Dr. Guy Smiley is a Beverly Hills plastic surgeon that can reverse the aging process for those willing and able to part with ... The rhinoplasty cost $35,000 (5 ...
Math-in-CTE Lesson Plan
|Lesson Title: “It’s All About Logic” |Lesson# H05 |
|Occupational Area: Health | |CTE Concept(s): Vital signs, CPR, and triage | |Math Concepts: Logical thinking using math models |
|Lesson |Student will demonstrate a working knowledge of | |Objective: |HEALTH: | | |Formulate solutions to problems using critical | | |thinking skills independently and in teams | | |Apply concepts of responding to given critical | | |situations appropriately as part of the medical team| | |MATH: | | |Similarities and generalize patterns | | |Use patterns to create models and make predictions | | |Describe the nature of patterns and relationships | | |Construct representations of mathematical | | |relationships and its application in Health Careers,| | |while recognizing it in other contexts. | |Supplies Needed:|Use Student Math Logic Worksheets A – S | | |Paper, pencils | | |Presentation Tool: White or black board, overhead or| | |computer projection device, etc. | | |Nichols, E. D., Schwartz, S. L. (1998). Mathematics| | |Dictionary and Handbook. (3rd ed.). Honesdale, PA: | | |Nichols Schwartz Publishing. (ISBN 1-882269-07-1) | |Link to Accompanying Materials: |Health Occupation H05 Downloads | |The "7 Elements" |Teacher Notes | | |(and answer key) | |Introduce the CTE lesson. |Health Concepts: Emergency | |The teacher will explain the |Procedures, Assessment, Triage, | |following: |CNA, Communication, Teamwork | |As part of the health curriculum, |Math Concepts: Patterns, logical | |you will be asked to assess |thinking, models, predictions, | |multiple clients requesting care in|decision making | |a variety of medical settings (i.e.| | |medical office, ER, nurse’s | | |station, telephone calls, dental | | |office, radiology, pharmacy, OB, | | |Lab). | | | | | |Have any of you ever spent time in | | |an emergency room? Did you have to| | |wait a long time to see a doctor? | | |Did you notice any patients who | | |came in after you received medical | | |treatment before you? The medical | | |staff must use logical thinking in | | |order to determine medical | | |priorities and give care to life | | |threatening situations first. For | | |example, a gunshot victim would | | |take precedence over a flu patient.| | |Logical clear thinking is needed | | |for professional practice across | | |all disciplines. Students need math| | |reasoning skills for making | | |decisions in the everyday delivery | | |of patient care. Students will need| | |to prioritize tasks in whatever | | |career choice they pursue. Using | | |math models will help students | | |analyze situations using logical | | |clear thinking. | | |You will have opportunity to | | |participate in activities in which | | |you will interpret between various | | |representations of mathematical | | |patterns and real-world phenomena. | | |Assess students’ math awareness as |Sample Dialogue for Teacher | |it relates to the CTE lesson. |This teaching strategy is used in | |Using the teaching strategy KWL |language arts to assess students’ | |(What do you Know? What do you |prior knowledge about a concept. | |Want to know? What did you Learn?)|Begin by asking the student “What | | |do you know about math models?” | |K |Record their responses in the | |W |chart on chalkboard, overhead or | |L |flip chart. | | |Then ask the students “What do you| | |want to know? Again write their | | |responses on the board or flip | | |chart in the chart. | | |After the lesson is over complete | | |the chart in the L column by | | |recording what they learned. Ask | | |the students “What did you learn | | |about math models?” | | |List Math Terms | | |Below are the basic terms used in | | |logic reasoning. It’s All About | | |Logic uses inductive and deductive| | |thinking to create and solve math | | |models. Logic can be subject of | | |study in its own right. We | | |provide teachers the following | | |terms to be able to talk to their | | |students about thinking strategies| | |we will utilize in the lessons to | | |follow. Our attempt is to provide| | |activities in math models that use| | |deductive and inductive logical | | |thinking without delving in depth | | |about these processes. | | |Logic | | |The study of laws governing valid | | |thinking patterns and of the | | |structure of statements Logical | | |thinking uses inductive and | | |deductive thinking to make | | |inferences to support valid | | |arguments. (Nichols/Schwartz, p. | | |232) | | |Inferences | | |A conclusion that logically | | |follows from premises. Commonly an| | |inference can be found from two | | |premises, e.g., All men are mortal| | |(major premise). Fernando is a man| | |(minor premise). Fernando is | | |mortal (inference, conclusion) | | |(Nichols/Schwartz, p. 202). | | |Deductive Thinking: | |Brainstorm with students a summary |To “deduce” is to reason from | |table of inductive and deductive |known facts. Coming to a | |reasoning. Include characteristics|conclusion using logic rules is | |of both and compare, contrast |deductive thinking. Starting with | |between the two types of thinking. |true statements and demonstrating | | |other statements follow logically | |Inductive Thinking |from these truths is to reason | |Deductive Thinking |deductively. | | |Inductive Thinking: | | |Inductive thinking is to reason | | |what has happened before will | | |happen again. Observing data, | | |recognizing patterns, and making | | |conjectures (guesses) from these | | |observations is inductive | | |thinking. Inductive reasoning is | | |the basis of the scientific | | |method. Scientists use | | |experimental data