Lesson Plan #:AELP-INT005
Author: Octaviano Garcia
School or Affiliation: Cuba Elementary School, Cuba, NM
Endorsed by: These lesson plans are the result of the work of the teachers who have attended the Columbia Education Center’s Summer Workshop. CEC is a consortium of teachers from 14 western states dedicated to improving the quality of education in the rural, western, United States, and particularly the quality of math and science Education. CEC uses Big Sky Telegraph as the hub of their telecommunications network that allows the participating teachers to stay in contact with their trainers and peers that they have met at the Workshops. Date: May 1994

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Grade Level(s): 4, 5, 6, 7, 8, 9, 10, 11, 12

Subject(s):

• Interdisciplinary

Overview:

Many students view problem solving, its process, and necessary skills as that task assigned by the teacher on Monday between the hours of 9:15 and 10:15 A.M. and to be completed with this set time or suffer the consequences— gradewise. They have not gotten into the habit of critically reviewing every recommendation and decision they make before executing on it. Therefore, the act of critically thinking through every significant idea that comes to mind is viewed as playing a very minor role in their daily lives.

Purpose:

The purpose of this activity, used as an introduction to a course at the very beginning of the year or an introduction to any unit of study, is to help students master the process of applying critical thinking to each and every problem/task that confronts them in their daily undertakings. Further, this activity can serve as a base reference and model for every problem/task assigned or any problem that a student or students might bring up.

Objective(s):

As a result of this activity, each student will:

Demonstrate her/his knowledge of the six basic steps to problem solving by listing them or reciting them orally.

Demonstrate his/her mastery of the six basic steps to problem solving by actively applying them in problem solving when the task lends itself to such a process.

Demonstrate her/his ability to apply these six basic steps to problem solving by guiding other students in the solution of a given problem or set of problems.

This activity works well as an introduction to a course, its objectives, requirements, and expectations. The activity can also serve to achieve the following secondary learning objectives given that the necessary follow through is provided during the course of the school year.

Demonstrate a high awareness of the need for the application of critical thinking skills to everyday problem solving.

Demonstrate an observable and measurable improvement in his/her problem solving skills by way of constantly and consistently applying this modeled process.

Show his/her understanding and mastery of the problem solving process by way of written or oral explanation of the critical steps in problem solving learned through this mode.

Show a marked improvement in the quality and completeness of his/her written and oral responses to other assigned, as well as, routine personal problems.

Materials: None are required if solution to the problem is assigned individuals other than pencil and paper. Large writing chart paper may be used for group work if assigned to small groups. Overhead transparencies may be use for easy viewing if the teacher works the solution through with the total class.

Procedure:

Set the stage by explaining the purpose of this story problem to the student. Orient students as to the expectations. Review with the students the basic strengths of a good problem solver. Emphasize a student’s ability to think critically; to identify, group, and classify information in an order and form that makes it relevant and applicable to a given solution. Alert them to the fact that ones ability to solve daily problems, simulated or real, depends on ones ability to separate useful from useless information; separate necessary from unnecessary information and then apply the pertinent information to the problem/task at hand. Remind them that their success in the course or unit of study heavily depends on their attention and critical thinking skills/habits. Tune-in; tune-out habits that will result in low quality solutions to assigned tasks while critical listening, critical thinking, and assertive problem solving processes will result in high quality solutions to any problem they solve. Tell them that the story problem you are about to share with them contains many fabricated distractors together with the pertinent and necessary information that they will need for solving the problem that the story posts for them as listeners.

The Story: The Shepherd and the Harvard Boys A few years ago, not counting those that came later, two Harvard sophomore students decided that they would spend their summer break traveling across the United States of North America, the same country that they had studied for years in books. In preparation for this long journey they were careful to pack the necessary credit cards, which their generous parents provided for them, maps, some light casual traveling clothes, and the friendliest Harvard smile they could muster. Their mode of travel was to be by way of an old 1961 Chevy panel truck that one of the boys had gotten, as a gift, from an uncle upon graduating from high school. The vehicle had made many trips between New Port, Connecticut, their home town, and the Harvard campus in Cambridge, Mass., therefore, the two agreed that the panel truck would make it to the west coast and back. All due caution was taken in preparing the vehicle for the trip also. Once all of these preparations were in place their journey was underway.

Traveling through the mid-west and southwestern states did provide much in the way of entertainment or challenge to their superior Harvard trained mind. The real fun began when they reached the far west coast in California. They spent four weeks in Hollywood, two weeks in the San Diego Zoo, a few days in San Fransisco, and many days in Disney Land. All too soon, it appeared, their summer had come to an end and it was time for them to start back to more familiar territory. So after picking up some supplies for the trip in Sacramento they headed east on Interstate 80. On the second day the panel truck made only 150 miles during a ten hour day. Repairs had taken up most of that day. On the third day the two decided to abandon the vehicle and hitch a ride home after having to stop six times for repairs within a sixty mile stretch of I-80.

