8.2 Getting Centered A Solidify Understanding Task
|
|
|
- Shana Mosley
- 5 years ago
- Views:
Transcription
1 8.2 Getting Centered A Solidify Understanding Task Malik s family has decided to put in a new sprinkling system in their yard. Malik has volunteered to lay the system out. Sprinklers are available at the hardware store in the following sizes: Full circle, maximum 15 radius Half circle, maximum 15 radius Quarter circle, maximum 15 radius All of the sprinklers can be adjusted so that they spray a smaller radius. Malik needs to be sure that the entire yard gets watered, which he knows will require that some of the circular water patterns will overlap. He gets out a piece of graph paper and begins with a scale diagram of the yard. In this diagram, the length of the side of each square represents 5 feet. 7 lawn
2 8 1. As he begins to think about locating sprinklers on the lawn, his parents tell him to try to cover the whole lawn with the fewest number of sprinklers possible so that they can save some money. The equation of the first circle that Malik draws to represent the area watered by the sprinkler is: (x + 25) + (y + 20) = 225 Draw this circle on the diagram using a compass. 2. Lay out a possible configuration for the sprinkling system that includes the first sprinkler pattern that you drew in #1. 3. Find the equation of each of the full circles that you have drawn. Malik wrote the equation of one of the circles and just because he likes messing with the algebra, he did this: Original equation: (x 3) + (y + 2) = 225 x 6x y + 4y + 4 = 225 x + y 6x + 4y 212 = 0 Malik thought, That s pretty cool. It s like a different form of the equation. I guess that there could be different forms of the equation of a circle like there are different forms of the equation of a parabola or the equation of a line. He showed his equation to his sister, Sapana, and she thought he was nuts. Sapana, said, That s a crazy equation. I can t even tell where the center is or the length of the radius anymore. Malik said, Now it s like a puzzle for you. I ll give you an equation in the new form. I ll bet you can t figure out where the center is.
3 9 Sapana said, Of course, I can. I ll just do the same thing you did, but work backwards. 4. Malik gave Sapana this equation of a circle: x + y 4x + 10y + 20 = 0 Help Sapana find the center and the length of the radius of the circle. 5. Sapana said, Ok. I made one for you. What s the center and length of the radius for this circle? x + y + 6x 14y 42 = 0 6. Sapana said, I still don t know why this form of the equation might be useful. When we had different forms for other equations like lines and parabolas, each of the various forms highlighted different features of the relationship. Why might this form of the equation of a circle be useful? x + y + Ax + By + C = 0
4 Getting Centered Teacher Notes A Solidify Understanding Task Purpose: The purpose of this task is to solidify understanding of the equation of the circle. The task begins with sketching circles and writing their equations. It proceeds with the idea of squaring the (x h) 2 and (y k) 2 expressions to obtain a new form of an equations. Students are then challenged to reverse the process to find the center of the circle. Core Standards Focus: G.GPE Expressing Geometric Properties with Equations Translate between the geometric description and the equation for a conic section G.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. Launch (Whole Class): Begin the task by helping students to understand the context of developing a diagram for a sprinkling system. The task begins with students drawing circles to cover the yard and writing equations for the circles that they have sketched. Allow students some time to work to make their diagrams and write their equations. As students are working, be sure that they are accounting for the scale as they name the center of their circles. Ask several students to share their equations. After several students have shared, ask one student to take the last equation shared and square the (x h) 2 and (y k) 2 expressions and simplify the remaining equation. Tell