Exploring Geometric Transformations in a Dynamic Environment Cheryll E. Crowe, Ph.D. Eastern Kentucky University
|
|
|
- Lily Elliott
- 7 years ago
- Views:
Transcription
1 Exploring Geometric Transformations in a Dynamic Environment Cheryll E. Crowe, Ph.D. Eastern Kentucky University Overview The GeoGebra documents allow exploration of four geometric transformations taught in middle and high school level geometry classes. The design of the applets provide flexibility of content and grade level with hidden elements that can be revealed to create additional topics for investigating reflections, rotations, translations, and glide-reflections. Suggested activities and exercises are included but can be altered or omitted to accommodate various levels of mathematical understanding. The interactive sketches were initially created for use with pre-service teachers in content mathematics education courses at the university level but can also be adapted for middle and high school students. Intended audience: Grades 6-12, Mathematics Teacher Education Courses Instruction & Activities General Instructions - The use of show buttons are identified in the directions with red font to correlate with the red letters on the button. - Calculations and coordinates are identified in the directions with green font to correlate with the green letters on the button. - Words in capital letters indicate selections from the menu at the top of the GeoGebra document. Activity 1: Exploring Reflections Part I Identifying Reflections Move the mirror line by clicking and dragging point K or L. Click on the Show Reflection button. Note the location of the reflection. Hide the reflection and repeat steps 1 and 2. Attempt to guess the location of the transformation. Note: You may need to use the zoom in/out tool to see the entire reflection. (Select this function from the last icon on the toolbar.) Investigate the connection between the location of the mirror line and the figures by dragging point K or L with the reflection visible. 1) Where is the mirror line located when the reflection and original figure intersect at a point? 2) Where is the mirror line located when the reflection and original figure overlap? 3) Can the mirror line be moved in such a way that the reflection and original are the same figure (identical, overlapped)?
2 Part II Mirror Lines & Distance Click on the Preimage to Mirror and Image to Mirror buttons. Drag point K or L and observe the changes for distance measurement. 1) What do you notice about the distance from the mirror line to reflection and the mirror line to the original figure? 2) Why do you think this relationship exists? Provide a thorough explanation. Part III Reflections & Coordinate Geometry Click on the Preimage Coordinates and Image Coordinates buttons. Drag points K and L in order to make the reflection line on the y-axis. Observe changes in the coordinates; answer questions #1 and #2 below. Drag points K and L in order to make the reflection line on the x-axis. Observe changes in the coordinates; answer questions #3 and #4 below. 1) State the connection between the x and y coordinates for the preimage and reflection when the reflection line is the y-axis. Preimage (x, y) Image 2) What conjecture(s) can you make regarding the coordinates of a figure reflected over the y-axis? 3) State the connection between the x and y coordinates for the preimage figure and reflection when the reflection line is the x-axis. Preimage (x, y) Image 4) What conjecture(s) can you make regarding coordinates of a figure reflected over the x-axis?
3 Activity 2: Exploring Rotations Part I Identifying Rotations Explore the rotation of the given figure about point O. Change the angle of rotation (α) by clicking and dragging on the slider. Click on the Show Rotation button. Note the location of the rotation. Hide the rotation and repeat steps 1 and 2. Attempt to guess the location of the transformation. 1) At what degree measure(s) is the rotated figure identical to the preimage? 2) Describe the result of the following combinations: a) A 90 rotation followed by another 90 rotation. b) A 180 rotation followed by another 180 rotation. c) A 270 rotation followed by a 180 rotation. Part II Rotations & Coordinate Geometry Click on the Preimage Coordinates and Image Coordinates buttons. Click and drag the slider to make m α = 90 Observe changes in the coordinates and answer question #1 below. Click and drag the slider to make m α = 180 Observe changes in the coordinates and answer question #2 below. Click and drag the slider to make m α = 270 Observe changes in the coordinates and answer question #3 below. 1) What conjecture can you make regarding the coordinates of a figure rotated 90? 2) What conjecture can you make regarding the coordinates of a figure rotated 180? 3) What conjecture can you make regarding the coordinates of a figure rotated 270?
