Lesson Central Limit Theorem for Sample Means
|
|
- Allan Johns
- 5 years ago
- Views:
Transcription
1 STATWAY STUDENT HANDOUT STUDENT NAME DATE INTRODUCTION Exploring Sampling Distributions In lesson you found random samples from a population of 400 real acorn weights. In this lesson you will use computer simulations to further your understanding of sampling distributions of sample means. You will pay special attention to the shape of the population distribution and how it compares to the shape of the sampling distribution for different sample sizes. This lesson uses the applet from your homework in Lesson : TRY THESE Sampling from a Uniformly Distributed Population To begin, we initially sample from a population that is uniformly distributed. We will simulate 1000 random samples using three different sample sizes. Set the population to uniform by adjusting the top input box. The population distribution is the top graph. Set the Population type to Uniform, and then click the Reset button. 1 Describe the shape of this population. What are the possible values in this population?
2 STATWAY STUDENT HANDOUT 2 2 Does it appear that some of the (discrete) population values are more likely to occur than others? Below the population curve is a plot of sample data. On the side there is a Sample button, and two input boxes. Set the sample size, n, to 2 Set the number of samples, N, to 1000 Click Sample In the Sample data plot, you see the results of a single sample of size 2. Below this, in the Sample means plot, you see the sample means from 1000 random samples of size 2. 3 What is the range of the sample means in this simulated sampling distribution? 4 What is the shape of the simulated sampling distribution? 5 Sketch the simulated sampling distribution, when n = 2, in the box below. Run the simulation for sample sizes n = 10, and n = 30. Sketch your results in the boxes below. For each simulation, set N = 1000 so 1000 random samples are created. Uniform Population n = 2 n = 10 n = 30
3 STATWAY STUDENT HANDOUT 3 6 What happens to the center and variability of the simulated sampling distribution when the sample size increases to n = 30? 7 Identify the mean and standard deviation (or error) of the simulated sampling distribution when n = 30. How do they compare to the mean and standard deviation of the population? Sampling from a Skewed Right Population We will now sample from a population whose distribution is skewed right. We will again simulate 1000 random samples using three different sample sizes. Set the Population type to Skewed, and then click the Reset button. If you want to make the population distribution more skewed, drag your mouse pointer along the population graph and adjust the shape. Set the sample size, n, to 2 and set the number of samples, N, to 1000 Click Sample 8 What is the range of the sample means in this simulated sampling distribution? 9 What is the shape of the simulated sampling distribution?
4 STATWAY STUDENT HANDOUT 4 10 Sketch the simulated sampling distribution, when n = 2, in the box below. Run the simulation for sample sizes n = 10, and n = 30. Sketch your results in the boxes below. For each simulation, set N = 1000 so 1000 random samples are created. Skewed Right Population n = 2 n = 10 n = What happens to the center and variability of the sampling distribution when the sample size increases to n = 30? 12 Identify the mean and standard deviation (or error) of the sampling distribution when n = 30. How do they compare to the mean and standard deviation of the population? Sampling from Any Population We now sample from a population with an unusual distribution. Try to create a population distribution so weird, so wild, that even when we increase the sample size, the sampling distribution will not become bell shaped. We will again simulate 1000 random samples using three different sample sizes. Set the Population type to Custom, and then click the Reset button. Click on the population graph to draw the wildest population you can imagine. Set the sample size, n, to 2 and set the number of samples, N, to Click Sample.
5 STATWAY STUDENT HANDOUT 5
6 STATWAY STUDENT HANDOUT 6 13 Sketch your population in the box below. 14 What is the range of the sample means in this simulated sampling distribution? 15 What is the shape of the sampling distribution? 16 Sketch the sampling distribution, when n = 2, in the box below. Run the simulation for sample sizes n = 10, and n = 30. Sketch your results in the boxes below. For each simulation, set N = 1000 so 1000 random samples are created. The Wild Population n =2 n =10 n = What happens to the center and variability of the sampling distribution when the sample size increases to n = 50?
