Section 5: Models and Representations
|
|
- Gilbert Atkinson
- 5 years ago
- Views:
Transcription
1 Section 5: Models and Representations Next comes one of the most important parts of learning to do math: building models. A model is something that makes the experience present to us. Since the experience is present again when we have the model, we say the experience is re-present. In other words, the model is a representation. We are interested in what kind of experience you had in trying to solve the puzzle. We want to give you a chance to express your ideas of what a representation of solving the puzzle could be. It doesn t matter what form you choose. If you like to draw, draw a picture that represents solving the puzzle. If you like music write a song. Or come up with your own ideas for a way to represent solving the puzzle. 28
2 Exercise 5.1. Each team should decide how they are going to represent solving the puzzle. Create your team s representation and present it to the class. Each of the models you and your classmates created has properties that reflect aspects of the experience of walking around your city attempting to get everyone to the same building. Later in this material we will discussthe representations which are used by the research mathematicians who study this puzzle. First of all, it is important to understand that this puzzle, or problem, is currently being studied at universities around the world. This is probably the first example that you have seen of a mathematics problem that is still being studied. In fact, no one knew the solution of the problem for almost 40 years. The problem was finally solved in 2007 by Professor Trahtman at Bar-Ilan University. What problem? For obvious reasons, the puzzle we have been discussing is called the Road Coloring Problem. 29
3 You may be saying to yourself, But wait, we ve also solved the problem a bunch of times already! In one sense, you are right. You and your classmates have found solutions for specific cities with three or four buildings. But to solve the Road Coloring Problem, Professor Trahtman had to prove that for every city there is a way to color its roads so that a set of directions can be found to get everyone to the same building. He had to show it works for cities with 100 buildings, or 1,000,000 buildings, or 1,000,000,000,000,000 buildings. He also had to prove that his technique works (Later in your high school careers, we will discuss what it means to prove something) You can go to the website to find out the latest news on the problem. 30
4 Let s explore this idea of a mathematical representation a little more. This idea is one of the most important concepts we will talk about in this class. A good mathematical representation finds the important features of a problem that need to be preserved and builds a model of them. For our cities, the features that are important are the buildings and the roads. This leads to the model called a directed graph. This type of model looks so much like the original city, it is usually the first representation most people build. For example, we could build the following city: The numbered circles represent the buildings and the one-way roads are shown as arrows. By representing the problem in this manner, we have concentrated on the key parts of our city. In mathematics, the circles are called vertices (one circle is a vertex) and the arrows are called directed edges. Let s start a dictionary of terms we ll use for the road coloring problem. You will find the dictionary at the back of these pages. 31
5 Whenever we use a new term that should go in the dictionary you will see this picture. Our first three dictionary terms are: vertex, directed edge, and directed graph Now that we have our directed graph representation of this city, let s begin to run some experiments. You see math, in many ways, is like other sciences. We need to perform experiments on our models to completely understand their properties. But the experiments in math are not done in laboratories. The experiments in math are thought-experiments. To do mathematics you don t need expensive equipment. Mathematics mainly requires careful observation and imagination. The second step of the puzzle involved coloring the roads of our city. Here is one possible way to color roads of the city on the last page. 32
6 Edge-colored directed graph You may have already experimented with this city and this particular way to color the roads. If someone in your class built this city during your experiments, they may have colored it differently, but let s use this as an example. We will refer to the directed graph of a city that is correctly colored as a city map. Now we ll carefully observe what happens when the command Blue is called out. We ll put names in each of the buildings to represent the people walking around the city. Candace Marcus Miguel When the command Blue is called out, here is what happens to the people in the city. a Candice leaves from building 1 and goes to building 2 a Miguel leaves from building 2 and goes to building 1 a Marcus leaves from building 3 and goes to building 2 33