4 Activity 3: Exploring Translations Part I Identifying Translations Change the distance of the translation by clicking and dragging point Q. Click on the Show Translation button. Note the location of the translation. Hide the translation and repeat steps 1 and 2. Attempt to guess the location of the transformation. Click on the Show Length of Vector and Distance from Preimage to Image button. Drag point Q and observe the changes for distance measurement. 1) How does the distance between points P and Q compare to the distance between the points in the preimage and transformation? Explain your observation. 2) At what distance is the translated figure identical to the preimage? 3) What happens to points P and Q in the case of question #2? Part II Translations and Coordinate Geometry Click on the Coordinates of Preimage and Coordinates of Image buttons. Drag point Q to the origin of the coordinate plane. Observe changes in the coordinates and answer question #1 below. Drag point Q to the coordinate (-6, -6). Observe changes in the coordinates and answer question #2 below. 1) What change do you notice happens to the coordinates of the preimage and the figure translated horizontally? 2) What change do you notice happens to the coordinates of the preimage and the figure translated vertically?
5 Activity 4: Exploring Glide-Reflections Part I Identifying Glide-Reflections Change the distance of vector PQ by clicking and dragging point Q. Click on the Show Translation and Show Glide-Reflection buttons. Note the location of the transformation. Hide the translation and glide-reflection. Repeat steps 1 and 2; attempt to guess the location of the transformation. Click on the Show Length of Vector button. Also click on Distance Preimage, Distance Translation, and Distance Image buttons. Observe the distance measurements. 1) State the two transformations used to create a glide-reflection. 2) What transformation occurs when point P and Q overlap? 3) What conjecture can you make regarding the distance between the vertices of the figure and vector PQ? Part II Glide-Reflections and Coordinate Geometry Click on Coordinates Preimage, Coordinates Translation, and Coordinates Image buttons. Drag point Q to the origin of the coordinate plane. Observe the coordinates. 1) What conjecture can you make regarding the coordinates of the three figures?
6 Activity 5: Exploring Two Reflections with Parallel Lines Before showing the reflections, answer question #1 below. Select the Show Reflection #1 and Show Reflection #2 buttons. Drag point L to change the slope of the parallel lines. Answer question #3 below. 1) What do you believe will be the final product of the two reflections? 2) What is the composition of two reflections through parallel lines? Activity 6: Exploring Three Reflections with Parallel Lines Before showing the reflections, answer question #1 below. Select the Show Reflection #1 and Show Reflection #2 and Show Reflection #3 buttons. Drag point L to change the slope of the parallel lines. Answer questions #3 and 4 below. 1) What do you believe will be the final product of the three reflections? 2) What is the composition of three reflections through parallel lines? 4) Make a conjecture about the number of parallel lines and the composition of reflections.
7 Activity 7: Exploring Reflections with Intersecting Lines Before showing the reflections, answer question #1. Select the Show Reflection #1 and Show Reflection #2 buttons. Drag point L to change the slope of the mirror lines. Answer question #3 below. 1) What do you believe will be the final product of the two reflections? 2) What is the composition of two reflections through intersecting lines? Activity 8: Exploring Reflections with Concurrent Lines Before showing the reflections, answer question #1. Select the Show Reflection #1 and Show Reflection #2 and Show Reflection #3 buttons. Drag point L to change the slope of the mirror lines. Answer question #3 below. 1) What do you believe will be the final product of the three reflections? 2) What is the composition of three reflections through concurrent lines?
GeoGebra Transformation Activities
GeoGebra Transformation Activities Move New Point Line Between Two Points Perpendicular Line Circle w/ Center Through Point If needed: Go to www.geogebra.org Click on Download Click on GeoGebra WebStart
Quickstart for Desktop Version
Quickstart for Desktop Version What is GeoGebra? Dynamic Mathematics Software in one easy-to-use package For learning and teaching at all levels of education Joins interactive 2D and 3D geometry, algebra,
What's the Spin? - Discover Properties of Geometric Rotations
What's the Spin? - Discover Properties of Geometric Rotations Geometry Major Topics: Rotations and their relation to reflections NCTM Principles and Standards: Content Standards Geometry Apply transformations
http://school-maths.com Gerrit Stols
For more info and downloads go to: http://school-maths.com Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It
GeoGebra. 10 lessons. Gerrit Stols
GeoGebra in 10 lessons Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It was developed by Markus Hohenwarter
Basic Understandings
Activity: TEKS: Exploring Transformations Basic understandings. (5) Tools for geometric thinking. Techniques for working with spatial figures and their properties are essential to understanding underlying
Pro/ENGINEER Wildfire 4.0 Basic Design
Introduction Datum features are non-solid features used during the construction of other features. The most common datum features include planes, axes, coordinate systems, and curves. Datum features do
CATIA: Navigating the CATIA V5 environment. D. CHABLAT / S. CARO Damien.Chablat@irccyn.ec-nantes.fr
CATIA: Navigating the CATIA V5 environment D. CHABLAT / S. CARO Damien.Chablat@irccyn.ec-nantes.fr Standard Screen Layout 5 4 6 7 1 2 3 8 9 10 11 12 13 14 15 D. Chablat / S. Caro -- Institut de Recherche
Understand the Sketcher workbench of CATIA V5.