students that this is what Malik did and now their job is to take the equation back to the form in which they can easily read the center and radius. Explore (Small Group): Since students have previously completed the square for parabolas, some students will think to apply the same process here. Monitor their work, watching for groups that have different answers for the same equation (hopefully, one of them is correct). Discuss (Whole Class): Begin the discussion by posting two different equations that answer question #4. Ask students how they can decide which equation is correct. They may suggest working backwards to the original equation, or possibly checking a point. Decide which equation is correct and ask that group to describe the process they used to get the answer. Ask another group that has a correct version of #5 to show how they obtained their answer. You may also wish to discuss #6. Wrap up the lesson up by working with the class to create a set of steps that they can follow to get the equation back to center/radius form. Aligned Ready, Set, Go: Circles and Other Conics 8.2
5 Name: Ready,'Set,'Go'' ' Circles(and(Other(Conics( 8.2( 10 Ready' Topic:Makingperfectsquaretrinomials. Fill'in'the'number'that'completes'the'square.''Then'write'the'trinomial'in'factored'form.' 1. x 2 + 6x + 2. x 2 14x + 3. x 2 50x + 4. x 2 28x + On'the'next'set'of'problems,'leave'the'number'that'completes'the'square'as'a'fraction.''Then' write'the'trinomial'in'factored'form.' 5. x 2 11x + 6. x 2 + 7x + 7. x 2 +15x + 8. x x + 9. x2 1 5 x x2 3 4 x + Set' ' 2013www.flickr.com/photos/paynomind/ Topic:Writingequationsofcircleswithcenter(h,k)andradiusr.' Write'the'equation'of'the'circle.' "2013"MATHEMATICS"VISION"PROJECT" "MV P" In"partnership"with"the"Utah"State"Office"of"Education""" LicensedundertheCreativeCommonsAttribution4NonCommercial4ShareAlike3.0Unportedlicense" "
6 Circles(and(Other(Conics( 8.2( Write'the'equation'of'the'circle'with'the'given'center'and'radius.''Then'write'it'in'expanded' form.' 14. Center:(5,2),Radius:13 15.Center:(46,410),Radius:9 16. Center:(0,8),Radius:15 17.Center:(19,413),Radius:1 18. Center:(41,2),Radius:10 19.Center:(43,44),Radius:8 11 Go' ' Topic:Verifyingifapointisasolution. Identify'which'point'is'a'solution'to'the'given'equation.''Show'your'work.' 20. y = 4 x 2 5 a.(415,414) b.(10,10) 21. y = 3 x a.(44,412) b. 5, y = x a. 7, 15 b. 7, y = 4x a. 5 3, 180 b. 5 3, x 2 + y 2 = 9 a. ( 8, 1) b. 2, x 2 y 2 = 16 a. 3, 10 b. 2 2, 4 "2013"MATHEMATICS"VISION"PROJECT" "MV P" In"partnership"with"the"Utah"State"Office"of"Education""" LicensedundertheCreativeCommonsAttribution4NonCommercial4ShareAlike3.0Unportedlicense" "
Secondary Two Mathematics: An Integrated Approach Module 8 Circles and Other Conics
1 Secondary Two Mathematics: An Integrated Approach Module 8 Circles and Other Conics By The Mathematics Vision Project: Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis Lemon, Janet Sutorius www.mathematicsvisionproject.org
Secondary Two Mathematics: An Integrated Approach Module 8 Circles and Other Conics
1 Secondary Two Mathematics: An Integrated Approach Module 8 Circles and Other Conics By The Mathematics Vision Project: Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis Lemon, Janet Sutorius www.mathematicsvisionproject.org
Circles & Other Conics
SECONDARY MATH TWO An Integrated Approach Standard Teacher Notes MODULE 8 HONORS Circles & Other Conics The Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis Lemon, Janet Sutorius 2017 Original work
1.6 The Tortoise and the Hare A Solidify Understanding Task
29 1.6 The Tortoise and the Hare A Solidify Understanding Task In the children s story of the tortoise and the hare, the hare mocks the tortoise for being slow. The tortoise replies, Slow and steady wins
When they compared their results, they had an interesting discussion:
27 2.5 Making My Point A Solidify Understanding Task Zac and Sione were working on predicting the number of quilt blocks in this pattern: CC BY Camille King https://flic.kr/p/hrfp When they compared their
CIRCLES: #1. What is an equation of the circle at the origin and radius 12?
