this equation on your Equation Mat using tiles. Using only legal moves, rearrange the tiles to get y by itself on the left side of the mat. Record each of your moves algebraically.
10 tiledata=bhcc3%205 2b cla2x boy aajqvqhajrmq1abpvtqaas5ssaasetv aar9svaarituabqfsjauwlppauwcqwauwnrfauw4qwauxjp9auxqpvaux5qmauxprra uyvqnauygrthf5 2b o9o9 IM 8 Ch How Can I Change It to y=mx+b Form.notebook 6x + 2y = b&c CHANGING FORMS Using only legal moves, rearrange the tiles to get y by itself on the left side of the mat. Record each of your moves algebraically. c) Now use your result from part (b) to find the growth pattern and y intercept of the line 6x + 2y = 10. Did your result match your prediction in part (a)?
11 2x + y = 3x 7 5 3a Draw & rearrange your tiles to create an equation that starts with y = Be sure to record all of your moves algebraically and be prepared to share your steps with the class. What is the pattern of growth for your line? What is the y intercept? How can you tell? growth = y intercept =
12 x + 2y = 3x b Draw & rearrange your tiles to create an equation that starts with y = Be sure to record all of your moves algebraically and be prepared to share your steps with the class. What is the pattern of growth for your line? What is the y intercept? How can you tell? growth = y intercept =
13 2(y 3) = 2x 6 5 3d Draw & rearrange your tiles to create an equation that starts with y = Be sure to record all of your moves algebraically and be prepared to share your steps with the class. What is the pattern of growth for your line? What is the y intercept? growth = y intercept =
14 5 3(x + 1) = 2y 3x e Draw & rearrange your tiles to create an equation that starts with y = Be sure to record all of your moves algebraically and be prepared to share your steps with the class. What is the pattern of growth for your line? What is the y intercept? growth = y intercept =
15 x (y + 2) = 2(2x + 1) 5 3f Draw & rearrange your tiles to create an equation that starts with y = Be sure to record all of your moves algebraically and be prepared to share your steps with the class. What is the pattern of growth for your line? What is the y intercept? growth = y intercept =
16 5 4a Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. 2(y 3) = 4 Solve for y
17 5 4b Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. 2x + 5y = 10 Solve for x
18 5 4c Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. 6x + 3y = 4y + 11 Solve for y
19 5 4d Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. Solve for x 3(2x + 4) = 2 + 6x + 10
20 5 4e Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. y = 3x + 6 Solve for x
21 5 4f Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. Solve for p m = 8 2(p m)
22 5 4g Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. 4(q 8) = 7q + 5 Solve for q
23 5 4h Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. Solve for y x 2 + 4y = 2(3x 6 x) + x 2
24 5 5 A tile pattern has 5 tiles in Figure 0 and adds 7 tiles in each new figure. Write the equation of the line that represents the growth of this pattern. Graph the equation and draw a growth triangle for the line. chapter/ch5/les Graph What is the rule? y = ( )x + ( ) How many tiles in Figure 0? Where's the y intercept? (, ) Describe the pattern:
25 5 6a Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. 2x + 22 = 12 Solve for x
26 5 6b Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. 2x y = 3 Solve for y
27 5 6c Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. 2x + 15 = 2x 15 Solve for x
28 5 6d Solve for the indicated variable. Use your Equation Mat if it is helpful. Write down each of your steps algebraically. 6x + 2y = 10 Solve for y
29 5 7 Solve each of the following equations for x. Then check each solution. a) x = b) 6 3 = 15 x c) 2x 12 = 5 8 d) 8 2 = 1 x
30 5 8 Graph the lines y = 4x + 3 and y = x 7 on the same set of axes. Then find their point of intersection. Graph y = 4x + 3 y intercept: rate of growth: y intercept: rate of growth: y = 1x 7 Where do the two lines intersect? chapter/ch5/lesson/5 ( 0, ) ( 0, ) (, )
31 5 9 Draw Figures 0, 1, 2, and 3 for a tile pattern that could be described by: y = 3x chapter/ch5/lesson/5.1.1 Draw the 0 figure. Draw the 1 st figure. Draw the 2 nd figure. Draw the 3 rd figure.
