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# Problem Solving and Mathematical Discovery

This courseware helps students to become better problem solvers. Students will learn about roughly a dozen problem techniques (such as Draw a useful diagram, Find a pattern, Consider cases) and explicitly look at problem solving in a number of major topic areas (such as Number Theory, Counting, Geometry). None of the problems presented in this course uses material beyond that covered in the Advanced Functions and Pre-Calculus courseware. The majority of the problems discussed would be accessible to strong and motivated students in Grades 10 and 11.

### Units

## Introduction

In this unit we solve one difficult problem and some easier variations of the problem. Through the development of the solutions we begin to think about problem solving strategies and techniques that will be formalized in the next unit.

Welcome video

Includes Problems 1-5

## Techniques

In this unit we explore a variety of problem solving techniques.

Includes Problem 6

Includes Problems 7-9

Includes Problems 10-12

Includes Problems 13-17

Includes Problems 18-25

Includes Problems 26-31

Includes Problems 32-35

Includes Problems 36-39

Includes Problems 40-45

Includes Problem 46-49

Includes Problems 50-54

Includes Problems 55-57

Includes Problems 58-61

Includes Problems 62-65

Includes Problems 66-67

Includes Problem 68

## Equations, Algebra, and Functions

We apply some of the techniques learned in the previous unit to solve problems involving equations, algebra, and functions.

Includes Problems 74-77

Includes Problems 78-81

Includes Problems 82-86

Includes Problems 87-91

Includes Problems 92-97

Includes Problems 98-100

Includes Problems 101-102

## Number Theory

We apply some of the techniques learned in the Techniques unit to solve problems involving number theory.

Includes Problems 103-105

Includes Problems 106-114

Includes Problems 115-119

## Counting

We apply some of the techniques learned in the Techniques unit to solve problems involving counting.

Includes Problems 124-125

Includes Problems 126-127

Includes Problems 128-130

Includes Problems 131-132

Includes Problems 133-136

## Geometry

We apply some of the techniques learned in the Techniques unit to solve problems involving geometry.

Includes Problems 137-142

Includes Problems 143-145

## Problem Solving Wrap-up

In this final unit we present some concluding thoughts and solve a set of challenging problems that highlight most of the techniques and topics covered throughout the course.

Includes Problems 150-160

## Additional Resources

A complete listing of problems used.