Transformations. Lesson Summary: Students will explore rotations, translations, and reflections in a plane.
|
|
- Valerie Little
- 6 years ago
- Views:
Transcription
1 Transformations Lesson Summary: Students will explore rotations, translations, and reflections in a plane. Key Words: Transformation, translation, reflection, rotation Background knowledge: Students should be familiar with Cabri software. NCTM Standards addressed in this lesson: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. Objectives: Students will be able to describe some of the properties of a plane figure and its reflection. Students will gain an understanding for what the reflection tool does in Cabri. Students will develop an appropriate definition for the word rotation. Students will analyze the properties of rotations. Students will recognize the difference between positive and negative rotations. Students will be able to describe a vector using ordered pair notation. Students will be able to translate objects by a given vector. Students will be able to derive the formula for the composition of two translations. Materials: Computer lab/calculators equipped with Cabri Paper Pencils Procedure: (suggestions) Pair students of varied ability levels. Allow students to work on this lab for one class period. Collect the lab sheets and discs from the students. Assessment: Grade questions based on clarity and demonstration of knowledge. Students who complete the lab extension could present their solutions in front of the class. Transformations
2 Activity One: Reflections Team member s names: File name: Goals: After completing this lab, you should: Be able to describe some of the properties of a plane figure and its reflection. Gain an understanding for what the reflection tool in Cabri does. Definitions: When a transformation is performed on a geometrical figure, the starting figure is called the preimage and the resulting figure is called the image. Procedure (Using Cabri): Part A: Reflecting a point over a line 1. Construct a line l. [Use the line and label tools] 2. Create a point not on l and label it A. [Use the point and label tools] 3. Reflect A over l and label the image A. [Use the reflection and label tools] 4. Measure the distance from A to l. [Use the distance and length tool] 5. Measure the distance from A to l. [Use the distance and length tool] 6. Compare these two distances. What do you notice? 7. Now draw a line from point A to point A. [Use the line tool] 8. Measure the four angles created by the [Use the angle tool] intersection of the two lines. 9. What do you notice? Repeat steps 1-8 with a new point. Do you get the same results? Why or why not? 10. Print and Save As Reflection4. Part B: Reflecting a line segment over a line 1. Go to File New.
3 2. Construct a line l. [Use line and label tools] 3. Draw a line segment and label it AB ' ' [Use the segment and label tools] 4. Reflect the segment AB over line l. [Use reflection tool] 5. Label the new segment AB. ' ' 6. Measure the length of segments AB and AB. ' ' [Use label tool] [Use dis tance and length tool] 7. Compare these two lengths. What do you notice? 8. Print and Save As Reflection5. Part C: Reflecting a pentagon over a line 1. Go to File New. 2. Construct a regular pentagon and label it ABCDE. [Use polygon and label tools] 3. Construct a line l that does not intersect the pentagon [Use line and label tools] ABCDE. 4. Reflect ABCDE over l. [Use reflection tool] 5. Label the new polygon A B C D E. [Use label tool] 6. What do you think the ratio of the area of ABCDE to the area of A B C D E will be? Why do you think this? 7. Test your hypothesis. Were you correct? [Use area tool] 8. Measure the sides in each pentagon. What do you notice about the corresponding sides? 9. Now measure the angles in each pentagon. What do you notice about the corresponding angles?
4 10. Repeat steps 1-8 with an irregular pentagon. Does your answer for #8 and #9 change? Why or why not? 11. In a paragraph of your own words, describe what the reflection tool in Cabri does. When an object is reflected, what changes? What remains the same? 12. In your own words, define reflection. 13.An isometry is a transformation in which the original figure and its image are congruent. Is reflection an isometry? Explain your reasoning. 14. Print and Save As Reflection6. Extension: Given a point A and its reflection A, How would one find the line over which point A was reflected? (It may be helpful to draw a picture.) Transformations
5 Activity Two: Translations Team member s names: File name: Goals: After completing this lab, you should be able to: Describe a vector in ordered pair notation. Translate objects by a given vector. Derive the formula for the composition of two translations. A vector like the one shown has an initial point (in this case A) and a terminal (or end) point (B). We write vectors as <x,y> where x is the horizontal change from the initial point to the terminal point, and y is the vertical change from the initial point to the terminal point. In the above example we would write the vector as <3,2>. When we translate an object by a vector <x,y> we move each point of the object x units horizontally and y units vertically. A negative x value will cause the image point to be moved to the left and a negative y value will cause the image point to be moved down. This is similar to the Cartesian coordinate system with which you are already familiar. Procedure (Using Cabri): Part A: Labeling and Constructing Vectors 1. Turn on the grid and axes. [Use the show axes and define grid tools] 2. Plot two vectors whose initial points [Use vector tool] and terminal points are points on your grid. 3. Using Cartesian coordinates, label the [Use label tool] initial points and terminal points of the vectors. 4. Label each vector using the ordered pair [Use label tool] notation: <x,y>.
