REASONS FOR REASONING

REASONS FOR REASONING

MASTER TEACHER Andrea Cantu

GRADES 6-8

OVERVIEW
This lesson provides students with an in-depth understanding in logical reasoning. During the lesson students will have hands on experience with logical reasoning when they play a game and solve a logic puzzle. The lesson will use video to show how reasoning skills are used in work and in play. Students will view how reasoning is used to solve criminal cases and problems in industry.

ETV SERIES
Mathemedia: #103 Logical Reasoning

LEARNING OBJECTIVES
Students will be able to:
* Use inductive and deductive reasoning processes to solve problems.

MATERIALS
Per student
logical reasoning worksheet

Per group of two
16 pennies or plastic disks

Per group of three
9 bottle caps (shampoo or soda)
black permanent marker
one candle or birthday candle

VOCABULARY
conjecture - an idea or guess
deductive - deriving a conclusion through reasoning
inductive - process of reasoning from a part to a whole

PRE-VIEWING ACTIVITIES
Prepare before hand enough candles for each groups of three or four to have one. Carefully remove 1/8 to 1/4 inch of the top of the candle leaving the wick in tack. Color the wick black with black permanent marker. Light a candle and drip wax on the candles that you have prepared. The candles have now been given the appearance of being used. Say, “Each group will be given a candle. Your job is to give 10 words to describe this candle.” (Many students will say that the candle has been burnt. If the candle had been burnt the wick would have been melted or fused together.) Have the groups take turns listing different descriptions of the candle on the board. Say, “The candle has not been burnt. If it had the wick would have been melted or fused together. Things are not always the way that they appear. This lesson is on logical thinking.”

FOCUS FOR VIEWING
To give students a specific responsibility while viewing say, “In various fields of investigation, criminal or scientific, the ability to think logically is essential to solve problems. Logical thinking is used to play strategy games or by engineers to design projects or solve problems. In this video you will see examples of deductive and inductive thinking used to solve a crime, to solve a shipping problem, and to play games or solve puzzles.”

VIEWING ACTIVITIES
Pass out worksheets to students. (Note that worksheet activities and questions are numbered through out pre-viewing, viewing, and post viewing periods.) Say, “A robbery has occurred at a convenience store. Under stressful times people do not remember all the details of the crime. So logical reasoning is used by investigators to solve crimes. For question 1 and 2 listen for the robberies of which the person in custody admitted and decide if this person committed more than he admitted. Begin tape where the visual is the words in yellow “Logical Reasoning” in a purple rectangle. The audio is machine noises. Pause the tape when the audio is, “How many of the robberies were committed by the person in custody?” and the video displays words. Say, “Of which crimes did the person in custody admit? (4 and 7) For question 2 write your explanation as to why you think the person committed some or all of the other crimes. In this next clip listen for the answers to questions 3 and 4 as to the logical reasons used by the investigators to resolve which crimes the robber committed. Resume the tape. Pause the tape when the audio is music and the visual is Mitchell and Yolanda sitting at a dining room table. The title is “You Go First.” Say, “What were the reasons that the investigator believed that the person in custody committed crimes 1, 3, and 5? (The robber had the victims place their hands under their shirts and that the robber took diapers.) What information was not very useful? (accent, and time of day) In this next segment Mitchell and Yolanda will play a game. See if you can find the secret to winning this game.” Resume the tape. Pause the tape when the audio and video says and shows “What is the secret to winning this game?” Say, “Can you figure out how to win this game? Let’s try this game ourselves. Remember that you can only take one or two pieces during your turn.” Pass out 16 small plastic disks or pennies to each group of two. Students may take one or two game pieces per turn. The person who takes the last coin loses. Have students play a few rounds of the game. Say, “For #5 tell if it matters who goes first?” (The person who goes first wins if they know the secret) Say, “Listen for the meaning of the word conjecture in the following clip.” Resume the tape. Pause the tape when Mitchell says, “Hmm, good question” as he puts his hand on his chin. Say, “What does conjecture mean? (an idea or guess) Record your answer on #6.”
Fast forward the tape to where the audio is,“Deere Reason, Too” and the video displays the phrase. While the video is fast forwarding say, “Let’s play the game again. Is there a way to win the game if you go first? Play the game with the rules that you can take 1, 2, or 3 coins on every turn. How does this new rule change the game? What would be the deadly number under this new rule? (5) Record your answers on questions 7-9.” Say, “ In this next clip, the John Deere company was shipping equipment over seas. For # 10 and 11, listen to what happened to the equipment when it arrived, and what they found that caused the problem.” Resume the tape. Pause the tape when the audio is, “Do you have any ideas for what’s causing this rust?” and the video displays the question. Say, “What was happening to the equipment being sent over seas? (white rust was corroding the exposed metal) Listen for the reasons why the method of shipping caused the problem and how they solved this problem.” Resume the tape. Pause the tape when the audio is piano music and the video displays the words “Who’s Who.” Say, “What was causing the white rust to occur? (acids from the oak crates and the moisture contained by the plastic) What four steps did the John Deere company take to prevent white rust? (kept moisture levels low in the wood, treated the wood, applied corrosion protection to the metal parts, and dried shipping containers) Record your answer on number 12. Your next challenge is to figure out which hobby goes with which person. The people are Andy, Brenda, Carol, and Dominic. Their hobbies are playing basketball, guitar, chess, and the trumpet. You have been provided with a chart on #13 to help you to organize the clues.” Resume the tape. Pause the tape after the last clue is given. The audio is, “Only 3 of them are old enough to drive, Dominic, the chess player, and the guitarist.” The video displays the same words. Have students work on their chart to figure out the solution. Say, “Listen to see if you matched the right person to their hobby.” Resume the tape. Stop the video when Dominic, Brenda, Andy and Carol are sitting on a bench in the gym. Under their names are their hobbies, trumpet, guitar, chess, and basketball respectively.