How can you find a rule? How can you compare two rules? How can you use what you know about solving? CPM Materials modified by Mr.
Common Core Standard: 8.EE.8b, 8.EE.8c How can you find a rule? How can you compare two rules? How can you use what you know about solving? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 5.2.4 What
More informationHow did you see it? How can you write it? Is your expression as simplified as possible? CPM Materials modified by Mr. Deyo
. Preparation for 8.EE.7a, 8.EE.7b in Lesson 2..8 How did you see it? How can you write it? Is your expression as simplified as possible? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 2..3 What Does
More informationHow are the angles related? Can I make a triangle? What if it is a right angle? What do I know about this triangle? CPM Materials modified by Mr.
Common Core Standard: 8.G.5 How are the angles related? Can I make a triangle? What if it is a right angle? What do I know about this triangle? CPM Materials modified by Mr. Deyo Title: IM8 Ch. 9.1.2 How
More informationWhat is the association of between the two variables? In what direction does the association go?
Common Core Standard: 8.SP.4 What is the association of between the two variables? In what direction does the association go? How strong is the association between the two variables? CPM Materials modified
More informationStudent Guide: Chapter 1
Student Guide: Chapter 1 1.1 1.1.1 I can solve puzzles in teams 1-4 to 1-8 1.1 1.1.2 1.1 1.1.3 I can investigate the growth of patterns 1-13 to 1-17 1-18 to 1-22 I can investigate the graphs of quadratic
More informationSample: Do Not Reproduce LF6 STUDENT PAGES LINEAR FUNCTIONS STUDENT PACKET 6: SYSTEMS OF LINEAR EQUATIONS. Name Period Date
Name Period Date LINEAR FUNCTIONS STUDENT PACKET 6: SYSTEMS OF LINEAR EQUATIONS LF6.1 LF6.2 LF6.3 Introduction to Systems of Linear Equations Understand the definition of a system of linear equations Understand
More informationMS Algebra Alg.: 1.0, 1.1 Gr. 7: AF 1.1, AF 1.2 Standards Review
MS Algebra Alg.: 1.0, 1.1 Gr. 7: AF 1.1, AF 1.2 Standards Review Mr. Deyo Gr. 7 AF 1.1 Use variables and appropriate operations to write an expression, an equation, an inequality that represents a verbal
More informationGUIDED NOTES 4.1 LINEAR FUNCTIONS
GUIDED NOTES 4.1 LINEAR FUNCTIONS LEARNING OBJECTIVES In this section, you will: Represent a linear function. Determine whether a linear function is increasing, decreasing, or constant. Interpret slope
More informationGraphing Linear Systems
Graphing Linear Systems Goal Estimate the solution of a system of linear equations by graphing. VOCABULARY System of linear equations A system of linear equations is two or more linear equations in the
More informationMS Algebra Ch Simplifying Rational Expressions. Mr. Deyo
MS Algebra Ch. 11.2 Simplifying Rational Expressions Mr. Deyo Title: 11.2 Simplifying Rational Expressions Date: Learning Target By the end of the period, I will simplify rational expressions and determine
More informationExpressions and Equations
Lesson 1 Expressions and Equations Name Use Color Tiles to model each number. Write the perfect square under the radical symbol. Write the square root. 1. 2. 5555 5 = 5 = Using Color Tiles, model each
More informationSay it with Symbols - Unit Test Review Shet
Name: Class: Date: ID: A Say it with Symbols - Unit Test Review Shet Short Answer 1. What does it mean to say that two algebraic expressions are equivalent? Evaluate the expression for the given value
More informationSection 1.4. Meaning of Slope for Equations, Graphs, and Tables
Section 1.4 Meaning of Slope for Equations, Graphs, and Tables Finding Slope from a Linear Equation Finding Slope from a Linear Equation Example Find the slope of the line Solution Create a table using
More informationMS Algebra A-F-IF-7 Ch. 7.3a Solve Linear Systems by Elimination through Addition or Subtraction