to look for | | |patterns that test a hypothesis. | | |Inductive thinking is a tool for | | |showing how patterns either | | |support or contradict a | | |hypothesis. | | |Answer Key: | | |Inductive Thinking | | |Deductive Thinking | | | | | |Starts with observations | | |Starts with true statements | | | | | |Assumption is that pattern will | | |continue (conjecture) | | |Facts logically point to true | | |statements using logic to reach a | | |conclusion. | | | | | |Conjecture may or may not be true | | |Conclusion must be true | | | | | |Use inductive thinking to make | | |educated guesses based on | | |observations of patterns | | |Use deductive thinking to follow | | |logic through | | | | | |Other student responses | | |Other student responses | | | | | |Examples of Inductive and | | |deductive reasoning are: | | |A PowerPoint is included for the | | |teacher’s use to introduce the | | |following math model terms and use| | |as an introduction to the lesson, | | |if so desired. | | | | | |Patterns enable students to | | |describe and understand the | | |physical world and to make | | |informed predictions. | | |Students should use mathematical | | |models of patterns to make | | |inferences, predictions and | | |decisions | | |A model is a representation of a | | |pattern or relationship used to | | |simplify a situation by focusing | | |on selected aspects of the | | |situation. Model could be a | | |picture, table, equation, or any | | |other method to represent a | | |situation. | |3. Work through the math example |In this lesson students recognize | |embedded in the CTE lesson. |similarities and generalize | |Read and present the following |patterns, use patterns to create | |classroom demonstration. |models and make predictions, | |“Three (3) medical office clients |describe the nature of patterns | |are seeking medical treatment at |and relationships, and construct | |Reception Desk. You are the Medical|representations of mathematical | |Assistant working at the front |relationships. | |desk. Your job is to determine the |Students should use models and | |priority for which the clients will|create their own models in order | |be served using a math logical |to answer a question or draw | |thinking model.” |conclusions about the situation | |Mrs. Smith, presents in the office,|that the model represents. | |with a request for a refill of |Be sure you go over the math | |blood pressure medication. |terms, concepts, and vocabulary | |Mr. Jones presents in the office, |listed above before asking | |complaining of abdominal pain and |students to use the models. | |needs a prescription refilled. |Instruct your students to read all| |Mrs. Nelson, on the telephone, and |the clues before they fill in the | |wants to speak to someone about her|table. Then as they fill in the | |bill. |table with clues, use the number | |Y=yes N=no |of the clue. Example Y(1) | | | | | |(Use the first handout– Student | | |Math Logic Worksheet A (Rated | |Prescri-ption |Basic). Review with students Y=yes| |Pain |and N=no. Have students indicate Y| |Present at Office |or N for the appropriate client in| |Billing |the correct column while you read | |Questions |the scenarios.) | | |Answer Key Classroom | |Mrs. Smith |Demonstration: | | | | | | | | |Prescrip-tion | | |Pain | | |Present at Office | |Mr. Jones |Billing | | |Questions | | | | | |Mrs. Smith | | |Y | | |N | |Mrs. Nelson |Y | | |N | | | | | |Mr. Jones | | |Y | | |Y | | |Y | | |N | | | | | |Mrs. Nelson | | |N | | |N | | |N | | |Y | | | | | | | | |First - Mr. Jones, complains of | | |pain, needs prescription (Rx), and| | |present in office | | |Second – Mrs. Smith, needs Rx, | | |present in office | | |Third – Mrs. Nelson, on phone re: | | |insurance | |EXAMPLE 1: |Examples of Inductive and | |Use the logical thinking |Deductive reasoning: | |mathematics model to analyze the |Inductive reasoning is based on | |following situation and decide who |knowledge and experience from | |you think the healthiest to least |observations: | |healthiest person is: (Y=yes and |Observation 1: Mary came to class| |N=no) |late one morning. | |Susan gets 8 hours of sleep |Observation 2: Mary’s hair was | |nightly, eats apples daily, and |uncombed. | |loves to play soccer. |Prior experience: Mary is careful | |Tom loves vegetables, rides a |about her appearance. | |motorcycle, and is lifts weights. |Conclusion: She overslept | |Helen eats one meal a day and runs.|Deductive reasoning is based on | |Peter prefers Krispy Kremes donuts |facts: | |and Mountain Dew and spends time in|Premise 1: All cats have four | |front of his computer. |legs | | |Premise 2: Misty is a cat. | | |Conclusion: Misty has four legs. | | |Have students try using the model | | |on their own following the | | |previous model format. | | |Continue using the first handout– | | |Student Math Logic Worksheet A | | |(Rated Basic). | |Name |Name | |Healthy Habits |Healthy Habits | |Healthy Diet |Healthy Diet | |Physical Exercise |Physical Exercise | | | | |Peter |Peter | | |N | | |N | | |N | | | | |Helen |Helen | | |N | | |N | | |Y | | | | |Tom |Tom | | |N | | |Y | | |Y | | | | |Susan |Susan | | |Y | | |Y | | |Y | | | | | |Answer Key EXAMPLE1: | | |First - Susan, No N’s | | |Second – Tom, 1 N | | |Third – Helen, 2 N’s | | |Fourth– Peter, 3 N’s | | | | | |Then complete the last part of the| | |KWL—the “what they have (L) | | |earned” part. Students should | | |share what they learned from doing| | |the logic problems. | |4. Work through related, contextual|Use Student Math Logic Worksheet B| |math-in-CTE exam |(Rated Intermediate). Review with| |EXAMPLE 1 – Who is the CNA? |students that Y = yes, N = no. | |Bess, Tara, Gerard, and Clifton all| | |work for the hospital. One is a | | |nurse, one a CNA, one an | | |administrator, and one a therapist.