7 Next, when the command Red is called here is what happens to the people in the city. a Candice leaves from building 2 and goes to building 3 a Miguel leaves from building 1 and goes to building 3 a Marcus leaves from building 2 and goes to building 3 We ve done it! The set of directions Blue - Red gets everyone to building 3. Mathematicians refer to a set of directions that solved the puzzle as synchronizing. (When your team answered exercise 4.4, did they decide on a different name?) The word synchronizing comes from the Greek language and means same time. [ Syn means same, like in synonym; chronos means time like in chronology.] For the exercises that follow choose some names of your classmates and place them in the vertices that represent the buildings of the three and four building cities your classes designed. Then record their movements around the city as the commands are called. 34
8 Exercise 5.2 Name Teacher Date Directions: (1) Draw in the colored directed edges of the city map for the 3 building city your team designed (2) Put the names of the players in their starting positions in the circles to the left. (3) In the boxes below, show how each player moved after the command was called by placing their names in the circles where they moved. Remember, all the player should move 1st command called: road 2nd command called: road 35
9 Exercise 5.2 Name Teacher Date 3rd command called: road 4th command called: road 5th command called: road 36
10 Exercise 5.3 Name Teacher Date Directions: (1) Draw in the colored directed edges of the city map of the 4 building your team designed (2) Put the names of the players in their starting positions in the circles to the left. (3) In the boxes below, show how each player moved after the command was called by placing their names in the circles where they moved. Remember, all the player should move at the same time when the command is called. 1st command called: road 2nd command called: road 37
11 Exercise 5.3 Name Teacher Date 3rd command called: road 4th command called: road 5th command called: road 38
Fibonacci Numbers ANSWERS Lesson 1 of 10, work individually or in pairs
Lesson 1 of 10, work individually or in pairs In 1202, the mathematician Leonardo Pisano Fibonacci (pronounced fi-buh-nah-chee) published a book with the famous Fibonacci sequence in it. (A sequence is
More informationThis chapter gives you everything you
Chapter 1 One, Two, Let s Sudoku In This Chapter Tackling the basic sudoku rules Solving squares Figuring out your options This chapter gives you everything you need to know to solve the three different
More informationKeeping secrets secret
Keeping s One of the most important concerns with using modern technology is how to keep your s. For instance, you wouldn t want anyone to intercept your emails and read them or to listen to your mobile
More informationMath 152: Applicable Mathematics and Computing
Math 152: Applicable Mathematics and Computing May 8, 2017 May 8, 2017 1 / 15 Extensive Form: Overview We have been studying the strategic form of a game: we considered only a player s overall strategy,
More information476 April 2015 teaching children mathematics Vol. 21, No. 8
476 April 2015 teaching children mathematics Vol. 21, No. 8 www.nctm.org Copyright 2015 The National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved. This material may not be
More informationGraph Theory: The Four Color Theorem
Graph Theory: The Four Color Theorem 9 April 2014 4 Color Theorem 9 April 2014 1/30 Today we are going to investigate the issue of coloring maps and how many colors are required. We ll see that this is
More informationThe Game of SET! (Solutions)
The Game of SET! (Solutions) Written by: David J. Bruce The Madison Math Circle is an outreach organization seeking to show middle and high schoolers the fun and excitement of math! For more information
More informationWipe Out Lesson 3 January 19/20 1
1 Large Group! Series at a Glance for Elevate About this Series: Jump! Duck! Dodge! Does life ever feel like an obstacle course? Push your way through this math quiz! Pick the right friends as your teammates,
More informationRefraction Inquiry. Background information: Refraction when a waves moves from one medium to another medium at an angle and changes speed.
Refraction Inquiry Direction: Copy down the purpose, background information and answer all the questions on notebook paper. Remember to put part of the question into your answers. Purpose: How does light
More informationMath Fundamentals for Statistics (Math 52) Unit 2:Number Line and Ordering. By Scott Fallstrom and Brent Pickett The How and Whys Guys.
Math Fundamentals for Statistics (Math 52) Unit 2:Number Line and Ordering By Scott Fallstrom and Brent Pickett The How and Whys Guys Unit 2 Page 1 2.1: Place Values We just looked at graphing ordered
More informationProblem Set 1: It s a New Year for Problem Solving!...