7 STATWAY STUDENT HANDOUT 7 18 Identify the mean and standard deviation (or error) of the sampling distribution when n = 50. How do they compare to the mean and standard deviation of the population? Sampling from a Normal Population For the last example, we sample from a normal population. Set the Population type to Bell shaped, and then click the Reset button. Set the sample size, n, to 2 and set the number of samples, N, to Click Sample 19 Does the distribution of sample means appear normal? 20 Experiment with different values of n, up to 100, clicking Sample for each. Are you able to construct any distribution of sample means that does not appear normal for any sample size? 21 When sampling from a normal population, is any restriction upon sample size necessary in order for the distribution of sample means to be normal?
8 STATWAY STUDENT HANDOUT 8 YOU NEED TO KNOW The Given any population with mean µ and standard deviation σ, the sampling distribution of sample means sampled with replacement from random samples of size n will have a distribution that approaches normality with increasing sample size. The mean and standard error of the sampling distribution are: The criteria for the approximate normality of a sampling distribution are that either the population from which we are sampling should be normal, or the sample size should be greater than 30. Very non-normal populations may require samples substantially larger than 30. TAKE IT HOME 1 A possible population distribution is one that is triangular. Use the applet to construct a triangular population distribution. A Use the Central Limit Theorem to calculate the mean and standard error of the sampling distribution when the sample size becomes very large. Use the population mean and standard deviation. B How does the shape of the sampling distribution change as the sample size increases?
9 STATWAY STUDENT HANDOUT 9 C How close are the values from (a) to the mean and standard error of your sampling distribution? 2 Yet another possible population distribution is one that is bimodal. For example, suppose you took samples of the length of human hair in your school. It is probable (but not certain!) that young women tend to have long hair and young men have short hair. Use the applet to construct a bimodal population distribution. A Use the Central Limit Theorem to calculate the mean and standard error of the sampling distribution when the sample size becomes very large. Use the population mean and standard deviation. B How does the shape of the sampling distribution change as the sample size increases? C How close are the values from (a) to the mean and standard error of your sampling distribution?
10 STATWAY STUDENT HANDOUT This lesson is part of STATWAY, A Pathway Through College Statistics, which is a product of a Carnegie Networked Improvement Community that seeks to advance student success. Version 1.0, A Pathway Through Statistics, Statway was created by the Charles A. Dana Center at the University of Texas at Austin under sponsorship of the Carnegie Foundation for the Advancement of Teaching. This version 1.5 and all subsequent versions, result from the continuous improvement efforts of the Carnegie Networked Improvement Community. The network brings together community college faculty and staff, designers, researchers and developers. It is an open-resource research and development community that seeks to harvest the wisdom of its diverse participants in systematic and disciplined inquiries to improve developmental mathematics instruction. For more information on the Statway Networked Improvement Community, please visit carnegiefoundation.org. For the most recent version of instructional materials, visit Statway.org/kernel STATWAY and the Carnegie Foundation logo are trademarks of the Carnegie Foundation for the Advancement of Teaching. A Pathway Through College Statistics may be used as provided in the CC BY license, but neither the Statway trademark nor the Carnegie Foundation logo may be used without the prior written consent of the Carnegie Foundation.
Lesson Least Squares Regression Line as Line of Best Fit
STATWAY STUDENT HANDOUT STUDENT NAME DATE INTRODUCTION Comparing Lines for Predicting Textbook Costs In the previous lesson, you predicted the value of the response variable knowing the value of the explanatory
More informationLesson Mathematical Linear Models
STATWAY STUDENT HANDOUT STUDENT NAME DATE INTRODUCTION Jean needs to buy some meat for her housing co-operative. She can go to the Fresh-Plus store to buy it for $3.50 per pound. Or she can go to the warehouse
More informationLesson Using Residuals to Determine If a Line Is a Good Fit
Ya STTWY STUDENT HNDOUT STUDENT NME DTE INTRODUCTION Recall that a residual (or error) is the difference between the actual value of the response variable and the value predicted by the regression line.