| | |Use the statements below to answer | | |the question that follows. (Y=yes, | | |N=no) | | |Bess and Gerard eat lunch with the | | |therapist. | | |Clifton and Tara carpool with the | | |CNA. | | |Gerard works in the same department| | |with the nurse and CNA. | | |Who is the CNA? |Answer Key EXAMPLE 1: | | | | | |Nurse | | |CNA | |Nurse |Administrator | |CNA |Therapist | |Administrator | | |Therapist |Bess | | |N | |Bess |Y | | |N | | |N | | | | | |Tara | | | | |Tara |N | | |N | | | | | | | | |Gerard | | |N | |Gerard |N | | |Y | | |N | | | | | |Clifton | | | | |Clifton |N | | |N | | | | | | | | | | | | | |EXAMPLE 2 - You Look Marvelous! |Use Student Math Logic Worksheet C| |Dr. Guy Smiley is a Beverly Hills |(Rated Intermediate). | |plastic surgeon that can reverse |Review with students that Y=yes, | |the aging process for those willing|N=no. | |and able to part with extraordinary|Wednesday’s procedure cost $30,000| |sums of money. On each of the five|(8). Tuesday’s didn’t cost $35,000| |days last week (Monday – Friday) he|or $40,000 (3); the doctor charged| |worked a different wonder for a |$25,000 or $20,000 for the | |client so famous we only dare refer|procedure he performed that day. | |to each by his/her initials. In |Suppose he charged $25,000. He | |each case, he charged a different |would have done the lip | |price ($20,000, $25,000, $30,000, |enhancement on Monday (1). Neither| |$35,000 or $40,000). Determine the|Tuesday’s nor Wednesday’s | |day on which he worked on each |procedure would have been the | |person, the procedure he performed |tummy tuck (3), the face-lift (6),| |and the price he charges. |or the rhinoplasty (5), so only | |1. Dr. Smiley performed lip |one procedure—the | |enhancement the day before he |liposuction—would have been left | |performed the $25,000. |for both days. This contradiction| |2. He saw Mr. N earlier in the week|implies our assumption was wrong. | |than he saw Mrs. C |Tuesday’s procedure cost $20,000 | |3. The doctor charged $10,000 more |rather than $25,000. Dr. Smiley | |for the tummy tuck than he charged |did the tummy tuck on Wednesday. | |on Tuesday. |Thus, the $25,000 procedure wasn’t| |4. He saw Mr. W either the day |performed on Monday or Thursday | |before or the day after he |(1). It was done on Friday, and | |performed the liposuction. |the lip enhancement was done on | |5. He charged $35,000 for the |Thursday (1). The rhinoplasty | |rhinoplasty. |cost $35,000 (5), so this was | |6. Mrs. R and the person on whom |Monday’s operation, since | |the doctor performed the face lift |procedure or price eliminates the | |are, in some order, the patient he |others. By elimination, the lip | |saw on Monday and a person he |enhancement cost $40,000. | |charged either $20,000 or $40,000 |Monday’s patient was Ms. R (6). | |7. Dr. Smiley charged Mrs. K more |The face-lift didn’t cost $40,000 | |than $25,000 |(see above), so it cost $20,000 | |8. On Wednesday, he charged $30,000|(6). By elimination, the doctor | | |did liposuction on Friday. | | |Thursday’s patient was Mr. W (4). | | |Ms. K wasn’t operated upon on | | |Tuesday or Friday (7 & above); she| | |got the tummy tuck on Wednesday. | | |Mr. N went under the knife on | | |Tuesday, and Ms. C. got the | | |liposuction on Friday (2). | | |Answer Key EXAMPLE 2 – See | | |Worksheet D for answer grid: | | |Monday: Mrs. R, rhinoplasty, | | |$35,000 | | |Tuesday: Mr. N, face lift, $20,000| | |Wednesday: Mrs. K, tummy tuck, | | |$30,000 | | |Thursday: Mr. W, lip enhancement, | | |$40,000 | | |Friday: Mrs. C, liposuction, | | |$25,000 | | |Use Student Math Logic Worksheets | | |E (Rated Advanced). | | |Review with students that Y=yes, | | |N=no. | |EXAMPLE 3 - Baby Boom |Example 3 - Answer Key Summary (see| |Next month is going to be a busy |Worksheet F for answer grid): | |and joyous one for five expectant |Logic Reasoning: Girls’ names are | |mothers who live on my block. |Dee, Gail & Willow, boys’ names are| |Each of the five (Anna Fran, Lisa,|Mike & Sean, & dates are 1st, 8th, | |Renee, and Yvette) is due to have |15th, 22nd & 29th (intro.). Bloom | |her baby on a different date in |[boy’s name (4)] isn’t Mike [29th | |November (the 1st, 8th, 22nd, or |[last] (5)] (4), that one’s Sean. | |29th). The mothers-to-be have |Gail isn’t 1st, 8th (4), or 22nd | |already decided on names for the |[Bloom [Sean] would be 8th (4), but| |babies, and no two women have |then Willow couldn’t be 1st (2) or | |picked the same name (three of |15th [Nye would be 8th [Bloom} | |which—Dee, Gail, and Willow—are |(2)], so couldn’t be placed]; Gail | |girls’ names, and two of |is 15th, so Bloom is 1st (4). | |which—Mike and Sean—are boys’ |Willow isn’t 8th [Nye would be 1st | |names). This is probably the |[Bloom] (2); she’s 22nd, so Nye is | |largest number of births in one |15th, and Lisa is 29th [last] (2). | |month that this neighborhood has |Dee is 8th, so Anna is 22nd (1). | |ever seen. In fact, you might say|Hess isn’t 22nd [Anna] (3) or 29th | |that we have hit the mother lode! |[Yvette would be 22nd [Anna] (3); | |From the information provided, can|that one’s 8th, so Yvette is 1st | |you determine the baby name chosen|(3). Vanmeer [girl’s name (5) | |by each mother (identified by |isn’t 29th [Mike]; that one’s 22nd.