6 5. Print and Save As Translation1 Part B: Translating Objects 1. Go to File New. 2. Draw a vector <x,y>on the screen. [Use vector tool] 4. Draw a point not on the vector and label it A. [Use point and label tools] 5. Translate the point by that vector. [Use translation tool] 6. Label the image A. [Use label tool] 7. Describe what you see. Do you notice any relationships between the objects? 8. Print and Save As Translation2 9. Go to File New. 10. Draw a line segment on the screen and label [Use the segment and label tools] it BC. 11. Draw a vector on the screen. [Use the vector tool] 12. Translate the segment by the vector. [Use the translations tool] 13. Label the image BC. ' ' [Use the label tool] 14. What do you notice? Is there a relationship betweenbc, BC, ' ' and the vector? 15. On the same screen, draw a quadrilateral. [Use the polygon tool] 16. Translate the quadrilateral by the vector. [Use the translation tool] 17. Describe what you see. Here are some things to consider. Are the images still arranged in the same order? Are the images the same size as their preimages? Are they oriented in the same way?
7 Part C: Compositions of Translations For any two translations, when the second translation is performed on the image of the first translation the resulting translation is called composition of translations. 1. Go to File New. 2. Turn on the grid and axes. [Use the show axes and define grid tools] 3. Construct a polygon wherever you choose [Use the polygon and vector tools] on the grid and two vectors whose terminal points and initial points are grid points. We will refer to this polygon as P. 4. Label the vectors using ordered pair notation. [Use the label tool] 5. Translate polygon P by one of the vectors. [Use the translate tool] We will refer to this image as P. 6. Translate P by the other vector. We will [Use the translate tool] refer to this image as P. 7. There exists a vector <x,y> that when P is translated by <x,y> the result is P. What is this vector? Use the grid to help you find it. 8. Repeat part C with a few more examples. Do you notice any patterns? Given two vectors <a,b> and <c,d>, what is the vector that would perform the same translation as the composition of these two translations? 9. An isometry is a transformation in which the original figure and its image are congruent. Is translation an isometry? Explain your reasoning. 10. Print and Save As Translation3 Extension: Draw a polygon and two parallel lines. Reflect the polygon over one line. Then reflect it over the other. Is there a translation that would produce the same image? If no, why not? If yes, show an example.
8 Transformations Activity Three: Rotations Team member s names: File name: Team member s names: Goals: After completing this lab you should have discovered the definition of a rotation and what its properties are. Procedure: (Using Cabri) Part A: Rotation of a polygon by 62 degrees 1. Draw a five-sided polygon and label each vertex point. We will refer to this polygon as P. [Use the polygon tool and label tool] 2. Use the numerical edit tool to insert the number 62 on the screen. [Use the numerical edit tool] 3. Rotate P about the vertex of your choice by 62 degrees. Label this polygon P. [Use the rotation tool] 4. Pick one of the vertices and measure the distances between it and its corresponding vertex in the image. Record the values on a blank section of the page [Use the distance and length tool] 4. Print and Save As Rotation1 Part B: Rotation of a polygon by negative 77 degrees 1. Go to File New. 2. Construct another polygon and label each vertex point. We will refer to this polygon as Q. [Use the polygon tool and the label tool] 3. Rotate Q about the vertex of your choice by 77 degrees. Don t forget to use the numerical edit tool before you do the rotation! Label this polygon Q.
9 [Use the rotation and numerical edit tools ] 4. Rotate Q about the vertex that corresponds to the one chosen in Part B #2 by negative 77 degrees. Don t forget to use the numerical edit tool before you do the rotation! [Use the rotation and numerical edit tools ] 5. Print and Save As Rotation2 Summarize your findings: 1. Consider P and P. What happened when you rotated by 62 degrees? 2. Consider Q and Q. What happened when you rotated by negative 77 degrees? 3. What were the similarities and differences between the two polygons when they were rotated? 4. An isometry is a transformation in which the original figure and its image are congruent. Is rotation an isometry? Explain your reasoning. 5. What did you notice about the distances between the original vertex point you picked and the corresponding vertex of the rotated polygon? Why do you think this is?
