Primary Objectives. Content Standards (CCSS) Mathematical Practices (CCMP) Materials


 Damian Bradford
 2 years ago
 Views:
Transcription
1 TRANSFORMERS What transformations do smartphones use? Mathalicious 2015 lesson guide Smartphones have to handle some complex calculations to do all the amazing things they do. One of those things is moving and resizing all of the elements on the screen when a user interacts with the device. In this lesson, students identify and categorize the different transformations that occur when a user manipulates a smartphone screen. They also use on screen coordinates to calculate the results of zooming within an application and to decide whether ponying up for a larger screen is worth it. Primary Objectives Identify and describe geometric transformations that occur on smartphone screens Determine whether given transformations (or a sequence of transformations) produce figures that are congruent, similar, or neither Reason about and discuss how smartphones determine the center of dilation for zooming applications Given various points and scale factors in the coordinate plane, calculate the images of points under dilation Construct arguments about whether larger screens are worth the additional cost, based on dilations Content Standards (CCSS) Mathematical Practices (CCMP) Materials Grade 8 G.2, G.3, G.4 MP.3 Student handout LCD projector Computer speakers Before Beginning This lesson focuses on developing concepts and language surrounding transformations, congruence, and similarity, but assumes no prior knowledge of those terms or ideas. If students already possess the vocabulary to identify particular transformations (e.g., translation ), that s great, but all that s really required is the ability to describe transformations with intuitive language (e.g., sliding ).
2 Lesson Guide: TRANSFORMERS 2 Preview & Guiding Questions This lesson is all about the geometric transformations that smartphones use, so begin by showing the clip of people interacting with the iphone 5 and have students pay special attention to what s happening on the (small) screens. Students may have varying levels of personal experience with smartphones, so this will either give them the opportunity to observe some user interaction, or to look more closely at something they might take for granted on a daily basis. Once they ve seen the ad, ask students to describe some of the different ways you can interact with a smartphone, and what kinds of changes happen on the screen. Has anyone here ever used an iphone? What about another kind of smartphone? What parts of the device can you interact with on a phone like that? What sorts of gestures change things on the screen? What do you think is the coolest thing that the screen does? Why? Act One In Act One, students look at several examples of transformations that occur on smartphone screens. They describe in their own words what s happening in each scenario, and then they tie those intuitive concepts to more technical language, categorizing each transformation as a rotation, reflection, translation, or dilation. Students then discuss the concepts of congruence and similarity in terms of transformations, and discuss which on screen scenarios produce congruent or similar results. Finally, students see an example that results in figures that are neither congruent nor similar and discuss the reasons why. Act Two In Act Two, students focus on dilations. They learn about the center of dilation and use examples to hypothesize how smartphones determine the center of dilation when a user zooms in or out. Students learn that a smartphone screen is essentially a coordinate plane, and the phone uses transformations to map pixels from their starting points to their end points when the user changes the screen. They examine this phenomenon in the context of a map application and use coordinate transformations to calculate where given points will end up after zooming in or out. Lastly, students use their knowledge about dilations to discuss whether or not it s worth the additional cost to get a smartphone with a larger screen.
3 Lesson Guide: TRANSFORMERS 3 Act One: Decept icons 1 Smartphone operating systems Android and ios use various transformations. Watch the screen recordings of someone using an iphone, and describe what s happening. For each effect, which transformation(s) do you see: rotation, reflection (i.e. flipping), dilation (i.e. scaling), or translation (i.e. shifting)? Description All of the icons slide toward the left. The baseball stadium gets larger in the center of the screen. The entire image rotates 90 clockwise. The video rotates 90 counterclockwise and also gets larger. Transform. Translation Dilation Rotation Rotation and Dilation Explanation & Guiding Questions This opening question has two goals: (1) get students to describe geometric transformations in their own words, and (2) begin to tie mathematical terminology to student intuition. For instance, although the idea of shifting the icons to the left succinctly captures what s happening in the first video, students may not have the technical vocabulary to classify such a change as translation. To help with the move from intuitive to technical vocabulary, the question text includes both. That way students can see a simpler description associated with its appropriate term. Of course it s impossible for the question to include every way students might describe the transformations in the videos, so it might be useful to have students relate other descriptive words to the ones provided. For example, if a student describes the first video as sliding between screens, see whether she can associate that with the synonymous shifting, and finally with translation. In your own words, how would you describe what s happening to the screen/icons in the first video? Could you best describe what s happening as rotating, flipping, scaling, or shifting? So which word rotation, reflection, dilation, or translation best matches what you see? What about in the other videos? Deeper Understanding When the image or video gets larger, why doesn t it look distorted? (It must be getting scaled by the same factor in every direction.) Can you think of an example of when your phone would perform a reflection? (Answers will vary, but some photography apps will let you flip photos horizontally or vertically, resulting in reflections.)