More informationWorksheet: Coulomb Force Simulation
Screen shot of simulation showing force between two charged particles. Worksheet: Coulomb Force Simulation Key Topic/Concept: Coulomb s Law and Newton s 3 rd Law Materials: One guide sheet for each student
More informationMoLE Gas Laws Activities
MoLE Gas Laws Activities To begin this assignment you must be able to log on to the Internet using Internet Explorer (Microsoft) 4.5 or higher. If you do not have the current version of the browser, go
More informationElectrostatic Fields and Forces Lab
Name Page 1 of 5 Period Electrostatic Fields and Forces Lab Go to http://tinyurl.com/337842 or http://linus.highpoint.edu/~atitus/physlets/em_field.html You should see the Electric Field Physlet. Your
More informationMoLE Gas Laws Activities *
MoLE Gas Laws Activities * To begin this assignment you must be able to log on to the Internet using Internet Explorer (Microsoft) 4.5 or higher. If you do not have the current version of the browser,
More informationTEACHER NOTES SCIENCE NSPIRED
Science Objectives Students will explore the force two charges exert on each other. Students will observe how the force depends upon the magnitude of the two charges and the distance separating them. Students
More informationCharles Law: V 1 = V 2 T 1 T 2
Name: Gas Laws Background In this investigation you will examine three gas laws including Boyle s Law, Charles Law and Gay-Lussac s Law. You will explore how manipulating the variables of volume (L), pressure
More information2, or x 5, 3 x 0, x 2
Pre-AP Algebra 2 Lesson 2 End Behavior and Polynomial Inequalities Objectives: Students will be able to: use a number line model to sketch polynomials that have repeated roots. use a number line model
More informationStudent Instruction Sheet: Unit 3, Lesson 3. Solving Quadratic Relations
Student Instruction Sheet: Unit 3, Lesson 3 Solving Quadratic Relations Suggested Time: 75 minutes What s important in this lesson: In this lesson, you will learn how to solve a variety of quadratic relations.
More informationBoyle s Law and Charles Law Activity
Boyle s Law and Charles Law Activity Introduction: This simulation helps you to help you fully understand 2 Gas Laws: Boyle s Law and Charles Law. These laws are very simple to understand, but are also
More informationStudent Instruction Sheet: Unit 2, Lesson 2. Equations of Lines, Part 2
Student Instruction Sheet: Unit 2, Lesson 2 Suggested Time: 50 minutes What s important in this lesson: Equations of Lines, Part 2 In this lesson, you will learn how to write equations of lines, given
More informationPea Patch Pollination Game
Pea Patch Pollination Game Classroom Activity: 5-8 Time: One 45-60-minute class period Overview: In this activity, students play a simulation game modeling changes in a plant population (a Pea Patch) caused
More informationObjective A: Mean, Median and Mode Three measures of central of tendency: the mean, the median, and the mode.
Chapter 3 Numerically Summarizing Data Chapter 3.1 Measures of Central Tendency Objective A: Mean, Median and Mode Three measures of central of tendency: the mean, the median, and the mode. A1. Mean The
More information. As x gets really large, the last terms drops off and f(x) ½x
Pre-AP Algebra 2 Unit 8 -Lesson 3 End behavior of rational functions Objectives: Students will be able to: Determine end behavior by dividing and seeing what terms drop out as x Know that there will be
More informationIntroduction to Gases Guided Inquiry
Introduction to Gases Guided Inquiry Part 1 - The Kinetic Molecular Theory Adapted from a POGIL authored by Linda Padwa and David Hanson, Stony Brook University Why? The kinetic-molecular theory is a model
More informationMath 361. Day 3 Traffic Fatalities Inv. A Random Babies Inv. B
Math 361 Day 3 Traffic Fatalities Inv. A Random Babies Inv. B Last Time Did traffic fatalities decrease after the Federal Speed Limit Law? we found the percent change in fatalities dropped by 17.14% after
More informationA Reinvention course for Calculus
A Reinvention course for Calculus 1 3 5 7 9 11 Working session at PME & PSI 2001, Utrecht, The Netherlands Michiel Doorman Freudenthal Institute, Utrecht University, The Netherlands email: michiel@fi.uu.nl
More informationThis module focuses on the logic of ANOVA with special attention given to variance components and the relationship between ANOVA and regression.