10 6. What do you see happen in part B? Extensions: 7. Using what you have learned, make up your own definition of rotation. Why do you think your definition is complete? 1. In the next class period you will be in groups of four. In your groups you will be asked to compare and contrast your definition of rotation. Try to formulate a definition within your groups that incorporates everybody s thoughts. Then the class will collectively decide on an appropriate definition. 2. Consider some art that you have seen. What are some famous paintings that use rotations? How can you tell?
Size Transformations in the Coordinate Plane
Size Transformations in the Coordinate Plane I.e. Dilations (adapted from Core Plus Math, Course 2) Concepts 21-26 Lesson Objectives In this investigation you will use coordinate methods to discover several
More informationChapter 2: Transformations. Chapter 2 Transformations Page 1
Chapter 2: Transformations Chapter 2 Transformations Page 1 Unit 2: Vocabulary 1) transformation 2) pre-image 3) image 4) map(ping) 5) rigid motion (isometry) 6) orientation 7) line reflection 8) line
More information12.4 Rotations. Learning Objectives. Review Queue. Defining Rotations Rotations
12.4. Rotations www.ck12.org 12.4 Rotations Learning Objectives Find the image of a figure in a rotation in a coordinate plane. Recognize that a rotation is an isometry. Review Queue 1. Reflect XY Z with
More informationGeometry Sixth Grade
Standard 6-4: The student will demonstrate through the mathematical processes an understanding of shape, location, and movement within a coordinate system; similarity, complementary, and supplementary
More informationProperties of Rotations
Properties of Rotations Student Probe Find the image of a 50 o counterclockwise rotation about point P. A P B Lesson Description The lesson examines rotations as the transformation obtained by reflecting
More informationR(-14, 4) R'(-10, -2) S(-10, 7) S'(-6, 1) T(-5, 4) T'(-1, -2)
1 Transformations Formative Assessment #1 - Translation Assessment Cluster & Content Standards What content standards can be addressed by this formative assessment? 8.G.3 Describe the effect of dilations
More informationProperties of Rotations
Properties of Rotations Student Probe Find the image of a 50 counterclockwise rotation about point P. Lesson Description The lesson examines rotations as the transformation obtained by reflecting an object
More informationModule 1 Topic C Lesson 14 Reflections
Geometry Module 1 Topic C Lesson 14 Reflections The purpose of lesson 14 is for students to identify the properties of reflection, to use constructions to find line of reflection, get familiar with notations
More informationUnit 1 Transformations in the Coordinate Plane
Unit 1 Transformations in the Coordinate Plane Table of Contents Title Page # Formula Sheet...2 Lesson 1 1: Introduction to Transformations and Rotations 3 Lesson 1 2: Reflections and Translations..9 Lesson
More informationSpecific Objectives Students will understand that that the family of equation corresponds with the shape of the graph. Students will be able to create a graph of an equation by plotting points. In lesson
More informationSet the Sails! Purpose: Overview. TExES Mathematics 4-8 Competencies. TEKS Mathematics Objectives.
Set the Sails! Purpose: Participants will use graphing technology to investigate reflections, translations, rotations, and sequences of reflections and translations in the coordinate plane. They will give
More informationChapter 12 Transformations: Shapes in Motion
Chapter 12 Transformations: Shapes in Motion 1 Table of Contents Reflections Day 1.... Pages 1-10 SWBAT: Graph Reflections in the Coordinate Plane HW: Pages #11-15 Translations Day 2....... Pages 16-21
More informationBeading Patterns Using Reflections
Beading Patterns Using Reflections Fast Facts Curriculum Area: Beading patterns Using Reflections Grade Level: Grade 10 Suggested Duration: 110 minutes Stage 1 Desired Results Established Goals Geometric
More information6th Grade Report Card Mathematics Skills: Students Will Know/ Students Will Be Able To...
6th Grade Report Card Mathematics Skills: Students Will Know/ Students Will Be Able To... Report Card Skill: Use ratio reasoning to solve problems a ratio compares two related quantities ratios can be
More informationDaily Warm-Ups GEOMETRY
WALCH EDUCATION Daily Warm-Ups GEOMETRY NCTM Standards Jillian Gregory Table of Contents iii Introduction............................................ v About the CD-ROM....................................
More informationConic Sections and Locii
Lesson Summary: Students will investigate the ellipse and the hyperbola as a locus of points. Activity One addresses the ellipse and the hyperbola is covered in lesson two. Key Words: Locus, ellipse, hyperbola
More informationShape & Space Part C: Transformations
Name: Homeroom: Shape & Space Part C: Transformations Student Learning Expectations Outcomes: I can describe and analyze position and motion of objects and shapes by Checking for Understanding identifying
More information6 Mathematics Curriculum
New York State Common Core 6 Mathematics Curriculum GRADE GRADE 6 MODULE 5 Table of Contents 1 Area, Surface Area, and Volume Problems... 3 Topic A: Area of Triangles, Quadrilaterals, and Polygons (6.G.A.1)...
