Lesson Plan for Henrico 21 Awards Teacher Name: Pete Anderson Collaborators: HCPS Math Teachers of Various Schools (summer book club lead by Pete Anderson, text: Problem Solving Strategies - Crossing the River with Dogs) Angie Branyon - GAHS Librarian Corbin Wright - GAHS English Department Chair/Teacher Lesson Title: Logic Target Grade/Subject: Honors Geometry Length: 13 hours Summary: Geometry is an investigative mathematics. Because of this, my students’ first impression must consist of scenarios of problems without obvious solutions. This is the heart of logic and the essence of my school years’ opening unit of study. We used Agatha Christie’s murder mystery novel “And Then There Were None” as a foundation for critical thinking. The nightly homework assignment was for every student to use deductive reasoning to solve the murders via an online discussion forum. During class time, students worked in teams to solve classic logic problems using essential problem solving skills while guided by rubrics. From there, we addressed formal logic and also found time for a cross-curricular application of topology (earth science) using the setting of the novel “Indian Island”. The unit was concluded with a group assessment where each class was divided into three teams of 7 to 9 students and tasked to solve a blend of open ended and traditional logic problems. [watch group assessment video: http://teachers.henrico.k12.va.us/glenallenhs/anderson_p/GroupAssessmentLogic2010.m4v ] Essential questions or objectives: Foundational Questions: What is deductive reasoning? When and why is deductive reasoning used? What are some common problem solving techniques? What is formal logic? Concepts or Skills that Provide Purpose: Students will learn of and utilize the following problem solving skills Draw a Diagram Create Systematic Lists Eliminate Possibilities Use Physical Representations Look for a Pattern Solve an Easier Related Problem Standards Addressed: SOL G.1 The student will construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include: a) identifying the converse, inverse, and contrapositive of a conditional statement; b) translating a short verbal argument into symbolic form; c) using Venn diagrams to represent set relationships; and d) using deductive reasoning, including the law of syllogism C/T 9-12.5 The student will demonstrate knowledge of technologies that support collaboration, personal pursuits, and productivity. • Respectfully collaborate with peers, experts, and others to contribute to an electronic community of learning. • Model responsible use and respect for equipment, resources, and facilities. Resources: Technology: Ubiquitous computing Schoolspace: https://www.schoolspace.henrico.k12.va.us o file distribution, discussion forums, calendar of events, assessments, and dropboxes Promethean Board, Slate, and Document Camera Promethean software (flipcharts) HCPS IGO (Investigating Geometry Online) web resources o http://teachers.henrico.k12.va.us/math/igo/02PerpendicularParallel/2_1.html o http://teachers.henrico.k12.va.us/math/igo/02PerpendicularParallel/2_2.html Teacher’s Vodcast for video instruction of SOL standards: o http://teachers.henrico.k12.va.us/glenallenhs/anderson_p/VideoLecture/Podcast/GeometryOnli nePodcast.xml o http://teachers.henrico.k12.va.us/glenallenhs/anderson_p/VideoLecture/GeometryOnlineVideos .html Various Problem Solving Web Applets o http://www.novelgames.com/flashgames/game.php?id=54 o http://www.mathcats.com/explore/river/crossing.html o http://web-ext.u-aizu.ac.jp/~niki/courses/sccp/venn/index.html ExamView Pro software: utilizing algorithms for generating dynamic SOL questions Other Required Resources: Ken Johnson and Ted Herr, Problem Solving Strategies - Crossing the River with Dogs. Key Press. 1st edition, 1994. Christie, Agatha, And Then There Were None. 1939 Lesson Development: Process/Tasks: The following is an excerpt from the letter that was sent to all parents of Mr. Anderson’s students. The wording is primarily that from the text: Problem Solving Strategies - Crossing the River with Dogs What is the role of the student? Collaboration is an essential element of a 21st century learning environment and will be emphasized throughout the school year. When you work with other students, you are free to make conjectures, ask questions, make mistakes, and express your ideas and opinions. You do not have to worry about being criticized for your thoughts or your wrong answers. You won’t always proceed down the correct path. Support each other, question each other, make another person explain what you don’t understand, and make sure the other members of your group understand, too. If others in your group make mistakes, don’t berate them; just help them to see why they are wrong. What is the role of the teacher? In most classes, the teacher is the final authority