The Evolution of Random Phenomena
|
|
- Sarah Norman
- 6 years ago
- Views:
Transcription
1 The Evolution of Random Phenomena A Look at Markov Chains Glen Wang glenw@uchicago.edu Splash! Chicago: Winter Cascade 2012 Lecture 1: What is Randomness?
2 What is randomness? Can you think of some examples of randomness?
3 What is randomness? Can you think of some examples of randomness? Rolling dice. Flipping coins. Card games. Picking numbers out of a hat.
4 What is randomness? Can you think of some examples of randomness? Rolling dice. Flipping coins. Card games. Picking numbers out of a hat. We use the word random in daily conversation.
5 What is randomness? Can you think of some examples of randomness? Rolling dice. Flipping coins. Card games. Picking numbers out of a hat. We use the word random in daily conversation. We just randomly met on the street and... Well, that was random...
6 What is randomness? Can you think of some examples of randomness? Rolling dice. Flipping coins. Card games. Picking numbers out of a hat. We use the word random in daily conversation. We just randomly met on the street and... Well, that was random... How much do we really know about randomness?
7 Let s do an experiment! In the beginning of class, I gave you a strip of paper with the numbers 1 to 20 on it. Randomly circle 4 numbers on your strip of paper.
8 Computer-generated selections I asked a computer to pick 4 numbers randomly just like in our experiment. Here are the computer s results:
9 Computer-generated selections I asked a computer to pick 4 numbers randomly just like in our experiment. Here are the computer s results:
10 Computer-generated selections I asked a computer to pick 4 numbers randomly just like in our experiment. Here are the computer s results:
11 Computer-generated selections I asked a computer to pick 4 numbers randomly just like in our experiment. Here are the computer s results:
12 Computer-generated selections I asked a computer to pick 4 numbers randomly just like in our experiment. Here are the computer s results:
13 Computer-generated selections I asked a computer to pick 4 numbers randomly just like in our experiment. Here are the computer s results:
14 Computer-generated selections I asked a computer to pick 4 numbers randomly just like in our experiment. Here are the computer s results: How do these results compare with ours?
15 The goals of this lecture 1 Define randomness. 2 Develop a mathematical language to talk about randomness,
16 The goals of this lecture 1 Define randomness. 2 Develop a mathematical language to talk about randomness, which means, probability.
17 Defining randomness What is a process? Q: Recall our examples of randomness. What do all of these have in common?
18 Defining randomness What is a process? Q: Recall our examples of randomness. What do all of these have in common? A: They are all actions and have outcomes. e.g. Rolling a die is an action, and outcomes could be any number from 1 to 6. e.g. Flipping a coin is an action, with heads or tails as outcomes.
19 Defining randomness What is a process? Q: Recall our examples of randomness. What do all of these have in common? A: They are all actions and have outcomes. e.g. Rolling a die is an action, and outcomes could be any number from 1 to 6. e.g. Flipping a coin is an action, with heads or tails as outcomes. Definition A process is anything that responds to action to produce outcomes.
20 Defining randomness What is a process? Q: Recall our examples of randomness. What do all of these have in common? A: They are all actions and have outcomes. e.g. Rolling a die is an action, and outcomes could be any number from 1 to 6. e.g. Flipping a coin is an action, with heads or tails as outcomes. Definition A process is anything that responds to action to produce outcomes. We can think of this as cause and effect, stimulus and response, input and output.
21 Defining randomness Function as a process
22 Defining randomness Function as a process What are some examples of functions?
23 Defining randomness Function as a process What are some examples of functions? How can we tell if something is a function?
24 Defining randomness Function as a process What are some examples of functions? How can we tell if something is a function? Vertical line test.
25 Defining randomness Function as a process What are some examples of functions? How can we tell if something is a function? Vertical line test. We can think of a function as a process. The action is what we give the function as input, and the outcome is the function s output.
26 Defining randomness Function as a process What are some examples of functions? How can we tell if something is a function? Vertical line test. We can think of a function as a process. The action is what we give the function as input, and the outcome is the function s output. Definition A function is a process that for every input, gives a unique (only one) output.
27 Defining randomness A traffic example Inputs Red Outputs Stop Green Go
28 Defining randomness A traffic example Inputs Red Outputs Stop Yellow Green Go
29 Defining randomness A traffic example Inputs Outputs Stop Yellow Go
30 Defining randomness We arrive at a definition! Definition A random variable is a process that associates inputs to possibly more than one output.
31 Defining randomness We arrive at a definition! Definition A random variable is a process that associates inputs to possibly more than one output. The definition of random variable captures what we know so far about randomness.