1 Pre-AP Algebra II Chapter 10 Test Review Standards/Goals: E.3.a.: I can identify conic sections (parabola, circle, ellipse, hyperbola) from their equations in standard form. E.3.b.: I can graph circles
5.3 It s All In Your Head A Solidify Understanding Task
16 5.3 It s All In Your Head A Solidify Understanding Task In the previous task you were asked to justify some claims by writing paragraphs explaining how various figures were constructed and how those
6.3 More Sine Language
6.3 More Sine Language A Solidify Understanding Task Clarita is helping Carlos calculate his height at different locations around a Ferris wheel. They have noticed when they use their formula h(t) = 30
6.3 More Sine Language
6.3 More Sine Language A Solidify Understanding Task Clarita is helping Carlos calculate his height at different locations around a Ferris wheel. They have noticed when they use their formula h(t) = 30
Parabolas and lines
Parabolas and lines Study the diagram at the right. I have drawn the graph y = x. The vertical line x = 1 is drawn and a number of secants to the parabola are drawn, all centred at x=1. By this I mean
x(t)*=*2t"+*1* y(t)*=*3t* *4**
47 7.8HParametrically8DefinedCurves A"Solidify"and"Practice"Understanding"Task" " Aparametriccurveisdefinedbyasetofequationsthatgivethe coordinatesofpointsonthecurveintermsofanothervariablecalleda parameter.
3.4 Pascal s Pride. A Solidify Understanding Task
3.4 Pascal s Pride A Solidify Understanding Task Multiplying polynomials can require a bit of skill in the algebra department, but since polynomials are structured like numbers, multiplication works very
Unit 4 Patterns and Algebra
Unit 4 Patterns and Algebra In this unit, students will solve equations with integer coefficients using a variety of methods, and apply their reasoning skills to find mistakes in solutions of these equations.
Exploring Graphs of Polynomial Functions
Name Period Exploring Graphs of Polynomial Functions Instructions: You will be responsible for completing this packet by the end of the period. You will have to read instructions for this activity. Please
1.4 Pulling a Rabbit Out of the Hat
1.4 Pulling a Rabbit Out of the Hat A Solidify Understanding Task I have a magic trick for you: Pick a number, any number. Add 6 Multiply the result by 2 Subtract 12 Divide by 2 The answer is the number
Name Period. Date: Topic: 9-2 Circles. Standard: G-GPE.1. Objective:
Name Period Date: Topic: 9-2 Circles Essential Question: If the coefficients of the x 2 and y 2 terms in the equation for a circle were different, how would that change the shape of the graph of the equation?
1.5 Look Out Below! A Solidify Understanding Task
22 1.5 Look Out Below A Solidify Understanding Task What happens when you drop a ball? It falls to the ground. That question sounds as silly as Why did the chicken cross the road? (To get to the other
Looking Ahead to Chapter 10
Looking Ahead to Chapter Focus In Chapter, you will learn about polynomials, including how to add, subtract, multiply, and divide polynomials. You will also learn about polynomial and rational functions.
3.3 It All Adds Up. A Develop Understanding Task
3.3 It All Adds Up A Develop Understanding Task Whenever we re thinking about algebra and working with variables, it is useful to consider how it relates to the number system and operations on numbers.
7.2"Circle"Dilations" A"Develop"Understanding"Task"
9 7.2CircleDilations ADevelopUnderstandingTask Thestatement allcirclesaresimilar mayseemintuitivelyobvious,sinceall circleshavethesameshapeeventhoughtheymaybedifferentsizes. However,wecanlearnalotaboutthepropertiesofcirclesbyworkingonthe
3.9 Is This The End? A Solidify Understanding Task
3.9 Is This The End? A Solidify Understanding Task In previous mathematics courses, you have compared and analyzed growth rates of polynomial (mostly linear and quadratic) and exponential functions. In
4.7$Graphing$Rational$Functions$$ A"Practice!Understanding+Task!