4 Lesson Guide: TRANSFORMERS 4 2 After a transformation, an object is congruent to the original if it s the same shape and size as before. An object is similar if it s the same shape, but not necessarily the same size. Choose one iphone transformation, and focus on a single screen element (e.g. an app icon, the stadium, etc.). After the transformation, what s different about the element, what s the same, and is it an example of congruence, similarity, or neither? Answers will vary. Sample responses: In the first video everything stays the same size and orientation, but each icon s position moves to the left, so each figure is congruent to its starting figure. In the second video the stadium s position and orientation stay the same, but its size changes, so the ending image is similar to the starting image. In the third video the building s position and size stay the same, but its orientation changes, so the final image is congruent to the original. In the last video, the orientation and size change, but its position stays the same, which means the resulting video is similar to the original video. Explanation & Guiding Questions Congruence and similarity make the idea of geometric sameness precise. They are also intimately bound up with and often defined in terms of transformations. So one way to talk about congruence and similarity is to talk about how shapes or objects are the same and different after a transformation (or a sequence of transformations), compared to before. For instance, in the video showing the image of the U.S. Capitol being rotated, its orientation changes, but everything about its size and fundamental shape remains the same. In the video where the user zooms in on the baseball stadium, the image s orientation and shape are unchanged, but its size increases. The goal is for students to realize that any combination of rotations, translations, and reflections of a figure will lead to a congruent figure, since all of those transformations preserve both shape and size. Dilations, however, produce similar figures, since a dilation doesn t change a figure s fundamental shape, but can change its size. One point that you might want to clarify with students is that every set of congruent figures is also a set of similar figures. After all, if two figures are the same shape and size (congruent), then they must necessarily be the same shape (similar). The converse isn t true, however, since figures can have the same shape, but at various scales. To put it simply: all congruent figures are similar, but not all similar figures are congruent. In each video, what kinds of transformations do you see? What changes about the image? What stays the same? Which transformation(s) will produce figures that are congruent to the original? Why? Which transformations will produce figures that are similar to the original? Why? Can figures be both congruent and similar? Why or why not? Deeper Understanding If you double all the dimensions of an image in a dilation, the scale factor is 2. What scale factor would produce a congruent figure from the original? (1 or  1)
5 Lesson Guide: TRANSFORMERS 5 3 Watch a slow motion recording of someone closing an app. As the screen collapses back into its icon, what transformation(s) do you notice, and do you think this is an example of congruence or similarity? Explain. The full screen image shrinks in size until it ends up as an icon, which makes it look like a dilation. But it can t actually be a dilation, because the resulting icon is a different shape than the original image (it s much closer to being a square). That means the resulting icon is neither congruent nor similar to the starting image. Explanation & Guiding Questions This question is tricky, because a transformation that starts out looking a lot like a dilation turns out not to be. But it highlights an important point: dilations change a figure s size, but they have to preserve its shape in order to be called dilations. In the first few frames, that s exactly what seems to be happening: the map begins to reduce in size, but it s hard to tell whether it s the same shape or not. By the end of the animation, though, it s clear that we can t be dealing with a dilation, because the original map roughly matches the phone screen s dimensions, while the final icon is nearly square. The key point here is that dilations don t just scale figures, they scale figures uniformly in all directions. In this case, the horizontal and vertical dimensions of the rectangle are being scaled by different factors, so the icon is neither congruent nor similar to the screen at the beginning of the video. What changes about the image as the app closes? What stays the same? What kinds of transformations do you notice? Are the before and after images congruent? Why or why not? Are the before and after images similar? How can you tell? Do you notice anything different about this set of transformations compared to the earlier ones? Deeper Understanding Here we have an example of something that looks like a dilation, but doesn t produce a similar figure. What s different about the scaling that s happening in this case? (The shape is scaled by different horizontal and vertical factors as it shrinks.)
6 Lesson Guide: TRANSFORMERS 6 Act Two: More Than Meets the i 4 When you zoom in or out, the screen scales around a center of dilation; the object at this point stays in place, while everything around it moves inwards or outwards. Watch as someone zooms in and out using two fingers. In each case, draw the center of dilation. How do you think the smartphone determines where this center is? The phone appears to make the center of dilation the midpoint of the user s fingers. For instance, the tennis ball in the dog s mouth seems to stay in the same place on the screen, so that must be about the center of dilation. Explanation & Guiding Questions Every dilation has a center: the fixed point of the transformation around which everything else changes. So if students can spot the part of the image that appears to stay in place, then they can locate the center of dilation. In the first video, the center of the tennis ball in the dog s mouth doesn t look like it changes position, so that must be the center of dilation. In the second video, the center of the plane appears to stay in place, so that must be the center of dilation. In both cases, the center of dilation looks as though it s halfway between the user s fingers. If students have trouble locating the center of dilation at first, you could start by pointing out some places where it couldn t be. For example, the tip of the dog s tail ends up much closer to the top of the screen than where it started, so it clearly isn t the fixed point. In the plane video, the little patches of grass that end up on the left aren t even on the screen when the video begins, so nothing on that whole side of the screen could be the center. In the first video, what part of the picture seems to stay in the same place? What about the second video? In each video, can you pick out anything that definitely can t be the center of dilation? How do you know? Where does the center of dilation appear to be, relative to the user s fingers? Deeper Understanding Why do you think the phone uses the midpoint of the user s fingers as the center of dilation? (If you think about what would happen if you tried to stretch a little section of tablecloth between your fingers, everything would spread out from the point halfway between them. The phone is probably trying to mimic what happens when you stretch something in real life.)