32 Defining randomness We arrive at a definition! Definition A random variable is a process that associates inputs to possibly more than one output. The definition of random variable captures what we know so far about randomness. Q: What can we do to better understand the behavior of random variables?
33 Defining randomness We arrive at a definition! Definition A random variable is a process that associates inputs to possibly more than one output. The definition of random variable captures what we know so far about randomness. Q: What can we do to better understand the behavior of random variables? e.g. Are cars more likely to stop when facing a yellow light, or are they more likely to go?
34 A: Math!
35 A: Math!... in particular, probability!
36 What is probability? What comes to mind when we say probability?
37 What is probability? What comes to mind when we say probability? A measurement of likelihood. How random phenomena are expected to behave.
38 What is probability? What comes to mind when we say probability? A measurement of likelihood. How random phenomena are expected to behave. Let s motivate the definition through an example!
39 We roll a die... Suppose we roll a fair, six-sided die. What could happen?
40 We roll a die... Suppose we roll a fair, six-sided die. What could happen? A: We get one of the following results:
41 We roll a die... Suppose we roll a fair, six-sided die. What could happen? A: We get one of the following results: So rolling a die is a random variable where the input (action) is the roll, and the possible outputs are 1 to 6.
42 Outcomes vs. events Definition An outcome of a random variable is one of the possible outputs of that random variable. So rolling a 1, rolling a 2, etc. are all outcomes of the rolling a die random variable.
43 Outcomes vs. events Definition An event is a collection of one or more outcomes.
44 Outcomes vs. events Definition An event is a collection of one or more outcomes. e.g. The event of rolling a number greater than 3.
45 Outcomes vs. events Definition An event is a collection of one or more outcomes. e.g. The event of rolling a number greater than 3. e.g. We make a distinction between the event of rolling a 1 and the outcome 1.
46 What is probability?
47 What is probability? Definition Given a random variable, a probability is a way to assign numbers to all possible events that could occur.
48 What is probability? Definition Given a random variable, a probability is a way to assign numbers to all possible events that could occur. The way that a probability assigns numbers follows specific rules:
49 What is probability? Definition Given a random variable, a probability is a way to assign numbers to all possible events that could occur. The way that a probability assigns numbers follows specific rules: The numbers assigned must be between 0 and 1.
50 What is probability? Definition Given a random variable, a probability is a way to assign numbers to all possible events that could occur. The way that a probability assigns numbers follows specific rules: The numbers assigned must be between 0 and 1. An event assigned with probability 0 will never occur.
51 What is probability? Definition Given a random variable, a probability is a way to assign numbers to all possible events that could occur. The way that a probability assigns numbers follows specific rules: The numbers assigned must be between 0 and 1. An event assigned with probability 0 will never occur. An event assigned with probability 1 will always occur.
52 What is probability? Definition Given a random variable, a probability is a way to assign numbers to all possible events that could occur. The way that a probability assigns numbers follows specific rules: The numbers assigned must be between 0 and 1. An event assigned with probability 0 will never occur. An event assigned with probability 1 will always occur. If every outcome in event A is also in event B, then P(A) P(B).
53 What is probability? Definition Given a random variable, a probability is a way to assign numbers to all possible events that could occur. The way that a probability assigns numbers follows specific rules: The numbers assigned must be between 0 and 1. An event assigned with probability 0 will never occur. An event assigned with probability 1 will always occur. If every outcome in event A is also in event B, then P(A) P(B). If two events A, B have no outcomes in common, then the probability that an outcome from one of the two events occurs equals the sum of the probabilities assigned to each event: P(A or B) = P(A) + P(B).
54 What is probability? Probability is a function! This function is defined differently for different random variables. The inputs are events and the outputs are numbers between 0 and 1.
55 Law of total probability Theorem (Law of total probability) For any random variable, the probability that some outcome occurs is 1. Inputs Yellow Outputs Stop Go
56 A quick example of a Markov chain
57 A quick example of a Markov chain 0.7 Red Red 1 Stop 0.3 Green Green 1 Go 0.3 Red 0.7 Green
58 A quick example of a Markov chain 0.7 Red Red Green Red 0.3 Red Green Green Red Green Green Red Green Red Green
59 Summary A process is any mechanism that gives outputs (responses) to certain inputs (actions). A function is a process that assigns every input only one output. A random variable is a process that assigns every input with possibly many outputs. One output of a random variable is called an outcome. A collection of outcomes is called an event. Probability is a specific way to assign events to numbers between 0 and 1. The probability that some event will occur is 1 (law of total probability).
60 Note card questions! Please take a minute to fill out the following questions on your note card. Your input will let me know how the class is going for you, so in the future I can set up the class according to your needs. 1 Was the pacing of this class too fast? Too slow? Just right? 2 Is there anything that you didn t quite understand? If so, please tell me what it is. 3 What were some of the things you liked about this lecture? Why? If you have questions for me, I will be sticking around after class. Please feel free to ask me anything! You can also me at glenw@uchicago.edu.