WISE ANOVA and Regression Lab Introduction to the WISE Correlation/Regression and ANOVA Applet This module focuses on the logic of ANOVA with special attention given to variance components and the relationship
More informationObjective: Recognize halves within a circular clock face and tell time to the half hour.
Lesson 13 1 5 Lesson 13 Objective: Recognize halves within a circular clock face and tell time to the half Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief
More informationGuided Inquiry Worksheet 2: Interacting Einstein Solids & Entropy
Guided Inquiry Worksheet 2: Interacting Einstein Solids & Entropy According to the fundamental assumption of statistical mechanics, AT EQUILIBRIUM, ALL ALLOWED MICROSTATES OF AN ISOLATED SYSTEM ARE EQUALLY
More informationLab: Electric Fields Hockey *
Name: Lab: Electric Fields Hockey * Objective: To investigate experimentally the concept of the electric field and to map (to represent graphically) some electric field lines for particular configurations
More informationInquiry Activity Thank you for purchasing this product! This resource is intended for use by a single teacher. If you would like to share it, you can download an additional license for 50% off. Visit your
More informationActivity 8b - Electric Field Exploration
Name Date Activity 8b - Electric Field Exploration Pd Go to the following website: http://phet.colorado.edu Find the heading Run our Simulations and click On Line. Under the Simulations heading, select
More informationLearning Outcomes in Focus
Contextual strand: CW Learning Outcomes in Focus Students should be able to describe and model the structure of the atom in terms of the nucleus, protons, neutrons and electrons; comparing mass and charge
More informationSimulation: Gas Laws FOR THE TEACHER
Simulation: Gas Laws FOR THE TEACHER Summary In this simulation, students will investigate three of the fundamental gas laws, including Boyle s Law, Charles Law and Gay-Lussac s Law. Students will have
More informationLesson 5: The Graph of the Equation y = f(x)
Lesson 5: The Graph of the Equation y = f(x) Learning targets: I can identify when a function is increasing, decreasing, positive and negative and use interval notation to describe intervals where the
More informationRichter Scale and Logarithms
activity 7.1 Richter Scale and Logarithms In this activity, you will investigate earthquake data and explore the Richter scale as a measure of the intensity of an earthquake. You will consider how numbers
More informationHere s the Graph of the Derivative. Tell me About the Function.
Here s the Graph of the Derivative. Tell me About the Function. Presented by Lin McMullin Using its derivatives to determine information about the graph of a function is a standard calculus topic and has
More informationLesson 2-6: Graphs of Absolute Value Equations
Where we re headed today Today we re going to take the net graphing step we ll learn how to graph absolute value equations. Here are the three things you are going to need to be able to do: 1. Match an
More informationIt s Just a Lunar Phase
Science Objectives Students will identify patterns in data associated with the lunar phases. Students will describe how the relative positions of the Earth, the Moon, and the Sun cause lunar phases. Students
More informationSunlight and Temperatures
Lesson Plan for Grades: 6 th 8 th Length of Lesson: 2 hours Authored by: UT Environmental Science Institute Date created: 08/01/2016 Subject area/course: Science, Earth Materials: Angle of the Sun and
More informationCatalysts. Lab Section. Log on to the Internet. Type the following address into the location-input line of your browser:
Catalysts Name Lab Section Log on to the Internet. Type the following address into the location-input line of your browser: http://cheminfo.chem.ou.edu/~mra/ccli2004/kcatbgm.htm This will load a Particulate
More informationLab 5 for Math 17: Sampling Distributions and Applications
Lab 5 for Math 17: Sampling Distributions and Applications Recall: The distribution formed by considering the value of a statistic for every possible sample of a given size n from the population is called
More informationExpressions and Equations
8 8.EE.7b Objective Common Core State Standards Expressions and Equations Solving Equations with Variables on Both Sides Another form of multi-step equations involves variables on both sides of the equation.
More informationUnit 1: Scientific Inquiry/Forces and Motion Newton s Laws Simulation Investigation
name: period: Learning Objective: Students will understand that the motion of objects depends on the sum of the forces on the object and the mass of the object. Background Information: Complete the following
More informationSection 2.3: One Quantitative Variable: Measures of Spread
Section 2.3: One Quantitative Variable: Measures of Spread Objectives: 1) Measures of spread, variability a. Range b. Standard deviation i. Formula ii. Notation for samples and population 2) The 95% rule
More informationField of dreams, the REAL reason you are safe in your car in a lightning storm!