| |first and last names—one surname |Plotkin is 29th. Fran isn’t Dee | |is Plot), as well as each woman’s |(1); she’s Gail. Renee is Dee. | |due date? | | |Anna’s baby is due to be born | | |exactly two weeks after Dee (who | | |isn’t Fran’s baby). | | |Willow is due to be born exactly | | |one week after Mrs. Nye’s baby but| | |at some point before Lisa’s baby. | | |Yvette is due to have her baby | | |exactly one week before Mrs. Hess | | |(who isn’t Anna). | | |Gail is due to be born exactly two| | |weeks after Mrs. Bloom will have | | |her baby boy. | | |Mike is due to be born on the | | |29th. Mrs. Vanmeer is having a | | |baby girl. | | |The math logic grid is on | | |worksheet E Students can use it to| | |define premises for recording | | |their inductive and deductive | | |thinking. | | |Name |Name | |Baby Name |Baby Name | |Due Date |Due Date | | | | | |Anna Vanmeer | | |Willow | | |22nd | | | | | |Fran Nye | | |Gail | | |15th | | | | | |Lisa Plot | | |Mike | | |29th | | | | | |Renee Hess | | |Dee | | |8th | | | | | |Yvette Bloom | | |Sean | | |1st | | | | |5. Work through traditional math | | |examples. |Dr. Math logical thinking | |Have the students try the enclosed|problem—Math Logic. Ask Dr. Math | |Dr. Math logical thinking problem.|http://mathforum.org/library/drmath| |EXAMPLE 1 - Math Logic |Use Student Math Logic Worksheet G | |Sally, Ron, Jim and Megan are the |(Rated Basic). Review with | |President, VP, Treasurer and |students that Y=yes, N=no. | |Captain of the cheerleading squad,|Answer Key EXAMPLE 1: | |but not necessarily in that order.|Sally – Treasurer | |Who is what? (Y = yes, N = no) |Ron - VP | |Sally loves money. |Jim – President | |Megan thinks she could not handle |Megan – Captain | |a whole class. | | |Jim was elected. | | |Ron is Jim’s partner. | | | |President | |President |VP | |VP |Treasurer | |Treasurer |Captain | |Captain | | | |Sally | |Sally |N | | |N | | |Y | | |N | | | | | |Ron | |Ron |N | | |Y | | |N | | |N | | | | | |Jim | |Jim |Y | | |N | | |N | | |N | | | | | |Megan | |Megan |N | | |N | | |N | | |Y | | | | | | | |EXAMPLE 2 - The Flower Show |Continue using Student Math Logic | |Jasmine, Rose, and Lilly each had |Worksheet G (Rated Intermediate). | |an entry in the county fair’s |Review with students that Y=yes | |flower competition. |,N=no. | |Coincidentally, the flowers they |EXAMPLE 2 Answer Key: | |entered were a jasmine, a rose, | | |and a lily, but not in that | | |order—in fact, none of the | | |competitors entered her namesake | | |flower. If, in addition, you know| | |that Jasmine did not enter a rose,|Jasmine | |can you figure out which flower |Rose | |each woman entered? (Y=yes, N=no) |Lily | | | | |Jasmine |Jasmine | |Rose |N | |Lily |N | | |Y | |Jasmine | | | |Rose | | |Y | | |N | | |N | |Rose | | | |Lily | | |N | | |Y | | |N | |Lily | | | | | | | | | | | | | | |EXAMPLE 3 – FAST-FOOD CHAIN |Use Student Math Logic Worksheet | |During the usual lunch rush at |H (Rated Advanced). Review with | |Mak’s Burgers, the five employees |students that Y=yes, N=no. | |like to switch jobs every |Logic Reasoning: Shifts are | |half-hour shift (11:00am, 11:30am,|11:00 a.m., 11:30 a.m., 12:00 | |12:00pm, 12:30pm and 1:00pm) so as|p.m., 12:30 p.m., and 1:00 p.m. | |to not get too frazzled. |(intro). | |Yesterday for example, during each|Drive-through shifts include 1 | |shift two of the employees manned |Mark (3), 1 Paul, 1 Rose, and 2 | |the main counter, another two |Fred (4); these are the only 5 | |workers cooked at the grill, and |drive-through shifts, so 11:00 | |the fifth person worked the |a.m. drive-through [1st] and 1:00| |drive-through window. When |p.m. drive-through [last] are | |lunchtime finally ends, the |Fred [only possible (2, above)],| |employees are usually the ones who|so Fred & Rose are counter at | |deserve a break! From the |least one shift (2), and Paul & | |information provided, determine |Rose are the same section 11:00 | |the employees who worked at the |a.m. and 1:00 p.m. (4). | |counter, the drive-through and the|Paul & Rose 11:00 a.m. [same | |grill during each shift. |section (above)] isn’t counter | |Kathy worked at the counter for |[Kathy 11:00 a.m. counter [1st] | |the first three shifts; she worked|(1)]; it’s grill. Mark 11:00 | |alongside Paul during at least one|a.m. is counter [only 11:00 a.m. | |of these shifts. |section unplaced]. | |The person who worked at the |Fred & Rose counter (above) isn’t| |drive-through for both the first |1:00 p.m. [Fred drive-through], | |and the last shift spent at least |11:30 a.m. [Kathy counter (1)], | |one shift working at the counter |or 12:00 p.m. [Kathy counter | |with Rose. |(1)]; it’s 12:30 p.m. | |Mark worked at the drive-through |Mark drive-through (3) isn’t | |the shift after he worked at the |11:30 a.m. Mark [11:00 a.m. | |grill alongside Rose but the shift|counter] would be 11:00 a.m. | |before he worked the grill again. |grill (3)] or 12:00 p.m. [11:30 | |Paul and Rose each worked at least|a.m. grill would be Mark & Rose | |one shift at the drive through. |(3), but then Rose drive-through | |During each of Fred’s two shifts |(4) couldn’t be 11:30 [Rose | |at the drive-through. Paul and |grill] or 12:30 p.m. [Rose | |Rose worked in the same section. |counter], so couldn’t be | | |placed]; Mark drive-through is | | |12:30 p.m., so 12:00 p.m. grill | | |is Mark & Rose and 1:00 p.m. | | |grill is Mark (3). | | |12:30 p.m. grill is Kathy & Paul | | |[only workers unplaced]. Rose | | |drive-through (4) isn’t 12:00 | | |p.m. [Rose grill]; it’s 11:30 | | |a.m. Paul drive-through (4) is | | |12:00 p.m. Fred 12:00 p.m. is | | |counter [only 12:00 p.m. section | | |unplaced]. Paul & Rose 1:00 p.m.