Mathematics Success Grade 7
T894 Mathematics Success Grade 7 [OBJECTIVE] The student will find probabilities of compound events using organized lists, tables, tree diagrams, and simulations. [PREREQUISITE SKILLS] Simple probability,
More informationContents. Foreword... 5
Contents Foreword... 5 Chapter 1: Addition Within 0-10 Introduction... 6 Two Groups and a Total... 10 Learn Symbols + and =... 13 Addition Practice... 15 Which is More?... 17 Missing Items... 19 Sums with
More informationManagerial Decision Making
Course Business Managerial Decision Making Session 4 Conditional Probability & Bayesian Updating Surveys in the future... attempt to participate is the important thing Work-load goals Average 6-7 hours,
More informationGrade 2: Using a Number Line to Order and Compare Numbers Place Value Horizontal Content Strand
Grade 2: Using a Number Line to Order and Compare Numbers Place Value Horizontal Content Strand Texas Essential Knowledge and Skills (TEKS): (2.1) Number, operation, and quantitative reasoning. The student
More informationCurriculum Design Project with Virtual Manipulatives. Gwenanne Salkind. George Mason University EDCI 856. Dr. Patricia Moyer-Packenham
Curriculum Design Project with Virtual Manipulatives Gwenanne Salkind George Mason University EDCI 856 Dr. Patricia Moyer-Packenham Spring 2006 Curriculum Design Project with Virtual Manipulatives Table
More informationEvaluating Statements About Probability
CONCEPT DEVELOPMENT Mathematics Assessment Project CLASSROOM CHALLENGES A Formative Assessment Lesson Evaluating Statements About Probability Mathematics Assessment Resource Service University of Nottingham
More informationEDEXCEL FUNCTIONAL SKILLS PILOT. Maths Level 2. Chapter 7. Working with probability
Working with probability 7 EDEXCEL FUNCTIONAL SKILLS PILOT Maths Level 2 Chapter 7 Working with probability SECTION K 1 Measuring probability 109 2 Experimental probability 111 3 Using tables to find the
More informationLeft, Left, Left, Right, Left
Lesson.1 Skills Practice Name Date Left, Left, Left, Right, Left Compound Probability for Data Displayed in Two-Way Tables Vocabulary Write the term that best completes each statement. 1. A two-way table
More informationACTIVITY: Comparing Combination Locks
5.4 Compound Events outcomes of one or more events? ow can you find the number of possible ACIVIY: Comparing Combination Locks Work with a partner. You are buying a combination lock. You have three choices.
More informationIn how many ways can one junior and one senior be selected from a group of 8 juniors and 6 seniors?
Counting Principle If one activity can occur in m way and another activity can occur in n ways, then the activities together can occur in mn ways. Permutations arrangements of objects in a specific order
More informationSight Word Assessment
Make, Take & Teach Sight Word Assessment Assessment and Progress Monitoring for the Dolch 220 Sight Words What are sight words? Sight words are words that are used frequently in reading and writing. Because
More informationPaper Reference. Edexcel GCSE Mathematics (Linear) 1380 Paper 1 (Non-Calculator) Foundation Tier. Monday 6 June 2011 Afternoon Time: 1 hour 30 minutes
Centre No. Candidate No. Paper Reference 1 3 8 0 1 F Paper Reference(s) 1380/1F Edexcel GCSE Mathematics (Linear) 1380 Paper 1 (Non-Calculator) Foundation Tier Monday 6 June 2011 Afternoon Time: 1 hour
More information4-3 Basic Skills and Concepts
4-3 Basic Skills and Concepts Identifying Binomial Distributions. In Exercises 1 8, determine whether the given procedure results in a binomial distribution. For those that are not binomial, identify at
More informationOne Way Draw a quick picture.