Field of dreams, the REAL reason you are safe in your car in a lightning storm! 1.1 Diagram Jeopardy. E field vectors due to one or more electrically charged objects are shown below. Indicate with circles,
More informationThe Normal Distribution. Chapter 6
+ The Normal Distribution Chapter 6 + Applications of the Normal Distribution Section 6-2 + The Standard Normal Distribution and Practical Applications! We can convert any variable that in normally distributed
More informationGas Pressure and Temperature Relationships *
Gas Pressure and Temperature Relationships * MoLE Activities To begin this assignment you must be able to log on to the Internet (the software requires OSX for mac users). Type the following address into
More informationAP Physics 1: Algebra-Based
2017 AP Physics 1: Algebra-Based Sample Student Responses and Scoring Commentary Inside: Free Response Question 5 Scoring Guideline Student Samples Scoring Commentary 2017 The College Board. College Board,
More informationLesson 5b Solving Quadratic Equations
Lesson 5b Solving Quadratic Equations In this lesson, we will continue our work with Quadratics in this lesson and will learn several methods for solving quadratic equations. The first section will introduce
More informationCenter of Mass. Evaluation copy
Center of Mass Experiment 19 INTRODUCTION In the most of the previous experiments you have examined the motion of a single object as it underwent a variety of motions. You learned that an object subject
More informationAP Calculus BC. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 5. Scoring Guideline.
017 AP Calculus BC Sample Student Responses and Scoring Commentary Inside: RR Free Response Question RR Scoring Guideline RR Student Samples RR Scoring Commentary 017 The College Board. College Board,
More informationHMH Fuse Algebra correlated to the. Texas Essential Knowledge and Skills for Mathematics High School Algebra 1
HMH Fuse Algebra 1 2012 correlated to the Texas Essential Knowledge and Skills for Mathematics High School Algebra 1 111.32. Algebra I (b) Knowledge and skills. (1) Foundations for functions. The student
More informationGEOMETRY (and Honors)
GEOMETRY (and Honors) Welcome to Geometry! Geometry will be challenging but rewarding!! This full year course requires that everyone work hard and study for the entirety of the class. You will need a large
More informationMath 261 Sampling Distributions Lab Spring 2009
Math 261 Sampling Distributions Lab Spring 2009 Name: Purpose After completing this lab, you should be able to distinguish between the distribution of the population, distribution of the sample, and the
More informationLesson Plan: Introduction to Quantum Mechanics via Wave Theory and the Photoelectric Effect
Lesson Plan: Introduction to Quantum Mechanics via Wave Theory and the Photoelectric Effect Will Stoll, Norcross High School Problem: To understand the basic principles of Quantum Mechanics through an
More informationUse your hypothesis (the mathematical model you created) from activity 4.1 to predict the man s position for the following scenarios:
4.1 Hypothesize Lesson 4: The Moving Man An object is moving in the positive direction at constant velocity v. It starts at clock reading t = 0 sec, at a position x 0. How would you write a function that
More information171S4.3 Polynomial Division; The Remainder and Factor Theorems. October 26, Polynomial Division; The Remainder and Factor Theorems
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions 4.3 Polynomial
More information171S4.3 Polynomial Division; The Remainder and Factor Theorems. March 24, Polynomial Division; The Remainder and Factor Theorems
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 4: Polynomial and Rational Functions 4.1 Polynomial Functions and Models 4.2 Graphing Polynomial Functions 4.3 Polynomial
More information!""""""""""""""""""""""""""""""""""""""""""""""""""#$%&'()*+",&-./'&%"0*".1&"2/*"
ENGAGING IN ASTRONOMICAL INQUIRY 89 """"""""""""""""""""""""""""""""""""""""""""""""""#$%&'()*+",&-./'&%"0*".1&"2/*" Big Idea: The Sun has surface features in different wavelengths and those features have
More informationTEACHER NOTES SCIENCE NSPIRED