MS Algebra A-F-IF-7 Ch. 7.3a Solve Linear Systems by Elimination through Addition or Subtraction Mr. Deyo Solve Linear Systems by Elimination through Addition or Subtraction Title: 7.3a Solve Linear Systems
More informationLesson ACTIVITY: Tree Growth
Lesson 3.1 - ACTIVITY: Tree Growth Obj.: use arrow diagrams to represent expressions. evaluate expressions. write expressions to model realworld situations. Algebraic expression - A symbol or combination
More informationInstruction. Student Activities Overview and Answer Key
Instruction Goal: To provide opportunities for students to develop concepts and skills related to solving systems of linear equations using substitution Common Core Standards Analyze and solve linear equations
More informationUNIT 8: LINEAR FUNCTIONS WEEK 31: Student Packet
Name Period Date UNIT 8: LINEAR FUNCTIONS WEEK 31: Student Packet 31.1 Introduction to Systems of Equations Use variables to write equations and systems of equations. Solve problems involving rate, distance,
More informationLesson 3-7: Absolute Value Equations Name:
Lesson 3-7: Absolute Value Equations Name: In this activity, we will learn to solve absolute value equations. An absolute value equation is any equation that contains an absolute value symbol. To start,
More informationAlgebra Ch. 9.2 Multiplying Polynomials. Mr. Deyo
Algebra Ch. 9.2 Multiplying Polynomials Mr. Deyo Learning Target By the end of the period, I will multiply polynomials by one of three methods: 1) by using a table, 2) by FOIL, or 3) by Vertical Multiplication.
More informationRoots are: Solving Quadratics. Graph: y = 2x 2 2 y = x 2 x 12 y = x 2 + 6x + 9 y = x 2 + 6x + 3. real, rational. real, rational. real, rational, equal
Solving Quadratics Graph: y = 2x 2 2 y = x 2 x 12 y = x 2 + 6x + 9 y = x 2 + 6x + 3 Roots are: real, rational real, rational real, rational, equal real, irrational 1 To find the roots algebraically, make
More informationGetting to the Core. A9 Functions Unit of Study. Algebra II. Updated on May 3, Student Name Period
Getting to the Core Algebra II A9 Functions Unit of Study Updated on May 3, 03 Student Name Period This page was intentionally left blank. Unit A9 Functions Table of Contents Lessons Description Page Title
More informationChapter 2 Linear Relationships. Vocabulary
Chapter 2 Linear Relationships Monday Tuesday Wednesday Thursday Friday Sept. 2 Lesson: 2.1.1/2.1.2 Sept. 3 Lesson: 2.1.3/2.1.4 Sept. 4 Lesson: 2.2.2 HW: Day 1 2-6 2-10 2-19 2-24 HW: Day 2 2-31 2-35 2-41
More informationUSING THE QUADRATIC FORMULA and 9.1.3
Chapter 9 USING THE QUADRATIC FORMULA 9.1.2 and 9.1.3 When a quadratic equation is not factorable, another method is needed to solve for x. The Quadratic Formula can be used to calculate the roots of a
More informationLearning Log Title: CHAPTER 6: SOLVING INEQUALITIES AND EQUATIONS. Date: Lesson: Chapter 6: Solving Inequalities and Equations
Chapter 6: Solving Inequalities and Equations CHAPTER 6: SOLVING INEQUALITIES AND EQUATIONS Date: Lesson: Learning Log Title: Date: Lesson: Learning Log Title: Chapter 6: Solving Inequalities and Equations
More informationB.3 Solving Equations Algebraically and Graphically
B.3 Solving Equations Algebraically and Graphically 1 Equations and Solutions of Equations An equation in x is a statement that two algebraic expressions are equal. To solve an equation in x means to find
More informationUnit 5. Linear equations and inequalities OUTLINE. Topic 13: Solving linear equations. Topic 14: Problem solving with slope triangles
Unit 5 Linear equations and inequalities In this unit, you will build your understanding of the connection between linear functions and linear equations and inequalities that can be used to represent and
More informationMath 10. Lesson 4 7 General Form of Linear Equation
Math 10 Lesson 7 General Form of Linear Equation I. Lesson Objectives: 1) To learn to use the general form of a linear equation. 2) To practice our algebra skills in order to manipulate equations. II.