Name Multiply Tens, Hundreds, and Thousands Essential Question How does understanding place value help you multiply tens, hundreds, and thousands? Lesson 2.3 Number and Operations in Base Ten 4.NBT.5 Also
More informationEnd-of-Module Assessment Task K 2
Student Name Topic A: Two-Dimensional Flat Shapes Date 1 Date 2 Date 3 Rubric Score: Time Elapsed: Topic A Topic B Materials: (S) Paper cutouts of typical triangles, squares, Topic C rectangles, hexagons,
More informationLesson plan for Maze Game 1: Using vector representations to move through a maze Time for activity: homework for 20 minutes
Lesson plan for Maze Game 1: Using vector representations to move through a maze Time for activity: homework for 20 minutes Learning Goals: Students will be able to: Maneuver through the maze controlling
More informationUnit 2. A whole-school approach to numeracy across the curriculum
Unit 2 A whole-school approach to numeracy across the curriculum 50 Numeracy across the curriculum Unit 2 Crown copyright 2001 Unit 2 A whole-school approach to numeracy across the curriculum Objectives
More informationNumber Line Moves Dash -- 1st Grade. Michelle Eckstein
Number Line Moves Dash -- 1st Grade Michelle Eckstein Common Core Standards CCSS.MATH.CONTENT.1.NBT.C.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit
More informationLearning to Think Mathematically With the Rekenrek
Learning to Think Mathematically With the Rekenrek A Resource for Teachers A Tool for Young Children Adapted from the work of Jeff Frykholm Overview Rekenrek, a simple, but powerful, manipulative to help
More informationActivity 2 Multiplying Fractions Math 33. Is it important to have common denominators when we multiply fraction? Why or why not?
Activity Multiplying Fractions Math Your Name: Partners Names:.. (.) Essential Question: Think about the question, but don t answer it. You will have an opportunity to answer this question at the end of
More informationSpinners at the School Carnival (Unequal Sections)
Spinners at the School Carnival (Unequal Sections) Maryann E. Huey Drake University maryann.huey@drake.edu Published: February 2012 Overview of the Lesson Students are asked to predict the outcomes of
More informationAlgebra 2- Semester 2 Review
Name Block Date Algebra 2- Semester 2 Review Non-Calculator 5.4 1. Consider the function f x 1 x 2. a) Describe the transformation of the graph of y 1 x. b) Identify the asymptotes. c) What is the domain
More informationStudent s Edition. Grade 6 Unit 6. Statistics. Eureka Math. Eureka Math
Student s Edition Grade 6 Unit 6 Statistics Eureka Math Eureka Math Lesson 1 Lesson 1: Posing Statistical Questions Statistics is about using data to answer questions. In this module, the following four
More informationRule-based Expert Systems
Rule-based Expert Systems What is knowledge? is a theoretical or practical understanding of a subject or a domain. is also the sim of what is currently known, and apparently knowledge is power. Those who
More informationCAN PICTORIAL REPRESENTATIONS SUPPORT PROPORTIONAL REASONING? THE CASE OF A MIXING PAINT PROBLEM
CAN PICTORIAL REPRESENTATIONS SUPPORT PROPORTIONAL REASONING? THE CASE OF A MIXING PAINT PROBLEM Christina Misailidou and Julian Williams University of Manchester Abstract In this paper we report on the
More informationAssociation Between Categorical Variables
Student Outcomes Students use row relative frequencies or column relative frequencies to informally determine whether there is an association between two categorical variables. Lesson Notes In this lesson,
More informationAssessing Children s Writing Connect with the Classroom Observation and Assessment
Written Expression Assessing Children s Writing Connect with the Classroom Observation and Assessment Overview In this activity, you will conduct two different types of writing assessments with two of
More information5 Guidelines for Learning to Spell
5 Guidelines for Learning to Spell 1. Practice makes permanent Did somebody tell you practice made perfect? That's only if you're practicing it right. Each time you spell a word wrong, you're 'practicing'
More informationWorking on the Bay Bridge.
Working on the Bay Bridge. Instructions for Teachers This lesson uses excerpts of oral histories from the museum exhibit. These histories can help students understand how some people felt about their jobs
More informationName: Class: Date: ID: A
Name: Class: _ Date: _ Test Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Members of a high school club sold hamburgers at a baseball game to
More informationMathematics process categories
Mathematics process categories All of the UK curricula define multiple categories of mathematical proficiency that require students to be able to use and apply mathematics, beyond simple recall of facts
More informationThe Implementation of a Consecutive Giving Recognition Program at the University of Florida
The Implementation of a Consecutive Giving Recognition Program at the University of Florida PROPOSAL Recognize donors who have given to UF s academic programs for 3+ years consecutively Use (CGP) as a
More informationExperience Corps. Mentor Toolkit
Experience Corps Mentor Toolkit 2 AARP Foundation Experience Corps Mentor Toolkit June 2015 Christian Rummell Ed. D., Senior Researcher, AIR 3 4 Contents Introduction and Overview...6 Tool 1: Definitions...8
More informationCS 598 Natural Language Processing
CS 598 Natural Language Processing Natural language is everywhere Natural language is everywhere Natural language is everywhere Natural language is everywhere!"#$%&'&()*+,-./012 34*5665756638/9:;< =>?@ABCDEFGHIJ5KL@
More informationSimilar Triangles. Developed by: M. Fahy, J. O Keeffe, J. Cooper
Similar Triangles Developed by: M. Fahy, J. O Keeffe, J. Cooper For the lesson on 1/3/2016 At Chanel College, Coolock Teacher: M. Fahy Lesson plan developed by: M. Fahy, J. O Keeffe, J. Cooper. 1. Title
More informationMultiplication of 2 and 3 digit numbers Multiply and SHOW WORK. EXAMPLE. Now try these on your own! Remember to show all work neatly!