35 4.7$Graphing$Rational$Functions$$ A"PracticeUnderstanding+Task PartI:SeeingStructure Foreachfunction,determineintercepts,domain,asymptotes,andcompleteasignline.Usethis informationtosketchthegraph. 1.
7.3 Getting on the Right Wavelength
7.3 Getting on the Right Wavelength A Practice Understanding Task The Ferris wheel in the following diagram has a radius of 40 feet, its center is 50 feet from the ground, and it makes one revolution counterclockwise
EXPLAINING AREA AND CIRCUMFERENCE OF A CIRCLE
1 EXPLAINING AREA AND CIRCUMFERENCE OF A CIRCLE INSTRUCTIONAL ACTIVITY Lesson 1 LEARNING GOAL Students will develop an understanding of diameter, radius, circumference, and pi and the relationships among
5.7 Justifying the Laws
SECONDARY MATH III // MODULE 5 The Pythagorean theorem makes a claim about the relationship between the areas of the three squares drawn on the sides of a right triangle: the sum of the area of the squares
3.6 Curbside Rivalry. A Solidify Understanding Task
Carlos and Clarita have a brilliant idea for how they will earn money this summer. Since the community in which they live includes many high schools, a couple of universities, and even some professional
Successful completion of the core function transformations unit. Algebra manipulation skills with squares and square roots.
Extension A: Circles and Ellipses Algebra ; Pre-Calculus Time required: 35 50 min. Learning Objectives Math Objectives Students will write the general forms of Cartesian equations for circles and ellipses,
Pure Math 30: Explained! 81
4 www.puremath30.com 81 Part I: General Form General Form of a Conic: Ax + Cy + Dx + Ey + F = 0 A & C are useful in finding out which conic is produced: A = C Circle AC > 0 Ellipse A or C = 0 Parabola
Unit 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
{ }. The dots mean they continue in that pattern to both
INTEGERS Integers are positive and negative whole numbers, that is they are;... 3, 2, 1,0,1,2,3... { }. The dots mean they continue in that pattern to both positive and negative infinity. Before starting
I started to think that maybe I could just distribute the log so that I get:
2.3 Chopping Logs A Solidify Understanding Task Abe and Mary were working on their math homework together when Abe has a brilliant idea Abe: I was just looking at this log function that we graphed in Falling
LHS Algebra Pre-Test
Your Name Teacher Block Grade (please circle): 9 10 11 12 Course level (please circle): Honors Level 1 Instructions LHS Algebra Pre-Test The purpose of this test is to see whether you know Algebra 1 well
Algebra II. A2.1.1 Recognize and graph various types of functions, including polynomial, rational, and algebraic functions.
Standard 1: Relations and Functions Students graph relations and functions and find zeros. They use function notation and combine functions by composition. They interpret functions in given situations.
Student Outcomes. Lesson Notes. Classwork. Opening Exercises 1 3 (5 minutes)
Student Outcomes Students calculate the decimal expansion of using basic properties of area. Students estimate the value of expressions such as. Lesson Notes For this lesson, students will need grid paper
Projects in Geometry for High School Students
Projects in Geometry for High School Students Goal: Our goal in more detail will be expressed on the next page. Our journey will force us to understand plane and three-dimensional geometry. We will take
7.4 Off on a Tangent. A Develop and Solidify Understanding Task. tan(%) = Recall that the right triangle definition of the tangent ratio is:
7.4 Off on a Tangent A Develop and Solidify Understanding Task Recall that the right triangle definition of the tangent ratio is: tan(%) = ()*+,- /0 123) /44/12,) 5*+() 6 ()*+,- /0 123) 53758)*,,/ 5*+()
Questioning Techniques. Multiply: (2a + 3) (2a 3) Find the binomial which multiplied by. 2a 3 equals 4a 2 9.