| | |[same section (above)] isn’t | | |grill [Mark 1:00 p.m. grill]; | | |it’s counter. | | |Kathy 1:00 p.m. is grill [only | | |1:00 p.m. section unplaced]. | | |Kathy & Paul counter (1) is 11:30| | |a.m. [only counter unplaced]. | | |11:30 a.m. grill is Fred and Mark| | |[only workers unplaced]. | | |Answer Key EXAMPLE 3: | |Shift |Shift | |Counter |Counter | |Drive-Through |Drive-Through | |Grill |Grill | | | | | |11:00am | | |Kathy & Mark | | |Fred | | |Paul & Rose | | | | | |11:30am | | |Kathy & Paul | | |Rose | | |Fred & Mark | | | | | |12:00pm | | |Fred & Kathy | | |Paul | | |Mark & Rose | | | | | |12:30pm | | |Fred & Rose | | |Mark | | |Kathy & Paul | | | | | |1:00pm | | |Paul & Rose | | |Fred | | |Kathy & Mark | | | | | |Summary (shift, counter, | | |drive-through, grill): | | |11:00 am: Kathy & Mark, Fred, | | |Paul & Rose | | |11:30 a.m., Kathy & Paul, Rose,| | |Fred & Mark | | |12:00 p.m., Fred & Kathy, Paul,| | |Mark & Rose | | |12:30 p.m., Fred & Rose, Mark, | | |Kathy & Paul | | |1:00 p.m., Paul & Rose, Fred, | | |Kathy & Mark | |EXAMPLE 4 - Bills, Bills, Bills |Use Student Math Logic Worksheet | |To deal with all my monthly bills,|I (Rated Advanced). Review with | |I’ve programmed my computer to |students that Y=yes, N=no. | |alert me three days before each |Answer Key EXAMPLE 4: | |bill is due, at which time I |BILL | |immediately log on to my checking |PAID DATE | |account and authorize an |AMOUNT | |electronic payment. This month, I| | |paid each utility bill on a |Telephone | |different date (the 1st, 4th, 7th,|12th | |12th, 15th, or 23rd). Each bill |$54.18 | |was for a different amount | | |($42.37, $54.18, $60.00, $94.98, |Gas | |98.64, or $106.50). From the |1st | |information provided, determine |$94.98 | |the date on which I paid each bill| | |(including the water bill) and the|Cable | |amount of each payment. |15th | |The telephone bill was due at some|$60.00 | |point before the date I paid the | | |$106.50 bill. |Sewer | |The gas bill was for a lower |7th | |amount than the bill that was due |$98.64 | |exactly six days after I paid the | | |electric bill. |Water | |I paid the cable bill on the day |23rd | |that the $54.18 bill was due. |$106.50 | |I paid the sewer bill at some | | |point after the due date of the |Electric | |$94.98 bill but at some point |4th | |before I paid the telephone bill. |$42.37 | |The bill due on October 18 was for| | |a higher amount that the bill I |In summary: | |paid exactly five days after the |Cable, 15th, $60.00 | |due date of the $42.37 bill. |Electric, 4th, $42.37 | | |Gas, 1st, $94.98 | | |Sewer, 7th, $98.64 | | |Telephone, 12th, $54.18 | | |Water, 23rd, $106.50 | | |Logic Reasoning: | |BILL |Paid dates are 1st[due 4th], | |PAID DATE |4th[due 7th], 7th[due 10th],12th | |AMOUNT |[due15th], 15th [due 18th], and | | |23rd [due 26th], and amounts are | | |$42.37, $54.18, $60.00, $94.98, | | |$98.64, and $106.50 (intro.). | | |$42.37 [least] isn’t paid 1st[due| | |4th, but no paid 9th], 7th | | |[due10th, but paid 15th is due | | |18th], 12th[due 15th but no paid | | |20th], 15th [due 18th], or 23rd | | |[due 26th, but no paid 31st] (5);| | |it’s paid 4th. | | |Sewer isn’t paid 15th [telephone | | |would be paid 23rd [due 26th, but| | |paid 23rd last (4)] (1), 1st, 4th| | |[4th is earliest due date], 23rd | | |[last] (4), OR 12th [telephone | | |couldn’t be paid 23rd [due 26th, | | |but paid 23rd last] (1), so would| | |be paid 15th [only paid left | | |after sewer paid] (4), and cable | | |couldn’t be paid 1st [no due | | |1st], 23rd [no due 23rd] (3), or | | |7th [$54.18 would be due 7th | | |[paid 4th [$42.37]] (3), so would| | |be paid 4th, but then electric | | |couldn’t be paid 1st [paid 4th | | |[due 7th] is $42.37 [least]], 7th| | |[no due 13th] , or 23rd [no due | | |29th] (2), so couldn’t be | | |placed]; sewer is paid 7th, so | | |$94.98 is ppaid 1st [due 4th, | | |only due left before sewer paid] | | |(4). | | |Cable isn’t paid 1st [no due | | |1st], 12th [no due 12th], 23rd | | |[no due 23rd] (3), or 4th | | |[$54.18 would be due 4th [paid | | |1st [$94.98]] (3); it’s paid | | |15th, so$54.18 is paid 12th [due | | |15th] (3). Telephone isn’t paid | | |23rd [due 26th, but paid 23rd | | |last] (1); it’s paid 12th | | |[due15th, only left after sewer | | |paid [7th]] (4), so $106.50 is | | |paid 23rd [only paid left after | | |telephone due] (1). Electric | | |isn’t paid 1st [paid 4th [due | | |7th] is$42.37 [least]] or 23rd | | |[no due 29th] (2); its paid 4th. | | | | | |Gas isn’t paid 23rd [$106.50 | | |[most]] (2); it’s paid 1st | | |[$94.98], so paid 7th [due 10th, | | |and electric paid 4th] is $98.64 | | |[only left more than gas] (2). | | |Water is paid 23rd. Cable is | | |$60.00. | |EXAMPLE 5-Where And With What | Use Student Math Logic Worksheet| |Weapon Was Each Man Murdered? |J (Rated Advanced). Review with | |One rainy evening, five military |students that Y=yes, N=no. | |men were murdered in an old | | |mansion on Willow Lane. The |Answer Key EXAMPLE 5: | |murdered took place in the |See Work sheet for the table and | |bedroom, basement, pantry, den and|answer key table Worksheet K. | |attic of the house. No two men |General – Den with the poker | |were murdered in the same room or |Sergeant – Basement with the | |with the same weapon. The weapons|shovel | |used were poison, a poker, a gun, |Captain – Pantry with the gun | |a knife, and a shovel. From the |Corporal – Attic with the knife | |clues given, try to determine the |Lieutenant – Bedroom with the | |room in which each man was killed |poison | |and the weapon used to do him in. |Find Logic Reasoning: Dr. Math | | |logical thinking problem—Math | |(Y = TRUE, N = FALSE) |Logic. | |The murder with shovel was not |Ask Dr.Math site: | |done in the den or the attic, the |http://mathforum.org/library/drma| |captain nor the lieutenant was |th | |killed with the shovel, nor was | | |either killed in the den or the | | |attic. | | |The captain was not murdered in | | |the bedroom. | | |The poker was not the murder | | |weapon in the attic. | | |Neither the general nor the | | |corporal was murdered with poison,| | |a gun, or a shovel. | | |The man murdered in the basement | | |had just had dinner with the | | |corporal, the captain, the man | | |done in with poison and the victim| | |of the poker. | | |6. Students