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 Billy Harrington. His topic, from Pre-Algebra: fractions, percents, and decimals.

Application:

1) Problems that arise with integrating fractions, percents, and decimals include instances such as shopping during a sale at a certain store or shop. The type of shop does not matter whether it is a flea market, or a high-end clothing store. A sale affects all types of stores in the same way. When an item is (1/3) of its original price, people must convert this into a fraction and then convert to a decimal to find out the whole dollar value which will most likely involve decimals as well as the fractions/percentages indicating the amount of money off the original price.

I used this website as an example of problems:

Another really good exercise in percentages, fractions, and decimals is budgeting a certain income over a year. Students should calculate the percent of their budget that they spend on a home, food, necessities, and their leisure activities. Some students can be told to start budgeting using fractions, while another group of students is told to budget based on percentages. When the class is done, students can come together for a class discussion, and share the benefits, and obstacles of budgeting using the method they performed.

2) For a full activity, each student will get one full sheet of printer paper, and a pair of scissors (or be split into small groups of 2 to 4 four people in each group to save paper). Each student/group will start by acknowledging that their full page represents 1 part of 1 whole and represent this as a fraction and a decimal. Students will then continue by cutting their paper in half and notice that there are now two pieces in front of them. They will continue to cut their paper in half another five to six times and then represent each stage by a fraction.

Stage 1 |
1 part of 1 |
Represented (1/1) |

Stage 2 |
1 part of 2 |
Represented (1/2) |

Stage 3 |
1 part of 4 |
Represented (1/4) |

Stage 4 |
1 part of 8 |
Represented (1/8) |

Stage 5 |
1 part of 16 |
Represented (1/16) |

Curriculum

1) When students get to their upper level math classes or even when they get to college, they must calculate their own grade/GPA. Not all classes or grades are going to be graded equally and on the same scale. Some classes are graded on a 1000 point scale where as some classes are weighted on a 75 point scale. To convert their weighted total number of points to calculate their letter grade, students must either set their percentage total in a proportion and weigh out the actual score on a 100 point scale to calculate their grade based on the letter grade scale. A student may say, “I have a 130 in this class, this must be an A!” This may be great, or it could be terrible depending on the grading scale, that’s why students must weigh it against the total point value, then convert it to a percent to find out their true letter grade and see in fact if their 130 is truly a good grade worthy of passing.

2) Students will always need basic math in their lives, even throughout adulthood. Percentages, fractions and decimals should be part of that foundation of mathematics that they know. A big part of this topic that students should learn is budgeting, even if it is a small allowance they receive on a weekly, or bi-weekly basis. If they’re given $20 every other week, how are they going to spend or save that money over the 2-week period they have? Students could spend it all, save it all, or spend some, and save some. Students could calculate the percent of money they did spend if they decided to spend money and see what fraction, percent or decimal value best represents what money they spent, and/or saved.

Culture

1 & 2) Percentages, fractions, and decimals is actually really important in the media world such as music and film industries. Take ITunes for example as the sole business that sells music, and also a different assortment of films. The consumers are drastically affected by other media sources, such as a television, or even a newspaper. If a “huge hit” is coming from this new movie coming out next Friday, chances are that a huge percentage of people are going to partake in the new film and go watch it at the local theater. If the movie is a success, then chances are that the movie will reach the top of the box office. The box office is determined by profits over a short amount of time when a movie/film is released into theaters. Movies such as Harry Potter and the Hunger Games were big sell-outs in the box office because there was such a huge profit made off of the films. Profits based on ticket sales are depicted by a percentage of average sales, which means the higher the percent of people that went and watched the new movie, means that the profits are going to be higher. Based on these statistics, movies are then ranked in the box office to see which movie was the most successful at the end of the year.

Rank 1 in Box Office for 2013 –

Hunger Games Catching Fire at over $420 million dollars

This concept applies in Theater as well such as Broadway plays they make huge profits on ticket sales

3) A huge way fractions, percents, and decimals has influenced the world and our culture is by our economy and our market system. Our current economic system is currently in shambles and is desperately trying to fix itself through many irregular and unorthodox ways that sometimes turn out for the worse. The economy is not easy to understand and explaining how the market works to an average citizen probably will not go well, so the market and its different branches are represented in simple, yet intricate graphs, percentages, and decimals to represent how the current day has progressed. There are some days where the DOWJONES may be below 13% where as some days the NASDAQ may be up 10%. Different branches of the economy are each shown in simple percentages, if people don’t understand the values of percents, fractions, and decimals; there is almost no hope for that person to understand the current economic situation.