Lesson Plans SET B for Grades 9-10-Lesson 7 Level 9-10- Logical Reasoning HW

Lesson 7 Level 9-10- Logical Reasoning HW

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This document outlines a set of logical reasoning problems designed for Level 9-10 students, likely as part of preparation for a Math Kangaroo competition or similar. It contains five problems, each engaging skills in logic, reasoning, and mathematical proof.<br /><br />1. **Tommy's Statements:** The first problem revolves around identifying which statement Tommy did not say. Given Tommy's nature to either fully lie or tell the truth on any given day, and analyzing the statements, it is deduced that today he is lying. Thus, the statement "Sometimes I lie" is not said by him today.<br /><br />2. **Friendship Paradox:** The second problem demonstrates using a contradiction to prove that in a class of 20 kindergarteners, at least two children must have the same number of friends. By assuming each child has a distinct number of friends ranging from 0 to 19 leads to logical inconsistencies, confirming the theorem.<br /><br />3. **Marathon Order:** Problem three involves analyzing the order of runners based on the number of times they pass each other. By recognizing passing patterns and using parity (odd/even passes), it is determined that Frank finishes first, followed by Brady, David, and Ethan.<br /><br />4. **Tic-Tac-Toe Analysis:** This problem is split into multiple parts, each asking for proofs regarding game frequency among three players—Anna, Bella, and Caddy. Using analysis on maximum game appearances and known quantities, it is concluded that Anna played 12 games, Bella played 23, and Caddy played 24 games; Anna lost the fourth game.<br /><br />5. **Identical Integers Proof:** The final problem is a mathematical proof demonstrating that a list of five positive integers must be equal if any subset of four can be paired to equal sums. Logical deduction and equalities between sums ensure that all integers in the list are the same.<br /><br />Overall, the solutions employ logical deductions, parity concepts, combinatorics, and algebraic proofs to convey clear mathematical reasoning processes.

Keywords

logical reasoning

math competition

problem solving

mathematical proof

parity

combinatorics

algebraic proofs

contradiction

game analysis

integer equality