Multiplication of 2 and digit numbers Multiply and SHOW WORK. EXAMPLE 205 12 10 2050 2,60 Now try these on your own! Remember to show all work neatly! 1. 6 2 2. 28 8. 95 7. 82 26 5. 905 15 6. 260 59 7.
More informationUse the Syllabus to tick off the things you know, and highlight the areas you are less clear on. Use BBC Bitesize Lessons, revision activities and
Use the Syllabus to tick off the things you know, and highlight the areas you are less clear on. Use BBC Bitesize Lessons, revision activities and tests to do. Use the websites recommended by your subject
More informationWhile you are waiting... socrative.com, room number SIMLANG2016
While you are waiting... socrative.com, room number SIMLANG2016 Simulating Language Lecture 4: When will optimal signalling evolve? Simon Kirby simon@ling.ed.ac.uk T H E U N I V E R S I T Y O H F R G E
More informationQuantitative analysis with statistics (and ponies) (Some slides, pony-based examples from Blase Ur)
Quantitative analysis with statistics (and ponies) (Some slides, pony-based examples from Blase Ur) 1 Interviews, diary studies Start stats Thursday: Ethics/IRB Tuesday: More stats New homework is available
More informationGrade Band: High School Unit 1 Unit Target: Government Unit Topic: The Constitution and Me. What Is the Constitution? The United States Government
The Constitution and Me This unit is based on a Social Studies Government topic. Students are introduced to the basic components of the U.S. Constitution, including the way the U.S. government was started
More informationWork Stations 101: Grades K-5 NCTM Regional Conference &
: Grades K-5 NCTM Regional Conference 11.20.14 & 11.21.14 Janet (Dodd) Nuzzie, Pasadena ISD District Instructional Specialist, K-4 President, Texas Association of Supervisors of jdodd@pasadenaisd.org PISD
More informationLearning to Think Mathematically with the Rekenrek Supplemental Activities
Learning to Think Mathematically with the Rekenrek Supplemental Activities Jeffrey Frykholm, Ph.D. Learning to Think Mathematically with the Rekenrek, Supplemental Activities A complementary resource to
More informationUtilizing FREE Internet Resources to Flip Your Classroom. Presenter: Shannon J. Holden
Utilizing FREE Internet Resources to Flip Your Classroom Presenter: Shannon J. Holden www.newteacherhelp.com This Presentation I gave this presentation to the Missouri Association of Secondary School Principals
More informationCase study Norway case 1
Case study Norway case 1 School : B (primary school) Theme: Science microorganisms Dates of lessons: March 26-27 th 2015 Age of students: 10-11 (grade 5) Data sources: Pre- and post-interview with 1 teacher
More informationSTAT 220 Midterm Exam, Friday, Feb. 24
STAT 220 Midterm Exam, Friday, Feb. 24 Name Please show all of your work on the exam itself. If you need more space, use the back of the page. Remember that partial credit will be awarded when appropriate.
More informationThe Use of Statistical, Computational and Modelling Tools in Higher Learning Institutions: A Case Study of the University of Dodoma
International Journal of Computer Applications (975 8887) The Use of Statistical, Computational and Modelling Tools in Higher Learning Institutions: A Case Study of the University of Dodoma Gilbert M.
