Lesson Plans SET A for Grades 7-8-Lesson 8 - Level 7-8 - Combinatorics

Lesson 8 - Level 7-8 - Combinatorics - Homework

Pdf Summary

This document contains a set of Level 7-8 combinatorics problems designed to reinforce skills learned in a Math Kangaroo class lesson. The problems test students' ability to use combinatorial reasoning to solve a variety of challenges, each with specific scenarios and constraints.<br /><br />1. **Distribution of Money**: The first problem involves distributing four one-dollar bills among three recipients. It is permissible for some individuals to receive nothing. The solution reveals that there are 15 different ways to achieve this distribution.<br /><br />2. **Party Handshakes**: In the second problem, five couples are attending a party where each person shakes hands with everyone else except their own partner. The challenge is to calculate the total number of handshakes that occur, with the answer being 40.<br /><br />3. **Triangle Formation**: The third problem presents the task of finding out how many triangles can be formed using four points each from two different lines, m and n. The solution to this problem indicates that there are 48 possible triangles.<br /><br />4. **Line Joining Problem**: The fourth problem involves determining the number of ways two students, Jaycee and Timothy, can join an existing line of five students waiting to buy lunch. The answer to this arrangement problem is 42.<br /><br />5. **Specific Six-Digit Numbers**: The fifth problem requires identifying six-digit numbers wherein each of the last three digits is twice the corresponding digit from the first three digits. Examples such as 430,860 illustrate the solution, with 100 valid combinations fitting the criteria.<br /><br />The problems are structured to encourage critical thinking and apply combinatorial concepts to different contexts, each with a distinct method for determining the count of possibilities.

Keywords

combinatorics

Math Kangaroo

problem-solving

distribution

handshakes

triangles

line joining

six-digit numbers

combinatorial reasoning

critical thinking