POST VIEWING ACTIVITY
Say, “We have seen how the police investigator used inductive reasoning to solve the burglary case and how the John Deere company’s engineers used inductive reasoning to solve their shipping problem. We have seen how deductive reasoning is used to solve logic puzzles or strategy games. In the following activity you will use deductive reasoning to solve this math strategy game.”   Give each group of three nine caps. Have them number the caps 1 to 9. Students will begin using the caps 1 to 6 first and then advance to using all nine caps. The caps are to be arranged into a triangle where there are three caps on each side (9 caps will have 4 caps on each side). The numbers on each side of the triangle must add up to the same number. Some examples for answers using six caps are the numbers: 9, 10, 11, and 12, and for nine some answers are: 17, 19, 20, 21, and 23.   The following is one example of the cap placement using six caps.
       5                               5 + 3 + 4 = 12
3        1                           5 + 1 + 6 = 12
4      2      6                       4 + 2 + 6 = 12

ACTION PLAN
1. Have a local police detective explain how they begin an investigation and how they use deductive and inductive reasoning to solve a case.
2. Have an engineer explain the engineering process of designing a project or solving a problem.

EXTENSIONS
Art
Create a drawing with a hidden picture(s) in its composition.
Social Studies
Learn about criminals in history and how they were caught.
Reading
Read a Sherlock Holmes or Agatha Christie novel.
Science
Read “When Scientists Become Sleuths” in the 1992 February / March issue of National Wildlife magazine pages 8 - 15 .
Internet
http://www.absudmath.inter.net/abmath/
http://alabanza.com/kabacoff/Inter-Links/fun/puzzles/real-life
http://alabanza.com/kabacoff/Inter-Links/fun/puzzles/logic
http://www.norfacad.pvt.k12.va.us/puzzles/sallys.htm
http:www.brainbasher.com/p/detail.as

Logical Reasoning Worksheet

Previewing Activity: Candle Observations

1. _________________ 6. ___________________

2. _________________ 7. ___________________

3. _________________ 8. ___________________

4. _________________ 9. ___________________

5. _________________ 10. ___________________

Viewing Activities

1. Of which crimes did the person in custody admit? ______

2. Explain why you think the person committed some or all of the crimes. ____________________________________________

3. What reasons were given to indicate that the person in custody committed crimes 1,3, and 5? ____________________________________________

4. What information was not useful in solving the case? _________________________

5. In the game, does it matter who goes first? ________________________________

6. Define conjecture. ____________________________________________

7. Is there a way to win the game if you go first? ______________________________

8. Explain how the new rule changes the game. _________________________________
___________________________________________

9. What is the deadly number for the new game? ____________________

10. What was happening to the equipment being sent over seas? ____________________

11. What was causing the white rust to occur? _________________________________
___________________________________________
12. What four steps did the John Deere company take to prevent white rust?
a) __________________ b)____________________

c) __________________ d)____________________

13.

Andy Brenda Carol Dominic

Basketball

Guitar

Chess

Trumpet

Post Viewing Activity

Using Six Numbers
Place your numbers in the blanks below. Circle your number answer to the right of the triangle.
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   __ __ __      __ __ __      __ __ __     __ __ __

Using Nine Numbers
Place your numbers in the blanks below. Circle your number answer to the right of the triangle.
         __                         __                         __
      __ __                   __ __                   __ __
   __        __             __        __             __        __
__ __ __ __       __ __ __ __       __ __ __ __

         __                         __                         __
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Updated: April 01, 2008