More informationMathematics: Algebra II Honors Unit 6: Radical Functions
Understandings Questions Knowledge Vocabulary Skills Radical functions can be used to model real-life situations. What are the properties of Algebra and how are these used to solve radical equations? How
More informationActivity 1 Multiply Binomials. Activity 2 Multiply Binomials. You can use algebra tiles to find the product of two binomials.
Algebra Lab Multiplying Polynomials You can use algebra tiles to find the product of two binomials. Virginia SOL A..b The student will perform operations on polynomials, including adding, subtracting,
More informationMATH 60 Course Notebook Chapter #1
MATH 60 Course Notebook Chapter #1 Integers and Real Numbers Before we start the journey into Algebra, we need to understand more about the numbers and number concepts, which form the foundation of Algebra.
More informationGrade Six Chapter 8 - Algebra: Equations and Inequalities Overview & Support
Standards: rade Six Chapter 8 - Algebra: and Overview & Support Reason about and solve one-variable equations and inequalities. 6.EE.5 Understand solving an equation or in as a process of answering a question:
More informationChapter 2 Linear Equations and Inequalities in One Variable
Chapter 2 Linear Equations and Inequalities in One Variable Section 2.1: Linear Equations in One Variable Section 2.3: Solving Formulas Section 2.5: Linear Inequalities in One Variable Section 2.6: Compound
More informationUnit 3 Functions HW #1 Mrs. Dailey
HW#1 Name Algebra II Unit Functions HW #1 Mrs. Dailey 1) In each of the following, the variable pair given are proportional to one another. Find the missing value. (a) b = 8 when a = 16 b =? when a = 18
More informationSimplifying Rational Expressions
.3 Simplifying Rational Epressions What are the ecluded values of a rational epression? How can you simplify a rational epression? ACTIVITY: Simplifying a Rational Epression Work with a partner. Sample:
More information7.7. Factoring Special Products. Essential Question How can you recognize and factor special products?
7.7 Factoring Special Products Essential Question How can you recognize and factor special products? Factoring Special Products LOOKING FOR STRUCTURE To be proficient in math, you need to see complicated
More information8.NS.1 Supporting Content Examples of Linking Supporting Clusters to the Major Work of the Grade: Examples of Major Within-Grade Dependencies
8.NS.1 Supporting Content Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion
More informationName Class Date. t = = 10m. n + 19 = = 2f + 9
1-4 Reteaching Solving Equations To solve an equation that contains a variable, find all of the values of the variable that make the equation true. Use the equality properties of real numbers and inverse
More informationChapter 3: Graphs and Equations CHAPTER 3: GRAPHS AND EQUATIONS. Date: Lesson: Learning Log Title:
Chapter 3: Graphs and Equations CHAPTER 3: GRAPHS AND EQUATIONS Date: Lesson: Learning Log Title: Date: Lesson: Learning Log Title: Chapter 3: Graphs and Equations Date: Lesson: Learning Log Title: Notes:
More informationMS Algebra A-SSE-1b Ch. 2.5 Expressions with Distributive Property
MS Algebra A-SSE-1b Ch. 2.5 Expressions with Distributive Property Mr. Deyo Apply the Distributive Property to algebraic expressions using appropriate terms, factors, and coefficients Title: 2.5 Apply
More informationCartesian Plane. Analytic Geometry. Unit Name
3.1cartesian Unit Name Analytic Geometry Unit Goals 1. Create table of values in order to graph &/or determine if a relation is linear. Determine slope 3. Calculate missing information for linearelationships.