Questioning Techniques Expressions Equations Standard Multiply: (2a + 3) (2a 3) Solve: 4a 9 = 27 Reversibility Thinking backwards. Given the answer and finding the problem. Generalization 1. Finding a
Algebra II. In this technological age, mathematics is more important than ever. When students
In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,
Fixed Perimeter Rectangles
Rectangles You have a flexible fence of length L = 13 meters. You want to use all of this fence to enclose a rectangular plot of land of at least 8 square meters in area. 1. Determine a function for the
Part 1: You are given the following system of two equations: x + 2y = 16 3x 4y = 2
Solving Systems of Equations Algebraically Teacher Notes Comment: As students solve equations throughout this task, have them continue to explain each step using properties of operations or properties
8.6 Translate and Classify Conic Sections
8.6 Translate and Classify Conic Sections Where are the symmetric lines of conic sections? What is the general 2 nd degree equation for any conic? What information can the discriminant tell you about a
Serena: I don t think that works because if n is 20 and you do 6 less than that you get 20 6 = 14. I think we should write! 6 > 4
24 4.6 Taking Sides A Practice Understanding Task Joaquin and Serena work together productively in their math class. They both contribute their thinking and when they disagree, they both give their reasons
Unit 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
CCGPS Frameworks Student Edition. Mathematics. CCGPS Analytic Geometry Unit 6: Modeling Geometry
CCGPS Frameworks Student Edition Mathematics CCGPS Analytic Geometry Unit 6: Modeling Geometry These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.
ALGEBRA 1 FINAL EXAM 2006
Overall instructions: Your Name Teacher ALGEBRA FINAL EXAM 2006 There is a mix of easier and harder problems. Don t give up if you see some questions that you don t know how to answer. Try moving on to
Name Period Date. polynomials of the form x ± bx ± c. Use guess and check and logic to factor polynomials of the form 2
Name Period Date POLYNOMIALS Student Packet 3: Factoring Polynomials POLY3 STUDENT PAGES POLY3.1 An Introduction to Factoring Polynomials Understand what it means to factor a polynomial Factor polynomials
Math101, Sections 2 and 3, Spring 2008 Review Sheet for Exam #2:
Math101, Sections 2 and 3, Spring 2008 Review Sheet for Exam #2: 03 17 08 3 All about lines 3.1 The Rectangular Coordinate System Know how to plot points in the rectangular coordinate system. Know the
Lesson 6-1: Relations and Functions
I ll bet you think numbers are pretty boring, don t you? I ll bet you think numbers have no life. For instance, numbers don t have relationships do they? And if you had no relationships, life would be
Secondary Two Mathematics: An Integrated Approach Module 3 - Part One Imaginary Number, Exponents, and Radicals
Secondary Two Mathematics: An Integrated Approach Module 3 - Part One Imaginary Number, Exponents, and Radicals By The Mathematics Vision Project: Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis
Flash Light Reflectors. Fountains and Projectiles. Algebraically, parabolas are usually defined in two different forms: Standard Form and Vertex Form
Sec 6.1 Conic Sections Parabolas Name: What is a parabola? It is geometrically defined by a set of points or locus of points that are equidistant from a point (the focus) and a line (the directri). To
Quarter 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
Solving Quadratic & Higher Degree Inequalities
Ch. 10 Solving Quadratic & Higher Degree Inequalities We solve quadratic and higher degree inequalities very much like we solve quadratic and higher degree equations. One method we often use to solve quadratic
Linear Functions, Equations, and Inequalities
CHAPTER Linear Functions, Equations, and Inequalities Inventory is the list of items that businesses stock in stores and warehouses to supply customers. Businesses in the United States keep about.5 trillion
