Lesson Plan – Learning Opportunity
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Lesson Plan- Learning Opportunity
Name: Wes Remley Date: 1/28/10 Course: Algebra I Grade Level: 9 _
I. Topic and General Goal
- Calculate the number of combinations and permutations for a specified event based on realistic scenarios.
II. Reference to PA or National Standard
- PA Standard 2.7.8.A - Determine the number of combinations and permutations for an event.
III. Pre-Assessment
- The students are assessed on their ability to recall the formula for a combination.
- The students are assessed on their ability to describe the difference between combination and permutation.
- The students are assessed on their ability to determine when to solve for combination and when to solve for permutation.
IV. Lesson Objectives
- The student will investigate the differences between combinations and permutations.
- The student will be able to explain the key word that helps to signify the difference that exists between combinations and permutations.
- The students will be able to determine if a problem is stating whether to solve for combinations or permutations.
V. Materials
- SmartBoard
- PowerPoint
- Combination/Permutation notes paper
- “Combinations or Permutation” activity sheet
VI. A. Introduction (Anticipatory Set)
- Recently, the students have been working with combination problems.
- Pass out the Combination/Permutation notes paper
- Give a simple example in which the students are to recreate the combination formula and solve for the number of combinations.
o Example: CLASS ELECTION
o “In how many ways can we select a committee of 3 people from a group of 5 candidates?”
o
o What does the n stand for? What is n for this problem?
o What does the r stand for? What is r for this problem?
o (Work out the problem on the board)
o
- In doing this exercise, you will review the formula for combinations and give an example for future review.
B. Lesson Development (Activities, Procedures)
- Today, we will be exploring permutations for a specified event.
- Continue with the same example, but with different parameters.
o Example: CLASS ELECTION
o “In how many ways can we select a committee consisting of a president, vice president, and treasurer from a group of 5 candidates?”
o Ask for 5 volunteers from the classroom.
o Explain that there are 5 possibilities (candidates) for a president to be chosen. (Write the “5” on the board)
o Ask one volunteer to vote the president into office. Ask the president to take their seat, and explain that there are now 4 possibilities for a vice president to be chosen. (Write “5 ∙ 4” on the board)
o Ask one more volunteer to elect the vice president in to office. Ask the vice president to take their seat, and explain that there are now 3 possibilities left for a treasurer to be chosen. The remaining two people do not get elected to office. (Write “5 ∙ 4 ∙ 3” on the board)
o Ask one last volunteer to vote the treasurer into office. Ask for round of applause for the remaining two participants.
o Ask the students to look at what has been written on the board. This equation represents the amount of ways we can choose these three officials (respectively) from the group of candidates. This represents the permutation in that there are 60 different ways to elect positions. Another, more familiar way to express permutation is this equation:
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o Keep in mind that permutations are different from combinations; permutations involve arranging and/or rearranging the order of a group, while combinations exist regardless of the order in a group. “Order” is the key term in explaining the difference, to the class.
o Visual Example:
PERMUTATION (for the election)abcde / bacde / cabde / dbcae / ecdab
acbde / bcade / cbade / dcbae / edcab
adebc / bcdea / cbdae / dceab / eadbc
aedbc / bdcea / cdbae / decab / edabc
abecd / baecd / cdeab / deabc / eabcd
aebcd / beacd / cedab / daebc / ebacd
acdbe / badce / cadbe / dabce / eacbd
adcbe / bdace / cdabe / dbace / ecabd
abdce / bdeac / caebd / dbeac / edbac
adbce / bedac / ceabd / debac / ebdac
acebd / bcead / cebad / dacbe / ebcad
aecbd / becad / cbead / dcabe / ecbad
- Pass out “Combination or Permutation” activity sheet
- Explain that this sheet contains some example problems of both permutations and combinations, but it is up to the student(s) to determine which is presented in each of the problems.
- Work out a few problems, as a class (ask whether a problem is describing a permutation or a combination), and tell the students to show their work.
- The activity sheet provides examples to help students differentiate between combinations and permutations.
C. Closure (Summary)
- Ask the students if they know what the main difference is between combinations and permutation. From the lesson, the students should be able to provide the answer, “Order.”
VII. Assessment/Evaluation
- The assessments, throughout the lesson, were mostly presented in the form of problems. This was done to give the students practice in deciding what denotes combination problems and permutations problems. Equations were discussed to make sure students stayed on task, and also to determine whether the students comprehended the placement of specific values within the equation.
- Initially, for the beginning of the permutation lesson, students were asked to consider an “election” scenario.
o This approach is used to get students involved in the actual example, and hopefully, help them gain a deeper, more visual depiction of what occurs in calculating a permutation.
- The remaining problems are hand-outs/worksheets. Incorporating the smartboard for this part of the lesson is a way for teacher and students to work through the problems to see if there are still confusing issues that need to be addressed.
- During this in-class activity, the students will be kept on task by answering questions posed to them when the problems are being solved on the smartboard. During this time, questions and answers should flow freely to get to the final answer of each problem presented from the power point. If there are any discrepancies in the answers among the students, there will be time to clarify and re-explain what the students are missing in the lesson at the time the problem is being reviewed.
- Through interactive discussion, the students are challenged to arrive at answers in order to solve each problem correctly for either combinations or permutations.
- At the end of the activity, the students should be able to answer one final question regarding combinations and permutations. Although not difficult to answer, the question represents the objective of the lesson.
VIII. Adaptations, Modifications, Extension Activities
- The in-class “work together” session on combinations and permutations is an attempt to eliminate the confusion that can arise between these two functions. The adaptations and modifications to the lesson will be handled if and/or when the students have questions during the smartboard lesson.
- Students of all levels have the opportunity to participate in today’s lesson.
IX. Interdisciplinary Connections
- The original lesson applies to the application of standards by addressing the idea that solving for combinations and permutations can be applied to everyday scenarios. This complies with PA Standard 2.7.8.A which states, Determine the number of combinations and permutations for an event.
X. Self-Evaluation
Fell off the page today during class, as I completely forgot to follow the protocol/routine of reviewing homework. I was preoccupied as to whether or not I would have enough time to get through the lesson because we were on a modified schedule due to testing again this morning. The lesson went well, and I was able to get in the “Class Election” activity (and worksheet) to demonstrate the permutation and combination concepts. I also had time to assign their homework for tomorrow. But, I need to stay focused and remember all the small details so that no student is left behind in understanding the objective of the lesson or the mathematical content we are trying to accomplish. It is vital for the students that I stay focused and remain driven to stay on task for the entire lesson no matter what external factors may interfere or deter from the lesson.