7 Lesson Guide: TRANSFORMERS 7 5 A smartphone screen is basically a coordinate plane; each pixel represents a point. Imagine you re zooming in and out on a map using an iphone 5 and an iphone 6. If the center of dilation is at the origin, determine the new coordinates of objects A and B for each scale factor: 0.5x, 2x, and 3x. Based on this, do you think it was smart for Apple to release the larger iphone 6? Screen Resolution: pixels Screen Resolution: pixels Original Coordinate Point A = (204,120) Point B = ( 284, 16) Scale Factor 0.5x 2x 3x 0.5x 2x 3x New Coordinate (102,60) (408,240) (612,360) ( 142, 8) ( 568, 32) ( 852, 48) On Screen? iphone 5? iphone 6 Answers will vary, but the larger screen obviously means that users will be able to see more of what s going on when they zoom in or out. Explanation & Guiding Questions Earlier in the lesson when students were talking about similar figures, they discussed how images maintain their shape when they are dilated. That means that any scaling must be applied equally in all directions, otherwise things will get distorted. When performing dilations with coordinates, that means each point must be scaled (in this case from the center) by the same factor along the x axis and the y axis. Since the center here is (0, 0), that simply means multiplying both coordinates by the scale factor to obtain the new point. Students will see that points on the larger screen stay in frame longer than points on the smaller screen. However, smaller screens may have the edge when it comes to convenience. Which phone students prefer will probably vary, depending on how they weigh these competing factors. Why do dilations preserve the shape of an object? What do you think it means to scale a point equally in all directions? What happens to the point (100, 60) when it gets twice the distance from (0, 0)? What would happen to the map if you only multiplied the x or y coordinates by the scale factor? Deeper Understanding How would the situation change if the center of dilation were some other point besides (0, 0)? (You could no longer just multiply the coordinates by the scale factor.)
Module 3 Congruency can be used to solve realworld problems. What happens when you apply more than one transformation to
Transforming and Congruence *CISD Safety Net Standards: G.3C, G.4C Title Big Ideas/Enduring Understandings Module 1 Tools of geometry can be used to solve realworld problems. Variety of representations
More informationGeometry. Unit 1. Transforming and Congruence. Suggested Time Frame 1 st Six Weeks 22 Days
Geometry Unit 1 Transforming and Congruence Title Suggested Time Frame 1 st Six Weeks 22 Days Big Ideas/Enduring Understandings Module 1 Tools of geometry can be used to solve realworld problems. Variety
More informationTransformations: 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)
More informationWIN AT ANY COST? How should sports teams spend their m oney to win more games?
Mathalicious 2014 lesson guide WIN AT ANY COST? How should sports teams spend their m oney to win more games? Professional sports teams drop serious cash to try and secure the very best talent, and the
More informationTransformations Worksheet. How many units and in which direction were the xcoordinates of parallelogram ABCD moved? C. D.
Name: ate: 1. Parallelogram ABC was translated to parallelogram A B C. 2. A shape is shown below. Which shows this shape transformed by a flip? A. B. How many units and in which direction were the xcoordinates
More informationHow to Create Your Own Rubik s Cube Mosaic
How to Create Your Own Rubik s Cube Mosaic Using GIMP a Free Photo Editing Program Written by Corey Milner HighSchool Math Colorado Springs, CO Materials GIMP software download for free at http://www.gimp.org/
More informationGeometry Unit 11 Notes Transformational Geometry
Geometry Unit 11 Notes Transformational Geometry Preimage the original figure in the transformation of a figure in a plane. Image the new figure that results from the transformation of a figure in a plane.
More informationIntroduction to PowerPoint in the Classroom Victoria Cross & Barbara Sommer, TRC PC: Office XP
Introduction to PowerPoint in the Classroom Victoria Cross & Barbara Sommer, TRC PC: Office XP PowerPoint vocabulary Slide: An individual screen in a presentation. Presentation: The file you save to disk
More informationReflective Symmetry. Lesson Plan
Reflective Symmetry Lesson Plan Lesson Plan: Reflective Symmetry Symmetry School encourages learners to use their intuition to explore symmetrical puzzles. Through gameplay, learners are aided in developing
More informationMATH 310 SelfTest Transformation Geometry SOLUTIONS & COMMENTS 1. From class notes!
