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1. THE ART AND SCIENCE OF SIGNIFICANT FIGURES HOW TO DO MATH IN CHEMISTRY This presentation is a sequence of scenes that take students from thinking about measurement to how to work with the numbers properly when using them to solve math problems 7 ie 12 12 2012 MELISSAGETZ 2012 ALL RIGHTS RESERVED TABLE OF CONTENTS Introduction Target learners Purpose and objectives Equipment you need Hardware Requirements Software Requirements Network connections Getting Started CD or network access Program startup procedure Normal running of the courseware Time to complete the courseware User Interface Components parts of the program Scene 1 Starting and About Measurement Scene 2 Rules Scene 3 Rounding Numbers Scene 4 Multiplication and Division with Significant Figures Scene 5 Dimensional Analysis Scene 6 Adding and Subtracting with Significant Figures Ending the program Troubleshooting Index 11 15 15 15 16 INTRODUCTION TARGET LEARNERS The target learners are chemistry students Ideally all high school chemistry students are taught about significant figures but some teachers do not teach about it In these situations there are students heading off to college where the professors expect students to use the correct significant figures in their answers but for many college students who have never seen the concept before it is very overwhelming The finished version will be pu2. Welcome Why do DA Let s convert oan Welcome to the segment Fm net doing it in my head tha Continuing example problem m sbi aan SPN on Dimensional Analysis Solving the problem done yet ates realization ae sig figs with DA ail i part 1 finished This is being done in Storyline by Articulate because Flash crashed and N want to see if it is easier to do an f interactive story here than in Flash Explanation route Welcome ta Explanations All conversion factors 1 Now where Practice route Welcome to the practice route Drag and Drop Drag and Drop Drag and Drop prag and Drop Note there are a couple frames that have a conversation or items zs a ie showing up at set times Please wait for everything to do its thing E before you click on the next button hope to have a click on Where to next message show up on frames that you need to advance after the animations are done Quiz route Welcome to the quiz route PREV NEXT gt Menu _ Dimensional Analysis Welcome Why do DA Let s convert Drag and Drop Drag and Drop Drag and Drop Drag and Drop Drag and Drop Drag and Drop Where to Quiz route Welcome to the quiz route Will become Continuing example Continuing example problem Solving the problem done yet realization sig figs with DA part 1 finished v Explanation route Welcome to Explanations All conversion factors 1 Now where v Practic
3. Scene click the words tha state where y want to go Rules for when the number next to the last one is less than 5 click the words th l a ART S Rules for when the number next to want to go the last one is 5 or greater click the words tha s state where you How to keep track of Significant eee figures when rounding Click on one of the three Rounding Scene categories or on a different scene using the buttons below Stat Rules Rounding Multiplication Dimensional Addition Numbers Division Analysis Subtraction nero i Cumulahwe gur Multiplication niytam Dimarakral ralysi Addition Subtraction Ci E T i figures The main rules for rounding are 4 and below round down or chop off and 5 and above round up Since those are even a bit vague each of those sections is full of examples of how to round various numbers The section on keeping track of significant figures when rounding is one of the more informative parts of the curriculum Even if students know how to round they should at least watch and read through the section on how to keep track of significant figures when also rounding a number To get to a section that describes the rule and gives examples click on the title of the section in the right column after the arrows Are you ready for a real quiz on rounding to the correct number of significant figures Keep this frame open so you can come back Start over and pick your next de