AS MATHEMATICS HOMEWORK C1
Student Teacher AS MATHEMATICS HOMEWORK C September 05 City and Islington Sixth Form College Mathematics Department www.candimaths.uk HOMEWORK INTRODUCTION You should attempt all the questions. If you
3.7"Perfecting"My"Quads" A"Practice"Understanding"Task"
42 3.7PerfectingMyQuads APracticeUnderstandingTask CarlosandClarita,TiaandTehani,andtheirbest friendzacarealldiscussingtheirfavoritemethods forsolvingquadraticequationsoftheform ax 2 + bx + c = 0.Eachstudentthinksaboutthe
Math Fundamentals for Statistics I (Math 52) Unit 7: Connections (Graphs, Equations and Inequalities)
Math Fundamentals for Statistics I (Math 52) Unit 7: Connections (Graphs, Equations and Inequalities) By Scott Fallstrom and Brent Pickett The How and Whys Guys This work is licensed under a Creative Commons
Grades Algebra 1. Polynomial Arithmetic Equations and Identities Quadratics. By Henri Picciotto. 395 Main Street Rowley, MA
Grades 7 10 ALGEBRA LAB GEAR Algebra 1 Polynomial Arithmetic Equations and Identities Quadratics Factoring Graphing Connections By Henri Picciotto 395 Main Street Rowley, MA 01969 www.didax.com Contents
In order to take a closer look at what I m talking about, grab a sheet of graph paper and graph: y = x 2 We ll come back to that graph in a minute.
Module 7: Conics Lesson Notes Part : Parabolas Parabola- The parabola is the net conic section we ll eamine. We talked about parabolas a little bit in our section on quadratics. Here, we eamine them more
Every positive two digit number is greater than the product of it s digits. Asks class is it true? can you find a counter-example etc.
Aim Activity Reasoning and Proof Introducing Proof Proof by Deduction Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion;
Unit 3, Lesson 2: Exploring Circles
Unit 3, Lesson 2: Exploring Circles Lesson Goals Describe the characteristics that make something a circle. Be introduced to the terms diameter, center, radius, and circumference. Required Materials rulers
Instructor Quick Check: Question Block 12
Instructor Quick Check: Question Block 2 How to Administer the Quick Check: The Quick Check consists of two parts: an Instructor portion which includes solutions and a Student portion with problems for
Investigation Find the area of the triangle. (See student text.)
Selected ACE: Looking For Pythagoras Investigation 1: #20, #32. Investigation 2: #18, #38, #42. Investigation 3: #8, #14, #18. Investigation 4: #12, #15, #23. ACE Problem Investigation 1 20. Find the area
Distributive property and its connection to areas
February 27, 2009 Distributive property and its connection to areas page 1 Distributive property and its connection to areas Recap: distributive property The distributive property says that when you multiply
Math Lab 10: Differential Equations and Direction Fields Complete before class Wed. Feb. 28; Due noon Thu. Mar. 1 in class
Matter & Motion Winter 2017 18 Name: Math Lab 10: Differential Equations and Direction Fields Complete before class Wed. Feb. 28; Due noon Thu. Mar. 1 in class Goals: 1. Gain exposure to terminology and
MA 1128: Lecture 08 03/02/2018. Linear Equations from Graphs And Linear Inequalities
MA 1128: Lecture 08 03/02/2018 Linear Equations from Graphs And Linear Inequalities Linear Equations from Graphs Given a line, we would like to be able to come up with an equation for it. I ll go over
Measuring Keepers S E S S I O N 1. 5 A
S E S S I O N 1. 5 A Measuring Keepers Math Focus Points Naming, notating, and telling time to the hour on a digital and an analog clock Understanding the meaning of at least in the context of linear measurement
Lesson Plan by: Stephanie Miller
Lesson: Pythagorean Theorem and Distance Formula Length: 45 minutes Grade: Geometry Academic Standards: MA.G.1.1 2000 Find the lengths and midpoints of line segments in one- or two-dimensional coordinate
{ }. The dots mean they continue in that pattern.