MATH 310 SelfTest Transformation Geometry SOLUTIONS & COMMENTS 1. From class notes! A transformat ion is a onetoone mapping of the point s of the plane to new points of the same plane. An isometry, also
More informationTarget Content Domain: Geometry, Similarity, Right Triangles, and Trigonometry (Geometry Conceptual Category)
About Illustrations: Illustrations of the Standards for Mathematical Practice (SMP) consist of several pieces, including a mathematics task, student dialogue, mathematical overview, teacher reflection
More informationStandards for Mathematical Practice in Kindergarten
Standards for Mathematical Practice in Kindergarten The Common Core State Standards for Mathematical Practice are expected to be integrated into every mathematics lesson for all students Grades K12. Below
More informationDiscovering Math: Exploring Geometry Teacher s Guide
Teacher s Guide Grade Level: 6 8 Curriculum Focus: Mathematics Lesson Duration: Three class periods Program Description Discovering Math: Exploring Geometry From methods of geometric construction and threedimensional
More information1. I have 4 sides. My opposite sides are equal. I have 4 right angles. Which shape am I?
Which Shape? This problem gives you the chance to: identify and describe shapes use clues to solve riddles Use shapes A, B, or C to solve the riddles. A B C 1. I have 4 sides. My opposite sides are equal.
More informationMath E301: Homework 4 Notes Due 10/5/09
Math E301: Homework 4 Notes Due 10/5/09 The notes for homeworks will vary. For some problems, I may give one solution, but there may be other ways to approach the problem. I will try to mention these
More informationVIDEO 1: BUILDING TEMPLATES IN HUBSPOT
VIDEO 1: BUILDING EMAIL TEMPLATES IN HUBSPOT Hello everyone and welcome to class two of the Design Certification. This is Building a World Class Email Template. Once again, this is Angela Hicks, your
More informationGEOMETRIC TRANSFORMATIONS ABACUS COEDITORS TABLE OF CONTENTS LINKS TO LITERATURE AND MANIPULATIVES. Volume 50 Number 3 March 2012
8 PAGE INSERT ELEMENTARY MATH O N T A R I O ASSOCIATION FOR M A T H E M A T I C S E D U C A T I O N Volume 50 Number 3 March 2012 GEOMETRIC TRANSFORMATIONS TABLE OF CONTENTS Abacus Editor Greetings......
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 00 national flags in the world. One of the largest is the flag of Brazil flown in Three Powers Plaza in Brasilia. This
More informationLesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations
Math Buddies Grade 4 131 Lesson #13 Congruence, Symmetry and Transformations: Translations, Reflections, and Rotations Goal: Identify congruent and noncongruent figures Recognize the congruence of plane
More informationPythagorean Theorem. Overview. Grade 8 Mathematics, Quarter 3, Unit 3.1. Number of instructional days: 15 (1 day = minutes) Essential questions
Grade 8 Mathematics, Quarter 3, Unit 3.1 Pythagorean Theorem Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Prove the Pythagorean Theorem. Given three side lengths,
More informationGeometry Using Manipulatives & Activities
1.1.5 What shapes can you find? Building a Kaleidoscope Today you will learn about geometric shapes as you study how a kaleidoscope works. 138. BUILDING A KALEIDOSCOPE How does a kaleidoscope create the
More informationSFUSD Mathematics Core Curriculum Development Project
1 SFUSD Mathematics Core Curriculum Development Project 2014 2015 Creating meaningful transformation in mathematics education Developing learners who are independent, assertive constructors of their own
More informationWhat is Green Screen by Do Ink?
What is Green Screen by Do Ink? You know what a green screen effect is, right? It s used in the movies to make it look like the actors have landed on an alien planet, and it s used on TV to make it look
More informationUnit 6 Geometry: Constructing Triangles and Scale Drawings
Unit 6 Geometry: Constructing Triangles and Scale Drawings Introduction In this unit, students will construct triangles from three measures of sides and/or angles, and will decide whether given conditions
More informationActivities Grades K 2 THE FOURSQUARE QUILT. Put triangles together to make patterns.
Activities Grades K 2 www.exploratorium.edu/geometryplayground/activities THE FOURSQUARE QUILT Put triangles together to make patterns. [45 minutes] Materials: FourSquare Quilt Template (attached) Triangle
More informationPowerPoint Contents 1.0 POWERPOINT INTRODUCTION POWERPOINT TERMS STARTING POWERPOINT POWERPOINT S OPENING WINDOW 4
Contents PowerPoint 2003 1.0 POWERPOINT INTRODUCTION 2 2.0 POWERPOINT TERMS 2 3.0 STARTING POWERPOINT 3 4.0 POWERPOINT S OPENING WINDOW 4 5.0 CREATE A NEW PRESENTATION 5 6.0 EDITING SLIDES 7 7.0 USING
More information0.75 75% ! 3 40% 0.65 65% Percent Cards. This problem gives you the chance to: relate fractions, decimals and percents
Percent Cards This problem gives you the chance to: relate fractions, decimals and percents Mrs. Lopez makes sets of cards for her math class. All the cards in a set have the same value. Set A 3 4 0.75
More informationState whether the figure appears to have line symmetry. Write yes or no. If so, copy the figure, draw all lines of symmetry, and state their number.