4. arrow Tou Sre here f wl Pikes Ranging Thi way for some Practice in Articulate F E AE S bbb Sun ulelrew Greclyaia Seb rmecsnneal Be careful about rounding Every time you round you are Incorporating some error Don t round until the very end Since conversion factors are shon Subtractiurt Analysis Addin Tilt nei meal ye This is one of the frames that has lots of examples Take the time to notice that first a problem is given then the answer before rounding When calculating to a specific number of Significant figures rounding is usually involved The third column identifies how many significant figures need to be in the final answer You learn how to determine this in the Multiplication Division scene Finally the last column shows you what the correct answer would be for that problem One frame in the Multiplication Division tounes scene has a few questions 380 that let students test themselves before they 32 0 move on to doing more 39 practice questions made in L the Articulate software Again leave this frame or 120 the next one open it has a 10 start over button and the answers so that upon 1 4 x 10 returning to the Flash presentation a new scene can be chosen unique the next scene focuses on how to do dimensional analysis and how to handle conversion factors Cumulate Quir 10 SCENE 5 DIMENSIONAL ANALYSIS Dimensional Analysis Sc
5. 735 has 7 significant fiqures 3 has 1 significant figure 25 93 has 4 significant figures Now you try H youa Soe nS and WOU are Peedy to taka the resi quiz on how many ag Ags are in a mambe cick on the button for the Fed Gur eshma Go to Real Quiz Questions You are r ur z harg 5 3 T De i 5 oe DE F This image shows you what the Practice page looks like for the numbers 1 9 rules Examples are provided so that players can make sense of what they see and connect how many digits are in the number with how many Significant figures are in the number Notice there is both a practice and a quiz button Both of these parts of the exercise were written in Articulate Practice Additianm Subtraction Dirmarskinal Analysis Tumulahwe Storyline because the software is easier to use than Flash to write questions You Should allow your browser to open a new tab or window so the exercises can load The main lesson file will remain open in Flash while you work Chun through the questions in Articulate unless you close your browser s window The idea is to leave the Flash lesson and go to a new window to practice what you have learned This also gives you an opportunity to go back to the explanations in Flash if you need to review the content Significant figures and Scientific Notation All numbers expressed in scientific notation ARE significant 2 349 x 10 has four significan
6. e route Welcome to the practice route Drag and Drop Drag and Drop Drag and Drop Drag and Drop Drag and Drop Drag and Drop Drag and Drop Where to Quiz route Welcome to the quiz route I m not doing it in my head that s for sure I m not doing it in my head that s for sure I ll do it on paper and will organize my work in a specific way that I ll be sure will i i If the viewer is give me the right answer patient and If we have 5 2 inches how waits for the The question many centimeters do we have frame to load The first thing we do is write down what we are given and the units we are looking for 5 2 inches centimeters please click next 12 M a pi DimensionalAnalysis gt Dimensional Analysis Resources v Explanation route Cine Explanations The Problem This IS an example of a All conversion factors 1 Stuff to know Convert 745 cm to meters saci setae ds Drag the object to their correct locations so that solving D ra g an d D ro p Practice route 414i he problem can be done co ly Note not all objects i Welcome to the practice route ee phe be Sie i m aiis q u esti on Al Ong the top Drag and Drop a ced 100cm 1meter 745cm 1000mm meters S SOMe Information Drag and Drop needed for the problem Drag and Drop Drag and Drop Drag and Drop Where to Quiz route Welcome to the quiz route X Do not assume that because the item
7. ene The Dimensional Analysis Scene in Flash ns IS one single frame Because there are Dimensional analysis is a tool d dd tivities in thi you can use to solve any problem B ag ARGAE ae ma ha PIENS that involves units section it was created in Articulate s Storyline software Leave this frame 45 q F iiki 45g x EMI m open in Flash to continue on to the last ag ag scene Addition and Subtraction Since Flash cashed while I ws making this project 1 went ower to Storyline to do the dimensional analysis fram s Pleas click om the geto Storyline button so tne sin var wyline story wil opan in wow browser Keep this presentation open so you can continue with its lick this button a go to Storyline content when you are done for the dimensia analysis story with the story Stat Rules Rounding Multiplication Dimensional Addition You are ki ay E F 5 z hore F 3 4 3 cs 5 z m et E E E oe ee C Ge te Eo mi 4 The Articulate Storyline software allows there to be a navigation screen in addition to buttons at the bottom of the frames Most people navigate through using the prev or next buttons Prev takes you to the previous frame whereas Next takes you to the next frame Some of the writing in these frames is set on a timer so a frame may look completely empty in the beginning but by the end of the frame it is full of content Meri 7 DimensionalAnalysis Dimensional Analysis Resources
