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

PDF Lesson 8 Level 7-8 Combinatorics-Class Teacher

Pdf Summary

This document is an instructional guide for teaching combinatorics to students participating in the Math Kangaroo contest, specifically targeting levels 7-8. It provides a comprehensive lesson plan structured into various segments, each with specific time allocations to cover the fundamentals of combinatorics, including the 4-step problem-solving method, permutations, combinations, factorials, and the fundamental counting principle.<br /><br />The lesson begins with a warm-up problem from the Math Kangaroo 2004 contest, exploring combinations of ice cream flavors chosen by children, leading to a total of 10 combinations. It uses this interactive example to introduce basic concepts.<br /><br />The core instruction phase introduces students to the 4-step problem-solving strategy, applying it to fundamental counting principles and calculating permutations and combinations. Examples provided include the use of factorials for arranging people and choosing students for tasks, highlighting the differences between ordered and unordered selections.<br /><br />The document includes several Math Kangaroo sample problems across different years that illustrate these concepts, like determining positions of numbers, forming groups without specific pairs, and number of triangles or palindromes possible under constraints.<br /><br />Additionally, strategies such as symmetrical counting, casework, and complementary counting are discussed to assist in solving more complex problems. Bonus questions, such as those from Math Kangaroo 2019 and 1998, challenge students further, navigating constraints in a chess tournament or counting palindromes on an odometer.<br /><br />The curriculum also incorporates a "Genius Hour" project where students present combinatorics problems and solutions to peers. The wrap-up emphasizes distinguishing between permutations and combinations and encourages using organized lists for smaller sets. The document aims to provide both theoretical knowledge and practical problem-solving techniques in combinatorics.

Keywords

combinatorics

Math Kangaroo

problem-solving

permutations

combinations

factorials

counting principle

symmetrical counting

casework

Genius Hour