PCMI Outreach, Jan 21 22, 2017 Problem Set 1: It s a New Year for Problem Solving!... Welcome to PCMI! We know you ll learn a great deal of mathematics here maybe some new tricks, maybe some new perspectives
More informationThree of these grids share a property that the other three do not. Can you find such a property? + mod
PPMTC 22 Session 6: Mad Vet Puzzles Session 6: Mad Veterinarian Puzzles There is a collection of problems that have come to be known as "Mad Veterinarian Puzzles", for reasons which will soon become obvious.
More informationWritten by Jacqueline Woodson. Created by: The Curriculum Corner
Written by Jacqueline Woodson Created by: The Curriculum Corner Task # 1 Read with Fluency Pick a page or pages to practice. Read the page over and over. Pay close attention to the punctuation. Task #
More informationThe World of Work. This is an survey, NOT a test. Place a check mark in the column that indicates your honest response for each of the items.
What do I know about... The World of Work Name Date This is an survey, NOT a test. Place a check mark in the column that indicates your honest response for each of the items. DIS DIS 1. Following the High
More informationPerformance Task. Asteroid Aim. Chapter 8. Instructional Overview
Instructional Overview Performance Task Launch Question Summary Teacher Notes Supplies Mathematical Discourse Writing/Discussion Prompts Apps take a long time to design and program. One app in development
More information2008 학년도대학수학능력시험 6 월모의평가듣기대본
2008 학년도대학수학능력시험 6 월모의평가듣기대본 M: The samples of our club logo are finally here. Take a look. W: Hey, they look pretty good! Which one do you like? M: I like the triangular one. W: I like it, too. But why
More informationGrade 7/8 Math Circles. Visual Group Theory
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles October 25 th /26 th Visual Group Theory Grouping Concepts Together We will start
More informationHOW TO PLAY Shape Card Games
HOW TO PLAY Math children are practicing Naming shapes Recognizing shape attributes Recognizing numerals Shifting rules, keeping track (working memory), regulating themselves during game play (executive
More informationCrossing the Pond A Probability Game BRIDGES BREAKOUT Excerpts From Bridges in Mathematics
Crossing the Pond A Probability Game BRIDGES BREAKOUT Excerpts From Bridges in Mathematics 200, The Math Learning Center Crossing the Pond: A Probability Game A Math Learning Center Publication by Allyn
More informationCPM EDUCATIONAL PROGRAM
CPM EDUCATIONAL PROGRAM SAMPLE LESSON: ALGEBRA TILES PART 1: INTRODUCTION TO ALGEBRA TILES The problems in Part 1 introduce algebra tiles to students. These first eleven problems will probably span two
More informationSet-up: Instructions:
Instructions Set-up: ü All players in personal space, scattered throughout the activity area. ü Be sure each player has enough room to do jumping jacks safely. Instructions: ü FITMAN is a fitness version
More informationReader s Notebook Name: Grade: School:
Reader s Notebook Name: Grade: School: 10 Genres I Read this year 9 8 7 6 5 4 3 2 1 0 Fantasy And Science Fiction Modern Realism Mystery & Suspense Informational Historical Fiction Biography or Autobiography
More informationMission: Accomplish a Goal
Mission: Accomplish a Goal What is an Essential Skills Mission? Missions are a great way to get real life experience while testing your skills. The world is your laboratory, your training ground, your
More informationHOW TO MANAGE THE MOVE FROM EMPLOYMENT TO SELF EMPLOYMENT
IF YOU RE IN BARNSLEY, DONCASTER, ROTHERHAM, CHESTERFIELD, BASSETLAW, BOLSOVER, DERBYSHIRE DALES, NORTH EAST DERBYSHIRE OR SHEFFIELD WE CAN HELP SUPPORT YOUR BUSINESS. HOW TO MANAGE THE MOVE FROM EMPLOYMENT
More informationExam Confidence! Prepare to get the best possible maths grade on the day of your exam!