8. figures in a number When you are done come back here and click on the start over button so you can pick another scene You ane welcome to review each of the J TE a Lae Rules sections before N umbers 7eroes scientific PTA 1 9 Notation Start over I want one last practice before I take the real quiz Practice 50 to Real Quiz Questions You are y heres A Aj SCENE 3 ROUNDING NUMBERS Wk Rounding Cumulaiwg Qui Muloplicabon Oihwisiam Dimensional Arial ysis Addition Subtraction Then comes along the last frame of the Rules Scene It looks chaotic but each button has a purpose Some people may want to review the rules so there is a button that will take players back to the first scene for each section of the rules Some may not want to do the practice or the quiz and would rather start over so they will start over The Start over button is also there because this ts the frame that will stay open when players go to the Articulate practice or quiz sessions Upon returning back from the Articulate questions players will need to choose another scene to visit Most will continue with the Rounding scene The first frame in the Rounding scene is a little chaotic Essentially there are two rules for rounding and since this is about significant figures there is a third rule just for significant Rounding Numbers scene There are three main parts to the Rounding
9. g Cumuladeg Qui Multiplication Divit Dimarsigmal Firial ysis Adgithan Subtraction The Art and Science of Significant Figures What are significant figures Are you Are you significant significant o a 9 1809600 1809600 7 4 im About Rules Measure ment Click button to advance cartoon Addition Subtraction Bo hE eee Rounding Multiplication Dimensional Numbers Division Analysis If you click on the About Measurement button you will be taken to a NASA video about something that happened when they did not do their original measurement correctly when designing the Hubble telescope After this scene the About Measurement button becomes Start and clicking on it will bring you back to the blank screen waiting for the cartoon to be loaded al Bld SCENE 2 RULES Most people will start off in the Rules scene and do each scene in order from left to right Here are Numbers 1 9 All numbers from i 9 are significant Any number that is a part of a some screenshots of some of the measurement is significant things you may find and what you A value of 1 2 3 4 5 6 7 B or 9 does can do with them not just magically appear in a measurement Here there are 4 buttons After reading the rules for numbers 1 9 They are actually a part of the measurement the players get to choose to start Where would you lka to goto ment over which takes them back to the Start screen go to the r
10. nt know that it is ok to come back and redo the question at a later time t Dimensional Analysis Resources l EEEE lanations Stuff to know The Problem ay os ii 35 wigs 4 oats Convert 400 wigs to flues conversion factors 1 45 gafe GS Flues Now where a l Drag the object to their correct locations so that solving the 70 flues 10 hoos aes problem can be done correctly ekeedeiie maces Note not all objects will be used Drag and Grop F i ae eaves 35 wigs 10 hoos wigs 400 flues Drag and Drop ba atin Tlues 400 wigs 400 Drag and Drop oafs Drag and Drop Drag and Drop eee 65 flues 70 flues Quiz route Welcome to the quiz route a 7 hoos ASoafs X Xx 7 4 oafs oats Do not assume that because the item stuck that it is in a right spot Click submit to find out if you are correct Not every item is used SUBMIT The dimensional analysis section covers how to set up not just one conversion factor but two Fictional equations are used so students can focus on the structure of dimensional analysis and not on the reality of what is being converted 14 SCENE 6 ADDING AND SUBTRACTING WITH SIGNIFICANT FIGURES Adding and Subtracting Scene Adding and subtracting with significant Finally the last scene Adding Figures is just really annoying Fortunately fee 8 Sime ears meeeecon and Subtracting explains how fice eed wel coerce eink values keeping track of significa nt figures when adding or ea ta
