Lesson Plans SET A for Grades 7-8-PDF Lesson 8 Level 7-8 Combinatorics-Class Student

PDF Lesson 8 Level 7-8 Combinatorics-Class Student

Pdf Summary

The Math Kangaroo Level 7-8 document focuses on teaching combinatorics through examples, problem-solving strategies, and progressively challenging problems. It begins with a warm-up question about selecting ice cream flavors, which introduces the concept of combination—choosing items without regard to order.<br /><br />The document outlines a 10-lesson curriculum that includes a variety of mathematical topics like algebra, geometry, and logic, with a specific lesson dedicated to combinatorics. The four-step problem-solving strategy emphasizes understanding the problem, planning a solution, executing the plan, and reflecting on the outcome to ensure accuracy.<br /><br />Combinatorial concepts include the fundamental counting principle, permutation, and combination. Examples illustrate these concepts, such as calculating outcomes for true/false questions (using multiplication for independent choices) and determining the number of ways to line up people (using factorials for permutations). Specific examples highlight the importance of order in permutations and its irrelevance in combinations.<br /><br />The document includes several Math Kangaroo contest questions exploring permutations and combinations in different scenarios, such as choosing members for a group, arranging people or numbers, and utilizing strategies like complimentary counting and symmetry. One question asks about the number of four-digit palindromes on an odometer, emphasizing pattern recognition.<br /><br />Additionally, students are encouraged to engage in a Genius Hour project to explore combinatorics further, requiring them to present a problem and solution with explanations of the techniques used. The wrap-up section suggests strategies for distinguishing permutations from combinations and leveraging lists or logical reasoning to simplify complex problems. The material aims to develop students' critical thinking and problem-solving skills in a structured yet engaging manner.

Keywords

combinatorics

problem-solving

permutations

combinations

Math Kangaroo

counting principle

algebra

geometry

logic

critical thinking