Exam Confidence! Prepare to get the best possible maths grade on the day of your exam! 2018 themathstutor.ie Ireland s Leading Online Support System for JC & LC Maths Introduction Exam technique is a key
More information4 th Grade Spring Break Math Activities Instructions
4 th Grade Spring Break Math Activities Instructions Indiana s College- and Career-Ready Academic Standards 2014 include one or more math fluency standards per grade level in Grades 1-8. Fluency will be
More informationCAREERS EDUCATION INFORMATION, ADVICE AND GUIDANCE
CAREERS EDUCATION INFORMATION, ADVICE AND GUIDANCE Year 9 Futures Name: Tutor Group: The road to your Career Booklet also available on school website 1 Options at Year 9: Introduction You are about to
More informationRestricted Choice In Bridge and Other Related Puzzles
Restricted Choice In Bridge and Other Related Puzzles P. Tobias, 9/4/2015 Before seeing how the principle of Restricted Choice can help us play suit combinations better let s look at the best way (in order
More informationMission 4 circles Materials
Mission 4 circles Materials Your fourth mission is to draw circles using the robot. Sounds simple enough, but you ll need to draw three different diameter circles using three different wheel motions. Good
More informationStand in Your Creative Power
Week 1 Coming into Alignment with YOU If you ve been working with the Law of Attraction for any length of time, you are already familiar with the steps you would take to manifest something you want. First,
More informationSpeaking Notes for Grades 4 to 6 Presentation
Speaking Notes for Grades 4 to 6 Presentation Understanding your online footprint: How to protect your personal information on the Internet SLIDE (1) Title Slide SLIDE (2) Key Points The Internet and you
More informationP1 Chapter 10 :: Trigonometric Identities & Equations
P1 Chapter 10 :: Trigonometric Identities & Equations jfrost@tiffin.kingston.sch.uk www.drfrostmaths.com @DrFrostMaths Last modified: 20 th August 2017 Use of DrFrostMaths for practice Register for free
More information6.1.2: Graphing Quadratic Equations
6.1.: Graphing Quadratic Equations 1. Obtain a pair of equations from your teacher.. Press the Zoom button and press 6 (for ZStandard) to set the window to make the max and min on both axes go from 10
More informationChapter 6.2: Trig Proofs
Chapter 6.2: Trig Proofs Proofs are fun, simply because they can be so challenging. No two are alike. While there are several common strategies for analytically proofing non-fundamental trig identities,
More informationTech Tips from Mr G Borrowing ebooks and Audiobooks Using OverDrive 3.2 on Apple ios Devices 2015
Tech Tips from Mr G Borrowing ebooks and Audiobooks Using OverDrive 3.2 on Apple ios Devices 2015 The Liverpool Public Library, the larger Onondaga County system, and libraries all over the country, subscribe
More informationby Barry Stebbing Sample
by Barry Stebbing From the Author Dear Boys and Girls, Moms and Dads, Grandpops and Grandmoms: Welcome to our beginning book on drawing, color, and painting. This text is intended for 6 year olds all the
More informationRubik s Revenge Solution Hints Booklet. Revenge - The Ultimate Challenge 2. Meet Your Revenge 3. Twisting Hints 5. General Hints 8. Notation System 12
Rubik s Revenge Solution Hints Booklet Revenge - The Ultimate Challenge 2 Meet Your Revenge 3 Twisting Hints 5 General Hints 8 Notation System 12 Revenge Sequences 19 Solving Rubik s Revenge 28 More Revenge
More informationMaking Middle School Math Come Alive with Games and Activities
Making Middle School Math Come Alive with Games and Activities For more information about the materials you find in this packet, contact: Chris Mikles 916-719-3077 chrismikles@cpm.org 1 2 2-51. SPECIAL
More informationMODULAR ARITHMETIC II: CONGRUENCES AND DIVISION
MODULAR ARITHMETIC II: CONGRUENCES AND DIVISION MATH CIRCLE (BEGINNERS) 02/05/2012 Modular arithmetic. Two whole numbers a and b are said to be congruent modulo n, often written a b (mod n), if they give
More informationGrade 7/8 Math Circles. Visual Group Theory
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles October 25 th /26 th Visual Group Theory Grouping Concepts Together We will start
More informationLower Elementary Family Projects
Dear Family, Every year, the students in Lower Elementary complete a family project. This project offers the children an opportunity to learn more about themselves and to celebrate their own family and
More information2.2. Special Angles and Postulates. Key Terms
And Now From a New Angle Special Angles and Postulates. Learning Goals Key Terms In this lesson, you will: Calculate the complement and supplement of an angle. Classify adjacent angles, linear pairs, and
More informationCreate Your Own World
Create Your Own World Introduction In this project you ll learn how to create your own open world adventure game. Step 1: Coding your player Let s start by creating a player that can move around your world.