to tell you whether you are right or wrong. In this unit, I will play that role at times, such as in grading your homework and assessments. However, there will be many times when I will not play that role. During student presentations, there may be days when several people get different answers. A natural student reaction at his point would be to ask the teacher who is correct. There will be moments when I will answer that question, and moments when I will not. The groups can discuss which answer they think is correct and why. Explaining why is a very important part of this class. When you stop relying on the teacher to verify your work, you will become a more powerful problem solver. Learn to evaluate your own work and the work of others carefully. Unit Outline Day 1 – September 8: Introduction to Problem Solving Intro to Problem Solving Various In-class problems Review of Course Syllabus Guest Speaker: Mrs. Branyon Assignment #1: “Round up the usual suspects.” And Then There Were None - by Agatha Christie Read chapters 1 and 2 [paper hand out]. As you read, make a list of every person mentioned for one of them is most definitely the murderer. Be wary of everyone and make a note of anything interesting, memorable, or “suspicious” about each character. Type this list in a Word document. I will explain in class how this document’s information will be shared with me and your classmates. Individual Work Grade: Homework (weighted twice) Due Date: Monday, September 13, 8:45 am (all classes) Day 2 – Friday, September 10: Drawing Diagrams Warm up Problem Review of Reading Today's Problems will emphasize the use of drawing diagrams Introduction to the grading Rubric for Problem Solving One problem will be collected for a group grade Assignment #2: WhoDunIt and Why? And Then There Were None - by Agatha Christie Read Chapters 3 and 4 and state who you think is the murderer and why. [Files for all readings are in the schoolspace folder in the "Lessons" tab] Your reasoning must include specific passages (chapter #, page #, and quote passage). You will post your “solution” online per the teacher’s instruction (TBA). You will read other classmates postings and respond to two stating your agreement/disagreement and why. Individual Work Grade: Homework Due Date: Monday, September 13. Time of posting due is 8:45 am. Day 3 – Monday, September 13: Technology Day Overview of Schoolspace How to download files How to turn in files (Virtual Share/ file names) How to post your work (Discussion Forums or Other) How to use the team Chat Room How to access my Virtual Office Hour. Assignment #3: WhoDunIt and Why? [chapters 5 and 6] Individual Work Grade: Homework Due Date: Prior to the beginning of the next scheduled class period. Day 4 – Wednesday, September 15: Systematic Lists Warm-Up: Draw a Diagram problem (using sketchpad) Several questions on systematic lists from the problem solving unit (chapter 2) Assignment #4: Read Chapters 7 and 8 Nobody dies in these chapters; therefore there is no WhoDunIt assignment. Throughout the reading, take notes on what you think the island looks like. Create a map of the island on paper. Include the location of the house and any other features of the terrain (mountains, coast, etc.) Be able to support your decisions with passages from the reading. Individual Work Grade: Homework Due Date: Prior to the beginning of the next scheduled class period. Day 5 – Friday, September 17: Quiz / Topographical Maps Problem Solving Quiz Create a Topographic Map of Easter Island Assignment #5: WhoDunIt and Why? [chapters 9 and 10] Day 6 – Monday, September 20: Read Regardless of whether we had class or not today, the reading schedule remains the same. Assignment #6: WhoDunIt and Why? [chapters 11 and 12] Day 7 – Wednesday, September 22: Formal Logic Go to Schoolspace and Lessons o "Pre-Test" (this is the warm-up) o Download the flipchart o Notes and Problems on Venn Diagrams o Truth Tables o Sentence Structure o We will finish the "two laws" of logic next class Assignment #7: WhoDunIt and Why? [chapters 13 and 14] Day 8 – Friday, September 24: Formal Logic Quiz Warm-Up on Schoolspace in the Logic folder Quick review of notes from the previous class Finish the lesson (notes on Two Laws of Logic) In Class Practice (classwork 2-2 found in the additional resources folder) Quiz: 20 questions / online / multiple choice / group work using chat room / no verbal communication) Assignment #8: WhoDunIt and Why? [chapters 15, 16 and the Epilogue] Day 9 – Monday, September 27: And the Murderer Is … Reading of the Manuscript by Mrs. Branyon Test Review Finish the Topographic Map Assignment #9: Clues and Red Herrings Discussion in the Test Folder Day 10 – Wednesday, September 29: Group Assessment Evaluation Procedure: Assessment of objectives: Assessment Expectations: Rubrics for all graded work are posted