10th Grade Permutation And Combination Lesson Plan (Math)

Topic: Permutation and Combination

Objectives & Outcomes

• By the end of this lesson, students will be able to identify and define permutation and combination, and use them to solve problems.

Materials

• Whiteboard and markers
• Handouts with examples of problems involving permutation and combination
• Calculator (optional)

Warm-up

• Ask students to think of a way to organize three objects (such as balls, toys, or mix-CDs) into a line, such that each object is next to only one other object.
• Have students share their ideas and write them on the board.
• Then, ask students to think of a way to organize four objects into a line, such that each object is next to only one other object.
• Have them share their ideas and write them on the board.
• Then, have students share their ideas for a way to organize five objects into a line, such that each object is next to only one other object.
• Have them share their ideas and write them on the board.
• After a few minutes, ask students to look at the list of ideas they came up with and see if they can notice any patterns.
• Do they notice any similarities between the ways to organize three objects and the ways to organize four objects? Or between the ways to organize four objects and the ways to organize five objects?
• Encourage them to share their observations with the class.

Direct Instruction

• Introduce the concept of permutation, explaining that it refers to the possible arrangements of objects when they are arranged in a line.
• Ask students to think of a way to organize three objects into a line, such that each object is next to only one other object.
• Have them share their ideas and write them on the board.
• Then, ask students to think of a way to organize four objects into a line, such that each object is next to only one other object.
• Have them share their ideas and write them on the board.
• Then, ask students to think of a way to organize five objects into a line, such that each object is next to only one other object.
• Have them share their ideas and write them on the board.
• Show students that the ways to organize the objects into a line form a pattern - the arrangement of objects in a line can be described using a mathematical formula, where n is the number of objects being arranged and r is the number of objects in each arrangement.
• For example, when arranging three objects into a line, the formula is n-r-n, where r is the number of objects that are next to only one other object.
• When arranging four objects into a line, the formula is n-r-n-r, where r is the number of objects that are next to only one other object.
• When arranging five objects into a line, the formula is n-r-n-r-r, where r is the number of objects that are next to only one other object.
• Explain that permutations can be understood as all the possible arrangements of objects when they are arranged in a line.
• Ask students to think of a way to organize three objects into a line, such that each object is next to only one other object.
• Have them share their ideas and write them on the board.
• Then, ask students to think of a way to organize four objects into a line, such that each object is next to only one other object.
• Have them share their ideas and write them on the board.
• Then, ask students to think of a way to organize five objects into a line, such that each object is next to only one other object.
• Have them share their ideas and write them on the board.
• Show students that the ways to organize the objects into a line form a pattern - the arrangement of objects in a line can be described using a mathematical formula, where n is the number of objects being arranged and r is the number of objects in each arrangement.
• For example, when arranging three objects into a line, the formula is n-r-n, where r is the number of objects that are next to only one other object.
• When arranging four objects into a line, the formula is n-r-n-r

Guided Practice:

• Have students work in pairs or small groups to arrange a certain number of objects into a line, such that each object is next to only one other object.
• Have them use the formula n-r-n to describe their arrangement.
• Have students share their arrangements with the class and discuss the formulas they used.
• Have students repeat the activity, this time using a different number of objects.

Independent Practice

• Have students work in pairs or small groups to arrange a certain number of objects into a line, such that each object is next to only one other object.
• Have them use the formula n-r-n to describe their arrangement.
• Have them present their arrangements to the class and explain their reasoning.
• Have students repeat the activity, this time using a different number of objects.

Closure

• Review the concepts of permutation and combination and how they are related to the identity of the UAE.
• Ask students to share something they found interesting or surprising about the lesson.

Assessment

• Use the class participation and the summary paragraph as formative assessment.
• For summative assessment, give a quiz or test that covers the concepts of permutation and combination.