More information, Eighth Grade Mathematics, Quarter 1
2017.18, Eighth Grade Mathematics, Quarter 1 The following Practice Standards and Literacy Skills will be used throughout the course: Standards for Mathematical Practice Literacy Skills for Mathematical
More informationUnit 5. Linear equations and inequalities OUTLINE. Topic 13: Solving linear equations. Topic 14: Problem solving with slope triangles
Unit 5 Linear equations and inequalities In this unit, you will build your understanding of the connection between linear functions and linear equations and inequalities that can be used to represent and
More informationChapter 1 Homework Problems
Chapter 1 Homework Problems Lesson 1.1.1 1-4. Angelica is working with function machines. She has the two machines shown at right. She wants to put them in order so that the output of the first machine
More informationAlgebra I Chapter 6: Solving and Graphing Linear Inequalities
Algebra I Chapter 6: Solving and Graphing Linear Inequalities Jun 10 9:21 AM Chapter 6 Lesson 1 Solve Inequalities Using Addition and Subtraction Vocabulary Words to Review: Inequality Solution of an Inequality
More informationMathematics Precalculus: Honors Unit 3: Analytic Trigonometry
Understandings Questions Knowledge Vocabulary Skills Mathematics can be used to model real-life situations. Trigonometric identities help lay the foundation for upper level mathematics. Trigonometric identities
More informationLadies and Gentlemen: Please Welcome the Quadratic Formula!
Lesson.1 Skills Practice Name Date Ladies and Gentlemen: Please Welcome the Quadratic Formula! The Quadratic Formula Vocabulary Complete the Quadratic Formula. Then, identify the discriminant and explain
More informationA constant is a value that is always the same. (This means that the value is constant / unchanging). o
Math 8 Unit 7 Algebra and Graphing Relations Solving Equations Using Models We will be using algebra tiles to help us solve equations. We will practice showing work appropriately symbolically and pictorially
More information8th Grade Math! 4th Quarter Pacing Guide LESSON PLANNING. Delivery Date
#8 Domain: Functions Standard: CC.8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of
More informationN5 R1.2 and R1.3 Quadratics - Revision
N5 R and R3 Quadratics - Revision This revision pack covers the skills at Unit Assessment and exam level for Quadratics so you can evaluate your learning of this outcome. It is important that you prepare
More informationMath 8 I CAN Statements
Math 8 I CAN Statements Valerie Bodily Unit 1 objectives: I can identify and distinguish rational and irrational numbers particularly by looking at their decimal expansion I can approximate irrational
More information12.3. Walking the... Curve? Domain, Range, Zeros, and Intercepts
Walking the... Curve? Domain, Range, Zeros, and Intercepts.3 Learning Goals In this lesson, you will: Describe the domain and range of quadratic functions. Determine the x-intercept(s) of a graph of a
More information21.1 Solving Equations by Factoring
Name Class Date 1.1 Solving Equations by Factoring x + bx + c Essential Question: How can you use factoring to solve quadratic equations in standard form for which a = 1? Resource Locker Explore 1 Using
More informationHIGLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL ALIGNMENT
HIGLEY UNIFIED SCHOOL DISTRICT INSTRUCTIONAL ALIGNMENT 8 th Grade Math Third Quarter Unit 3: Equations Topic C: Equations in Two Variables and Their Graphs (Continued) This topic focuses on extending the
More informationSolution Choose several values for x, and find the corresponding values of (x), or y.
Example 1 GRAPHING FUNCTIONS OF THE FORM (x) = ax n Graph the function. 3 a. f ( x) x Solution Choose several values for x, and find the corresponding values of (x), or y. f ( x) x 3 x (x) 2 8 1 1 0 0
More informationLesson 23: Complicated Quadratics
: Complicated Quadratics Opening Discussion 1. The quadratic expression 2x 2 + 4x + 3 can be modeled with the algebra tiles as shown below. Discuss with your group a method to complete the square with
More informationSYSTEMS OF THREE EQUATIONS
SYSTEMS OF THREE EQUATIONS 11.2.1 11.2.4 This section begins with students using technology to eplore graphing in three dimensions. By using strategies that they used for graphing in two dimensions, students
More informationSection 1.4 Circles. Objective #1: Writing the Equation of a Circle in Standard Form.
