Engaging students: Adding and subtracting decimals

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 Sydney Araujo. Her topic, from Pre-Algebra: adding and subtracting decimals.

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

I have been riding horses since I was 5 years old, when I was around 12 years old I got into the equine sport called barrel racing. The sport is an equine speed event. Essentially horse and rider go through a clover leaf pattern as fast as possible. Placings are separated by 1000ths of a second. At competitions, there are different divisions, typically 4-5. These divisions are separated by half a second. For example, if the winning time of the barrel race was 15.536 seconds, then the winning times of the different divisions would be as follows, 16.036, 16.536, 17.036, and so on by simply adding half a second. It was always interesting to compare times and to see where I could possibly stand in different divisions based on my time and the winning time. I could see myself creating an activity that had my students be given different scenarios like being given a winning time and determining the winning times of the different divisions, determining which division a certain time would be in, how much faster or slower at time needs to be to place, and so on. This was an activity I did regularly at barrel races for myself and other people when watching.

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How has this topic appeared in pop culture (movies, TV, current music, video games, etc.)?

One of the more popular movies I can think of is the movie Hidden Figures. The movie is about a team of African American women mathematicians who work for NASA to help launch an astronaut into orbit. There are several different scenes in the movie where math problems are being solved and this involves the adding and subtracting of decimals. It shows that doing math by hand and math itself is very important in the real world and has helped us make great discoveries and progress. Another movie where adding and subtracting decimals appeared is in the movie called Gifted, where an uncle of an extremely math gifted child suddenly becomes her guardian. She solves several advanced math problems and proofs throughout the movie. The topic also appears in the classic sci-fi TV show Star Trek. It is constantly brought up throughout the series, typically from the character Spock who will make calculations on the spot. As he is a very smart and logical character, he is often the one who must do the required math in the series.

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

Adding and subtracting decimals is constantly used in both mathematics courses and science courses throughout high school and eventually college. We see adding and subtracting decimals in some trigonometry concepts when solving for theta and using different trig functions. Students will also see this very often in algebra when dealing with real world situations that forces them to have to use decimals. It appears quite a bit when students approach quadratic equations as once, they learn the quadratic formula to solve quadratic equations that don’t have integers, they will run into many decimals and having to add and subtract. Looking even further into the future of student’s math courses, we often must add and subtract decimals when evaluating different limits and integrals. Adding and subtracting decimals also appears in physics courses. Students will often see many decimals in physics when solving problems using force, density, displacement, and so on. You often see more imperfect numbers and situations in physics as it is more often seen in the real world.

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