Chapter 1 Drawing Sketches in Learning Objectives the Sketcher Workbench-I After completing this chapter you will be able to: Understand the Sketcher workbench of CATIA V5. Start a new file in the Part
Chapter 9. Editing Features. Learning Objectives
Chapter 9 Editing Features Learning Objectives After completing this chapter, you will be able to: Edit features. Edit sketches of the sketch based features. Edit the sketch plane of the sketch based features.
3D-GIS in the Cloud USER MANUAL. August, 2014
3D-GIS in the Cloud USER MANUAL August, 2014 3D GIS in the Cloud User Manual August, 2014 Table of Contents 1. Quick Reference: Navigating and Exploring in the 3D GIS in the Cloud... 2 1.1 Using the Mouse...
CATIA Basic Concepts TABLE OF CONTENTS
TABLE OF CONTENTS Introduction...1 Manual Format...2 Log on/off procedures for Windows...3 To log on...3 To logoff...7 Assembly Design Screen...8 Part Design Screen...9 Pull-down Menus...10 Start...10
Teacher Page. 1. Reflect a figure with vertices across the x-axis. Find the coordinates of the new image.
Teacher Page Geometr / Da # 10 oordinate Geometr (5 min.) 9-.G.3.1 9-.G.3.2 9-.G.3.3 9-.G.3. Use rigid motions (compositions of reflections, translations and rotations) to determine whether two geometric
Wireframe and Surface
Wireframe and Surface Preface What's New Getting Started Basic Tasks Workbench Description Glossary Index Dassault Systèmes 1994-99. All rights reserved. Preface CATIA Version 5 Wireframe and Surface allows
The Use of Dynamic Geometry Software in the Teaching and Learning of Geometry through Transformations
The Use of Dynamic Geometry Software in the Teaching and Learning of Geometry through Transformations Dynamic geometry technology should be used to maximize student learning in geometry. Such technology
(Least Squares Investigation)
(Least Squares Investigation) o Open a new sketch. Select Preferences under the Edit menu. Select the Text Tab at the top. Uncheck both boxes under the title Show Labels Automatically o Create two points
Creating a Guided Tour with Google Earth
Creating a Guided Tour with Google Earth Before creating a tour, first orient yourself to basic Google Earth functions. To start, download Google Earth to your desktop. This is free through earth.google.com.