State whether the figure appears to have line symmetry. Write yes or no. If so, copy the figure, draw all lines of symmetry, and state their number. esolutions Manual  Powered by Cognero Page 1 1. A figure
More informationAXIS Mobile Viewer for Hosted Video
AXIS Hosted Video USER MANUAL AXIS Mobile Viewer for Hosted Video AXIS Mobile Viewer for Hosted Video Created: November 07, 2014 Last updated: November 19, 2014 Rev: 0.3 TABLE OF CONTENTS SYSTEM REQUIREMENTS
More informationSection 12.1 Translations and Rotations
Section 12.1 Translations and Rotations Any rigid motion that preserves length or distance is an isometry (meaning equal measure ). In this section, we will investigate two types of isometries: translations
More informationGeometric Transformations Grade Four
Ohio Standards Connection Geometry and Spatial Sense Benchmark I Describe, identify and model reflections, rotations and translations, using physical materials. Indicator 7 Identify, describe and use reflections
More informationPSS 27.2 The Electric Field of a Continuous Distribution of Charge
Chapter 27 Solutions PSS 27.2 The Electric Field of a Continuous Distribution of Charge Description: Knight ProblemSolving Strategy 27.2 The Electric Field of a Continuous Distribution of Charge is illustrated.
More informationStandard Form of Quadratic Functions
Math Objectives Students will be able to predict how a specific change in the value of a will affect the shape of the graph of the quadratic ax bxc. Students will be able to predict how a specific change
More informationProblem of the Month The Shape of Things
Problem of the Month The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards:
More informationUnit 2 Module 3: Generating Examples and Nonexamples
Unit 2 Module 3: Generating Examples and Nonexamples Section 1 Slide 1 Title Slide Welcome to the third module in the Vocabulary Instructional Routines unit, Generating Examples and Nonexamples. Slide
More informationFinding Parallelogram Vertices
About Illustrations: Illustrations of the Standards for Mathematical Practice (SMP) consist of several pieces, including a mathematics task, student dialogue, mathematical overview, teacher reflection
More informationMA.7.G.4.2 Predict the results of transformations and draw transformed figures with and without the coordinate plane.
MA.7.G.4.2 Predict the results of transformations and draw transformed figures with and without the coordinate plane. Symmetry When you can fold a figure in half, with both sides congruent, the fold line
More information1 st Grade Mathematics
1 st Grade Mathematics Unit # 5: Composing and Partitioning Shapes/Time Pacing: 15 days Unit Overview 1 In lessons 13, students identify the defining parts, or attributes, of two and threedimensional
More informationThe Geometer s Sketchpad: NonEuclidean Geometry & The Poincaré Disk
The Geometer s Sketchpad: NonEuclidean Geometry & The Poincaré Disk Nicholas Jackiw njackiw@kcptech.com KCP Technologies, Inc. ICTMT11 2013 Bari Overview. The study of hyperbolic geometry and noneuclidean
More informationRESIZE SENSE User Guide. VeprIT.
RESIZE SENSE User Guide VeprIT http://veprit.com support@veprit.com Based on version 1.6.2. January 11, 2014 VeprIT  Resize Sense User Guide Page 1 Contents 1 Main Concepts 3 2 User Interface Overview
More informationMicrosoft PowerPoint 2013 Part 2: Notes, Links, & Graphics. Choosing a Design. Adding Content Exercise. Inserting Screen Shots.
Microsoft PowerPoint 2013 Part 2: Notes, Links, & Graphics Choosing a Design Open PowerPoint. Click on Blank Presentation. Click on the Design tab. Click on the design tab of your choice. Adding Content
More informationPermutation Groups. Rubik s Cube
Permutation Groups and Rubik s Cube Tom Davis tomrdavis@earthlink.net May 6, 2000 Abstract In this paper we ll discuss permutations (rearrangements of objects), how to combine them, and how to construct
More informationDilation Teacher Notes
Dilation Teacher Notes Teacher demonstrations using GeoGebra are essential at the beginning of this unit. 1. Dilation The definition of a dilation is more complicated than the definitions of the isometries.
