# Engaging students: Fractions and 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 again comes from my former student Samantha Offutt. Her topic, from Algebra: fractions and decimals. How can this topic be used in your students’ future courses in mathematics or science?

Students will use/convert fractions and decimals in a number of ways in future courses in mathematics and science. The best example is percentages. In a probability/statistics class, percentages are a major component for answering many types of problems. For example, in the college course Math 3680, percentages are used frequently. So in a large set of data, one is asked to record the frequency of a certain number, take the frequency and divide it by the total number of entries, and one is almost always ask for them to be written as decimals to the 4th number. After determining the relative frequency, you can tell what proportions of the data are between certain stipulations. For example, if there were 50 numbers that are between 1 and 20, one can be asked, “What proportion of the numbers are between 7 and 13.” So even to this day in college, students still use this pre-algebra topic. How could you as a teacher create an activity or project that involves your topic?

I found this awesome project on a teachers blog: http://teachinginroom6.blogspot.com/2012/02/math-social-studies-awesomeness.html, This certain teacher did a social studies spin on colonial era quilts. I think it was awesome. “I then had the students create a 20 cm x 20 cm square (we have cm graph paper available at school).  Choosing either 2, 4, or 5 colors, the students created a square that had at least one triangle, quadrilateral, was bright, and symmetrical (Stephanie).” Then the students created fractions by counting how many squares, of the 400 squares, took up each color. Later found the decimal of those fractions, and finally determined the percentage each color owned on their square. The teacher took each square and made a quilt. I’m in love with this project and I think it’d look fantastic in the classroom. Students get to practice multiple skills and are given the opportunity to have their work displayed in the classroom. How can technology (YouTube, Khan Academy [khanacademy.org], Vi Hart, Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic?

Technology is a very useful tool for students. Instead of a teacher lecturing, they can find videos of all sorts on the Internet. If a teacher simply wanted to let Khan Academy engage students and do examples for the kids in a short 8 minutes, then they could use this very helpful video (that the students can reference later at home if they have any questions):

Students get to dive right into the topic and see how it is done, but later when they are at home and have forgotten some things, they have access to the exact video. Technology is very useful both in the classroom and at home. Also this video shows more than just one, simple example. I think it’s great the video shows problems of different levels of difficulty.

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