More informationUnit 14: Transformations (Geometry) Date Topic Page
Unit 14: Transformations (Geometry) Date Topic Page image pre-image transformation translation image pre-image reflection clockwise counterclockwise origin rotate 180 degrees rotate 270 degrees rotate
More informationWhy Can t We Use SSA to Prove Triangles Congruent?
Why Can t We Use SSA to Prove Triangles Congruent? Lesson Summary: When proving triangles congruent by applying the SSS, ASA, and SAS theorems and postulates, students often asked why is there no SSA property.
More informationUnit 7. Transformations
Unit 7 Transformations 1 A transformation moves or changes a figure in some way to produce a new figure called an. Another name for the original figure is the. Recall that a translation moves every point
More information4-7 Study Guide and Intervention Congruence Transformations
4-7 Study Guide and Intervention Congruence Transformations Identify Congruence Transformations A congruence transformation is a transformation where the original figure, or preimage, and the transformed
More informationArizona Academic Standards
Arizona Academic Standards This chart correlates the Grade 8 performance objectives from the mathematics standard of the Arizona Academic Standards to the lessons in Review, Practice, and Mastery. Lesson
More informationShapes & Transformations and Angles & Measurements Spatial Visualization and Reflections a.) b.) c.) d.) a.) b.) c.)
Chapters 1 & 2 Team Number Name Shapes & Transformations and Angles & Measurements 1.2.1 Spatial Visualization and Reflections 1-47. d.) 1-48. 1-49. 1-50. 1-51. d.) 1-52. On the axes at right, graph the
More informationNumber Sense and Operations Curriculum Framework Learning Standard
Grade 5 Expectations in Mathematics Learning Standards from the MA Mathematics Curriculum Framework for the end of Grade 6 are numbered and printed in bold. The Franklin Public School System s grade level
More informationCourse Guide (/8/teachers/teacher_course_guide.html) Print (/8/teachers/print_materials.html) LMS (/8
(http://openupresources.org)menu Close OUR Curriculum (http://openupresources.org) Professional Development (http://openupresources.org/illustrative-mathematics-professional-development) Implementation
More informationTable of Contents. Introduction to the Math Practice Series...1
Table of Contents Table of Contents Introduction to the Math Practice Series...1 Common Mathematics/Geometry Symbols and Terms...2 Chapter 1: Introduction To Geometry...13 Shapes, Congruence, Similarity,
More informationCCM6+/7+ - Unit 13 - Page 1 UNIT 13. Transformations CCM6+/7+ Name: Math Teacher: Projected Test Date:
CCM6+/7+ - Unit 13 - Page 1 UNIT 13 Transformations CCM6+/7+ Name: Math Teacher: Projected Test Date: Main Idea Pages Unit 9 Vocabulary 2 Translations 3 10 Rotations 11 17 Reflections 18 22 Transformations
More informationSection 12.1 Translations and Rotations
Section 12.1 Translations and Rotations Any rigid motion that preserves length or distance is an isometry. We look at two types of isometries in this section: translations and rotations. Translations A
More informationContents COORDINATE METHODS REGRESSION AND CORRELATION
Contents UNIT 3 UNIT 4 COORDINATE METHODS Lesson 1 A Coordinate Model of a Plane.............. 162 Investigations 1 Representing Geometric Ideas with Coordinates............... 164 2 Reasoning with Slopes
More informationMontana City School GRADE 5
Montana City School GRADE 5 Montana Standard 1: Students engage in the mathematical processes of problem solving and reasoning, estimation, communication, connections and applications, and using appropriate
More informationChapter 5. Transforming Shapes
Chapter 5 Transforming Shapes It is difficult to walk through daily life without being able to see geometric transformations in your surroundings. Notice how the leaves of plants, for example, are almost
More informationUnit 4 Guided Notes Part 2 Geometry
Unit 4 Guided Notes Part 2 Geometry Name: Important Vocabulary: Transformation: A change in,, or of a geometric figure. Rigid transformation: A transformation that preserves measures and of segments. Transformation
More informationChapter 2 Rigid Transformations Geometry. For 1-10, determine if the following statements are always, sometimes, or never true.
Chapter 2 Rigid Transformations Geometry Name For 1-10, determine if the following statements are always, sometimes, or never true. 1. Right triangles have line symmetry. 2. Isosceles triangles have line
More information9 Transformations CHAPTER. Chapter Outline.
