# Real Numbers: Problem Solving and Quizzes

## Problem Solving

Often, when students hear the words *problem solving* in a mathematics class, they assume that we are talking about word problems. While word problems are included in problem solving, the concept is much broader than that. In the **Problem Solving Assignments** you will find word problems, but you'll also find other types of problems.

For example, if you were asked to evaluate , you could solve that easily using the Order of Operations. This activity would be called an *exercise*, since you are practicing what you have already learned. However, if you were given the expression and were asked to insert grouping symbols to make it equal to 13, then you have a *problem*. This type of question requires you to apply what you know about the Order of Operations in a creative way. These types of problems allow you to demonstrate a thorough grasp of the material that you have been studying.

Go to the Lesson 1: Problem Solving Assignment.

## Lesson Quiz

After reviewing the key concepts from this lesson, take the Lesson 1: Quiz with your mentor. Your mentor will check your work and provide feedback for this quiz.

## Solve It! Quiz

The Solve It! Quiz will give you a chance to demonstrate your problem-solving skills. Take the Lesson 1: Solve It! Quiz with your mentor.

## Digging Deeper

The Four 4s Activity (Wheeler) is a puzzle that has intrigued mathematicians for at least one hundred years. Warning: Be careful or you will spend all your free time thinking about the number 4!

*Note*: The **Digging Deeper** activity is purposely written to challenge you. Don't expect to solve these problems quickly. These problems are meant to be pondered. Andrew Wiles described his method of pondering: "When I got stuck, and I didn't know what to do next, I would go out for a walk.... Walking has a very good effect in that you're in this state of relaxation, but at the same time you're allowing the sub-conscious to work on you" (Wiles, *NOVA*).

Work on these problems for a while; when you get stuck, take a break. Go for a walk. Take a snack break. Put your pencil down, relax, and think. Ponder. Contemplate. Then pick up your pencil and try again.

## Solutions

Solutions to the

- Problem Solving Assignment,
- Lesson Quiz,
- Solve It! Quiz, and
- Digging Deeper Problem Set

are available on the Mentor Guidelines Web site. (Mentors, if you have not already done so, please register on the **Duke TIP Mentor Registration** page to access the answer keys.)

**Please proceed to Lesson 2.**

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