More informationBroken Circles, Broken Squares
Broken Circles, Broken Squares LEARNING TO COOPERATE The most basic lesson that students must learn when working in groups is to be sensitive and responsive to the needs of other members of the group.
More informationJourney through Game Design
Simulation Games in Education Spring 2010 Introduction At the very beginning of semester we were required to choose a final project to work on. I found this a bit odd and had the slightest idea what to
More informationThe Unlimited Licks System
The Unlimited Licks System Classical compositions in the style of Vivaldi, Bach, Handel are based on sequences - groups of notes that repeat themselves through a scale. Some of these sequences has been
More informationAnd I Quote. By: Vitchel Toussaint
And I Quote 100 By: Vitchel Toussaint Copyright 2016 Vitchel Toussaint All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means including photocopying,
More informationA year ago I investigated a mathematical problem relating to Latin squares. Most people, whether knowing it or not, have actually seen a Latin square
1 How I Got Started: A year ago I investigated a mathematical problem relating to Latin squares. Most people, whether knowing it or not, have actually seen a Latin square at some point in their lives and
More informationBelieve, Achieve and Succeed at Test Time. Standardized Test Taking
Believe, Achieve and Succeed at Test Time Standardized Test Taking Types of Tests Taking tests is a big part of school. There are many different types of tests in school. Some subjects are tested often
More informationHow to Set and Achieve Your Goals
How to Set and Achieve Your Goals 1 www.projecthatch.com.au Goal Setting We, as humans, have the ability to look forward in life and imagine how we want things to be in the future. We learn through our
More informationGrade 7/8 Math Circles Game Theory October 27/28, 2015
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Game Theory October 27/28, 2015 Chomp Chomp is a simple 2-player game. There is
More informationThis is a one-week excerpt from the Starfall Kindergarten Mathematics Teacher s Guide. If you have questions or comments, please contact us.
UNIT 7 WEEK 16 This is a one-week excerpt from the Starfall Kindergarten Mathematics Teacher s Guide. If you have questions or comments, please contact us. Email: helpdesk@starfall.com Phone: 1-888-857-8990
More informationBy Scott Fallstrom and Brent Pickett The How and Whys Guys
Math Fundamentals for Statistics I (Math 52) Unit 2:Number Line and Ordering By Scott Fallstrom and Brent Pickett The How and Whys Guys This work is licensed under a Creative Commons Attribution- NonCommercial-ShareAlike
More informationProAgenda.com Factsheet
ProAgenda.com Factsheet The Tool ProAgenda.com offers the best online diary and booking system for teaching professionals in golf, and any other sport or profession. It offers everything you need for your
More informationDefinition 1 (Game). For us, a game will be any series of alternating moves between two players where one player must win.
