Math Problem Solving Strategies

When students develop the ability to solve problems either in written or picture form, then they truly understand related mathematical concept or concepts.

The best approach that I used as a teacher, was to provide my students with a problem or the day or problem of the week. Problems of the day were not as complex as problems of the week.

Problems of the day dealt with a specific math concept related to the previous day’s class work or homework.

Problems of the week combined several concepts together to help students make connections between concepts, which is critical to long term understanding.

Sample Problems

Problem 1

A loop of rope is lying on the ground in the position show in the figure below: You are too far away to see which section of the rope is above or below at each of the crossovers at A, B and C.

If we assume that it is equally likely that either section is on top at each crossover, what is the probability that the rope is knotted?

Problem 2

Three intelligent women, Alice, Barb and Carol, sit down to try out a test in logical reasoning. They are so arranged that each can see the color of a label which is either red or blue, attached to the hats worn by the other two but no one of them can see the color of the label attached to her own hat. They are told that at least one of the labels is red. If any one of them can logically deduce the color of the label on her hat, she is to declare it. Carol decides to play this game with her eyes closed, knowing that the other two women have their eyes open. After a little time Carol, who has not seen the label on any of the hats declares her label is red. How can she deduce this?

Problem 3

For this tower of nine squares, determine a line passing through point P that will split the area of the nine squares into two equal parts.