11. nts who do not already understand how to do calculations with significant figures and is more of a tutorial than a summative assessment If students take time to read each scene it could take them anywhere from an hour to get through all of the scenes and exercises that have been written to a couple or even a few hours to reread the rules and redo the exercises USER INTERFACE COMPONENTS PARTS OF THE PROGRAM General operation The presentation is packed with buttons and choices Here are some screenshots to help explain what you are about to encounter The presentation starts off looking empty If you click on the button like it suggests you will get to see the introductory cartoon SCENE 1 STARTING AND ABOUT MEASUREMENT The Art and Science of Significant Figures Click button toadvance becomes cartoon LE SS About Rules Rounding Multiplication Dimensional Addition Measure Numbers Division Analysis Subtraction ment mrp i f h kb g i 3 a 2E Be ES lt 3 3 EON HE E EE E The art and science of Significant Figures This video is here to give you an idea of why measurement is important The video was produced by NASA When yau are ready ta leam mone about hon bo use numbers involwed with measurements click on the section you would like to go to a Se E Start Rules Addition Subtraction a Rounding Numbers D Multiplication Dimensional Division Analysis Yuu are 5 n here x Riles Roundin
12. rart pane M The dot subtracting is different than tells when multiplying or dividing Start Rules Rounding Multiplication Dimensional Bo Mumbers Division Analysis Wa oO er 4 F amp ouncing TL ei Limenaiznz Anari Ful idia i ENDING THE PROGRAM There is no official end of the program although if things were perfect there would be a summative assessment at the end made of many of the formative assessment questions as well as some new ones TROUBLESHOOTI NG Hopefully nothing will go wrong but these are some things that might 1 The sound effects don t work If that happens it is no big deal They were there mainly for entertainment purposes anyway 2 The video does not load That would be unfortunate because a lot of care was done to make sure it was properly embedded and was viewable An online version of the video with podcasting notes can be found at http www nasa gov multimedia podcasting jpl wfpc 20090507 html 3 Articulate scenes may not open in a new window like I tried to program them to do In that case the students may want to use two different browsers one for the Flash presentation and another one just to launch the quizzes or parts made in Articulate Storyline 4 Some of the buttons may not work even though I ve gone through it many times to make sure each one takes you somewhere Ideally there will be more than one way to approach any scene and there are hopefully many opportunitie
13. s to return to the original starting page so students can start over if they choose 5 A where am I mini map was added to the bottom so people would at least know which scene they were in 15 Program startup procedure 4 Equipment You Need 3 Hardware Requirements 3 Network Connections 4 Introduction 2 Software Requirements 3 Purpose and Objectives 3 Target Learners 2 G N General Operation Scene 1 Normal running of the courseware 4 About Measurement 5 Ending the program 15 Scene 1 Time to complete the courseware 4 Starting Out 5 User interface components 4 Scene 2 Rules 6 Scene 3 Rounding Scene 8 Scene 4 Multiplication and Division 9 Scene 5 U Dimensional Analysis 11 Scene 6 Addition and Subtraction Scene 15 User Interface Components Getting Started 4 General Operation 4 CD or Network Access 4 T Troubleshooting 15