demonstrate their |Use Student Math Logic Worksheet | |understanding. |L (Rated Advanced). Review with | |Work individually or in a group to|students that Y=yes, N=no. | |solve the following childcare |Answer Key – Example 1: | |logic puzzle. Provided is a table| | |for recording your findings. Be |Assertiveness | |aware you will need a math logic |Gestalt | |grid to solve the dilemma. |Teen | | |Women’s | |EXAMPLE 1 – GROUP THERAPY |Four | |Patricia is a psychotherapist who |Six | |runs four evening group therapy |Seven | |sessions each week; there is one |Eight | |each evening from Monday through | | |Thursday. Each group has a |Mon. | |different focus, and each |Y | |currently includes a different |N | |number of participants (four, six,|N | |seven or eight). Can you figure |N | |out, for each night, the focus |N | |group meeting and how many |Y | |participants it currently |N | |includes? (Y=Yes, N=No) |N | |Patricia’s women’s group meets on | | |Tuesday. |Tues. | |Her assertiveness group (which |N | |doesn’t meet on Wednesday) |N | |includes six regular participants.|N | |Patricia’s teen group (which meets|Y | |on Thursday) includes an even |N | |number of people. |N | |Her gestalt group is the largest, |Y | |with eight regular participants. |N | | | | | |Wed. | |Assertiveness |N | |Gestalt |Y | |Teen |N | |Women’s |N | |Four |N | |Six |N | |S e v e n |N | |Eight |Y | | | | |Mon. |Thurs. | | |N | | |N | | |Y | | |N | | |Y | | |N | | |N | | |N | | | | |Tues. |Four | | |N | | |N | | |Y | | |N | | | | | |Six | | |Y | | |N | | |N | |Wed. |N | | | | | |Seven | | |N | | |N | | |N | | |Y | | | | | |Eight | | |N | |Thurs. |Y | | |N | | |N | | | | | | | | | | | | | | | | | | | | | | |Four | | | | | | | | | | | | | | | | | |Six | | | | | | | | | | | | | | | | | |Seven | | | | | | | | | | | | | | | | | |Eight | | | | | | | | | | | | | | | | | | |Patricia’s women’s group meets on| | |Tuesday, has 7 members. | | |Her assertiveness group (which | | |doesn’t meet on Wednesday) | | |includes six regular | | |participants. Meets on Monday | | |Patricia’s teen group (which | | |meets on Thursday) includes an | | |even number of people (4). | | |Her gestalt group is the largest,| | |with eight regular participants,| | |meets on Wednesday. | | | | | |Note gestalt is a term that | | |simply means the “whole is more | | |than the sum of it’s parts”. | | |Gestalt provides a foundation for| | |cognitive theory in education | | |today. According to Brek Hufnus,| | |Department of Educational | | |Technology, San Diego State | | |University, the essence of | | |Gestalt theory is that people | | |perceive objects as wholes. When| | |we see a triangle, we view it not| | |as three lines and three angles | | |but as one thing, a triangle. | | |One simple application to | | |teaching is known as | | |whole-part-whole. The overview | | |of the subject is presented first| | |and then broke down into various | | |component parts. Then finally | | |the entire subject is again | | |taught showing the relationship | | |between the parts connected to | | |the whole. | | |Group Therapy | | |Logic Reasoning: | | |Patricia’s women’s group meets on| | |Tuesday (10. Patricia’s teen | | |group meets on Thursday (3). Her| | |assertiveness group doesn’t meet | | |on Wednesday (2), so it meets on | | |Monday. By elimination, her | | |gestalt group meets on Wednesday.| | |It includes eight people (4). | | |The assertiveness group includes | | |six people (2). The teen group | | |includes four people (3); by | | |elimination, the women’s group | | |has seven people. | |EXAMPLE 2 - Adventures in |Use Student Math Logic Worksheet | |Babysitting |M (Rated Advanced) | |Because Evan’s homework load is a | | |little light this semester, he’s |Answer Key Example 2: | |been able to pick up quite a bit |Day | |of money babysitting for families |Family Name | |in his neighborhood. Over five |# Children | |nights (Thursday through Monday), |Children’s Names | |he sat for five families | | |(including the Cerrones), each |Thurs. | |with a different number of |Montenero | |children (from one to five). For |3 | |each night, determine the family |Sheila, Victoria, Walt | |he sat for, the number of children| | |in that family, and their names. |Fri. | |The Jawalul’s have one more child |O’Neill | |than Brandon’s family. |4 | |Evan babysat for the Montenegro’s |Brandon, Greg, Harriet, Isaac | |two days before he babysat for | | |Tim’s family. |Sat. | |The O’Neill family has three more |Jawalul | |children than Joel’s family. |5 | |The family for whom Evan babysat |Angela, Luther, Mark, Polly, Tim | |on Saturday has at least two | | |girls. |Sun. | |He looked after Shayla at least |Rolchevski | |two days before he minded Luther. |2 | |The Rolchevskis have one more |Cindy, Emily | |child than the family for whom | | |Evan babysat on Monday. |Mon. | |Harriet’s family has more children|Cerrone | |than Cindy’s family. |1 | |Evan babysat for the Jawaluls on |Joel | |either Saturday or Sunday. | | |Angela has at least one brother | | |and at least one sister. | | |Emily and her sister are the only | | |two children Evan looked after on | | |Sunday evening. | | |Mark’s last name is either | | |Rolchevski or Jawalul. | | |Isaac has more siblings than Walt.| | |Evan watched Polly on Thursday or | | |Saturday. |Logic Reasoning: | |He babysat for Victoria’s family |Emily & her sister are the only | |before he sat for Greg’s. |two children Evan babysat on Sun.