More informationAnswer Key For The California Mathematics Standards Grade 1
Introduction: Summary of Goals GRADE ONE By the end of grade one, students learn to understand and use the concept of ones and tens in the place value number system. Students add and subtract small numbers
More informationAP Statistics Summer Assignment 17-18
AP Statistics Summer Assignment 17-18 Welcome to AP Statistics. This course will be unlike any other math class you have ever taken before! Before taking this course you will need to be competent in basic
More informationSTUDENT PERCEPTION SURVEYS ACTIONABLE STUDENT FEEDBACK PROMOTING EXCELLENCE IN TEACHING AND LEARNING
1 STUDENT PERCEPTION SURVEYS ACTIONABLE STUDENT FEEDBACK PROMOTING EXCELLENCE IN TEACHING AND LEARNING Presentation to STLE Grantees: December 20, 2013 Information Recorded on: December 26, 2013 Please
More informationCS Machine Learning
CS 478 - Machine Learning Projects Data Representation Basic testing and evaluation schemes CS 478 Data and Testing 1 Programming Issues l Program in any platform you want l Realize that you will be doing
More informationProbability and Statistics Curriculum Pacing Guide
Unit 1 Terms PS.SPMJ.3 PS.SPMJ.5 Plan and conduct a survey to answer a statistical question. Recognize how the plan addresses sampling technique, randomization, measurement of experimental error and methods
More informationPreliminary Chapter survey experiment an observational study that is not a survey
1 Preliminary Chapter P.1 Getting data from Jamie and her friends is convenient, but it does not provide a good snapshot of the opinions held by all young people. In short, Jamie and her friends are not
More informationUnit Lesson Plan: Native Americans 4th grade (SS and ELA)
Unit Lesson Plan: Native Americans 4th grade (SS and ELA) Angie- comments in red Emily's comments in purple Sue's in orange Kasi Frenton-Comments in green-kas_122@hotmail.com 10/6/09 9:03 PM Unit Lesson
More informationEnd-of-Module Assessment Task
Student Name Date 1 Date 2 Date 3 Topic E: Decompositions of 9 and 10 into Number Pairs Topic E Rubric Score: Time Elapsed: Topic F Topic G Topic H Materials: (S) Personal white board, number bond mat,
More informationSchool Size and the Quality of Teaching and Learning
School Size and the Quality of Teaching and Learning An Analysis of Relationships between School Size and Assessments of Factors Related to the Quality of Teaching and Learning in Primary Schools Undertaken
More informationCommon Core Exemplar for English Language Arts and Social Studies: GRADE 1
The Common Core State Standards and the Social Studies: Preparing Young Students for College, Career, and Citizenship Common Core Exemplar for English Language Arts and Social Studies: Why We Need Rules
More informationMYCIN. The MYCIN Task
MYCIN Developed at Stanford University in 1972 Regarded as the first true expert system Assists physicians in the treatment of blood infections Many revisions and extensions over the years The MYCIN Task
More informationA Pumpkin Grows. Written by Linda D. Bullock and illustrated by Debby Fisher
GUIDED READING REPORT A Pumpkin Grows Written by Linda D. Bullock and illustrated by Debby Fisher KEY IDEA This nonfiction text traces the stages a pumpkin goes through as it grows from a seed to become
More informationProcedia - Social and Behavioral Sciences 237 ( 2017 )
Available online at www.sciencedirect.com ScienceDirect Procedia - Social and Behavioral Sciences 237 ( 2017 ) 613 617 7th International Conference on Intercultural Education Education, Health and ICT
More informationMe on the Map. Standards: Objectives: Learning Activities:
Me on the Map Grade level: 1 st Grade Subject(s) Area: Reading, Writing, and Social Studies Materials needed: One sheet of construction paper per child, yarn or string, crayons or colored pencils, pencils,
More informationPART C: ENERGIZERS & TEAM-BUILDING ACTIVITIES TO SUPPORT YOUTH-ADULT PARTNERSHIPS
PART C: ENERGIZERS & TEAM-BUILDING ACTIVITIES TO SUPPORT YOUTH-ADULT PARTNERSHIPS The following energizers and team-building activities can help strengthen the core team and help the participants get to
More informationPREP S SPEAKER LISTENER TECHNIQUE COACHING MANUAL
1 PREP S SPEAKER LISTENER TECHNIQUE COACHING MANUAL IMPORTANCE OF THE SPEAKER LISTENER TECHNIQUE The Speaker Listener Technique (SLT) is a structured communication strategy that promotes clarity, understanding,
More information12- A whirlwind tour of statistics
CyLab HT 05-436 / 05-836 / 08-534 / 08-734 / 19-534 / 19-734 Usable Privacy and Security TP :// C DU February 22, 2016 y & Secu rivac rity P le ratory bo La Lujo Bauer, Nicolas Christin, and Abby Marsh
More informationA BEGINNERS GUIDE TO SUCCESSFUL ONLINE SURVEYS
A BEGINNERS GUIDE TO SUCCESSFUL ONLINE SURVEYS EVERYTHING YOU NEED TO KNOW TO CONDUCT CUSTOMER AND EMPLOYEE SURVEYS THAT GROW YOUR BUSINESS 1 CONTENTS PLANNING 3 Planning 3 Respondents 4 THE SURVEY 6 Visual
More informationUnited States Symbols First Grade By Rachel Horen. Featured Selection:
United States Symbols First Grade By Rachel Horen Featured Selection: Easy Reader Biographies: Betsy Ross: The Story of Our Flag by Pamela Chanko Scholastic Teaching Resources 2007 Betsy Ross is given
