My husband came home from work today and asked me in which grade students start studying probability. I thought, "Where did that question come from? I didn't even think he knew what probability was."
It seems that the secretary of their department was babysitting her grandchildren last night. She offered to help them with their math homework. The question they needed help with was "What is the probability of rolling snake eyes on a pair of dice?" Her grandchildren are in fourth grade.
She brought the question to work with her today, wanting to know the correct answer. As a group, they came up with 1/36. My husband wanted to know if they had done it right. The secretary wanted to know why students are learning probability in fourth grade.
So, I'll answer those questions. Yes, you worked the problem correctly. There are 36 possible combinations that can be rolled with a pair of dice. Only one of them can be snake eyes. That means that there is one possible combination out of 36, or 1/36. Another way to calculate this is that there is one "1" on the first die out of six numbers. There is also one"1" on the second die out of six numbers. In probability, you multiply these together. 1/6 times 1/6 is 1/36.
As for the secretary's question as to why 4th graders are learning probability, there are several answers.
First, there are several major industries that are big users of probability (and statistics). The first of those is the gambling, sports, and games industry. All gambling, sports, and many other games rely heavily on the use of probabilities to predict winning combinations and numbers of winners. Poker players know the odds of any particular hand winning over any other hand. Probabilities are used to determine how much and how often a slot machine pays out. Stats are calculated on every sport and sports figure. Even the odds of me having to put my left foot on red in a game of Twister is 1 out of 16.
The second major industry using probabilities is the insurance industry. All insurance rates are determined by the probability that a certain person of a certain age doing a certain activity will have an accident or a heart attack or get diabetes or die at a certain age.
The third big user of probability is meteorology and weather forecasting. Every time the weather person says there's an 80% chance of snow, he or she has studied the weather patterns, applied the mathematics and science and formulas, and made the prediction.
A fourth area where probabilities are used, but may not be widely known, is in the area of research. Research is done in almost every field of study from agriculture to business trends to education to psychology to medicine. Even fashion and food follow trends that can be studied. The data is gathered and analyzed and predictions are made using probability and statistics.
A second reason 4th graders study probability is so that they learn the basics they will need as they move on to more advanced courses in high school. The mathematics will get harder, as will the probability, so they need to learn the fundamentals at an early age.
A third reason 4th graders study probability is that it gives them practice with fractions and multiplication of those fractions. Students need to practice these concepts, and studying probabilities gives them another opportunity. Students also get to see how what they're studying can be applied to real-life situations.
And a final reason for all students studying probability and statistics is that it is one of the major standards that must be met in all mathematics educational programs. As far as I know, all state standards for mathematics include a statistics and probability component at every grade level. Students are tested in these different components (numbers and number sense, computation, algebra, geometry, and data) and are expected to be proficient.
No Child Left Behind states that all children must be proficient in mathematics by the year 2014. If schools do not make adequate yearly progress, then staff may be replaced or the school may be closed and turned into a charter school.
So, yes, probability study is very important and the earlier a student starts studying it, the better for everyone.