14. stination Click Start over to go back to the first screen where you can then pick another set of lessons to explore Click Practice to go to an Articulate practice session that will open in your Browser Practice Click Take the quiz to go to an Articulate quiz question session that will open in your Browser on TJ Sre heres B Rikas Curulative Quiz Dira res bo rel ddiin Subtraction furl esis Mulbplicasen Nive kom The last frame is similar to the last Rules frame in that it provides students with an opportunity to do practice and quiz questions that involve rounding to a specific number of Significant digits This page should be left open so that after doing the exercises in Articulate s stories a new scene can be chosen Most people will continue on to the Multiplication Division scene because knowing how to round to a certain number of Significant figures is not good enough Students also need to know when to apply the rules and how to do it correctly SCENE 4 MULTIPLICATION AND DIVISION WITH SIGNIFICANT FIGURES Multiplication and Division Scene Main points for Multiplication 1 Conversion factors have an unlimited amount of significant figures 2 Your answer can never be more precise than your least precise measurement 3 This means your given determines the number of sig figs in your final answer The Dot tells you where you are ES eee Rounding Again le
15. stuck that it is in a right spot Click submit to find out if you are correct SUBMIT Invalid Answer If the submit button is clicked while the structure is still empty an error You must complete the question before statement comes up telling the students submitting to answer the question before submitting it OK Menu g n 2 DimensionalAnalysis gt Dimensional Analysis Resources Explanation route Welcome to Explanations The Problem All conversion factors 1 Stuff to know Convert 745 cm to meters Th j S iS wh at a fi led j n Now where 100 cm 1 meter 1000 mm 1 meter Drag the object to their correct locations so that solving Practice route 1000 mL 1 liter the problem can be done correctly Note not all objects d rag a nd d rop fra me Welcome to the practice route will be used Drag and Drop can look like Drag and Drop 1 meter Drag and Drop Drag and Drop dD These answers are Drag and Drop Drag and Drop 745 cm wrong Where to Quiz route Welcome to the quiz route 100 cm x 1 000 mm meters Do not assume that because the item stuck that it is in a right spot Click submit to find out if you are correct SUBMIT 13 Incorrect Since you are in a series of questions go ahead and try the next one You can always come back to redo this route Continue site DimensionalAnalysis When the answer is wrong another dialog box pops up to let the stude
16. t figures 5 00 x 10 has three significant figures 9 6031 x 10 has five significant figures One way to illustrate the significant digits in a number is to express the number in scientific notation Start over Oops I did not realize I d be starting with scientific notation I think want to start ower Then click the Start over button You are a q E 5 J here z B E H Pi gn I c founding Curmulative Qua mersiona Aralysi Addition Subtrarctiurn Multiplication Division Some frames have extra buttons that let you escape Start Over or jump ahead to the quiz without having to continue reading the lesson Significant figures and Scientific Notation One way to indicate zeroes are significant is to put the number in scientific notation 789000 becomes 7 89 x 10 if none of the zeroes are significant 789000 becomes 7 890 x 10 if the first zero is significant examples continue on the next page If you ve seer enough and you ae ready to take the roal quiron how many sg figs wein a number dick onthe button for the Ras Quiz Questions Go to Real Quiz Questions Yuu are e 3 E T ti amp 2 e3 hare 8 c RE Sa a 2 y S P gz ef o a Pa 3 fas vi Are you ready to take a real quiz on how many significant figures are in a number Once again you will be heading off to an Articulate Quiz to show how much you know about determining the number of significant
17. t the dot help you figure out where you are The Multiplication and Division scene is not very long but it is very dense Those who learn by example will appreciate the frames because they are packed with information Those who are overwhelmed easily will want to take a deep breath and Slowly progress through the examples line by line The examples are there so you can compare them to each Start Rules Mulgplication Dimensional Addition Numbers ision Analysis Subtraction other and look for patterns S p a za a E a D Ep E TI What do you think the final answer is 4 692 x 987 4631 004 0 0098 4 72 0 002076271 1000 27 37 0370370 900 3 x 45900 41 323 770 1 7 x 20 62 385 594 0 00731 x 0 0462 0 00033 7722 keep this page TPE aG eee H you want bo rev har come back after some of the lesson the quiz and lick the return arrow Start Over and head back to look IE oer Start over T y For simplicity ssanie starting numbers sre measurenents of some sor Tou a P lera z 2 E E E ENIE More examples Problem Answer before rounding 3 Te E a EE T EEE SMP ene aiaa E a a 659 PLP ceeeeceneees OO 70470568 4 3 x 7 2 2 31 x 8 13 30 96 18 7803 1 648535 2 sf 200 73 x3 00 5 1 602 34 5 1 118 1058824 2 sf 65 24 60 liaas 10 873333333 6 79 x 107 2 1 10 1 4259 x 107 To go back and review rules for rounding In Multiplication and Division click the back