Science Objectives Students will investigate the effects of mass, spring constant, and initial displacement on the motion of an object oscillating on a spring. Students will observe the relationships between
More informationAP Biology. Sample Student Responses and Scoring Commentary. Inside: Free Response Question 5. Scoring Guideline. Student Samples. Scoring Commentary
2017 AP Biology Sample Student Responses and Scoring Commentary Inside: Free Response Question 5 Scoring Guideline Student Samples Scoring Commentary 2017 The College Board. College Board, Advanced Placement
More informationADVANCED ALGEBRA (and Honors)
ADVANCED ALGEBRA (and Honors) Welcome to Advanced Algebra! Advanced Algebra will be challenging but rewarding!! This full year course requires that everyone work hard and study for the entirety of the
More information6 THE NORMAL DISTRIBUTION
CHAPTER 6 THE NORMAL DISTRIBUTION 341 6 THE NORMAL DISTRIBUTION Figure 6.1 If you ask enough people about their shoe size, you will find that your graphed data is shaped like a bell curve and can be described
More informationWhat Is a Sampling Distribution? DISTINGUISH between a parameter and a statistic
Section 8.1A What Is a Sampling Distribution? Learning Objectives After this section, you should be able to DISTINGUISH between a parameter and a statistic DEFINE sampling distribution DISTINGUISH between
More informationShow all work on separate grid and lined paper. Number each question clearly.
Algebra summer homework 2015 In addition to the practice problems below, students are to work in IXL.com in the 8 th grade content. Students must know all of the perfect squares from 1 to 625 for automatic
More information10.1.1Theorem: Module 4 : Local / Global Maximum / Minimum and Curve Sketching
\ Module 4 : Local / Global Maximum / Minimum and Curve Sketching Lecture 10 : Sufficient conditions for increasing / decreasing [Section 10.1] Objectives In this section you will learn the following :
More information5.2.3 Systems of Equations (Substitution Method)
Lesson: 5.2.3 Systems of Equations (Substitution Method) 5.2.3 Alternate Systems of Equations (Substitution Method) Teacher Lesson Plan CC Standards 8.EE.8b 8.EE.8c Solve systems of two linear equations
More informationMATH 1314 College Algebra Scott Travis Fall 2014 Review for Exam #2
MATH 1314 College Algebra Scott Travis Fall 2014 Review for Exam #2 There are eight sections from Chapters 4 and 5 included in the exam: 4.1, 4.3, 5.1 to 5.6. This review should help you prepare. For each
More informationAP Calculus AB 2006 Free-Response Questions Form B
AP Calculus AB 006 Free-Response Questions Form B The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students
More informationOPEN LESSON SAMPLE LESSONS FOR THE CLASSROOM FROM LAYING THE FOUNDATION
OPEN LESSON SAMPLE LESSONS FOR THE CLASSROOM FROM LAYING THE FOUNDATION Middle Grades Science Sugar and Salt Solutions Exploring Common Substances Using a PhET Simulation About this Lesson This activity
More informationCHEM 1413 Course Syllabus (CurricUNET) Course Syllabus
Semester with Course Reference Number (CRN) CHEM 1413 Course Syllabus (CurricUNET) Course Syllabus College Chemistry I CHEM 1413 Instructor contact information (phone number and email address) Office Location
More informationWISE Regression/Correlation Interactive Lab. Introduction to the WISE Correlation/Regression Applet
WISE Regression/Correlation Interactive Lab Introduction to the WISE Correlation/Regression Applet This tutorial focuses on the logic of regression analysis with special attention given to variance components.
More informationAP Calculus. Limits, Continuity, and Differentiability
AP Calculus Limits, Continuity, and Differentiability Student Handout 016 017 EDITION Click on the following link or scan the QR code to complete the evaluation for the Study Session https://www.surveymonkey.com/r/s_sss
More informationStudent Exploration: Seasons in 3D
Name: Date: Student Exploration: Seasons in 3D Vocabulary: axis, equinox, latitude, Northern Hemisphere, revolve, rotate, solar energy, solar intensity, Southern Hemisphere, summer solstice, winter solstice
More informationUsing the computer simulation, be able to define and apply vectors appropriately.