Chapter 9 www.ck12.org CHAPTER 9 Transformations Chapter Outline 9.1 EXPLORING SYMMETRY 9.2 TRANSLATIONS AND VECTORS 9.3 REFLECTIONS 9.4 ROTATIONS 9.5 COMPOSITION OF TRANSFORMATIONS 9.6 DILATIONS 9.7 TESSELLATIONS
More informationGeometry ~ Unit 4
Title Quadrilaterals and Coordinate Proof CISD Safety Net Standards: G.5A Big Ideas/Enduring Understandings Module 9 Properties of quadrilaterals can be used to solve real-world problems. Suggested Time
More informationVisual Representations: Geometry in Art. Common Core State Standards. Students will decompose polygons into triangles, rectangles, and trapezoids.
Lesson in Action Visual Representations: Geometry in Art AT A GLANCE Launch Warm up with a review Have students demonstrate and explain different solutions to the Compare and contrast the two visual representations.
More informationLesson 1. Unit 2 Practice Problems. Problem 2. Problem 1. Solution 1, 4, 5. Solution. Problem 3
Unit 2 Practice Problems Lesson 1 Problem 1 Rectangle measures 12 cm by 3 cm. Rectangle is a scaled copy of Rectangle. Select all of the measurement pairs that could be the dimensions of Rectangle. 1.
More informationUNIT PLAN. Big Idea/Theme: Polygons can be identified, classified, and described.
UNIT PLAN Grade Level: 5 Unit #: 11 Unit Name Geometry Polygons Time: 15 lessons, 18 days Big Idea/Theme: Polygons can be identified, classified, and described. Culminating Assessment: (requirements of
More informationAngles of Polygons. Essential Question What is the sum of the measures of the interior angles of a polygon?
7.1 Angles of Polygons Essential Question What is the sum of the measures of the interior angles of a polygon? The Sum of the Angle Measures of a Polygon Work with a partner. Use dynamic geometry software.
More informationStandard 1 Students will expand number sense to include integers and perform operations with whole numbers, simple fractions, and decimals.
Stretch Standard 1 Students will expand number sense to include integers and perform operations with whole numbers, simple fractions, and decimals. Objective 1: Represent whole numbers and decimals from
More informationa) Draw a line through points A and B. What is one symbol or name for it?
Lesson 1A: Geometric Notation Name: Use correct notation when referring to lines, segments, rays, and angles. 1. Lines P A C D Q E F G H I a) Draw a line through points A and. What is one symbol or name
More informationName Hr. Honors Geometry Lesson 9-1: Translate Figures and Use Vectors
Name Hr Honors Geometry Lesson 9-1: Translate Figures and Use Vectors Learning Target: By the end of today s lesson we will be able to successfully use a vector to translate a figure. Isometry: An isometry
More informationClassifying Quadrilaterals
Practice A 1. List the six major special quadrilaterals. Give all of the names that apply to each quadrilateral. 2. 3. 4. Give the name that best describes each quadrilateral. 5. 6. 7. Draw each figure.
More informationGeometry. Standardized Practice Have students try the following problem.
1 Students need a basic understanding of angles to learn the properties of twodimensional shapes. In this lesson, students use models to represent, measure, and classify angles. Objective Recognize types
More informationPrinciples and Standards for School Mathematics. Content Standards. Process Standards. Emphasis across the Grades. Principles
1 Navigating through Geometry Grades 3-5 Principles and Standards for School Mathematics Presented by Dr. Karol L. Yeatts Navigations Writer Navigating through Algebra Grades 3-5 Navigating through Number
More information2-1 Transformations and Rigid Motions. ENGAGE 1 ~ Introducing Transformations REFLECT
2-1 Transformations and Rigid Motions Essential question: How do you identify transformations that are rigid motions? ENGAGE 1 ~ Introducing Transformations A transformation is a function that changes
More informationPerimeter and Area of Geometric Figures on the Coordinate Plane
Perimeter and Area of Geometric Figures on the Coordinate Plane There are more than 200 national flags in the world. One of the largest is the flag of Brazil flown in Three Powers Plaza in Brasilia. This
More informationUnit 1 NOTES Honors Math 2 1
Unit 1 NOTES Honors Math 2 1 Day 1: Introduction to Transformations and Translations Warm-Up: Prerequisite Skill: Graphing Lines Graph the following lines. 1) x = 2 2) y = 4 3) y = x (Hint: this is y =
More informationXVIII. AMC 8 Practice Questions
XVIII. AMC 8 Practice Questions - A circle and two distinct lines are drawn on a sheet of paper. What is the largest possible number of points of intersection of these figures? (A) (B) 3 (C) 4 (D) 5 (E)
More informationPolygons. L E S S O N 1.4
Page 1 of 5 L E S S O N 1.4 Polygons A polygon is a closed figure in a plane, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others. Each line segment
More informationStudent Mathematician: Date: Some, All or None Tell whether each statement below is true or false by circling the correct answer. If the statement is false, give a counterexample using words and/or pictures.