INTEGERS Integers are positive and negative whole numbers, that is they are;... 3, 2, 1,0,1,2,3... { }. The dots mean they continue in that pattern. Like all number sets, integers were invented to describe
Composition of Functions
Math 120 Intermediate Algebra Sec 9.1: Composite and Inverse Functions Composition of Functions The composite function f g, the composition of f and g, is defined as (f g)(x) = f(g(x)). Recall that a function
Lesson 6 Plane Geometry Practice Test Answer Explanations
Lesson 6 Plane Geometry Practice Test Answer Explanations Question 1 One revolution is equal to one circumference: C = r = 6 = 1, which is approximately 37.68 inches. Multiply that by 100 to get 3,768
Sums of Squares (FNS 195-S) Fall 2014
Sums of Squares (FNS 195-S) Fall 014 Record of What We Did Drew Armstrong Vectors When we tried to apply Cartesian coordinates in 3 dimensions we ran into some difficulty tryiing to describe lines and
Lesson 18: Recognizing Equations of Circles
Student Outcomes Students complete the square in order to write the equation of a circle in center-radius form. Students recognize when a quadratic in xx and yy is the equation for a circle. Lesson Notes
8.1 Absolute Value Functions
8.1 Absolute Value Functions We will explore one final function family this year known as piecewise functions. Piecewise functions are functions that are defined a piece at a time. In other words, for
Lesson 20B: Absolute Value Equations and Inequalities
: Absolute Value Equations and Inequalities Warm-Up Exercise 1. Watch the absolute value video on YouTube Math Shorts Episode 10 and then answer the questions below. https://www.youtube.com/watch?v=wrof6dw63es
DARE TO BE. FORMULA: e = distance between foci length of major axis VOCABULARY: ECCENTRIC. ellipse: eccentricity: focus (plural is foci): major axis:
NAME: DATE: DARE TO BE ECCENTRIC INTRODUCTION: Have you ever heard the phrase dare to be different? Well that's what eccentricity is all about: deviating from the norm - or in other words, being different!
CHAPTER 1. Introduction
CHAPTER 1 Introduction A typical Modern Geometry course will focus on some variation of a set of axioms for Euclidean geometry due to Hilbert. At the end of such a course, non-euclidean geometries (always
Expressions 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.
Task Type Grouping Strategy. Scaffolding Task Individual/Partner Task. Practice Task Individual/Partner Task. Scaffolding Task Individual/Partner Task
SELECTED TASKS The following tasks represent the level of depth, rigor, and complexity expected of all Coordinate Algebra students. These tasks, or tasks of similar depth and rigor, should be used to demonstrate
ACTIVITY 3. Learning Targets: 38 Unit 1 Equations and Inequalities. Solving Inequalities. continued. My Notes
Learning Targets: Write inequalities to represent real-world situations. Solve multi-step inequalities. SUGGESTED LEARNING STRATEGIES: Create Representations, Guess and Check, Look for a Pattern, Think-Pair-Share,
FACTORING AND QUADRATIC EQUATIONS
Topic 24: Factoring and quadratic equations 409 FACTORING AND QUADRATIC EQUATIONS Lesson 24.1 Rectangles and factors 24.1 OPENER Write the length and width for each algebra tile rectangle. 1. 2. 3. 4.
Lab 8 Impulse and Momentum
b Lab 8 Impulse and Momentum What You Need To Know: The Physics There are many concepts in physics that are defined purely by an equation and not by a description. In some cases, this is a source of much
2.4 Log-Arithm-etic. A Practice Understanding Task
2.4 Log-Arithm-etic A Practice Understanding Task Abe and Mary are feeling good about their log rules and bragging about their mathematical prowess to all of their friends when this exchange occurs: CC
Unit 3, Lesson 3: Exploring Circumference
Unit 3, Lesson 3: Exploring Circumference Lesson Goals Understand diameter and circumference of a circle. as the constant of proportionality in the relationship between the Recognize that the relationship
6.2 Sine Language. A Solidify Understanding Task. In the previous task, George W. Ferris Day Off, you
In the previous task, George W. Ferris Day Off, you probably found Carlos height at different positions on the Ferris wheel using right triangles, as illustrated in the following diagram. Recall the following
4.5$Watch$Your$ Behavior $ A"Develop!Understanding+Task!