Pro/ENGINEER Wildfire 5.0 Introduction to Surface Modeling
Introduction Several advanced surface types are available as listed below. Variable Section Sweep Boundary Blend Section to Surfaces Blend Surface to Surface Blend A surface is created by sweeping a single
Lecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20
Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding
Tutorial 1: The Freehand Tools
UNC Charlotte Tutorial 1: The Freehand Tools In this tutorial you ll learn how to draw and construct geometric figures using Sketchpad s freehand construction tools. You ll also learn how to undo your
Geometry Unit 1 Geometric Transformations Lesson Plan (10 days)
Geometry Unit 1 Geometric Transformations Lesson Plan (10 days) Stage 1 Desired Results Learning Goal: Students will be able to draw, describe, specify the sequence, develop definitions, and predict the
Activity 6 Graphing Linear Equations
Activity 6 Graphing Linear Equations TEACHER NOTES Topic Area: Algebra NCTM Standard: Represent and analyze mathematical situations and structures using algebraic symbols Objective: The student will be
Geometer s Sketchpad. Discovering the incenter of a triangle
Geometer s Sketchpad Discovering the incenter of a triangle Name: Date: 1.) Open Geometer s Sketchpad (GSP 4.02) by double clicking the icon in the Start menu. The icon looks like this: 2.) Once the program
SketchUp Instructions
SketchUp Instructions Every architect needs to know how to use SketchUp! SketchUp is free from Google just Google it and download to your computer. You can do just about anything with it, but it is especially
Chapter 1. Creating Sketches in. the Sketch Mode-I. Evaluation chapter. Logon to www.cadcim.com for more details. Learning Objectives
Chapter 1 Creating Sketches in Learning Objectives the Sketch Mode-I After completing this chapter you will be able to: Use various tools to create a geometry. Dimension a sketch. Apply constraints to
SolidWorks Implementation Guides. Sketching Concepts
SolidWorks Implementation Guides Sketching Concepts Sketching in SolidWorks is the basis for creating features. Features are the basis for creating parts, which can be put together into assemblies. Sketch
Introduction to CATIA V5
Introduction to CATIA V5 Release 16 (A Hands-On Tutorial Approach) Kirstie Plantenberg University of Detroit Mercy SDC PUBLICATIONS Schroff Development Corporation www.schroff.com www.schroff-europe.com
Cabri Geometry Application User Guide
Cabri Geometry Application User Guide Preview of Geometry... 2 Learning the Basics... 3 Managing File Operations... 12 Setting Application Preferences... 14 Selecting and Moving Objects... 17 Deleting
Scientific Graphing in Excel 2010
Scientific Graphing in Excel 2010 When you start Excel, you will see the screen below. Various parts of the display are labelled in red, with arrows, to define the terms used in the remainder of this overview.
2. Select Point B and rotate it by 15 degrees. A new Point B' appears. 3. Drag each of the three points in turn.
In this activity you will use Sketchpad s Iterate command (on the Transform menu) to produce a spiral design. You ll also learn how to use parameters, and how to create animation action buttons for parameters.
Connecting Transformational Geometry and Transformations of Functions
Connecting Transformational Geometr and Transformations of Functions Introductor Statements and Assumptions Isometries are rigid transformations that preserve distance and angles and therefore shapes.
SolidWorks: Mirror, Revolve, and. Introduction to Robotics
SolidWorks: Mirror, Revolve, and Circular Pattern Introduction to Robotics Let s Review At this point we have learned the following: Extrude Boss/Base Extruded Cut Adding Relations and Dimensions Linear
Click on various options: Publications by Wizard Publications by Design Blank Publication
Click on various options: Publications by Wizard Publications by Design Blank Publication Select the Blank Publications Tab: Choose a blank full page Click on Create New Page Insert > Page Select the number
Example SECTION 13-1. X-AXIS - the horizontal number line. Y-AXIS - the vertical number line ORIGIN - the point where the x-axis and y-axis cross
CHAPTER 13 SECTION 13-1 Geometry and Algebra The Distance Formula COORDINATE PLANE consists of two perpendicular number lines, dividing the plane into four regions called quadrants X-AXIS - the horizontal
Introduction to the TI-Nspire CX
Introduction to the TI-Nspire CX Activity Overview: In this activity, you will become familiar with the layout of the TI-Nspire CX. Step 1: Locate the Touchpad. The Touchpad is used to navigate the cursor
Volumes of Revolution
Mathematics Volumes of Revolution About this Lesson This lesson provides students with a physical method to visualize -dimensional solids and a specific procedure to sketch a solid of revolution. Students
Tessellating with Regular Polygons
Tessellating with Regular Polygons You ve probably seen a floor tiled with square tiles. Squares make good tiles because they can cover a surface without any gaps or overlapping. This kind of tiling is
Investigating Relationships of Area and Perimeter in Similar Polygons
Investigating Relationships of Area and Perimeter in Similar Polygons Lesson Summary: This lesson investigates the relationships between the area and perimeter of similar polygons using geometry software.