1 Section 1. Circles Objective #1: Writing the Equation of a Circle in Standard Form. We begin by giving a definition of a circle: Definition: A Circle is the set of all points that are equidistant from
More informationHerndon High School Geometry Honors Summer Assignment
Welcome to Geometry! This summer packet is for all students enrolled in Geometry Honors at Herndon High School for Fall 07. The packet contains prerequisite skills that you will need to be successful in
More informationControlling the Population
Lesson.1 Skills Practice Name Date Controlling the Population Adding and Subtracting Polynomials Vocabulary Match each definition with its corresponding term. 1. polynomial a. a polynomial with only 1
More informationMS Algebra A-F-IF-7 Ch. 6.3b Solving Real World Problems with the Point-Slope Form
MS Algebra A-F-IF-7 Ch. 6.3b Solving Real World Problems with the Point-Slope Form ALGEBRA SUPPORT (Homework) Solving Problems by Writing Equations in Point-Slope Form Title: 6.3b Apply Point-Slope Form
More informationComplex Numbers. Essential Question What are the subsets of the set of complex numbers? Integers. Whole Numbers. Natural Numbers
3.4 Complex Numbers Essential Question What are the subsets of the set of complex numbers? In your study of mathematics, you have probably worked with only real numbers, which can be represented graphically
More information1-1. Expressions and Formulas. Lesson 1-1. What You ll Learn. Active Vocabulary
1-1 Expressions and Formulas What You ll Learn Skim the lesson. Write two things you already know about expressions and formulas. 1. Active Vocabulary 2. Review Vocabulary Identify the four grouping symbols
More informationAdvanced Precalculus Summer Assignment
Advanced Precalculus Summer Assignment The following packet of material contains prerequisite skills and concepts that will be drawn upon from Algebra II as well as a preview of Precalculus. This summer
More informationMaintaining Mathematical Proficiency
Chapter 7 Maintaining Mathematical Proficiency Simplify the expression. 1. 5x 6 + 3x. 3t + 7 3t 4 3. 8s 4 + 4s 6 5s 4. 9m + 3 + m 3 + 5m 5. 4 3p 7 3p 4 1 z 1 + 4 6. ( ) 7. 6( x + ) 4 8. 3( h + 4) 3( h
More informationExpressions and Equations
8 8.EE.7b Objective Common Core State Standards Expressions and Equations Solving Equations with Variables on Both Sides Another form of multi-step equations involves variables on both sides of the equation.
More information8 Mathematics Curriculum
New York State Common Core 8 Mathematics Curriculum G R A D E GRADE 8 MODULE 4 Table of Contents 1... 3 Topic A: Writing and Solving (8.EE.C.7)... 11 Lesson 1: Writing Equations Using Symbols... 13 Lesson
More informationUnit 7: It s in the System
Unit 7: It s in the System Investigation 1: Linear Equations with Two Variables I can convert between standard and slope intercept forms, and graph systems of equations. Solving equations is one of the
More informationGrade 8 Curriculum Map
Grade 8 Curriculum Map 2007-2008 Moving Straight Ahead 25 Days Curriculum Map 2007-2008 CMP2 Investigations Notes Standards 1.2 Finding and Using Rates Walking Rates and Linear Relationships 1.3 Raising
More information= 9 = x + 8 = = -5x 19. For today: 2.5 (Review) and. 4.4a (also review) Objectives:
Math 65 / Notes & Practice #1 / 20 points / Due. / Name: Home Work Practice: Simplify the following expressions by reducing the fractions: 16 = 4 = 8xy =? = 9 40 32 38x 64 16 Solve the following equations
More informationFoundations of Math II Unit 5: Solving Equations
Foundations of Math II Unit 5: Solving Equations Academics High School Mathematics 5.1 Warm Up Solving Linear Equations Using Graphing, Tables, and Algebraic Properties On the graph below, graph the following
More informationTable of contents. Jakayla Robbins & Beth Kelly (UK) Precalculus Notes Fall / 53
Table of contents The Cartesian Coordinate System - Pictures of Equations Your Personal Review Graphs of Equations with Two Variables Distance Equations of Circles Midpoints Quantifying the Steepness of
More informationgraphs, Equations, and inequalities 2
graphs, Equations, and inequalities You might think that New York or Los Angeles or Chicago has the busiest airport in the U.S., but actually it s Hartsfield-Jackson Airport in Atlanta, Georgia. In 010,
More informationName Period. Date: have an. Essential Question: Does the function ( ) inverse function? Explain your answer.
