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 Ethan Gomez. His topic, from Pre-Algebra: absolute value.

**How does this topic extend what your students should have learned in previous courses?**

This topic extends students understanding of distance relative to positive and negative integers. First, students learn the positive integers — the counting numbers. Then, students are introduced to negative numbers. Visually, positive integers are to the right of zero, and negative integers are to the left of zero; students understand that these numbers exist and where they lie relative to each other. Essentially, students start by having a directional sense of numbers. Also, students also have a good understand of distance. With the concept of absolute value, students are able to associate distance with positive/negative numbers. Negative numbers aren’t just randomly placed but are rather a certain unit away from the number zero. For example, the absolute value of -5 is 5. So, -5 is not just a number that happens to be to the left of zero, but it is also 5 units away from zero. We now have a spatial sense of integers along with the directional intuition, making the numbers feel a bit more tangible and less abstract.

**How can technology be used to effectively engage students with this topic?**

Technology can be used to effectively engage students with the concept of absolute value since it allows students to explore its meaning. Students can discover the connection between distance and integers on their own, which reinforces the meaning-making process that teachers strive to provide students. For example, Gizmos has a wonderful tool that displays integers on a number line. On this gizmo, students are provided a visual that portrays the spatial and directional aspect of integers. This gizmo also makes students take note of the similarities between the absolute value of positive and negative numbers, forcing them to think about why they happen to be the same number sometimes.

https://gizmos.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=210

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

I could create a documentation sheet for students to keep track of what time they get home from school. They will keep track of this information for a week. The first time that they record will be the “reference time.” Every day after that, the students will document the time they get home, and how many minutes off it was from the first time, as well as if it was earlier or later than the first time. Having students think about “how many minutes off” they were from the first recorded time get them used to the idea of a magnitude, and how the number they are using tends to always be positive; the only difference is in the description of that number, which can be associated with the positive and negative characteristic of integers.