# Engaging students: Independent and dependent events

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Emily Bruce. Her topic, from Probability: independent and dependent events.

How can this topic be used in your students’ future courses in mathematics or science?

The concept of probability can be used in a variety of different courses and professions. In sciences classes, the students might want to calculate the probability that the universe was created from the big bang, or they might want to use probability to predict phenotypes. This can later be used by biologists and doctors to determine the chances that a certain disease or genetic mutation will be passed on to a child. Probability and statistics are also commonly used in meteorology to predict weather patterns. In reality, we use the concepts of probability every day when we determine the best choice to make or a reasonable risk to take. Since it correlates with statistics and data analysis well, one could argue that every future course has the potential to expand on this topic.

What interesting things can you say about the people who contributed to the discovery and/or the development of this topic?

Probability has been around for several hundred years. The first time we see probability address was in the fifteenth century. Italian mathematicians published two works on the subject, but the calculations of probabilities were not commonly known. It wasn’t until the seventeenth century that probability really came to light and became a branch of mathematics. It all started with gambling! A man named Chevalier de Méré was a big gambler. He bet that if he rolled a dice four times he could roll at least one 6. He won a lot of money using this bet. Then he wanted to go a step further and started betting that if he rolled two dice twenty four times, he would get two sixes at least once. Similarly, he won the bet more often than not. Eventually he wanted to know why this was happening, so he called on some mathematician friends to research it. That was the start of hundreds of years of researching and developing what we know today as probability.

References:

Brief History of Probability. (2000). Retrieved September 4, 2014. http://www.teacherlink.org/content/math/interactive/probability/history/briefhistory/home.html.

A2. How could you as a teacher create an activity or project that involves your topic?

One way I, as a teacher, can create an activity that involves decimals, fractions and percents is to incorporate it with art. I found inspiration from an article titled, “Masterpieces to Mathematics: Using Art to Teach Fraction, Decimal, and Percent Equivalents.” Each student would receive a 100 square grid and a large amount of colored squares (red, green, blue, purple, orange) to create and glue on their square grid paper in a design of their choosing:

As seen on the image above, when the students were done with their masterpiece, they would have another sheet consisting of columns: color, number, fraction, decimal, and percent. They would list the colors they used under the color column, and then count the amount of squares of each color and record it in the number column. They would then convert the number of each color used compared to the total amount of squares (100) to a fraction, decimal, and percent. To further their understanding, I could ask the students to block out the outer squares and ask to calculate the new number of each color, fraction, decimal, and percent from the new total (64).

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