23 4.5$Watch$Your$ Behavior $ A"DevelopUnderstanding+Task Inthistask,youwilldevelopyourunderstandingoftheendbehaviorofrationalfunctionsaswellas discoverthebehaviorofevenandoddfunctions. PartI:Endbehaviorofrationalfunctions
COMMON 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
Math 112 Group Activity: The Vertical Speed of a Shell
Name: Section: Math 112 Group Activity: The Vertical Speed of a Shell A shell is fired straight up by a mortar. The graph below shows its altitude as a function of time. 400 300 altitude (in feet) 200
Egyptian Fractions: Part I
Egyptian Fractions: Part I Prepared by: Eli Jaffe October 8, 2017 1 Cutting Cakes 1. Imagine you are a teacher. Your class of 10 students is on a field trip to the bakery. At the end of the tour, the baker
Assignment 1 and 2: Complete practice worksheet: Simplifying Radicals and check your answers
Geometry 0-03 Summary Notes Right Triangles and Trigonometry These notes are intended to be a guide and a help as you work through Chapter 8. These are not the only thing you need to read, however. Rely
Lesson 11: Using the Zero Product Property to Find Horizontal Intercepts
: Using the Zero Product Property to Find Horizontal Intercepts Opening Discussion 1. A. Jenna said the product of two numbers is 20. Would the factors have to be 4 and 5? Why? B. Julie said the product
Chapter 1 Review of Equations and Inequalities
Chapter 1 Review of Equations and Inequalities Part I Review of Basic Equations Recall that an equation is an expression with an equal sign in the middle. Also recall that, if a question asks you to solve
For Exercises 1 4, identify the part of the circle drawn in red as its circumference, diameter, or radius. Then, measure that part in centimeters.
A C E Applications Connections Extensions Applications For Exercises 1 4, identify the part of the circle drawn in red as its circumference, diameter, or radius. Then, measure that part in centimeters.
Manipulating Radicals
Lesson 40 Mathematics Assessment Project Formative Assessment Lesson Materials Manipulating Radicals MARS Shell Center University of Nottingham & UC Berkeley Alpha Version Please Note: These materials
USING 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
Chapter 5: Measurement of Circles
Chapter 5: Measurement of Circles Getting Started, p. 151 1. a) Perimeter, since the word around is used. b) Area, since since the word wrap is used. c) Perimeter, since the word wrap is used. 2. a) 5
Recall the following facts for the Ferris wheel Carlos is riding:
In spite of his nervousness, Carlos enjoys his first ride on the amusement park Ferris wheel. He does, however, spend much of his time with his eyes fixed on the ground below him. After a while, he becomes
G-GPE Explaining the equation for a circle
G-GPE Explaining the equation for a circle Alignments to Content Standards: G-GPE.A.1 Task This problem examines equations defining different circles in the - plane. a. Use the Pythagorean theorem to find
Solving Quadratic & Higher Degree Equations
Chapter 9 Solving Quadratic & Higher Degree Equations Sec 1. Zero Product Property Back in the third grade students were taught when they multiplied a number by zero, the product would be zero. In algebra,
Math 3 Unit 7: Parabolas & Circles
Math 3 Unit 7: Parabolas & Circles Unit Title Standards 7.1 Introduction to Circles G.GPE.1, F.IF.8.a, F.IF.8 7.2 Converting Circles to Descriptive Form G.GPE.1, A.CED.4, F.IF.8 7.3 Definition of a Parabola
Marina s Fish Shop Student Worksheet Name
Marina s Fish Shop Student Worksheet Name Marina owns a fish shop, and wants to create a new sign above the shop. She likes geometric ideas, and thinks a square with a triangle looks like a fish. Marina