in Schoolspace prior to the assessed activity. Rubric for “Round up the usual suspects.” Total Points = 30 [with an opportunity for bonus points] List of Suspects: 1 point for each name listed (12 minimum, more than twelve will be bonus points) Information for each suspect: 1 point per suspect Suspect list posted correctly: 6 points Rubric for all WhoDunIt and Why Discussion Forum postings Total Points = 10 Name of “murder” - 1 point Reasoning – 6 points o Must use correct grammar and spelling (1 point deduction for errors) o Must cite passages to support the claim (2 point deduction if not included) Posting – 1 point Responses – 2 points o One point per response o Must use correct grammar and spelling (1 point deduction for errors) o Must be respectful to the opinions of others (2 point deduction if not) NOTE: Late postings will be deducted 3 points per day (24 hours) late Rubric for Problem Solving Activities and Assessments Process: 6 points How did you solve this problem? Describe what your first ideas were and any false starts you had. Include any diagrams and tables you may have used. If you used manipulatives, describe how you used them, and how they were helpful. STATE YOUR IDEA! 0 Points 1 Point 2 Points 3 Points Ideas No work shown Very little thought is shown. Ideas are shown but not thoroughly explored. All ideas are clearly stated, and worked out. Organization No work shown The process is very difficult to follow Some clarity is needed. The process is very clear and easy to follow RUBRIC Solution: 3 points What is your answer to the problem? How do you know that your answer is correct? RUBRIC 0 points No Solution 1 point Solution does not relate to the process. 2 points 3 points Incorrect solution, Correct Solution but is appropriate for that matches the the stated process process. Evaluation / Self-Assessment: 1 point RUBRIC 0 points No response. Did you like this problem? Why or why not? What skills were required in order to solve this problem? Was this hard or easy for you? Why? 1 point Responded to any or all of the questions given above. TIPC Assessment: Research and Information Fluency: Rubric: Students use information and resources to apply knowledge to real-world situations and accomplish real-world tasks. Reasoning: Throughout the lesson, students were asked “WhoDunIt?” and had to use all of their resources to answer the question. Communication and Collaboration: Rubric: [target] Students communicate ethically within and beyond the classroom in ways that produce collaboration in real and non-real time Reasoning: The original plan was for each student to have their own blog from which they would post their solution and opinions. Unfortunately, HCPS had placed too many restrictions on student access of technology for this to occur. Thanks to Gaynell Lyman and Tom Woodward, a solution was found, but the unit of study had already begun. Schoolspace (a closed system) was the only option left. Rubric: [developing] Students work productively in teacher-created collaborative teams to solve basic problems and / or create original works. Reasoning: Students were grouped by the teacher in order to mix the student population. Being a new school it was important to create a sense of belonging to GAHS and not teams of friends from our feeder schools. Critical Thinking and Problem Solving: Rubric: [Target] Students use resources to solve real-world problems and reflect on their product and their process. Reasoning: Even though “real world” problems are considered the “target” for Henrico 21, they are not the “target”, per se, for mathematics. Source: Mathematical Association of America, featured article my Paul Lockhart: “A Mathematician’s Lament”, page 4. [http://www.maa.org/devlin/LockhartsLament.pdf] Rubric: [Target] Students use prior research [experiences] to develop and answer open-ended questions using higher order thinking skills. Reasoning: The unit exposes students to many different problem solving strategies. Students draw from the experiences from learning these strategies to best choose a method (or combination of methods) to solve problems. It is my belief that “research” implies real information, which is irrelevant to the objectives of the unit. [see source above] Creativity and Innovation: Rubric: [Target] Students work collaboratively to produce products that offer novel solutions to “realworld” problems. Reasoning: The entire unit and formal assessment focused on student collaboration to solve problems in creative ways. While the problems were specific to the novel, they represent real-world situations. Brief Sample of Student Work Assignment: WhoDunIt and Why? Donna’s Post: And the murder is ... Mr. Wargrave Mr. Wargrave was running it all like a trial. He could be the voice because the voice on the gramophone had stated all the facts like a trial would begin. Also