More informationHi I m Ryan O Donnell, I m with Florida Tech s Orlando Campus, and today I am going to review a book titled Standard Celeration Charting 2002 by
Hi I m Ryan O Donnell, I m with Florida Tech s Orlando Campus, and today I am going to review a book titled Standard Celeration Charting 2002 by Steve Graf and Ogden Lindsley. 1 The book was written by
More informationEngineers and Engineering Brand Monitor 2015
Engineers and Engineering Brand Monitor 2015 Key Findings Prepared for Engineering UK By IFF Research 7 September 2015 We gratefully acknowledge the support of Pearson in delivering this study Contact
More informationInstructional Supports for Common Core and Beyond: FORMATIVE ASSESMENT
Instructional Supports for Common Core and Beyond: FORMATIVE ASSESMENT Defining Date Guiding Question: Why is it important for everyone to have a common understanding of data and how they are used? Importance
More informationThe Editor s Corner. The. Articles. Workshops. Editor. Associate Editors. Also In This Issue
The S tatistics T eacher N etwork www.amstat.org/education/stn Number 73 ASA/NCTM Joint Committee on the Curriculum in Statistics and Probability Fall 2008 The Editor s Corner We hope you enjoy Issue 73
More informationHentai High School A Game Guide
Hentai High School A Game Guide Hentai High School is a sex game where you are the Principal of a high school with the goal of turning the students into sex crazed people within 15 years. The game is difficult
More informationIntroduction to the Revised Mathematics TEKS (2012) Module 1
Introduction to the Revised Mathematics TEKS (2012) Module 1 This is the first of four modules to introduce the Revised TEKS for grades K 8. The goals for participation are to become familiar with the
More informationNUMBERS AND OPERATIONS
SAT TIER / MODULE I: M a t h e m a t i c s NUMBERS AND OPERATIONS MODULE ONE COUNTING AND PROBABILITY Before You Begin When preparing for the SAT at this level, it is important to be aware of the big picture
More informationShockwheat. Statistics 1, Activity 1
Statistics 1, Activity 1 Shockwheat Students require real experiences with situations involving data and with situations involving chance. They will best learn about these concepts on an intuitive or informal
More informationUsing focal point learning to improve human machine tacit coordination
DOI 10.1007/s10458-010-9126-5 Using focal point learning to improve human machine tacit coordination InonZuckerman SaritKraus Jeffrey S. Rosenschein The Author(s) 2010 Abstract We consider an automated
More informationThe open source development model has unique characteristics that make it in some
Is the Development Model Right for Your Organization? A roadmap to open source adoption by Ibrahim Haddad The open source development model has unique characteristics that make it in some instances a superior
More informationThe Task. A Guide for Tutors in the Rutgers Writing Centers Written and edited by Michael Goeller and Karen Kalteissen
The Task A Guide for Tutors in the Rutgers Writing Centers Written and edited by Michael Goeller and Karen Kalteissen Reading Tasks As many experienced tutors will tell you, reading the texts and understanding
More informationSocratic Seminar (Inner/Outer Circle Method)
Socratic Seminar (Inner/Outer Circle Method) Why? Because, as Socrates said, The unexamined life is not worth living. Freedom of expression is essential to enlightenment, and it s high time many of you
More informationContext Free Grammars. Many slides from Michael Collins
Context Free Grammars Many slides from Michael Collins Overview I An introduction to the parsing problem I Context free grammars I A brief(!) sketch of the syntax of English I Examples of ambiguous structures
More informationJigsaw- Yellow- Red White- Grey- Orange- Brown- Gold- Blue- Green Pink
Jigsaw- For autism awareness Silver- For dyslexia awareness Yellow- Support for the army Red HIV/AIDS awareness symbolizing passion, a heart and love White- Raises awareness for the right to life Grey-
More informationg to onsultant t Learners rkshop o W tional C ces.net I Appealin eren Nancy Mikhail esour Educa Diff Curriculum Resources CurriculumR
Curriculum Resources www.curriculumresources.net 714.406.3522 Follow Us for FREE resources, current educational topics, tips, and more! Appealing to Different Learners Workshop Nancy Mikhail Educational
More informationMinitab Tutorial (Version 17+)
Minitab Tutorial (Version 17+) Basic Commands and Data Entry Graphical Tools Descriptive Statistics Outline Minitab Basics Basic Commands, Data Entry, and Organization Minitab Project Files (*.MPJ) vs.
More informationStochastic Calculus for Finance I (46-944) Spring 2008 Syllabus
Stochastic Calculus for Finance I (46-944) Spring 2008 Syllabus Introduction. This is a first course in stochastic calculus for finance. It assumes students are familiar with the material in Introduction
More informationSTT 231 Test 1. Fill in the Letter of Your Choice to Each Question in the Scantron. Each question is worth 2 point.
