Lesson Plans SET B for Grades 9-10-Lesson 1 Problem solving strategies HW

Lesson 1 Problem solving strategies HW

Pdf Summary

This document outlines a set of math problems intended for students at levels 9-10, covering various problem-solving strategies as part of a Math Kangaroo class. Here's a summary of the problems and their solutions:<br /><br />1. **Number Sequence Problem:** Attempt to insert addition and subtraction signs between numbers 1 to 20 to result in 1. The solution explains that it's impossible to obtain 1 due to the parity (odd/even nature) of the total sum and changes that can be made.<br />   <br />2. **Car Problem:** Two cars travel between towns A and B, meeting at points C and D. Given AC is 40 miles out of 100, the solution involves velocity equations to determine BD is 20 miles.<br /><br />3. **Sum of Numbers Problem:** With 2024 numbers, any sum of 100 is positive. Two solution strategies are provided: <br />   - A smaller problem is solved, showing symmetry leads to the total sum being positive.<br />   - Considering extreme values, demonstrating positive sums due to repeating smaller sets of numbers.<br /><br />4. **Pencil Distribution:** The task involves dividing 6 identical pencils among 3 children. Solutions are provided via listing and combinatorial methods (stars and bars/sticks and stones), yielding 28 ways.<br /><br />5. **Marble Machine Problems:**<br />   - Part (a) involves reaching 40 marbles with machines outputting 4 or 5 marbles. It's possible by strategic use of each output.<br />   - Part (b) asks about reaching 200 marbles with alternative outputs of 4 and 7, proving impossible due to remainders when divided by 3.<br />   - Part (c) confirms that starting from one marble, any number ≥8 is accessible using outputs of 4 and 5 through modular arithmetic logic.<br />   - Part (d) explores generalized conditions for achieving any marble count beyond a threshold with machines characterized by outputs d and e.<br /><br />Each section teaches problem-solving methods through a combination of mathematical reasoning, algebraic manipulation, and logical deduction.

Keywords

math problems

problem-solving strategies

Math Kangaroo

number sequence

car problem

sum of numbers

pencil distribution

marble machine

algebraic manipulation

logical deduction