The highly prized skills that employers look for today are problem-solving, reasoning and decision making, and logical approaches to challenges. Fortunately, mathematics challenges are the perfect way to hone your skills in these areas, especially when you challenge yourself to a new "Problem of the Week" each week like this classic one listed below, "The Horse Problem."

Though they may seem simple at first, problems of the week from such sites as MathCounts and Math Forum challenge mathematicians to deductively reason the best approach to solving these word problems correctly, but oftentimes, phrasing is meant to trip up the challenge-taker, but careful reasoning and a good process for solving the equation will help ensure you answer questions like these correctly.

Teachers should guide students toward a solution to problems like "The Horse Problem" by encouraging them to devise methods for solving the puzzle, which might include drawing graphs or charts or using a variety of formulas to determine missing number values.

### The Horse Problem: A Sequential Math Challenge

The following math challenge is a classic example of one of these problems of the week. In this case, the question poses a sequential math challenge in which the mathematician is expected to calculate the final net result of a series of transactions.

**The situation**: A man buys a horse for 50 dollars. Decides he wants to sell his horse later and gets 60 dollars. He then decides to buy it back again and paid 70 dollars. However, he could no longer keep it and he sold it for 80 dollars.

**The questions:** Did he make money, lose money, or break even? Why?

There's an old Marilyn Burns video titled "About Teaching Mathematics" in which this particular question was taken to the street and there were as many answers as there were strategies to solve it—why is this problem such a problem for so many?

**The answer: **The man ultimately saw a net profit of 20 dollars—whether you use a number line or a debit and credit approach, the answer should always amount to the same. I have yet to see a group of people come up with the same answer!

### Guiding Students to the Solution

When presenting problems like this one to students or individuals, let them devise a plan for solving it, because some students will need to act out the problem while others will need to draw charts or graphs; additionally, thinking skills are needed for a lifetime, and by letting students devise their own plans and strategies in problem-solving, teachers are allowing them to improve these critical skills.

Good problems like "The Horse Problem" are tasks that allow students to devise their own methods to solve them. They should not be presented with the strategy to solve them nor should they be told that there is a specific strategy to solve the problem, however, students should be required to explain their reasoning and logic once they believe they have solved the problem.

Teachers should want their students to stretch their thinking and move toward understanding as math should be problematic as its nature suggests. After all, the single most important principle for improving the teaching of math is to allow math to be pragmatic for students.