More informationIllinois Math Assessment Framework, Grade 7. correlated to
Illinois Math Assessment Framework, Grade 7 correlated to Grade 7 correlated to Chapter 1 Variables, Expressions, and Integers (pp. 1 61) Lesson 1.1 (pp. 5 9) Expressions and Variables Evaluate and write
More informationLesson 1. Rigid Transformations and Congruence. Problem 1. Problem 2. Problem 3. Solution. Solution
Rigid Transformations and Congruence Lesson 1 The six frames show a shape's di erent positions. Describe how the shape moves to get from its position in each frame to the next. To get from Position 1 to
More informationRational Numbers: Graphing: The Coordinate Plane
Rational Numbers: Graphing: The Coordinate Plane A special kind of plane used in mathematics is the coordinate plane, sometimes called the Cartesian plane after its inventor, René Descartes. It is one
More informationGEOMETRY. Background Knowledge/Prior Skills. Knows ab = a b. b =
GEOMETRY Numbers and Operations Standard: 1 Understands and applies concepts of numbers and operations Power 1: Understands numbers, ways of representing numbers, relationships among numbers, and number
More informationWednesday, November 7, 2018
Wednesday, November 7, 2018 Warm-up Use the grid from yesterday s warm-up space to plot the pre-image ABCD and the points that are transformed by the rule (x, y) (2x, 2y) 5 2 2 5 2 4 0 0 Talk about quiz
More informationGrade Level Expectations for the Sunshine State Standards
for the Sunshine State Standards FLORIDA DEPARTMENT OF EDUCATION http://www.myfloridaeducation.com/ The seventh grade student: Number Sense, Concepts, and Operations knows word names and standard numerals
More informationGrade 8 Mathematics Item Specifications Florida Standards Assessments
MAFS.8.G.1 Understand congruence and similarity using physical models, transparencies, or geometry software. MAFS.8.G.1.2 Understand that a two-dimensional figure is congruent to another if the second
More informationIntroduction A young woman uses her reflection in a mirror to give herself a facial.
Algebra/Geometry Blend Unit #2: Transformations Lesson 2: Reflections Introduction A young woman uses her reflection in a mirror to give herself a facial. [page 1] Name Period Date Have you ever mimicked
More informationChapters 7 & 8. Parallel and Perpendicular Lines/Triangles and Transformations
Chapters 7 & 8 Parallel and Perpendicular Lines/Triangles and Transformations 7-2B Lines I can identify relationships of angles formed by two parallel lines cut by a transversal. 8.G.5 Symbolic Representations
More informationName: Period 2/3/2012 2/16/2012 PreAP
Name: Period 2/3/2012 2/16/2012 PreP UNIT 11: TRNSFORMTIONS I can define, identify and illustrate the following terms: Symmetry Line of Symmetry Rotational Symmetry Translation Symmetry Isometry Pre-Image
More informationHandout 1: Viewing an Animation
Handout 1: Viewing an Animation Answer the following questions about the animation your teacher shows in class. 1. Choose one character to focus on. Describe this character s range of motion and emotions,
More informationTranslations, Reflections, and Rotations
* Translations, Reflections, and Rotations Vocabulary Transformation- changes the position or orientation of a figure. Image- the resulting figure after a transformation. Preimage- the original figure.
More information5th Grade Mathematics Essential Standards
Standard 1 Number Sense (10-20% of ISTEP/Acuity) Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions, and percents. They understand the
More informationAn Overview of Mathematics 6
An Overview of Mathematics 6 Number (N) read, write, represent, and describe numbers greater than one million and less than one-thousandth using symbols, expressions, expanded notation, decimal notation,
More informationGrade Level: 6-8 Sunshine State Standard: MA.A.1.3.3, MA.A.3.3.1, MA.B.1.3.2, MA.B.4.3.2, MA.C Time: 45 minutes
Rotations Grade Level: 6-8 Sunshine State Standard: MA.A.1.3.3, MA.A.3.3.1, MA.B.1.3.2, MA.B.4.3.2, MA.C.3.3.2 Time: 45 minutes Materials: Students: Paper, pencil, graph paper, computer with GeoGebra (if
More informationIntroduction : Applying Lines of Symmetry
Introduction A line of symmetry,, is a line separating a figure into two halves that are mirror images. Line symmetry exists for a figure if for every point P on one side of the line, there is a corresponding
More informationAbout Finish Line Mathematics 5
Table of COntents About Finish Line Mathematics 5 Unit 1: Big Ideas from Grade 1 7 Lesson 1 1.NBT.2.a c Understanding Tens and Ones [connects to 2.NBT.1.a, b] 8 Lesson 2 1.OA.6 Strategies to Add and Subtract
More informationIsometries: Teacher Notes
Isometries: Teacher Notes Henri Picciotto Acknowledgments Vinci Daro, Ann Shannon, and Celia Stevenson helped me with the original version of this document. Zalman Usiskin offered valuable feedback, some
More informationSimi imilar Shapes lar Shapes Nesting Squares Poly lyhedr hedra and E a and Euler ler s Form s Formula ula
TABLE OF CONTENTS Introduction......................................................... 5 Teacher s Notes....................................................... 6 NCTM Standards Alignment Chart......................................