Name Period Date: Topic: 10-3 Composition and Inverses of Functions Essential Question: Does the function inverse function? Explain your answer. have an Standard: F-BF.1c Objective: Compose functions.
More information2 P a g e. Essential Questions:
NC Math 1 Unit 5 Quadratic Functions Main Concepts Study Guide & Vocabulary Classifying, Adding, & Subtracting Polynomials Multiplying Polynomials Factoring Polynomials Review of Multiplying and Factoring
More informationStudy Guide and Intervention. The Quadratic Formula and the Discriminant. Quadratic Formula. Replace a with 1, b with -5, and c with -14.
4-6 Study Guide and Intervention Quadratic Formula The Quadratic Formula can be used to solve any quadratic equation once it is written in the form ax 2 + bx + c = 0. Quadratic Formula The solutions of
More informationPut the following equations to slope-intercept form then use 2 points to graph
Tuesday September 23, 2014 Warm-up: Put the following equations to slope-intercept form then use 2 points to graph 1. 4x - 3y = 8 8 x 6y = 16 2. 2x + y = 4 2x + y = 1 Tuesday September 23, 2014 Warm-up:
More informationGive algebraic and numeric examples to support your answer. Which property is demonstrated when one combines like terms in an algebraic expression?
Big Idea(s): Algebra is distinguished from arithmetic by the systematic use of symbols for values. Writing and evaluating expressions with algebraic notation follows the same rules/properties as in arithmetic.
More informationUNIT 3 CIRCLES AND VOLUME Lesson 1: Introducing Circles Instruction
Prerequisite Skills This lesson requires the use of the following skills: performing operations with fractions understanding slope, both algebraically and graphically understanding the relationship of
More informationOverview Ratios, Rates, Proportions, and Percents Polynomials Equations Overview Statistics...
Overview... 5 1. Integers and Real Numbers... 6 2. Ratios, Rates, Proportions, and Percents... 10 3. Laws of Exponents... 14 4. Algebraic Expressions... 18 5. Polynomials... 22 6. Equations... 26 7. Graphs
More informationUnit 6 Quadratic Relations of the Form y = ax 2 + bx + c
Unit 6 Quadratic Relations of the Form y = ax 2 + bx + c Lesson Outline BIG PICTURE Students will: manipulate algebraic expressions, as needed to understand quadratic relations; identify characteristics
More informationQuarter 2 400, , , , , , ,000 50,000
Algebra 2 Quarter 2 Quadratic Functions Introduction to Polynomial Functions Hybrid Electric Vehicles Since 1999, there has been a growing trend in the sales of hybrid electric vehicles. These data show
More informationAbsolute Value Inequalities
LESSON 16 Absolute Value Inequalities LEARNING OBJECTIVES Today I am: reviewing solving and graphing inequalities. So that I can: determine the steps to solve absolute value inequalities. I ll know I have
More information2.1 Identifying Patterns
I. Foundations for Functions 2.1 Identifying Patterns: Leaders' Notes 2.1 Identifying Patterns Overview: Objective: s: Materials: Participants represent linear relationships among quantities using concrete
More information4.6 Model Direct Variation
4.6 Model Direct Variation Goal p Write and graph direct variation equations. Your Notes VOCABULARY Direct variation Constant of variation Eample Identif direct variation equations Tell whether the equation
More informationFall 09/MAT 140/Worksheet 1 Name: Show all your work. 1. (6pts) Simplify and write the answer so all exponents are positive:
Fall 09/MAT 140/Worksheet 1 Name: Show all your work. 1. (6pts) Simplify and write the answer so all exponents are positive: a) (x 3 y 6 ) 3 x 4 y 5 = b) 4x 2 (3y) 2 (6x 3 y 4 ) 2 = 2. (2pts) Convert to
More informationx y x y 15 y is directly proportional to x. a Draw the graph of y against x.