he seemed unmoved by the voice and very levelheaded about the whole affair. (chp. 4 pg 1 "We will now proceed to the next stage of our inquiry”) (chp.3 pg. 4 “Only Mr. Justice Wargrave and Miss Brent seemed comparatively unmoved.”) Jessica’s Reply I disagree. I think he was handling the situation like it was a trial because he was a judge and that's just how he handles things. Lindsay’s Reply I halfway agree with you, it does seem suspicious that he was running it like a trial, but at the same time, he seems like the least suspicious person. Marc’s Reply I agree because since he is the judge he knows about everyones murders and it was possibly him that said all the stuff Kristen’s Reply I agree but maybe he was holding his thoughts in about the voice. Chloe’s Reply I agree with Donna but at the same time I don't because Mr. Wargrave was trying to lead it and figure it out who it was not sabotage them. Detailed Sample of Student Work Assignment: WhoDunIt and Why? Block 7 The postings of one particular student and the replies that followed. Grade: Homework Due Date: Prior to the beginning of the next regularly scheduled class period. Rubric: Name of “murder” - 1 point Reasoning – 6 points Must use correct grammar and spelling (1 point deduction for errors) Must cite passages to support the claim (2 point deduction if not included) Posting – 1 point Responses – 2 points One point per response Must use correct grammar and spelling (1 point deduction for errors) Must be respectful to the opinions of others (2 point deduction if not) NOTE: Late postings will be deducted 3 points per day (24 hours) late Chapters 3 and 4 Philip Lombard Anderson, Kristin W. 9/13/2010 I think that Philip Lombard is the murder because of the way he was acting after dinner when everyone else was enjoying themselves with each other. In chapter 3 page 1 it says, “Once or twice he looked up quickly, and his eyes narrowed. Now and then his eyes played round the table, studying the others.” This makes me think that he is the murderer because he is acting paranoid, like he is expecting something to happen. I also think that he is the murderer because he was unwilling to tell how he was invited to Indian Island in chapter 3, page 12. “Lombard's brain had been active. Was he to come out in the open, or not?” If he was not the murderer, why would he not tell why he came to the island? Detres, Cristina Marie 9/14/2010 I agree that it is a possibility that Lombard is the killer because it seems like he feels no remorse for the other people that he left to starve, so why wouldn't he kill again? Gammon, Heather Elizabeth 9/13/2010 I agree with this. Lombard had been acting very suspicious and he wouldn't tell the others why he had been invited to the Island. Mr. Owen could have easily asked him to come so he could kill everyone else for him. Jahn, Tyler K. 9/13/2010 These were very good reasons which makes Phillip Lombard the killer. Sitison, Rachel C 9/13/2010 I didn't think that Phillip Lombard sounded like the murderer but you pointed out some spots in the reading that sounded like he could possibly be the murderer. Pou, Kaelah Sheldonia 9/13/2010 I agree with this because of the suspicious way that he studied everyone else. Also, he didn't act surprised when Mrs. Rogers passed out aand he found the gramaphone. It seemed like he kind or expected it. Anderson, Peter G. 9/13/2010 I agree with your "hunch", but how is it possible that he put the poison in the glass? Vest, Helen T. 9/13/2010 I agree because he was acting very paranoid, and had to think about concealing something. Chapters 5 and 6 Mr. Roberts Anderson, Kristin W. 9/13/2010 I think that Mr. Roberts is the murderer of Mrs. Roberts. The way he was acting when Dr. Armstrong examined her was proof in itself. Chapter 6 page 2 Mr. Roberts asks, “’Was it-was it-‘er ‘eart, doctor?’” but when asked by the doctor if he had and reason to believe that she had heart problems he responded, “’No, doctor. I never knew of anything.’” Roger also responds, in chapter 6 page 3, when asked if his wife took medicine to help her sleep, “’Not that I knew of. I’m sure she didn’t.’” I agree with Mr. Blore on the cause of her murder. Robert must have been afraid that she would blab their secret. Kumar, Virang Ketan 9/13/2010 I strongly disagree with you for many reasons. One reason that I disagree is that you may have mistaken Mr. Roberts with Mr. Rogers. Another reason I disagree is that Mr. Rogers noticed the china figures missing when each person died so why would he be the one to kill someone if he wondered where the china figures have gone. The final reason I disagree, is that Mr. Rogers said Dr. Armstrong gave Mrs. Rogers the last thing she ate, so there might have been poison in it. Tinsley, Tianna Lonai 9/20/2010 I did not notice that. Very interesting Chapters 9 and 10 Mr. Justice