More informationChapter 12 Transformations: Shapes in Motion
Name Geometry Honors Date Per. Teacher Chapter 12 Transformations: Shapes in Motion 1 Table of Contents Reflections Day 1.... Page 3 Translations Day 2....... Page 10 Rotations/Dilations Day 3.... Page
More informationZome Symmetry & Tilings
Zome Symmetry & Tilings Tia Baker San Francisco State tiab@mail.sfsu.edu 1 Introduction Tessellations also known as tilings are a collection of polygons that fill the plane with no overlaps or gaps. There
More informationB ABC is mapped into A'B'C'
h. 00 Transformations Sec. 1 Mappings & ongruence Mappings Moving a figure around a plane is called mapping. In the figure below, was moved (mapped) to a new position in the plane and the new triangle
More informationMCAS/DCCAS Mathematics Correlation Chart Grade 6
MCAS/DCCAS Mathematics Correlation Chart Grade 6 MCAS Finish Line Mathematics Grade 6 MCAS Standard DCCAS Standard DCCAS Standard Description Unit 1: Number Sense Lesson 1: Whole Number and Decimal Place
More informationSlammin Sammy. Name Date. Finger. Shoulder. Back. Toe. Heel
Name Date Slammin Sammy Finger Shoulder Back Toe Heel (0, 0) Fist 1. Give the coordinates of Sammy s six body parts: Finger (, ) Shoulder (, ) Back (, ) Toe (, ) Heel (, ) Fist (, ) Classroom Strategies
More informationAmarillo ISD Math Curriculum
Amarillo Independent School District follows the Texas Essential Knowledge and Skills (TEKS). All of AISD curriculum and documents and resources are aligned to the TEKS. The State of Texas State Board
More informationB ABC is mapped into A'B'C'
h. 00 Transformations Sec. 1 Mappings & ongruence Mappings Moving a figure around a plane is called mapping. In the figure below, was moved (mapped) to a new position in the plane and the new triangle
More informationHIGH ORDER QUESTION STEMS STUDENT SCALE QUESTIONS FCAT ITEM SPECIFICATION
Benchmark Support Task Cards MA.3.A.1.1 BENCHMARK: MA.3.A.1.1 Model multiplication and division, including problems presented in context: repeated addition, multiplicative comparison, array, how many combinations,
More informationMathematics Curriculum
6 G R A D E Mathematics Curriculum GRADE 6 5 Table of Contents 1... 1 Topic A: Area of Triangles, Quadrilaterals, and Polygons (6.G.A.1)... 11 Lesson 1: The Area of Parallelograms Through Rectangle Facts...