3 8.1 Direct proportion 1 x 2 3 5 10 12 y 6 9 15 30 36 B a Draw the graph of y against x. y 40 30 20 10 0 0 5 10 15 20 x b Write down a rule for y in terms of x.... c Explain why y is directly proportional
More informationLesson 5: The Graph of the Equation y = f(x)
Lesson 5: The Graph of the Equation y = f(x) Learning targets: I can identify when a function is increasing, decreasing, positive and negative and use interval notation to describe intervals where the
More information8.EE The Intersection of Two
8.EE The Intersection of Two Lines Alignments to Content Standards: 8.EE.C.8.a Task a. Draw the two lines that intersect only at the point. One of the lines should pass (0, ) through the point. b. Write
More informationI can demonstrate for rational numbers that the decimal expansion repeats eventually.
Grade 8 Math Length of Class: School Year Program/Text Used: Competency 1: The Number Systems - Students will demonstrate the ability to know that there are numbers that are not rational and approximate
More informationCOMMON CORE MATHEMATICS CURRICULUM
COMMON CORE MATHEMATICS CURRICULUM Lesson 1 8 4 Lesson 1: Writing Equations Using Symbols Write each of the following statements using symbolic language. 1. When you square five times a number you get
More informationAP CALCULUS Summer Assignment 2014
Name AP CALCULUS Summer Assignment 014 Welcome to AP Calculus. In order to complete the curriculum before the AP Exam in May, it is necessary to do some preparatory work this summer. The following assignment
More informationToday I am: reviewing solving and graphing inequalities. So that I can: determine the steps to solve absolute value inequalities.
2tI o LESSON 16 Absolute Value Inequalities LEARNING OBJECTIVES Today I am: reviewing solving and graphing inequalities. So that I can: determine the steps to solve absolute value inequalities. I ll know
More informationSection Page(s) Problems to Complete Points Section 1 Exercises Section 2 Exercises Section 3 Exercises
To help you prepare for AP Calculus AB, you are required to complete this assignment. These problems will allow you to review and master the prerequisite skills necessary for this rigorous course so that
More informationUnit 5: Proportions and Lines. Activities: Resources:
Timeline: 2 nd nine weeks Vocabulary: Slope Formula, Rate of Change, Y Intercept, Slope intercept form, Vertical, Horizontal Linear Function Slope Slope of a Line Unit 5: Proportions and Lines New State
More informationOverview (90 Days) Properties of Equality Properties of Inequality Solve Linear Function
Pre- Requisites Skills: Overview (90 Days) Students need to know the meanings of exponents (2 4 = 2 2 2 2) Students need to know how to graph a simple inequality on a number line (i.e. x > 4) Students
More informationMathematics Curriculum
New York State Common Core Mathematics Curriculum ALGEBRA I MODULE 3 Linear Functions Module Overview... 3 Topic A: Linear Sequences (F-IF.A.1, F-IF.A.2, F-IF.A.3, F-IF.B.6, F-BF.A.1a, F-LE.A.1, F-LE.A.2,
More informationLesson 3-6: Compound Inequalities Name:
Lesson 3-6: Compound Inequalities Name: W hen people plan a house, they often have many requirements in mind that can be written as inequalities. Such requirements could be the dimensions of rooms or the
More informationEquations With Two or More Variables
! Equations With Two or More Variables You have done a lot of work with relationships involving two related variables. However, many real-world relationships involve three or more variables. For example,
More informationLesson 3-1: Solving Linear Systems by Graphing
For the past several weeks we ve been working with linear equations. We ve learned how to graph them and the three main forms they can take. Today we re going to begin considering what happens when we
More informationName: Date: Period: A2H.L5-7.WU. Find the roots of the equation using two methods. Quick Review SOLVING QUADRATICS
Name: Date: Period: A2H.L5-7.WU Quick Review SOLVING QUADRATICS Find the roots of the equation using two methods. 2x 2 + 4x 6 = 0 Algebra Objective Language Objective A2H.L5-7.NOTES LESSON 5-7: USING QUADRATIC
More information