Abstract In this Circles, we play and describe the game of Nim and some of its friends. In German, the word nimm! is an excited form of the verb to take. For example to tell someone to take it all you
More information8 Fraction Book. 8.1 About this part. 8.2 Pieces of Cake. Name 55
Name 8 Fraction Book 8. About this part This book is intended to be an enjoyable supplement to the standard text and workbook material on fractions. Understanding why the rules are what they are, and why
More informationApplying the 7 Habits of Highly Effective Teens
NAME CLASS # DATE Applying the 7 Habits of Highly Effective Teens Directions: Please complete this worksheet as you are reading p.3-28! Answer in thoughtful, complete sentences. Part I (Get in the Habit
More informationTHE PROCESS. Steps to Finding and Using the Right Information. Anytime. Anywhere.
CHAPTER ONE THE PROCESS Steps to Finding and Using the Right Information. Anytime. Anywhere. Nervous yet? Don t worry. We re here to help. in this chapter, we ll discuss how to dive into that giant mess
More informationGetting Started with Osmo Coding Jam. Updated
Updated 8.1.17 1.1.0 What s Included Each set contains 23 magnetic coding blocks. Snap them together in coding sequences to create an endless variety of musical compositions! Walk Quantity: 3 Repeat Quantity:
More information12. 6 jokes are minimal.
Pigeonhole Principle Pigeonhole Principle: When you organize n things into k categories, one of the categories has at least n/k things in it. Proof: If each category had fewer than n/k things in it then
More informationPA3 Part 2: BLM List. Workbook 3 - Patterns & Algebra, Part 2 1 BLACKLINE MASTERS
PA Part : BLM List Calendars Colouring Exercise Hanji Puzzles Hundreds Charts 8 Mini Sudoku 9 Sudoku The Real Thing Sudoku Warm Up Venn Diagram BLACKLINE MASTERS Workbook - Patterns & Algebra, Part Calendars
More informationThe #1 HR Expert Answers the Top Interview Questions to Land the Job!
The #1 HR Expert Answers the Top Interview Questions to Land the Job! Angela Anderson Table of Contents 3 4 5 8 9 Letter from the author Angela Anderson Interview preparation Top interview questions and
More informationThank you, Honorable Chairperson- Being a good team member
Session 32 Thank you, Honorable Chairperson- Being a good team member WHOSE FUTURE GOAL 22: You will learn how to plan for a successful Welcome back! You re one step closer to taking more control in your
More informationWhy do people set goals?
Note: to save space this file has been saved without the picture borders. Name: 1-2 Why do people set goals? Materials needed: piece of blank paper or cardboard for each group of 4 students Activity 1
More informationSemester 2 F i n a l Project Create a Math Board Game Due: May 11 th and 13 th
Semester 2 F i n a l Project Create a Math Board Game Due: May 11 th and 13 th May 1, 2015 Dear students and families, As my final project, students are creating a math board game that supports the content
More informationkeys to thrive and create you desire
5Anthony Robbins the life keys to thrive and create you desire It s no surprise that so many people today are in a state of uncertainty. We re going through massive changes in the economy, the world, and
More informationAnger How do I manage it?
Where can I get further help? If you are concerned about managing your anger, make an appointment to see your GP or take a look at the Trust s website to see what services we offer. If you cannot get online
More informationPART I: Emmett s teacher asked him to analyze the table of values of a quadratic function to find key features. The table of values is shown below:
Math (L-3a) Learning Targets: I can find the vertex from intercept solutions calculated by quadratic formula. PART I: Emmett s teacher asked him to analyze the table of values of a quadratic function to
More informationDAY 1 READ PSALM 139:13. THANK God for creating you to be exactly who He wanted you to be. DAY 2 READ PSALM 139:14 WEEK
1 READ PSALM 139:13 DAY 1 This month is all about individuality which we define as: discovering who you are meant to be so you can make a difference. Of all the people in the whole world, there is NO ONE
More informationDaily Announcements. M T W Th F
Daily Announcements A week of Never Giving Up! Make it a NEVER GIVE UP WEEK at school! Read an announcement every day of the week to reinforce the theme. Announcements can be made by the principal, the
More information5 0 I N S I D E R T I P S T O G O F R O M M A K I N G A L I V I N G T O M A K I N G A L I F E
5 0 I N S I D E R T I P S T O G O F R O M M A K I N G A L I V I N G T O M A K I N G A L I F E F R O M P E O P L E T H A T H A V E G O N E B E F O R E Y O U Hi, thank you for signing up and welcome in our
More informationTo Get You From Crayons to College.