More informationUnit 6: Quadrilaterals
Name: Geometry Period Unit 6: Quadrilaterals Part 1 of 2: Coordinate Geometry Proof and Properties! In this unit you must bring the following materials with you to class every day: Please note: Calculator
More informationHelpful Hint When you are given a frieze pattern, you may assume that the pattern continues forever in both directions Notes: Tessellations
A pattern has translation symmetry if it can be translated along a vector so that the image coincides with the preimage. A frieze pattern is a pattern that has translation symmetry along a line. Both of
More informationUnit 7: Quadrilaterals
Name: Geometry Period Unit 7: Quadrilaterals Part 1 of 2: Coordinate Geometry Proof and Properties! In this unit you must bring the following materials with you to class every day: Please note: Calculator
More informationGuided Problem Solving
-1 Guided Problem Solving GPS Student Page 57, Exercises 1 1: Match each rule with the correct translation. A. (x, y) (x, y 1 ) I. P(, 1) P (3, ) B. (x, y) (x 1 3, y) II. Q(3, 0) Q (3, ) C. (x, y) (x 1,
More informationUnit Lesson Plan: Measuring Length and Area: Area of shapes
Unit Lesson Plan: Measuring Length and Area: Area of shapes Day 1: Area of Square, Rectangles, and Parallelograms Day 2: Area of Triangles Trapezoids, Rhombuses, and Kites Day 3: Quiz over Area of those
More informationIsometries and Congruence
Honors Geometr Section.1 Name: Date: Period: Isometries and Congruence transformation of a geometric figure is a change in its position, shape, or size.. The original figure is called the preimage. The
More informationNumber/Computation. addend Any number being added. digit Any one of the ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
14 Number/Computation addend Any number being added algorithm A step-by-step method for computing array A picture that shows a number of items arranged in rows and columns to form a rectangle associative
More informationGeometry. 4.4 Congruence and Transformations
Geometry 4.4 Congruence and Transformations 4.4 Warm Up Day 1 Plot and connect the points in a coordinate plane to make a polygon. Name the polygon. 1. A( 3, 2), B( 2, 1), C(3, 3) 2. E(1, 2), F(3, 1),
More informationGeometry. 4.4 Congruence and Transformations
Geometry 4.4 Congruence and Transformations 4.4 Warm Up Day 1 Plot and connect the points in a coordinate plane to make a polygon. Name the polygon. 1. A(-3, 2), B(-2, 1), C(3, 3) 2. E(1, 2), F(3, 1),
More informationChapter 1. Linear Equations and Straight Lines. 2 of 71. Copyright 2014, 2010, 2007 Pearson Education, Inc.
Chapter 1 Linear Equations and Straight Lines 2 of 71 Outline 1.1 Coordinate Systems and Graphs 1.4 The Slope of a Straight Line 1.3 The Intersection Point of a Pair of Lines 1.2 Linear Inequalities 1.5
More informationArchdiocese of Washington Catholic Schools Academic Standards Mathematics
5 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions,
More information7 th Grade STAAR Crunch March 30, 2016
Reporting Category UMATHX Suggested Lessons and Activities Access UMath X with the URL that your group was given. Login with a valid user name and password. Category 1:Numbers, Operations, and Quantitative
More informationMathematics - LV 6 Correlation of the ALEKS course Mathematics MS/LV 6 to the Massachusetts Curriculum Framework Learning Standards for Grade 5-6
Mathematics - LV 6 Correlation of the ALEKS course Mathematics MS/LV 6 to the Massachusetts Curriculum Framework Learning Standards for Grade 5-6 Numbers Sense and Operations TD = Teacher Directed 6.N.1:
More informationAre You Ready? Ordered Pairs
SKILL 79 Ordered Pairs Teaching Skill 79 Objective Plot ordered pairs on a coordinate plane. Remind students that all points in the coordinate plane have two coordinates, an x-coordinate and a y-coordinate.
More information8 TH GRADE MATHEMATICS CHECKLIST Goals 6 10 Illinois Learning Standards A-D Assessment Frameworks Calculators Allowed on ISAT
8 TH GRADE MATHEMATICS CHECKLIST Goals 6 10 Illinois Learning Standards A-D Assessment Frameworks Calculators Allowed on ISAT ISAT test questions are derived from this checklist. Use as a curriculum guide.
More informationChapter 9 Transformations
Section 9-1: Reflections SOL: G.2 The student will use pictorial representations, including computer software, constructions, and coordinate methods, to solve problems involving smmetr and transformation.
More informationSecond Grade Report Card Teacher Rubric Mathematics
Mathematics Numbers and Operations Emerging (1) Progressing (2) Meets (3) Exceeds (4) Comments/Evidence Understands and uses Can do none or one of the Can do two or more but not all of Can consistently
More informationUsing the Best of Both!
Using the Best of Both! A Guide to Using Connected Mathematics 2 with Prentice Hall Mathematics Courses 1, 2, 3 2012, and Algebra Readiness MatBro111707BestOfBothPH10&CMP2.indd 1 6/7/11 11:59 AM Using
More informationCCGPS UNIT 5 Semester 2 COORDINATE ALGEBRA Page 1 of 38. Transformations in the Coordinate Plane
CCGPS UNIT 5 Semester 2 COORDINATE ALGEBRA Page 1 of 38 Transformations in the Coordinate Plane Name: Date: MCC9-12.G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line,
More informationA Correlation of Pearson Mathematics Geometry Common Core, 2015 To the Missouri Learning Standards for Mathematics Geometry
A Correlation of Pearson Mathematics Common Core, 2015 To the Missouri Learning Standards for Mathematics A Correlation of Common Core 2015 To the Introduction This document demonstrates how Pearson, Common
More information