More informationSession 9 Solids. congruent regular polygon vertex. cross section edge face net Platonic solid polyhedron
Key Terms for This Session Session 9 Solids Previously Introduced congruent regular polygon vertex New in This Session cross section edge face net Platonic solid polyhedron Introduction In this session,
More informationLESSON TITLE: Math in Special Effects (by Deborah L. Ives, Ed.D)
LESSON TITLE: Math in Special Effects (by Deborah L. Ives, Ed.D) GRADE LEVEL/COURSE: Grades 710 Algebra TIME ALLOTMENT: Two 45minute class periods OVERVIEW Using video segments and web interactives from
More informationAbove: Lanscape Orientation 3:2 Ratio
Aspect Ratios in Photography Although we now live in a digital age where most images are viewed on a computer screen rather than in print, we must always acknowledge that for a single photograph, it can
More informationWIDESCREEN PRESENTATON CONTENTS
Tips for creating a presentation in widescreen format PRESENTING IN WIDESCREEN FORMAT WIDESCREEN PRESENTATON CONTENTS WHAT IS ASPECT RATIO? SO WHAT IS THE DIFFERENCE? WHAT ARE THE ADVANTAGES OF USING 16:9
More informationUnit 8 Grade 7 Similarity, Congruency, and Transformations
Unit 8 Grade 7 Similarity, Congruency, and Transformations Lesson Outline BIG PICTURE Students will: understand location using four quadrants of the coordinate axis; investigate and apply transformations
More informationXbox Xponential Lesson by Mathalicious; Annotation by Student Achievement Partners
Xbox Xponential Lesson by Mathalicious; Annotation by Student Achievement Partners GRADE LEVEL High School IN THE STANDARDS FIF.C.8b, FBF.A.1a, FLE.A.2, FLE.B.5, SID.B.6a WHAT WE LIKE ABOUT THIS LESSON
More informationCabri 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
More informationMODELING A CONSTELLATION IN TWO AND THREE DIMENSIONS grades 4 6
MODELING A CONSTELLATION IN TWO AND THREE DIMENSIONS grades 4 6 Objectives Thinking and acting like a scientist: By building an accurate threedimensional model of a constellation, students will practice
More informationCREATING A CUBEMAP AND CUBE FACES FOR USE IN PHOENIX RC SCENERY CREATION
TUTORIAL 2 CREATING A CUBEMAP AND CUBE FACES FOR USE IN PHOENIX RC SCENERY CREATION This document is copyrighted to the author and may only be reproduced or copied with the author s consent. It is free
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 00 national flags in the world. One of the largest is the flag of Brazil flown in Three Powers Plaza in Brasilia. This
More informationCOORDINATE GEOMETRY AND TRANSFORMATIONS
COORDINATE GEOMETRY AND TRANSFORMATIONS i 2 t 2 Final Project 5Day Unit Plan 8 th Grade Math Lab Helen Roseler December 1, 2003 1 Preface Math Lab is an additional math class designed to deliver Academic
More informationA Teacher Resource Package for the Primary Grades
A Teacher Resource Package for the Primary Grades Notes for Teachers: These are intended to be a starting point to help your class apply what they have learned in the Geometry and Spatial Sense strand
More informationActivities Grades 3 5 ROTATING STRING SHAPES. Make multisided shapes with string. [45 minutes]
Activities Grades 3 5 www.exploratorium.edu/geometryplayground/activities ROTATING STRING SHAPES Make multisided shapes with string. [45 minutes] Materials: String, about 2.5 meters (8 feet) long, tied
More informationBLOSSOMS MODULE ARE RANDOM TRIANGLES ACUTE OR OBTUSE? By Gilbert Strang Professor of Mathematics Massachusetts Institute of Technology
BLOSSOMS MODULE ARE RANDOM TRIANGLES ACUTE OR OBTUSE? By Gilbert Strang Professor of Mathematics Massachusetts Institute of Technology Hi! I m Gilbert Strang. I teach math at MIT. Mostly what I teach is
More information4a.2 Digital Media Fundamentals
4a.1 With film photography, most people s creative involvement with their photos stops with clicking the shutter. With digital photography, the equivalent moment to dropping your film off for developing
More informationMobile Remote Monitoring Using QS View for ios and Android
Mobile Remote Monitoring Using QS View for ios and Android Setup and Users Guide for Mobile Remote Monitoring QS Series Security DVRs on the iphone and ipad as well as Android devices. ENABLING MOBILE
More informationGolden Tee Fundamental Principles of Alignment
Golden Tee Fundamental Principles of Alignment Introduction The biggest difference between Golden Tee and real golf is something very basic  Alignment. YES NO YES NO YES The game gives us superpowers
More informationascending order decimal denominator descending order Numbers listed from largest to smallest equivalent fraction greater than or equal to SOL 7.
