# Engaging students: Using the point-slope equation of a line

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 Johnny Aviles. His topic, from Algebra: using the point-slope equation of a line.

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

On the 1987 NBA Dunk Contest, Michael Jordan won by dunking all the way from the free throw line. (I will play them a clip). Now can anyone tell me how high the hoop is from the ground? And how far is the free throw line from the base of the hoop? So, in total he went 10 feet in the air while jumping 15 feet! This is incredibly difficult and was why he won the contest. Now lets just compute that slope. With rise/ run we get that the slope was 2/3. Another example I can use is the time I took to get to school. I live 30 miles away and it took me 40 minutes to get to school. would anyone be able to find the average speed? (45 MPH) Then I will make it more complex and say I went 60 miles an hour for the first 20 minutes, how fast was I going the last 20 minutes?(30 MPH) Then I will have a round robin activity where I will give 5 min for my students to discuss amongst their groups where they can create a scenario where they can use point-slope equation of a line.

C3 How has this topic appeared in the news?

We all have many factors that interest us and the news’ job is to keep us updated. For many people, the stock market is a very serious subject of interest. Everything is shown in charts and done on points and percentages for simplicity reasons. This uses the concept of point-slope equation of a line to create this data. The news also covers may other topics like the rise of current temperature from given years to see if factors like global warming may have played a role to create the next leading story. The data from previous years can create point-slope equation that can predict the rain and snow fall amount for a given city or town. The weather initially can use point-slope equation of a line to predict all factors all data collected over decades. There is a copious amount of data that the news has to be used in all aspects of the news, one that has been shown is the rise of mass shootings. This is a very controversial matter as many people seek reform of the second amendment. Overall, point-slope equation of a line is widely used in many platforms of our news programs.

D4 What are the contributions of various cultures to this topic?

Architecture has been the biggest contribution that point-slope equation of a line and has to be applied. Various cultures have their own specific style of how they have their cities, towns and neighborhoods but all will apply the basics of point-slope equation of a line. For example, when creating a building, they use materials with large mass and need to be supported. If the slope of a beam is even slightly off, it can generally cause the building to collapse under its own weight causing the lives of many. Every aspect of the building needs to be measured in a precise way to create a solid structure. Styles then range from all cultures and can have tilted and rounded with elaborate beams to add more diversity. Overall, all cultures have their own specific style of houses that all require the same point-slope equation of a lines that contributes them to remain standing.

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