To Get You From Crayons to College. Reproduced with Permission from The Corner on Character - http://corneroncharacter.blogspot.com/2011/08/from-crayons-to-college.html Attitude Build a strong bridge between
More informationMaking Middle School Math Come Alive with Games and Activities
Making Middle School Math Come Alive with Games and Activities For more information about the materials you find in this packet, contact: Sharon Rendon (605) 431-0216 sharonrendon@cpm.org 1 2-51. SPECIAL
More informationUse the following games to help students practice the following [and many other] grade-level appropriate math skills.
ON Target! Math Games with Impact Students will: Practice grade-level appropriate math skills. Develop mathematical reasoning. Move flexibly between concrete and abstract representations of mathematical
More informationC l o u d C o a c h Same Mentor Messages. Table of Contents
C l o u d C o a c h Same Mentor Messages The Gateway Prompts suggest mentors confine their messages to three paragraphs. We know that working out how to write an impactful message in three paragraphs can
More informationRevision Techniques. or how to pass exams
Revision Techniques or how to pass exams Let s start with what not to do! Don t imagine you can learn everything you need to know the night before the exam. Your memory won t cope and, apart from anything
More informationLot totalk. About. There s a. Family. Friends. Hopes. Dreams. Accomplishments. Pleasures. Talents. Values. The little details.
Life. There s a Lot totalk About There s so much we experience in our lives. There are the big moments that shape us graduation, a first job, falling in love and getting married, having children, seeing
More informationGirl Scout Cookie Boss Packet
Girl Scout Cookie Boss Packet Are you ready? Let s rock this cookie season! Everyone knows how delicious Girl Scout Cookies are, but a lot of people don t realize how much girls learn when they sell them.
More informationhttps://www.teachersp ayteachers.com/store/ Worksheetjunkie
https://www.teachersp ayteachers.com/store/ Worksheetjunkie Copyright 2017 IDEA GALAXY. All rights reserved by author. Permission to copy for single classroom use only. Electronic distribution limited
More informationStarting from LEARNER NOTES edited version. An Introduction to Computing Science by Jeremy Scott
Starting from 2013 edited version An Introduction to Computing Science by Jeremy Scott LEARNER NOTES 4: Get the picture? 3: A Mazing Game This lesson will cover Game creation Collision detection Introduction
More informationIELTS Listening Pick from a list
NGOẠI NGỮ 24H WWW.NGOAINGU24H.VN 1 IELTS Listening Pick from a list The Basic Pick from a list is essentially a version of multiple choice questions. The main difference is, while traditional multiple
More informationTo begin you need to log on to the Missouri Connections website.
Missouri Connections is a website that students can use to help determine and prepare for a career. You will be using this website to complete a budgeting exercise called "Get a Reality Check" to learn
More information10 Tips for Law School Success. Law School Toolbox LawSchoolToolbox.com
10 Tips for Law School Success Law School Toolbox Thanks for downloading! Law school isn t easy, but it doesn t have to be impossible. With these tips, and your own hard work, you ll be well on your way
More informationHappiness & Attitude. Kids Activities
Happiness & Attitude Kids Activities Thousands of teachers worldwide have learned how fun and helpful it can be to have Happy Kids Songs in their classrooms. These full-production songs are both highly
More informationMath Circle: Logic Puzzles
Math Circle: Logic Puzzles June 4, 2017 The Missing $1 Three people rent a room for the night for a total of $30. They each pay $10 and go upstairs. The owner then realizes the room was only supposed to
More informationTeachers Pack Whitechapel Gallery. British Council Collection: Great Early Buys. 5 April June whitechapelgallery.