18. t up at YouTube so that any chemistry student can play with the presentation and become comfortable with what significant figures are and how to do calculations with them PURPOSE AND OBJECTIVES 1 Students will identify how many significant digits or significant figures are ina particular number made of numbers 1 9 2 Students will identify how many significant digits or significant figures are in numbers that include zero 3 Students will identify how many significant digits or significant figures are in numbers expressed in scientific notation 4 Students will be able to determine how to round numbers to a specific amount of Significant digits figures 5 Students will follow rules of significant figures when doing multiplication or division to round final answers correctly 6 Students will use dimensional analysis to determine how many significant figures Should be in a final answer 7 Students will be able to round final answers to the correct amount of significant figures after performing addition or subtraction EQUIPMENT YOU NEED HARDWARE REQUIREMENTS a Computer a computer that can handle Flash player 10 3 and higher b Peripherals i Speakers to hear sound effects ii mouse to maneuver through the scenes c Monitor that will let an 800 x 800 screen be seen in one piece SOFTWARE REQUIREMENTS a Operating System Any that can handle playing Flash documents and Articulate documents Both should be able to be
19. ules on zeroes or go to the rules on scientific notation Scientific Notation pa start feroes over zoma Questions about aet 1 9 and sig igs salect the practica button Practice In the Rules scene each part has its own practice because being able to use significant figures requires a thorough understanding of what to do with each type of number you JLaL ound ng Cunnilaaec uc ido tion SubE act an heiim L memini na ele Pul idiali come across Numbers 1 9 All numbers from 1 9 are significant This image is here to emphasize the guide Any number that is a part of a that goes along the measurement is significant bottom of each page A value of 1 2 3 4 5 6 7 8 or 9 does There is a dot next to not just magically appear in a the name of the scene measurement you are in For the Rules scene it They are actually a part of the measurement happens to be a green Where would you like to go to next dot The dot lets SEREA Al NTE scientific you know Zeroes M 0e Notation To try some questions about numbers 1 9 and sig figs where you select the practice button Pra ctl Ce dic Aawnding Cumulative Cui Addin Subtraction Ciinnen res bo mal Arial ysis Multiplication Dirim Practice for numbers 1 9 starts here Examples 242 has 3 significant figures 899 99 has 5 significant figures 397295 has 6 significant figures 1 798
20. viewed in a common browser like Firefox or Internet Explorer that have Flash Player add ons plug INS b Application Programs A Brower that can handle Flash animations and playing videos should be needed il Flash Player version 10 3 or newer c Specific Web Browser Firefox recommended il Internet Explorer 9 or higher iii Safari 5 or higher IV Depending on the computer s settings the screen resolution may need to be made smaller by using control minus Ctrl to shrink the viewable screen The program s dimensions are set to 800 px x 800 px NETWORK CONNECTIONS Naturally high speed is always better than dial up The program has been tested on wired and wireless connections and worked smoothly in both GETTING STARTED CD OR NETWORK ACCESS a Not necessary for a CD player to be available b It does need Internet access PROGRAM STARTUP PROCEDURE a Click on the link to the web address for the html or swf file b Give it a minute to load c Click on any of the scenes to start reading or hearing about measurement or significant figures NORMAL RUNNING OF THE COURSEWARE TIME TO COMPLETE THE COURSEWARE It depends on the students interest levels The presentation is set up so that students have several opportunities to do formative assessment exercises There Is actually more emphasis on practicing the rules than on getting a single correct answer This courseware IS Supposed to be used by stude
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