Using the computer simulation, be able to define and apply vectors appropriately. Please visit the vector addition site at: http://phet.colorado.edu/en/simulation/vector-addition Before you begin these
More informationTechnologies for Learning - Velocity and Acceleration
Technologies for Learning - Velocity and Acceleration The goal of this unit is to understand how different technologies and approaches can contribute to the understanding of velocity and acceleration.
More informationUnit 1: Applications of Matter & Chemical Change
Unit 1: Applications of Matter & Chemical Change Lesson 4 - Word Equations & Types of Chemical Reactions Approximate Lesson Length: 75 minutes Subject Line for Email: SCI24U1L4 Lesson Objectives: Upon
More informationWeb sites and Worksheets
Introduction Web sites and Worksheets Sandra Woodward Oakhill College Castle Hill (swoodward@oakhill.nsw.edu.au) Astronomy is a practical subject by nature. Unfortunately for teachers, many of the practical
More informationUnit 3: Principles of Mechanical Engineering. LO5: Understand principles of dynamic systems
Unit 3: Principles of Mechanical Engineering LO5: Understand principles of dynamic systems Coefficient of friction/limiting friction Instructions and answers for teachers These instructions should accompany
More informationSignificant Figures. CK12 Editor. Say Thanks to the Authors Click (No sign in required)
Significant Figures CK12 Editor Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content,
More information60 C From Bicycle to Space. Dionysis Konstantinou Corina Toma. Space Travel
60 C From Bicycle to Space Dionysis Konstantinou Corina Toma C Space Travel From Bicycle Length to Space of the CDay61 introduction Imagine travelling from one planet to another Why is it that we have
More informationLO6: Know the basic principles of thermal physics Boyle s Law, Charles Law and the Pressure Law Instructions and answers for teachers
Unit 2: Science for Engineering LO6: Know the basic principles of thermal physics Boyle s Law, Charles Law and the Pressure Law Instructions and answers for teachers These instructions should accompany
More informationEnhanced Instructional Transition Guide
1-1 Enhanced Instructional Transition Guide High School Courses Unit Number: 7 /Mathematics Suggested Duration: 9 days Unit 7: Polynomial Functions and Applications (15 days) Possible Lesson 1 (6 days)
More informationAir Resistance. Experiment OBJECTIVES MATERIALS
Air Resistance Experiment 13 When you solve physics problems involving free fall, often you are told to ignore air resistance and to assume the acceleration is constant and unending. In the real world,
More informationAP Calculus AB 2015 Free-Response Questions
AP Calculus AB 015 Free-Response Questions College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online
More informationAP Physics 1 Summer Assignment Packet
AP Physics 1 Summer Assignment Packet 2017-18 Welcome to AP Physics 1 at David Posnack Jewish Day School. The concepts of physics are the most fundamental found in the sciences. By the end of the year,
More informationRecommended Grade Level: 8 Earth/Environmental Science Weather vs. Climate
Lab Activity Title: Climate Factors Past and Present Recommended Grade Level: 8 Discipline: Earth/Environmental Science Topic: Weather vs. Climate Time Requirements: 90 minutes Submitted by: Karen McCabe
More informationUsing Exploration and Technology to Teach Graph Translations
Using Eploration and Technology to Teach Graph Translations Rutgers Precalculus Conference March 16, 2018 Frank Forte Raritan Valley Community College Opening Introduction Motivation learning the alphabet
More informationES205 Analysis and Design of Engineering Systems: Lab 1: An Introductory Tutorial: Getting Started with SIMULINK
ES205 Analysis and Design of Engineering Systems: Lab 1: An Introductory Tutorial: Getting Started with SIMULINK What is SIMULINK? SIMULINK is a software package for modeling, simulating, and analyzing
More informationLesson 12: Position of an Accelerating Object as a Function of Time
Lesson 12: Position of an Accelerating Object as a Function of Time 12.1 Hypothesize (Derive a Mathematical Model) Recall the initial position and clock reading data from the previous lab. When considering
