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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.

### Equations, Algebra, and Functions

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

### Number Theory

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

### Counting

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

### Geometry

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

### 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.