SOL 7.1 ascending order Numbers listed in order from smallest to largest decimal The numbers in the base 10 number system, having one or more places to the right of a decimal point denominator The bottom
More informationSolving Simultaneous Equations and Matrices
Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering
More informationSwapping Units 1) X = = 2) X = = 3) X = = 4) X = = Name: Period: MULTIPLYING BY ONE
Name: Period: Swapping Units Swap Meet is a game about trading one thing for another. In the game, we are not trying to end up with stuff that is worth MORE than what we started with. Instead, we simply
More informationBASICS OF BETTER UNDERWATER PHOTOGRAPHY TIPS FOR SHOOTING VIDEO
BASICS OF BETTER UNDERWATER PHOTOGRAPHY TIPS FOR SHOOTING VIDEO MOTION CHANGING YOUR APPROACH Some scenes that don t make good still photos can actually make great video! Examples: You just can t get close
More informationSession 6 Area. area midline similar figures
Key Terms in This Session Session 6 Area Previously Introduced scale factor New in This Session area midline similar figures Introduction Area is a measure of how much surface is covered by a particular
More informationDrawing Lines of Symmetry Grade Three
Ohio Standards Connection Geometry and Spatial Sense Benchmark H Identify and describe line and rotational symmetry in twodimensional shapes and designs. Indicator 4 Draw lines of symmetry to verify symmetrical
More informationAwesome PowerPoint Tricks for Effective Presentations
Awesome PowerPoint Tricks for Effective Presentations Visualization Identify all the individual elements that could be represented by a single object, icon, or picture Role Person Company X Y Z Graph X
More information1.16 Factors, Multiples, Prime Numbers and Divisibility
1.16 Factors, Multiples, Prime Numbers and Divisibility Factor an integer that goes into another integer exactly without any remainder. Need to be able to find them all for a particular integer it s usually
More informationPocantico Hills School District Grade 1 Math Curriculum Draft
Pocantico Hills School District Grade 1 Math Curriculum Draft Patterns /Number Sense/Statistics Content Strands: Performance Indicators 1.A.1 Determine and discuss patterns in arithmetic (what comes next
More informationBefore We Begin. Feel free to interrupt and ask questions The only dumb question is the one that you don t ask
Powerpoint 2003 Before We Begin Feel free to interrupt and ask questions The only dumb question is the one that you don t ask For Next Week Create an outline for a PP presentation containing 515 slides
More informationintroduction to waves on page 3.) This animation can be created with Microsoft PowerPoint (PC) or Apple Keynote (Mac).
Lesson Plan 22 Making Waves In deep water,* every water molecule moves in a circular orbit and returns to its starting position as a wave passes by. In this activity, students build a simple computer model
More informationWelcome to the Quick Start Guide for TrialPad 2.0, the leading trial presentation and legal file management app for the ipad!
trialpad.com facebook.com/trialpad twitter.com/trialpad Welcome to the Quick Start Guide for TrialPad 2.0, the leading trial presentation and legal file management app for the ipad! We re very excited
More informationSIXTH SENSE TECHNOLOGY
1 SIXTH SENSE TECHNOLOGY INTRODUCTION 1. 'Sixth Sense' is a wearable gestural interface that augments the physical world around us with digital Information and lets us use natural hand gestures to interact
More informationSketchUp 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
More informationTEACHER NOTES MATH NSPIRED
Math Objectives Students will predict and identify the shapes of twodimensional crosssections are formed when threedimensional figures are cut by horizontal and vertical planes. Students will draw,
More informationBaseball Classroom Activity
Baseball Classroom Activity The Classroom Activity introduces students to the context of a performance task, so they are not disadvantaged in demonstrating the skills the task intends to assess. Contextual
More informationPerformance Assessment Task Parking Cars Grade 3. Common Core State Standards Math  Content Standards
Performance Assessment Task Parking Cars Grade 3 This task challenges a student to use their understanding of scale to read and interpret data in a bar graph. A student must be able to use knowledge of
More informationTEACHER S GUIDE TO RUSH HOUR
Using Puzzles to Teach Problem Solving TEACHER S GUIDE TO RUSH HOUR Includes Rush Hour 2, 3, 4, Rush Hour Jr., Railroad Rush Hour and Safari Rush Hour BENEFITS Rush Hour is a sliding piece puzzle that
More informationCARMEL CLAY SCHOOLS MATHEMATICS CURRICULUM
GRADE 4 Standard 1 Number Sense Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers 1 and decimals relate to simple fractions. 4.1.1 Read and write
More informationPhotoshop Image Editing
Photoshop Image Editing Opening a file: File Menu > Open Photoshop Workspace A: Menus B: Application Bar view options, etc. C: Options bar controls specific to the tool you are using at the time. D:
More informationVueZone Mobile for iphone/itouch. User Guide Version 2.1.5
VueZone Mobile for iphone/itouch User Guide Version 2.1.5 Contents The VueZone personal video network and your smartphone are a powerful combination. With VueZone Mobile apps, you can take remote video