Wargrave Anderson, Kristin W. 9/19/2010 I think that Mr. Wargrave is the murderer because he is the one who had the greatest amount of time away from the others, as stated in chapter 9 pages 21 and 22 when Mr. Wargrave himself said, “I sat on that chair on the terrace for the whole morning until the gong went, but there were, I should imagine, several periods during the morning when I was quite unobserved and during which it would have been possible for me to walk down to the sea, kill the General, and return to my chair.” Why would an innocent man tell others that it is quite possible that he himself could be the murderer? What would he gain from that? What he said is true, though. No one saw him for more than a moment at most. Everyone else has an alibi, such as Vera Claythorne and Emily Brent, in chapter 9 page 147 when Emily Brent says, “I took a walk with Miss Claythorne up to the top of the island.” [no replys] Chapters 11 and 12 Doctor Armstrong Anderson, Kristin W. 9/20/2010 I believe that Dr. Armstrong is the murderer. He is the murderer because, as Dr. Armstrong said in chapter 12 page 184, “‘[I] Always travel with… [a hypodermic syringe].’” In chapter 12 page 185, you learn that the needle was not there. The doctor was the only one who knew where the needle was, so how could anyone else taken it? Therefore, Dr. Armstrong must be the murderer. Adams, Kara Noelle 9/20/2010 You have to keep in mind that the murderer is definately going to try to frame people, to draw attention away from themselves. Dr. Armstrong is a perfect setup for framing. Anyone could have gone through his stuff, knowing that he was a doctor and would most likely have that equipment. Alst, obviously the murderer has done his reaserch and homework on his victims. So, he or she would definately have enough knowledge to get away with that. Dr. Armstrong wouldn't be that obvious if he were the murderer. Bruce, Kaytlyn Christina 9/21/2010 I think its Mr. Justice Wargrave, but you make a really good point. Carter, Olivia Spiller Christian 9/20/2010 Oh... you’re kind of right Jahn, Tyler K. 9/20/2010 I strongly agree with this poin of view. Jones, Ian D. 9/20/2010 I disagree completely. The doctor is the least likely to murder everyone, especially since he is the one diagnosing the COD (Cause of Death). Sitison, Rachel C 9/20/2010 He could possibly be the murderer but I think that it wasn't him that used the syringe. I think someone used his syringe so that they could make it seem as if it was Dr. Armstrong and not themselves. You do make a good point when you say that no one else knew that it was there but I think it was probably not hard to find. I think the real murderer framed Dr. Armstrong in this chapter. Chapters 13 and 14 Mr. Justice Wargrave Anderson, Kristin W. 9/22/2010 I know, I know, he has been murdered. However, the description in chapter 13 page 202 does not state that there was actual evidence of a bullet hole in his head. Instead, it states, "Then, with a swift movement, he raised the wig. It fell to the floor, revealing the high bald forehead with, in the very middle, a round stainde mark from which something trickled." It says a "stained mark", not a hole or anything else of the sort. It also says in chapter 14 page 219, "People moving about downstairs--doors opening and shutting--feet going up to the attic overhead." What reason would someone have to go to the attic? The only reason that I can think of is that they are supposed to be dead, but indeed they are alive. Blackwell, Kelly A. 9/22/2010 This is a very interesting point. I have been contemplating the same thing myself Bruce, Kaytlyn Christina 9/23/2010 I agree with you, you make a really good point about the attic part. Jahn, Tyler K. 9/22/2010 What the book is trying to say is that he was shot in the head and he is dead. Sitison, Rachel C 9/22/2010 I guess it is a possibility but I don't agree with you because Mr. Wargrave seemed pretty dead to me. It would be hard to fake being dead. Chapters 15 and 16 Mr. Justice Wargrave Anderson, Kristin W. 9/25/2010 Again, I know he is dead. Someone had to drop the marble on Blore's head, but Vera and Philip were both outside. It could not have been Armstrong because, as stated in the Epilogue on page 6, "...Armstrong must have gone into the sea sometime during the night of the 10th-11th..." Armstong could not be the murderer because he was already dead. Who else could have been the murderer but Mr. Wargrave. Blore heard footsteps going into the attic, but Armstrong was dead by then. The footsteps were Mr. Wargrave and Mr. Wargrave pushed Armstrong into the sea. Also in the Epilogue on page 7 it says, "For that revolver was found up in the house just inside the door at the top of the stairs - Wargrave's room." It also says, "But that chair wasn't found kicked over. It was, like all the other