Inking in MS Office 2013
VIRGINIA TECH Inking in MS Office 2013 Getting Started Guide Instructional Technology Team, College of Engineering Last Updated: Fall 2013 Email tabletteam@vt.edu if you need additional assistance after
Prentice Hall Connected Mathematics 2, 7th Grade Units 2009
Prentice Hall Connected Mathematics 2, 7th Grade Units 2009 Grade 7 C O R R E L A T E D T O from March 2009 Grade 7 Problem Solving Build new mathematical knowledge through problem solving. Solve problems
SpaceClaim Introduction Training Session. A SpaceClaim Support Document
SpaceClaim Introduction Training Session A SpaceClaim Support Document In this class we will walk through the basic tools used to create and modify models in SpaceClaim. Introduction We will focus on:
Sketcher. Preface What's New? Getting Started Basic Tasks Customizing Workbench Description Glossary Index
Sketcher Preface What's New? Getting Started Basic Tasks Customizing Workbench Description Glossary Index Dassault Systèmes 1994-99. All rights reserved. Preface CATIA Version 5 Sketcher application makes
A Correlation of Pearson Texas Geometry Digital, 2015
A Correlation of Pearson Texas Geometry Digital, 2015 To the Texas Essential Knowledge and Skills (TEKS) for Geometry, High School, and the Texas English Language Proficiency Standards (ELPS) Correlations
Geometry: Unit 1 Vocabulary TERM DEFINITION GEOMETRIC FIGURE. Cannot be defined by using other figures.
Geometry: Unit 1 Vocabulary 1.1 Undefined terms Cannot be defined by using other figures. Point A specific location. It has no dimension and is represented by a dot. Line Plane A connected straight path.
Canterbury Maps Quick Start - Drawing and Printing Tools
Canterbury Maps Canterbury Maps Quick Start - Drawing and Printing Tools Quick Start Guide Standard GIS Viewer 2 Canterbury Maps Quick Start - Drawing and Printing Tools Introduction This document will
Tip of the Week: Creating Geometry from AutoCAD Drawings
PTC Email Newsletter March 4, 2002 PTC Product Focus: Assembly Performance Extension (APX) Tip of the Week: Creating Geometry from AutoCAD Drawings Training: Upcoming Training Classes PTC Product Focus:
Volume. Revolutionary. Online. Cool. Scheduling
Volume Revolutionary. Online. Cool. Scheduling H E A L T H I N N O V A T I O N T E C H O N O L O G I E S, I N C EyeCodeRight v4.0 Tutorial EyeCodeRight 2717 Emerson Ave South Minneapolis, MN 877-370-6906
Optical Illusions Essay Angela Wall EMAT 6690
Optical Illusions Essay Angela Wall EMAT 6690! Optical illusions are images that are visually perceived differently than how they actually appear in reality. These images can be very entertaining, but
Using GeoGebra to create applets for visualization and exploration.
Handouts for ICTCM workshop on GeoGebra, March 2007 By Mike May, S.J. mikemaysj@gmail.com Using GeoGebra to create applets for visualization and exploration. Overview: I) We will start with a fast tour
Course Project Lab 3 - Creating a Logo (Illustrator)
Course Project Lab 3 - Creating a Logo (Illustrator) In this lab you will learn to use Adobe Illustrator to create a vector-based design logo. 1. Start Illustrator. Open the lizard.ai file via the File>Open
Project Setup and Data Management Tutorial
Project Setup and Heavy Construction Edition Version 1.20 Corporate Office Trimble Navigation Limited Engineering and Construction Division 5475 Kellenburger Road Dayton, Ohio 45424-1099 U.S.A. Phone:
Slopes and Equations of Lines with GeoGebra
Student Name(s): Introduction Today you are going to review how to calculate the slope of a line using 2 different methods. Then you will access the Internet and use a software tool for Geometry and Algebra
Math 241 Lines and Planes (Solutions) x = 3 3t. z = 1 t. x = 5 + t. z = 7 + 3t
Math 241 Lines and Planes (Solutions) The equations for planes P 1, P 2 and P are P 1 : x 2y + z = 7 P 2 : x 4y + 5z = 6 P : (x 5) 2(y 6) + (z 7) = 0 The equations for lines L 1, L 2, L, L 4 and L 5 are
Welcome to CorelDRAW, a comprehensive vector-based drawing and graphic-design program for the graphics professional.
Creating a logo Welcome to CorelDRAW, a comprehensive vector-based drawing and graphic-design program for the graphics professional. In this tutorial, you will create a logo for an imaginary coffee shop.