More informationPowerpoint Guide Office 2000
Powerpoint Guide Office 2000 Powerpoint is a presentation tool, combining great visual effects, sound, videos and motion. It will allow you to make an otherwise dry lesson/presentation come to life. GETTING
More informationLearning to Juggle and Picking the Right Balls (AKA adapting organizations for the future of digital publishing)
Learning to Juggle and Picking the Right Balls (AKA adapting organizations for the future of digital publishing) Liisa McCloyKelley VP, Director ebook Production Strategy & Operations 1 If We ve Learned
More informationSTRAND: Number and Operations Algebra Geometry Measurement Data Analysis and Probability STANDARD:
how August/September Demonstrate an understanding of the placevalue structure of the baseten number system by; (a) counting with understanding and recognizing how many in sets of objects up to 50, (b)
More informationAUDACITY SOUND EDITOR SOFTWARE A USER GUIDE FOR AUDIOVISUAL WORKERS
AUDACITY SOUND EDITOR SOFTWARE A USER GUIDE FOR AUDIOVISUAL WORKERS Prepared by Peter Appleton Copyright 2008 All illustrations in this guide were created using Audacity v1.2.6 Version 0.5 Page 1 of 18
More informationGrade 7 Mathematics. Unit 8. Geometry. Estimated Time: 18 Hours
Grade 7 Mathematics Geometry Estimated Time: 18 Hours [C] Communication [CN] Connections [ME] Mental Mathematics and Estimation [PS] Problem Solving [R] Reasoning [T] Technology [V] Visualization Grade
More informationGetting Started With Adobe Photoshop CS3
Getting Started With Adobe Photoshop CS3 Pictures in photoshop are measured in inches orpixels. A pixel is one screen dot. If your work is sized at (W) 300 pixels by (H) 200 pixels, it means there are
More informationGeorgia Standards of Excellence Curriculum Frameworks. Mathematics. GSE Geometry. Unit 1: Transformations in the Coordinate Plane
Georgia Standards of Excellence Curriculum Frameworks GSE Geometry Mathematics Unit 1: Transformations in the Coordinate Plane Unit 1 Transformations in the Coordinate Plane Table of Contents OVERVIEW...
More informationEmbroidering is fun, but creating your own designs provides an even more exciting way to unleash your creativity!
September 2013 Embroidering is fun, but creating your own designs provides an even more exciting way to unleash your creativity! Fall is here and the kids have gone back to school, so it s a perfect time
More informationMathematics Kindergarten
Mathematics Kindergarten In Kindergarten, instructional time should focus on two critical areas: (1) representing, relating, and operating on whole numbers, initially with sets of objects; (2) describing
More informationTip: if you type up your narration, then you can use it as part of your captioning. Captioning keeps you in line with the 508 Disabilities Act.
Launching Camtasia Open Camtasia from the Programs folder. The default screen to appear is the Camtasia Studio Start Up. This splash screen will appear every time you launch Camtasia unless you deselect
More informationGraphing Quadratic Functions
About the Lesson In this activity, students plot data and use the Transformation Graphing app to explore the parent function y = x. As a result, students will: Graph a quadratic function y = ax + bx +
More information1.4 Exponential and logarithm graphs.
1.4 Exponential and logarithm graphs. Example 1. Recall that b = 2 a if and only if a = log 2 (b) That tells us that the functions f(x) = 2 x and g(x) = log 2 (x) are inverse functions. It also tells us
More informationFor example, estimate the population of the United States as 3 times 10⁸ and the
CCSS: Mathematics The Number System CCSS: Grade 8 8.NS.A. Know that there are numbers that are not rational, and approximate them by rational numbers. 8.NS.A.1. Understand informally that every number
More informationUsing Microsoft Word. Working With Objects
Using Microsoft Word Many Word documents will require elements that were created in programs other than Word, such as the picture to the right. Nontext elements in a document are referred to as Objects
More informationCombinatorics: The Fine Art of Counting
Combinatorics: The Fine Art of Counting Week 7 Lecture Notes Discrete Probability Continued Note Binomial coefficients are written horizontally. The symbol ~ is used to mean approximately equal. The Bernoulli
More informationFROM THE SPECIFIC TO THE GENERAL
CONNECT: Algebra FROM THE SPECIFIC TO THE GENERAL How do you react when you see the word Algebra? Many people find the concept of Algebra difficult, so if you are one of them, please relax, as you have
More informationManyCam 4.0 for Windows. User Guide
ManyCam 4.0 for Windows User Guide Table of Contents ManyCam the Ultimate Webcam Utility... 3 ManyCam Pro features... 3 Installation... 3 Tray Icon and Menu... 4 Main ManyCam window... 4 Main Live window...
More informationGrowing Patterns and Sequences
Growing Patterns and Sequences Reporting Category Topic Primary SOL Patterns, Functions, and Algebra Identifying and extending arithmetic and geometric sequences 6.17 The student will identify and extend
More informationIsometries of the Plane Teacher s Notes
Isometries of the Plane Teacher s Notes Henri Picciotto This unit is intended to be consistent with the Common Core State Standards for Mathematics (CCSSM), but it does go quite a bit further than is required
More information