More informationMathematics E-15 Seminar on Limits Suggested Lesson Topics
Mathematics E-15 Seminar on Limits Suggested Lesson Topics Lesson Presentation Guidelines Each lesson should last approximately 45 minutes. This will leave us with some time at the end for constructive
More informationDP Physics Torque Simulation
DP Physics Torque Simulation Name Go to Phet Simulation: ( http://phet.colorado.edu/simulations/sims.php?sim=torque ) Part I: Torque 1. Click the tab at the top that says torque 2. Set the force equal
More informationAP Calculus AB. Free-Response Questions
2018 AP Calculus AB Free-Response Questions College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online
More informationCC Algebra 2H Transforming the parent function
CC Algebra H Transforming the Name: March. Open up the geometer s sketchpad document on Mr. March s website (It s under CC Algebra Unit Algebra Review). Make sure ou maimize both windows once ou open the
More informationActivity 2 MODELING LAB
Activity 2 MODELING LAB PURPOSE. This activity sets up the rest of the ExoLab investigation, and is intended to help your students predict what the signal of an alien world might look like. They use the
More informationACCUPLACER Sample Questions for Students
ACCUPLACER Sample Questions for Students 0 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn logo are registered trademarks of the College Board. All other products and services may
More information1 What s Way Out There? The Hubble Ultra Deep Field
ENGAGING IN ASTRONOMICAL INQUIRY 5 1 What s Way Out There? The Hubble Ultra Deep Field Big Idea: The Hubble Space Telescope image Hubble Ultra Deep Field reveals a variety of previously unknown objects
More informationTASC Transition Curriculum Project
TASC Transition Curriculum Project MODULE 3: WORKSHOP 9 REVIEWING THE CROSS-CUTTING CONCEPTS INVOLVED IN SOLVING PROBLEMS PLACED ON STUDENTS IN TASC ABOUT DISCIPLINARY CORE IDEAS POSED IN THE PHYSICAL
More informationName: Block: Date: Electrical Potentials and Electrical Fields: Potentially Dangerous Situations
Name: Block: Date: Electrical Potentials and Electrical Fields: Potentially Dangerous Situations Part A: Introduction 1. Open the Charges and Fields application. 2. On the right-hand-side, activate the
More informationAir Resistance. Experiment OBJECTIVES MATERIALS
Air Resistance Experiment 13 When you solve physics problems involving free fall, often you are told to ignore air resistance and to assume the acceleration is constant and unending. In the real world,
More informationPLEASANTON UNIFIED SCHOOL DISTRICT 8 Course Outline Form
PLEASANTON UNIFIED SCHOOL DISTRICT 8 Course Outline Form Course Title: Math 8 Course Number/CBED Number: Grade Levels: Length of Course: Eighth Grade One Year Credit: 10 Meets Graduation Requirements:
More informationAppearances Can Be Deceiving!
Appearances Can Be Deceiving! Overview: Students explore the relationship between angular width, actual size, and distance by using their finger, thumb and fist as a unit of angular measurement in this
More informationx 2 = 4 x = ± 4 x = +2 The graph shows that in each case the related function intersects the x-axis in two places.
Algebra II: Strand 3. Quadratic Functions; Topic. Digging Deeper; Task 3.. 1 TASK 3..: WHEN DOES A QUADRATIC FUNCTION DO THAT? Solutions 1. Consider quadratic equations of the form x + c = 0, where c is
More informationACCUPLACER Sample Questions for Students
ACCUPLACER Sample Questions for Students 0 The College Board. College Board, ACCUPLACER, WritePlacer and the acorn logo are registered trademarks of the College Board. All other products and services may
More informationStudent Exploration: Air Track
Name: Date: Student Exploration: Air Track Vocabulary: air track, approach velocity, conservation of energy, conservation of momentum, elasticity, kinetic energy, momentum, separation velocity, velocity
More informationMath 1241, Spring 2014 Section 3.3. Rates of Change Average vs. Instantaneous Rates
Math 1241, Spring 2014 Section 3.3 Rates of Change Average vs. Instantaneous Rates Average Speed The concept of speed (distance traveled divided by time traveled) is a familiar instance of a rate of change.
More information