Teachers Pack Whitechapel Gallery British Council Collection: Great Early Buys 5 April 2009 14 June 2009 Whitechapel Gallery 77 82 Whitechapel High Street London E1 7QX Aldgate East whitechapelgallery.org
More informationLesson 8 Tic-Tac-Toe (Noughts and Crosses)
Lesson Game requirements: There will need to be nine sprites each with three costumes (blank, cross, circle). There needs to be a sprite to show who has won. There will need to be a variable used for switching
More informationHOW TO ORDER AND DOWNLOAD YOUR MUSIC FROM THE WENDELL BROOKS WOOCOMMERCE STORE
HOW TO ORDER AND DOWNLOAD YOUR MUSIC FROM THE WENDELL BROOKS WOOCOMMERCE STORE AT https://www.wendellbrooks.com First of all, I want to thank EVERYONE who is supporting my project. I am EXTRAORDINARILY
More informationHome Connection 5 Activity
Blackline HC 5.1 Use after Unit 2, Session 3. Run on cardstock. Have students attach paper clip spinners at school. Home Connection 5 Activity An Hour or Bust! Game Rules 1 Get a partner, a spinner, 1
More informationUsing Structure I: Multiplication Puzzles
PS6-5 Using Structure I: Multiplication Puzzles Teach this lesson after: 6.2 Measurement Goals: Students will mentally compute the ones digit of a product of multi-digit numbers. Students will solve multi-digit
More informationFootball writing exercises
Football writing exercises Written by Tom Palmer ONE: FOOTBALL ARGUMENTS There are lots of arguments in football. Watch Match of the Day and you ll see players shouting at each other on the pitch, as well
More informationObjectives. Materials
. Objectives Activity 8 To plot a mathematical relationship that defines a spiral To use technology to create a spiral similar to that found in a snail To use technology to plot a set of ordered pairs
More informationTEACHER SHEET TOPICS: SIMPLE STRATEGY AND SPATIAL GEOMETRY LEARN THROUGH PLAY PLACE, MOVE, SAVE
TEACHER SHEET & 1991 GIGAMIC F - TOPICS: SIMPLE STRATEGY AND SPATIAL GEOMETRY Objectives: - learn to anticipate and develop short and long term strategies; - situate an object in relation to yourself or
More informationKenken For Teachers. Tom Davis January 8, Abstract
Kenken For Teachers Tom Davis tomrdavis@earthlink.net http://www.geometer.org/mathcircles January 8, 00 Abstract Kenken is a puzzle whose solution requires a combination of logic and simple arithmetic
More informationGo to Kindergarten Everyday Mathematics Sample Lessons
McGraw-Hill makes no representations or warranties as to the accuracy of any information contained in this McGraw-Hill Material, including any warranties of merchantability or fitness for a particular
More informationIn addition to one-point perespective, another common perspective
CHAPTR 5 Two-Point Perspective In addition to one-point perespective, another common perspective drawing technique is two-point perspective, illustrated in Figure 5.1. Unless otherwise stated, we will
More informationPart 1: Big Decisions
Excerpts from Part 1: Big Decisions Should you build it yourself or with help? To build, or not to build? That is the question. The answer depends on you. Yes, you. The mantra of the tiny house movement
More informationWeek 3. Week 3. Overview Card. Overview Card. February. February
Overview Card Basic Truth: Jesus wants to be my friend forever. Key Question: How do you love God? Bottom Line: Love God with all your heart. Memory Verse: Love... God with all your heart. Matthew 22:37,
More informationDocuments for the Winning Job Search
Table of Content 1 2 3 5 6 7 Documents for the Winning Job Search Resumes Brag Books 30/60/90 Day Sales Plan References Letters of Recommendation Cover Letters Thank You Notes Technology Sheet What Do
More informationFolding Activity 3. Compass Colored paper Tape or glue stick
Folding Activity 3 Part 1 You re not done until everyone in your group is done! If you finish before someone else, help them finish before starting on the next part. You ll need: Patty paper Ruler Sharpie
More information