| |Day |(10). Joe’s family doesn’t have | |Family Name |3, 4, or 5 children (3), so he is| |# Children |an only child. | |Children’s Names |Brandon’s family can be the third| | |in our enumeration. He isn’t one | | |of five children (1). If he were | | |one of three, there would be 4 | | |Jawalul children (1). However, | | |there’d also be 4 O’Neill | | |children (3), so we’d have a | | |contradiction (intro). Thus, | | |Brandon is one of 4 children (see| | |above). His last name is O’Neill | | |(3), and there are 5 Jawaluls | | |(1). | | | | | |Evan babysat for the Jawaluls on | | |Sat. (8). Because the Jawaluls | | |and O’Neills have 5 & 4 children,| | |respectively, the family that | | |Evan sat for on Mon. doesn’t | | |include exactly 3 or 4 children | | |(6); this family has one child, | | |since day or last name eliminates| | |the others. The Rolchevskis are | | |the family with 2 children (6). | | |The family he worked for on Mon. | | |isn’t the Monteneros (2); it’s | | |the Cerrones (Intro), and, by | | |elimination, there are 3 | | |Montenero children. Since Tim | | |isn’t one of the two Rolchevski | | |children (see above), Evan didn’t| | |sit for the Monteneros on Fri. | | |(2); he sat for the O’Neills on | | |Fri., and, by elimination, he sat| | |for the Monteneros on Thurs. | | | | | |Tim is one of the 5 Jawalul | | |children (2 & above), as is Mark | | |(11 & above). Evan didn’t | | |babysit Luther on Sun. or Mon. | | |(see above), nor did he babysit | | |Luther on Thurs. or Fri. (5); | | |Luther is another of the Jawalul | | |children, and Shayla is one of | | |the Monteneros (5). | | |Isaac isn’t one of three children| | |(12 & above) & he isn’t a Jawalul| | |(4 & above), so he’s an O’Neill. | | |Walt is a Montenero (12 & above).| | |Evan didn’t watch Greg on Thurs.| | |(14) or Sat. (4 & above). Evan | | |didn’t watch Greg on Thurs. (14) | | |or Sat. (4 & above); Greg is an | | |O’Neill (see above). Victoria is | | |the final Montenero child (14). | | | | | |Emily’s sister (see above) isn’t | | |Harriet (7), Angela (9), or Polly| | |(13); she’s Cindy. Since at most | | |one O’Neill child is a girl (see | | |above), Angela isn’t an O’Neill | | |(9); she’s a Jawalul. | | |Polly is the final Jawalul (13). | | |By elimination, Harriet’s last | | |name is O’Neill. | |EXAMPLE 3 – ER Triage |Distribute Student Worksheet N | |Give the following patient |(Rated Intermediate). | |sCNArios to students. | | |Read or have students read the |Example 3 is the culminating | |following: |assessment for the lesson. If | |“TRIAGE is a French term meaning |students can create their own | |“picking or sorting”. In |logic problems and solutions they| |medicine, it is a process of |have achieved success. | |sorting and classifying sick and | | |in injured patients for medical |Challenge students to write and | |treatment. Those who work the |solve their own example problems | |front line with patients use |and demonstrate competency in a | |triage when there are more victims|test situation. They are to | |than medical staff. Victims are |determine the categories on their| |classified as lowest priority, |own and set priorities using the | |second priority, and highest |math logical thinking model. | |priority. See the table.” |**Be sure you do not provide the | |Priority |categories for the model. | |Condition |Students should do this on their | | |own to develop their reasoning | |Highest |abilities and mathematical model | |Airway and breathing difficulties |development skills. | |Cardiac arrest |It is important that students | |Uncontrolled or suspected sever |make their own model and | |bleeding |categories. Don’t be surprised | |Severe head injuries |if they do not end up with all of| |Open chest or abdominal wounds |the patients in the same order as| |Shock |above. My students ended with | | |Mary last, but reasoned she | |Second |should be second. They went back| |Burns |and adjusted their categories in | |Major or multiple fractures |their model until she ended up | |Back injuries |second. They used their own | | |reasoning process to determine | |Lowest |that the first model couldn’t be | |Fractures |correct | |Minor wounds | | | | | |“Assess the following six (6) |Answer Key Example 3: | |Emergency Room clients seeking | | |medical treatment. Determine the |Unconscious | |priority order of delivering care |Bleeding | |using a math logical thinking |C/O | |model. Be sure to use the |Pain | |principles of First Aid/CPR ABC’s.|Abnormal | |(Y=yes, N=no) |Skin Color | |Tom, 55 year-old male, working at |Impaired Airway | |home using a power saw. Presents | | |in the ER bleeding from his left |Tom | |hand. Unconscious, not breathing.|Y | |Perspiring profusely, skin color |Y | |gray. |Y | | |Y | |Sue, 26 year-old female, 8 months |Y | |pregnant. Presents in the ER with| | |fever. Complains of dizziness and|Sue | |headache. Skin color pale. |N | |Jenny, 32 year-old female, auto |N | |accident. Conscious, bleeding |Y | |from the right leg with bone |Y | |protruding. Crying and moaning |N | |loudly. Skin color pale | | |Mary, 7 year-old, presents in the |Jenny | |ER with fever, nausea & vomiting. |N | |Unconscious and having a seizure. |Y | |Skin color pale, breathing shallow|Y | |and irregular. |Y | |Joe, 17-year-ond-male, presents in|N | |the ER after falling off the roof,| | |unconscious, bleeding from a left |Sam | |arm laceration, breathing shallow |N | |and noisy. Skin color pale Sam, |N | |21-year-old male, motor vehicle |Y | |accident. Came in to the ER |Y | |complaining of leg pain. Skin |N | |color pale. | | | |Joe | | |Y | | |Y | | |N | | |Y | | |Y | | | | | |Mary | | |Y | | |N | | |N | | |Y | | |Y | | | | | |First (5 Y’s)– Tom – | | |unconscious, apnea, bleeding, | | |shock | | | | | |Second (4 Y’s) – Joe – | | |unconscious, dyspnea, bleeding | | |Discuss third and fourth | | |position: | | |(3 Y’s) - Jenny - bleeding | | |fracture, pain | | |(3 Y’s) – Mary – unconscious, | | |seizure and vomiting for | | |potential airway obstruction | | |Fifth (2 Y’s) – Sue – fever, | | |pain | | |Sixth (2 Y’s)– Sam – pain | | |Have students explain the | | |solutions to the problems, or | | |demonstrate what they did to show| | |understanding. | | |Teacher will collect the | | |worksheets to demonstrate | | |students’ understanding of the | | |math model concepts. A | | |teacher/student discussion should| | |show student understanding | |Optional Example Family Tree |Key - Tree Challenge Recording | |Challenge Attached is a scanned |Summary(Rated Intermediate). | |problem (Worksheet 0 and Grid |CHILD | |Sheet P) to use for those students|A G E | |who like a challenge. It may also|MONTH | |be used as group problem solving |HAIR | |challenge. |COLOR | |CHILD |EYE COLOR | |AGE | | |MONTH |Brinley | |HAIR COLOR |6 | |EYE COLOR |May | | |Black | | |Blue | | | | | |Carlen | | |8 | | |Oct. | | |Black | | |Green | | | | | |Devan | | |4 | | |Jan. | | |Blonde | | |Green | | | | | |Farren | | |3 | | |June | | |Red | | |Brown | | | | | |Hilaire | | |7 | | |Sept. | | |Blonde | | |Blue | | | | | |Peregrine | | |14 | | |July | | |Brown | | |Hazel | | | | | |Romy | | |12 | | |Aug. | | |Black | | |Brown | | | | | |Skylar | | |9 | | |April | | |Brown | | |Blue | | | | | |Tait | | |10 | | |March | | |Red | | |Green | | | | | |Tannis | | |7 | | |Sept. | | |Red | | |Blue | | | | | |Wynne | | |11 | | |Nov. | | |Red | | |Hazel | | | | | |Zephan | | |10 | | |March | | |Blonde | | |Brown | | | | | | | | | | | | | | | | |7. Formal assessment |Distribute Student Worksheet Q | |CNA Long Term Care Assignment | | |This activity can be done |Mobility | |individually or as a group |Feed Assist | |project. Students are to develop |Appointment | |their own math logic grid and |AM care assist | |premises (can vary from example |X’s | |given) | | |“You are a CNA assigned to provide|Anna | |AM care to 6 residents with |N | |different levels of function. |N | |Prioritize the care you are to |N | |deliver within your 4 hour shift |Y total | |7:00 am – 11:00 am. Some |1 | |residents will have appointments.”| | |Anna, is a 75-year-old female who |Tom | |is semi-conscious, total assist |Y | |with AM care, bed bound, receives |N | |nutrition through a feeding tube. |Y 9:00am | |Tom, is a 65-year-old male |Y partial | |paraplegic, alert, wheelchair |3 | |bound, self-feeder, partial assist| | |with AM care, who attends physical|Mary | |therapy at 9:00 am. |Y | |Mary, is an 80-year-old female |N | |with right hemi-plegia, alert, w/c|N | |bound, self-feeder, partial assist|Y partial | |with AM care |2 | |John, is an 82-year-old male | | |double amputee, alert, bed bound, |John | |needs assistance with feeding and |N | |is a total assist with AM care. |Y | |Kathryn, is a 90-year-old female |N | |with dementia, ambulatory, NPO, |Y total | |needs assistance with AM care, |2 | |hospital appointment at 8:00 am. | | |Liz, is a 70-year-old with |Kathryn | |dementia, ambulatory, self-feeder,|Y | |needs assistance with AM care, |N | |family coming to visit at 10:00am.|Y 8:00am | | |Y partial | | |3 | | | | | |Liz | | |Y | | |N | | |Y 10:00am | | |Y partial | | |3 | | | | | |ANSWER KEY at Teacher’s | | |discretion, Y=yes, N=no | | |Kathryn, (3 Y’s) 8:00 am appt., | | |NPO | | |John, feed assist come back later| | |for AM care | | |Tom, (3 Y’s) 9:00 am appt, | | |self-feeder | | |Liz, (3 Y’s) 10:00 am appt., self| | |feeder | | |Mary (2 Y’s) ambulatory | | |John, (2 Y’s) finish AM care, bed| | |bound | | |7. Anna (1 Y) tube feeder, bed | | |bound | | |Back-To-School Clothes (Basic | | |Level Assessment) | | |Answer Key Summary (Worksheet R –| | |Back-to-School Clothes) (Rated | | |Basic) | | |Review with students that Y=yes, | | |N=no. | | | | | |Allan | | |Grant | | |Jeremy | | |Ryan | | |Dress Pants | | |Jeans | | |Shirts | | |Shoes | | | | | |Mon. | | | | | | | | | | | |Y | | | | | |Y | | | | | | | | | | | |Tues. | | |N | | |Y | | | | | |N | | | | | | | | | | | |Y | | | | | |Wed. | | | | | | | | |Y | | | | | | | | | | | |Y | | | | | | | | |Thurs. | | |Y | | | | | | | | |N | | |Y | | | | | | | | | | | | | | |Dress Pants | | |Y | | | | | | | | | | | | | | | | | |Jeans | | |N | | | | | |N | | |Y | | | | | | | | |Shirts | | |N | | | | | |Y | | | | | | | | | | | |Shoes | | | | | |Y | | | | | | | | | | | | | | |Logic Reasoning: Marian took | | |Jeremy shopping on Wednesday (3).| | |She didn’t take Ryan shopping on | | |Tuesday or Thursday (4), so she | | |took him out on Monday. She | | |didn’t take Allan shopping on | | |Tuesday (2), so she took him on | | |Thursday. By elimination, she | | |took Grant shopping on Tuesday. | | |She bought him shoes (1). Allan | | |didn’t need jeans or shirts (2), | | |so he needed dress pants. Jeremy| | |didn’t need jeans (3), so he | | |needed shirts. By elimination, | | |Ryan needed jeans. | | |References: We cited some sources| | |throughout the document but need | | |to give particular credit to… | | |The Original Logic and Math | | |Puzzles, Vol. 14 Fall 2004 (Group| | |Therapy, p.9, You Look | | |Marvelous!, p. 29). The | | |Original Logic Problems, No. 107,| | |Oct. 2004 (Baby Boom, p. 30, Fast| | |Food Chain, p. 55 and Bills, | | |Bills, Bills, p.61). | | |For additional problems you may | | |want to browse the websites | | |listed. | | |Michigan Curriculum Framework. | | |Michigan Dept. of Education. | | |www.michigan.gov | | | | | |MI CliMB. Clarification of | | |Benchmarks, Michigan Dept. of | | |Education. www.michigan.gov | | | | | |Mathematics and Science Education| | |Reform | | |http://www.svsu.edu/mathsci-cente| | |r/maser.htm | | | | | |Michigan Teacher Network | | |http://mtn.merit.edu | | | | | |Illuminations | | |http://illuminations.nctm.org/ind| | |ex2.html | | |A book recommendation is Logic | | |Problems for Student Groups, | | |ISBN: 08251-51-3817-5, | | |www.walch.com or 1-800-341-6094, | | |$22.45. |