DWIN DGUS Applications Example
DWIN DGUS Applications Example 1 DGUS Key Functions Preview... 1 2 Application Examples... 3 2.1 Display, input and adjustment of parameters... 3 2.2 Display and adjust the curve... 4 2.3 Time display
Generative Drafting. Page 1 1997 2001 DASSAULT SYSTEMES. IBM Product Lifecycle Management Solutions / Dassault Systemes
Generative Drafting Page 1 Tutorial Objectives Description This Tutorial is an introduction to Generative Drafting. Message To show how CATIA V5 allows the user to automatically generate associative drafting
Lesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations
Math Buddies -Grade 4 13-1 Lesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations Goal: Identify congruent and noncongruent figures Recognize the congruence of plane
3D Viewer. user's manual 10017352_2
EN 3D Viewer user's manual 10017352_2 TABLE OF CONTENTS 1 SYSTEM REQUIREMENTS...1 2 STARTING PLANMECA 3D VIEWER...2 3 PLANMECA 3D VIEWER INTRODUCTION...3 3.1 Menu Toolbar... 4 4 EXPLORER...6 4.1 3D Volume
Kaplan Higher Education Seminar Student User Guide
Kaplan Higher Education Seminar Student User Guide Kaplan Higher Education and Professional Education R08.05.15 Table of Contents Getting Started... 1 Software Requirements... 1 Seminar Types... 1 Accessing
Introduction to Autodesk Inventor for F1 in Schools
Introduction to Autodesk Inventor for F1 in Schools F1 in Schools Race Car In this course you will be introduced to Autodesk Inventor, which is the centerpiece of Autodesk s digital prototyping strategy
Brava 5.3 X Client User
Brava 5.3 X Client User Guide Table Of Contents Help Contents...1 New Features in this Release...3 What is CSF?...5 Why CSF?...7 All Toolbars...9 Viewing Tools...11 Magnification Tools...11 Zoom and Pan
Graphic Designing with Transformed Functions
Math Objectives Students will be able to identify a restricted domain interval and use function translations and dilations to choose and position a portion of the graph accurately in the plane to match
GEOMETRY CONCEPT MAP. Suggested Sequence:
CONCEPT MAP GEOMETRY August 2011 Suggested Sequence: 1. Tools of Geometry 2. Reasoning and Proof 3. Parallel and Perpendicular Lines 4. Congruent Triangles 5. Relationships Within Triangles 6. Polygons
Spotfire v6 New Features. TIBCO Spotfire Delta Training Jumpstart
Spotfire v6 New Features TIBCO Spotfire Delta Training Jumpstart Map charts New map chart Layers control Navigation control Interaction mode control Scale Web map Creating a map chart Layers are added
Twelve. Figure 12.1: 3D Curved MPR Viewer Window
Twelve The 3D Curved MPR Viewer This Chapter describes how to visualize and reformat a 3D dataset in a Curved MPR plane: Curved Planar Reformation (CPR). The 3D Curved MPR Viewer is a window opened from
GeoGebra Help Official Manual 3.2
GeoGebra Help Official Manual 3.2 Markus Hohenwarter and Judith Hohenwarter www.geogebra.org GeoGebra Help 3.2 Last modified: April 22, 2009 Authors Markus Hohenwarter, markus@geogebra.org Judith Hohenwarter,
Tutorial: 3D Pipe Junction Using Hexa Meshing
Tutorial: 3D Pipe Junction Using Hexa Meshing Introduction In this tutorial, you will generate a mesh for a three-dimensional pipe junction. After checking the quality of the first mesh, you will create
Solving Equations Involving Parallel and Perpendicular Lines Examples
Solving Equations Involving Parallel and Perpendicular Lines Examples. The graphs of y = x, y = x, and y = x + are lines that have the same slope. They are parallel lines. Definition of Parallel Lines
Introduction to ANSYS ICEM CFD
Workshop 8.2 3D Pipe Junction 14.5 Release Introduction to ANSYS ICEM CFD 2012 ANSYS, Inc. April 1, 2013 1 Release 14.5 3D Pipe Junction 3D Pipe Junction This is a simple 4-way pipe intersection with two
This activity will show you how to draw graphs of algebraic functions in Excel.
