Lesson Plans SET B for Grades 9-10-Lesson 5 Minimum Maximum Values HW

Lesson 5 Minimum Maximum Values HW

Pdf Summary

This document contains a set of math problems and solutions aimed at students practicing concepts from a Math Kangaroo class, specifically targeting lessons on minimum and maximum values. Here's a summary of the problems and their solutions:<br /><br />1. **Pens and Pencils Packing Problem**: The task is to determine the maximum number of boxes that can be used to pack 90 pens and 90 pencils where each box contains the same number of pens but differing numbers of pencils. The solution involves finding divisors of 90, determining that the largest possible number of boxes is 10, and verifying that this arrangement is achievable by distributing pencils variably among these boxes.<br /><br />2. **Square Coloring Problem**: Peter needs to color a 5x5 square ensuring no row, column, or diagonal has repeated colors. The minimum number of colors required is five. This result draws on knowledge of coloring smaller squares and strategizing to cover the entire 5x5 grid.<br /><br />3. **Perfect Cube Element Deletion**: From the set {5, 10, 15, 25, 30, 35, 40, 45, 50}, the task is to find the least number of deletions necessary so that the product of the remaining numbers is a perfect cube. Through factor analysis, the numbers 15, 20, and 35 need removal to make the product a perfect cube, achieving the result by maintaining balanced prime factors across the set.<br /><br />4. & 5. **Divisibility Selection Problems**: For a chosen range, students need to pick numbers such that one remains divisible by the other. The lessons consist of establishing thresholds; where the set {1, 2, 3, …, 15} requires at least 9 numbers and the set {1, 2, 3, …, 100} demands at least 51 to ensure at least two numbers maintain divisibility relationships. The solutions leverage pigeonhole principles and divisibility tactics. <br /><br />The exercises blend combinatorial reasoning, divisibility rules, and strategic counting principles, developing the students’ problem-solving skills.

Keywords

Math Kangaroo

minimum values

maximum values

pens and pencils

square coloring

perfect cube

divisibility

combinatorial reasoning

strategic counting

problem-solving skills