The hour was marching on to four o’clock in the afternoon when they had bade their panel truck goodbye. Both boys were silent for the first hour of walking but each was thinking of the night ahead and having to round up a meal or go without. The more timid of the two was re-experiencing fears that he thought he had left behind at the age of twelve when he was in seventh grade. He began envisioning attacks by wild lions, tigers, panthers, and the like. When he spoke up his first question to his partner was, Where are we going to sleep tonight and what are we going to eat? Fear not my good friend, responded his partner, I shall teach you how the pioneers of the frontier survived in these desolate plains long before there was even a highway through here. Just keep your eyes alert for sheep and when you spot some hopefully their shepherd let me do the talking. For I fear that in your condition you might jeopardize our chances for an evening meal and perhaps even a bed to sleep in.

Our timid friend did not speak up but he did not much fancy chasing and wrestling a sheep down for their dinner not to mention having to butcher and prepare it over an open fire. He was deep in his thoughts when his traveling companion’s shout of glee brought him back to reality. There, there, by those trees on that other slope! he shouted as he pointed with excitement at some white spots that, in Mr. Timid’s eyes looked like rocks. Those are nothing but rocks, he retorted with the air of certainty that he often used on the Harvard campus. Nonetheless, he was very happy to accept his error when they approached the white spots and they turned out to be sheep as his companion had predicted from the opposite side of the valley.

No sooner had they arrived at the herd’s northern most edge when out of a scrub oak thicket came two Australian Shepherd dogs. Both stopped and assayed the valley for the whereabouts of the shepherd and sure enough, from under the tallest pine tree there emerged what looked like a person. As they got closer they could recognize him as the lone shepherd of this large herd. The man looked as if he had needed a shave, a haircut, and probably a bath for several weeks but they left all that aside and decided that here was a good opportunity for them to cash in on that evening meal they so badly needed and perhaps even a place to spend the night if they applied their best manners and savvy.

Mr. Timid’s partner took a quick glance over the entire herd and in his mind made the best estimate of the number of sheep in the herd that his bright mind could compute in the time he had and when they were a dozen or so yards from the shepherd he greeted him. A very good afternoon to you Mr. Shepherd of two thousand sheep, he offered, not knowing the man’s name. Your greetings are kindly accepted my traveling friends but you error Mr. Bright Boy. I am not the shepherd of two thousand sheep. If I had that many sheep out there plus another herd as large as that then again half as many as I have out there I should be the shepherd of two thousand sheep.

Mr. Timid immediately set his mathematical mind to the problem and by the time they had arrived at the shepherd’s tent, which was a few hundred yards away he had figured out how many sheep the shepherd actually had in that herd.

Problem and Solution:

Question to students: How many sheep were in this shepherd’s herd?

Direct the students to apply the six basic steps to problem solving in solving this problem. To do so, students must list each step and next to it or immediately following they must list the information from this story that applies and is pertinent to that particular step. Remind students that at the out set you warned them that the point of the story was to see how well they can separate useful information from useless information given a particular task/problem to solve.

You may wish to accept a solution that is arrived by guess and test (trial and error) method or you may direct the students to apply their algebra skills and produce an algebraic formula/equation: Example: 1X + 1/2X = 2,000 sheep.

You may wish to have students attempt the solution to this problem on an individual basis or on a small group basis. If you feel the group is very unfamiliar with the six basic steps to problem solving you may want to use this story problem to establish familiarity with these steps and do a total group problem solving exercise. This problem lends itself well to any of the above approaches in arriving at a solution.

A reward may be offered to the person or group that produces the most complete and well formulated solution first. Extra points is a good reward for this problem or physical objects may also be offered.

Tying It All Together:

Review by having students re-state and review the purpose (objectives) associated with this story problem.

Be sure to review the best solution (problem solving process) with the students before this story problem is set aside for the day or the week.

Remind students that there will be constant reference made to the components of this problem and especially the process followed in solving it as other problems of similar character come up during the course of the year or unit, whichever applies.

Encourage students to share the results of this activity with their parents or guardian person(s).

Use this story problem to introduce or review the problem solving process with any lesson, unit or course. Remember you can vary it by level. Example: the number of sheep that Mr. Bright Boy, as the shepherd calls him, may be 20; 200; 2,000; etc.

Useful Internet Resources:
* Group Problem Solving Six Steps
http://mauicc.hawaii.edu/staff/stjohn/publicspeakers/pdf/gpssteps.pdf * What are the Steps in Problem Solving?
http://www.esu11.k12.ne.us/fps/6stps.html