This activity will show you how to draw graphs of algebraic functions in Excel. Open a new Excel workbook. This is Excel in Office 2007. You may not have used this version before but it is very much the
Vector Treasure Hunt Teacher s Guide
Vector Treasure Hunt Teacher s Guide 1.0 Summary Vector Treasure Hunt is the first activity to be done after the Pre-Test. This activity should take approximately 30 minutes. 2.0 Learning Goals Driving
Section 11.4: Equations of Lines and Planes
Section 11.4: Equations of Lines and Planes Definition: The line containing the point ( 0, 0, 0 ) and parallel to the vector v = A, B, C has parametric equations = 0 + At, = 0 + Bt, = 0 + Ct, where t R
Cricut Design Space Reference Guide & Glossary
Cricut Design Space Reference Guide & Glossary Top Menu Bar Grid On/Off button Panel Menu Side Menu Bar 1 Cricut logo click the Cricut logo at any time to return to the Cricut Design Space landing page.
Designing instructional tools by Flash MX ActionScript some examples to teach basic geometric concepts Yuan, Yuan Lee, Chun-Yi
Designing instructional tools by Flash MX ActionScript some examples to teach basic geometric concepts Yuan, Yuan Lee, Chun-Yi It is believed that technology will transform how we view teaching, and it
An introduction to 3D draughting & solid modelling using AutoCAD
An introduction to 3D draughting & solid modelling using AutoCAD Faculty of Technology University of Plymouth Drake Circus Plymouth PL4 8AA These notes are to be used in conjunction with the AutoCAD software
Lesson 18: Looking More Carefully at Parallel Lines
Student Outcomes Students learn to construct a line parallel to a given line through a point not on that line using a rotation by 180. They learn how to prove the alternate interior angles theorem using
PRE SERVICE TEACHERS' USAGE OF DYNAMIC MATHEMATICS SOFTWARE
PRE SERVICE TEACHERS' USAGE OF DYNAMIC MATHEMATICS SOFTWARE Mehmet BULUT Faculty of Gazi Education Gazi University Turkey mbulut@gazi.edu.tr Neslihan BULUT Faculty of Gazi Education Gazi University Turkey
Civil 3D 2009 New Features
Civil 3D 2009 New Features User Interface Workspaces and menus Menu Browser Using the large icon in the upper left corner of your screen, you can access all menus and also search for any command, recent
Interactive Voting System. www.ivsystem.nl. IVS-Basic IVS-Professional 4.4
Interactive Voting System www.ivsystem.nl IVS-Basic IVS-Professional 4.4 Manual IVS-Basic 4.4 IVS-Professional 4.4 1213 Interactive Voting System The Interactive Voting System (IVS ) is an interactive
with functions, expressions and equations which follow in units 3 and 4.
Grade 8 Overview View unit yearlong overview here The unit design was created in line with the areas of focus for grade 8 Mathematics as identified by the Common Core State Standards and the PARCC Model
CATIA Drafting TABLE OF CONTENTS
TABLE OF CONTENTS Introduction...1 Drafting...2 Drawing Screen...3 Pull-down Menus...4 File...4 Edit...5 View...6 Insert...7 Tools...8 Drafting Workbench...9 Views and Sheets...9 Dimensions and Annotations...10
I n t e r a c t i n g G a l a x i e s - Making Ellipticals Te a c h e r N o t e s
I n t e r a c t i n g G a l a x i e s - Making Ellipticals Te a c h e r N o t e s Author: Sarah Roberts Interacting - Making Ellipticals - Teacher Notes Making Ellipticals Making Ellipticals - Changing
GeoGebra Workshop for the Initial Teacher Training in Primary Education
GeoGebra Workshop for the Initial Teacher Training in Primary Education N. Ruiz natalia.ruiz@uam.es Facultad de Formación de Profesorado y Educación (Faculty of Education) Universidad Autónoma de Madrid
Creating Charts in Microsoft Excel A supplement to Chapter 5 of Quantitative Approaches in Business Studies
Creating Charts in Microsoft Excel A supplement to Chapter 5 of Quantitative Approaches in Business Studies Components of a Chart 1 Chart types 2 Data tables 4 The Chart Wizard 5 Column Charts 7 Line charts
CATIA Functional Tolerancing & Annotation TABLE OF CONTENTS
TABLE OF CONTENTS Introduction...1 Functional Tolerancing and Annotation...2 Pull-down Menus...3 Insert...3 Functional Tolerancing and Annotation Workbench...4 Bottom Toolbar Changes...5 3D Grid Toolbar...5
SolidWorks Tutorial 4 CANDLESTICK
SolidWorks Tutorial 4 CANDLESTICK Candlestick In this tutorial you will make a simple container and a candlestick out of sheetmetal. You will learn about working with sheet metal in SolidWorks. We will
CATIA for Design and Engineering. Version 5 Releases 14 & 15. David S. Kelley. Central Michigan University SDC
CATIA for Design and Engineering ersion 5 Releases 4 & 5 David S. Kelley Central Michigan University SDC PUBLICATIONS Schroff Development Corporation www.schroff.com www.schroff-europe.com TUTORIAL Extruded
Transformations: Rotations
Math Objectives Students will identify a rotation as an isometry, also called a congruence transformation. Students will identify which properties (side length, angle measure, perimeter, area, and orientation)
Vector Notation: AB represents the vector from point A to point B on a graph. The vector can be computed by B A.