STT 231 Test 1 Fill in the Letter of Your Choice to Each Question in the Scantron. Each question is worth 2 point. 1. A professor has kept records on grades that students have earned in his class. If he
More informationHow to Use Vocabulary Maps to Deliver Explicit Vocabulary Instruction: A Guide for Teachers
How to Use Vocabulary Maps to Deliver Explicit Vocabulary Instruction: A Guide for Teachers Overview and Materials Objective Students will increase academic vocabulary knowledge through teacher-provided
More informationACADEMIC ALIGNMENT. Ongoing - Revised
ACADEMIC ALIGNMENT Sandra Andrews December 2012 Erin Busscher, John Dersch, William Faber, Lorraine Fortuna, Laurie Foster, Wilfred Gooch, Fiona Hert, Diane Patrick, Paula Sullivan and Vince James Part
More informationSMARTboard: The SMART Way To Engage Students
SMARTboard: The SMART Way To Engage Students Emily Goettler 2nd Grade Gray s Woods Elementary School State College Area School District esg5016@psu.edu Penn State Professional Development School Intern
More informationLahore University of Management Sciences. FINN 321 Econometrics Fall Semester 2017
Instructor Syed Zahid Ali Room No. 247 Economics Wing First Floor Office Hours Email szahid@lums.edu.pk Telephone Ext. 8074 Secretary/TA TA Office Hours Course URL (if any) Suraj.lums.edu.pk FINN 321 Econometrics
More informationAlberta Police Cognitive Ability Test (APCAT) General Information
Alberta Police Cognitive Ability Test (APCAT) General Information 1. What does the APCAT measure? The APCAT test measures one s potential to successfully complete police recruit training and to perform
More informationUnit 1: Scientific Investigation-Asking Questions
Unit 1: Scientific Investigation-Asking Questions Standards: OKC 3 Process Standard 3: Experimental design - Understanding experimental designs requires that students recognize the components of a valid
More informationBlank Table Of Contents Template Interactive Notebook
Blank Template Free PDF ebook Download: Blank Template Download or Read Online ebook blank table of contents template interactive notebook in PDF Format From The Best User Guide Database Table of Contents
More informationLongman English Interactive
Longman English Interactive Level 3 Orientation Quick Start 2 Microphone for Speaking Activities 2 Course Navigation 3 Course Home Page 3 Course Overview 4 Course Outline 5 Navigating the Course Page 6
More informationEvidence-based Practice: A Workshop for Training Adult Basic Education, TANF and One Stop Practitioners and Program Administrators
Evidence-based Practice: A Workshop for Training Adult Basic Education, TANF and One Stop Practitioners and Program Administrators May 2007 Developed by Cristine Smith, Beth Bingman, Lennox McLendon and
More informationGenevieve L. Hartman, Ph.D.
Curriculum Development and the Teaching-Learning Process: The Development of Mathematical Thinking for all children Genevieve L. Hartman, Ph.D. Topics for today Part 1: Background and rationale Current
More informationEnglish Nexus Offender Learning
Working as a catering assistant Topic Vocabulary and functional language for a catering assistant s role. Level: Entry 3 / National 4 Time: 90 minutes Aim To become more familiar with the job description
More informationWASHINGTON Does your school know where you are? In class? On the bus? Paying for lunch in the cafeteria?
(870 Lexile) Instructions: COMPLETE ALL QUESTIONS AND MARGIN NOTES using the CLOSE reading strategies practiced in class. This requires reading of the article three times. Step 1: Skim the article using
More informationE-3: Check for academic understanding
Respond instructively After you check student understanding, it is time to respond - through feedback and follow-up questions. Doing this allows you to gauge how much students actually comprehend and push
More informationSecret Code for Mazes
Secret Code for Mazes ACTIVITY TIME 30-45 minutes MATERIALS NEEDED Pencil Paper Secret Code Sample Maze worksheet A set of mazes (optional) page 1 Background Information It s a scene we see all the time
More informationWHAT ARE VIRTUAL MANIPULATIVES?
by SCOTT PIERSON AA, Community College of the Air Force, 1992 BS, Eastern Connecticut State University, 2010 A VIRTUAL MANIPULATIVES PROJECT SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR TECHNOLOGY
More informationConsequences of Your Good Behavior Free & Frequent Praise
Statement of Purpose The aim of this classroom is to be a comfortable, respectful and friendly atmosphere in which we can learn about social studies. It is okay if you make mistakes because it is often
More informationEmpiricism as Unifying Theme in the Standards for Mathematical Practice. Glenn Stevens Department of Mathematics Boston University
Empiricism as Unifying Theme in the Standards for Mathematical Practice Glenn Stevens Department of Mathematics Boston University Joint Mathematics Meetings Special Session: Creating Coherence in K-12
More information