chairs, neatly put back against the wall. That was done after Vera Claythorne's death - by some one else." It the revolver that Vera used to kill Philip was in Mr. Wargrave's room and Vera's chair was found put up again, who else could it have been but Mr. Wargrave. I think that after he moved the chair, he committed suicide with the revolver, making it appear that he was shot in the head. Bruce, Kaytlyn Christina 9/28/2010 I agree Jahn, Tyler K. 9/26/2010 Wargrave was dead along time ago he was shot in the head there is no way to fake that . Also Armstrong wasn’t found dead before Mr. Blore was killed so he was still a suspect in Mr. Blores death. Pre-Assessment Group Collaboration The following is an excerpt of an online discussion of one team’s preparation for one of the assessment questions. Submit at least 1 clue that should have told you that Justice Wargrave was the murdered. Also find 1 “red herring” that led you away from Justice Wargrave as a viable suspect. Be certain to quote the passages from the reading, stating their chapter and page number, for each clue and red herring. FOR THE TEST GRADE, YOUR TEAM WILL SUBMIT 3 CLUES AND 3 RED HERRINGS. Clue and Red herring Sitison, Rachel C 9/28/2010 Clue- chapter 13 page 202 it doesn’t say anything about a wound in his head it just says a stain "Then, with a swift movement, he raised the wig. It fell to the floor, revealing the high bald forehead with, in the very middle, a round stained mark” it just says a mark not a wound or anything. Red herring- in chapter 15 Vera Claythorne shot Philip Lombard which makes her seem like the murderer Clues and Red Herrings Carter, Olivia Spiller Christian 9/28/2010 Mr. Justice Wargrave was the only one for whom it was explicitly reveled that did not wrongly cause a death. And a red herring was he faked his death clue Miller, Tess E 9/27/2010 that he was always the one quizing everyone else and did very good making himself look inisant. (ex. chapter 9 pg. 12) red herring Miller, Tess E 9/27/2010 For instance maybe when he "died" and we did not know that it was all planned. Chapter 13 pg8 Red Herring Anderson, Kristin W. 9/27/2010 Poison was used to kill Anthony Marston (chapter 4 page 11), Mrs. Rogers (chapter 6 page 4), and Emily Brent (chapter 12 page 6) and only a doctor would have been thought capapble of killing them with a medicine. "A human hand held the syringe." "At a guess, one of the cyanides. Probably Potassium Cyanide, same as Anthony Marston." (chapter 12 page 6) Clue Anderson, Kristin W. 9/27/2010 Wargrave was unobserved for long periods of time when he was sitting on the chair in chapter 9 pages 21 and 22. RE: Clue Anderson, Kristin W. 9/27/2010 "'I sat on that chair on the terrace for the whole morning until the gong went, but there were, I should imagine, several periods during the morning when I was quite unobserved and during which it would have been possible for me to walk down to the sea, kill the General, and return to my chair." How would he know that it was possible if he did not do it? red herring Jones, Mikala Lachelle 9/27/2010 "They had carried Mr. Justice Wargrave up to his room and laid him on the bed." chapter 14, page 1. Wargrave made it look like he was dead. They thought if he was dead, then he couldn't be the killer. clue Jones, Mikala Lachelle 9/27/2010 9--under twenty-four hours--and even then only if the wind drops." Dr. Armstrong dropped his head in his hands and groaned. He said: "And in the meantime we may all be murdered in our beds?" "I hope not," said Mr. Justice Wargrave. "I intend to take every possible precaution against such a thing happening." ch. 10,passage 3, page 4. We should have known it was wargrave because he was too calm about the murders happening around him. "I do not, of course, profess to be a weather prophet. But I should say that it is very unlikely that a boat could reach us--even if they knew of our plight Group Assessment Submission Team Alpha The following is the actually assessment submission by the group. Clues and Red Herrings Submitted by Jones, Mikala Lachelle (hcps-jonesml4) on 9/28/2010 3:03:39 PM Clues: Wargrave was the only one who had not wrongfully committed a crime; the man he hanged was later without a doubt proved innocent. Wargrave's fake gunshot wound was described as "... a round stained mark." not a wound. Also... this mark was symbolic of the mark God bestowed upon Cain for killing Abel. Wargrave spent alot of time by himself in Chapter 9 pages 21 and 22. Red Herrings: The "red herring" line in the poem suggests Armstrong was killed by someone he trusted, and the only presumable person is Wargrave. Poison was used to kill Mrs. Rogers, Miss Brent, and Marsden, leading suspision to Dr.Armstrong, especially after a syringe was used on Miss Brent. Vera shoots Lombard and it seems as though she is the murder Chapter 16 page 3