1 Linear Transformations Prepared by: Robin Michelle King A transformation of an object is a change in position or dimension (or both) of the object. The resulting object after the transformation is called
Pennsylvania System of School Assessment
Pennsylvania System of School Assessment The Assessment Anchors, as defined by the Eligible Content, are organized into cohesive blueprints, each structured with a common labeling system that can be read
Graphing Quadratic Functions
Problem 1 The Parabola Examine the data in L 1 and L to the right. Let L 1 be the x- value and L be the y-values for a graph. 1. How are the x and y-values related? What pattern do you see? To enter the
Making Visio Diagrams Come Alive with Data
Making Visio Diagrams Come Alive with Data An Information Commons Workshop Making Visio Diagrams Come Alive with Data Page Workshop Why Add Data to A Diagram? Here are comparisons of a flow chart with
Determine whether the following lines intersect, are parallel, or skew. L 1 : x = 6t y = 1 + 9t z = 3t. x = 1 + 2s y = 4 3s z = s
Homework Solutions 5/20 10.5.17 Determine whether the following lines intersect, are parallel, or skew. L 1 : L 2 : x = 6t y = 1 + 9t z = 3t x = 1 + 2s y = 4 3s z = s A vector parallel to L 1 is 6, 9,
INTRODUCTION TO DESKTOP PUBLISHING
INTRODUCTION TO DESKTOP PUBLISHING Desktop publishing uses page layout software and a personal computer to combine text, type, drawings, and images on a page to create books, newsletters, marketing brochures,
Geometric Transformations
Geometric Transformations Definitions Def: f is a mapping (function) of a set A into a set B if for every element a of A there exists a unique element b of B that is paired with a; this pairing is denoted
Performance Based Learning and Assessment Task Triangles in Parallelograms I. ASSESSSMENT TASK OVERVIEW & PURPOSE: In this task, students will
Performance Based Learning and Assessment Task Triangles in Parallelograms I. ASSESSSMENT TASK OVERVIEW & PURPOSE: In this task, students will discover and prove the relationship between the triangles
ADOBE DREAMWEAVER CS3 TUTORIAL
ADOBE DREAMWEAVER CS3 TUTORIAL 1 TABLE OF CONTENTS I. GETTING S TARTED... 2 II. CREATING A WEBPAGE... 2 III. DESIGN AND LAYOUT... 3 IV. INSERTING AND USING TABLES... 4 A. WHY USE TABLES... 4 B. HOW TO
MODERN APPLICATIONS OF PYTHAGORAS S THEOREM
UNIT SIX MODERN APPLICATIONS OF PYTHAGORAS S THEOREM Coordinate Systems 124 Distance Formula 127 Midpoint Formula 131 SUMMARY 134 Exercises 135 UNIT SIX: 124 COORDINATE GEOMETRY Geometry, as presented
ClassLink ClassMate. Introduction to: Attendance A Teachers Guide
ClassLink ClassMate Introduction to: Attendance A Teachers Guide My Folders My Favorites Recently Viewed My Modules My Reports Teacher Daily Attendance Putting it all Together Reporting 2 www.classlink.com/products/classmate/