I use the warm up above when teaching Absolute Value in my Algebra 2 course. It bothers me that many students define absolute value as “always positive.” My next question to them is always “Why is it always positive?” That’s a question you will find on my assessments as well. I want the key word to be distance for students when they think of absolute value. I want them to understand signs of positive and negative as describing direction. And those distances and directions are from zero (a pretty intuitive starting place for students in “the middle” of our number line).
I put together a few questions that hopefully lead students to think about absolute value in this way. The two questions at the bottom of the first page help identify 2 different situations: one where direction matters and one where direction does not matter. On the second page, I try to emphasize the idea of more than one possible solution. When the direction is not given or specified, there can be many possible solutions. These questions usually lead to some great conversations. It’s also nice to reference these questions later by asking students to remember how many directions Bart could skateboard or Otto could drive. By talking about concepts in everyday situations without the distractions of notation, students can get a firm grasp of the concept before diving into problems where they will just try and memorize steps.
With my move to a new area this summer, I have spent a lot of time at Lowe’s. The math teacher in me saw a great lesson idea with my 2 coupons.
What is the better deal?
Describe which deal you would use in words:
Use a table to compare the two deals:
Use a graph to compare the two deals:
Use equations to compare the two deals:
What is significant about where the two graphs meet?
What does the x-coordinate of that point represent?
What does the y-coordinate of that point represent?
This year I would like to continue to focus on using multiple represenations with real life application problems. I hope to incorporate more problems that start with natural and intuitive responses before moving towards other notation (equations, tables, graphs). Ideally, the students will move in that direction themselves and see why notation is useful in providing a clear and concise representation of situations.
The questions above were just a few thoughts of how I would like the lesson to progress. I will develop the lesson further before using it. Ultimately, I think the students will be able to make connections with all the different representations in a natural and intuitive way. I also think the concept of a solution to a system of equations takes on more meaning in this context.
Next week I will start my 5th year of teaching (wow…) at a new school. For my first 4 years of teaching I worked in an awesome school with a staff that was supportive and helped me grow into the teacher I am now. I learned a lot from my peers and was given the freedom to try new things. Last year was by far my best year. I felt comfortable and confident from the first day. I had my own classroom and no new preps for the first time. I had great students. I no longer felt like the “new guy” and had established a reputation. Throughout the year I noticed I no longer had to focus on a lot of the “small things.” I knew the basic routines of the daily operations of the school and the routines and expectations I wanted in my own classroom. I felt like I finally could put a lot of my time and energy towards creating more engaging, interactive, and relavent lessons.
I have mixed emotions as I anxiously await the start of this school year. I know that I am about the be overwhelmed by all the information thrown my way during the neverending orientations. A lot of my time and energy this year will be spent familiarizing myself with my new environment. All of this change is also refreshing. Everyone in my new school that I have met so far is great. I look forward to being with a new administration and staff with new ideas and philosophies. I am excited to go out of my comfort zone. The challenges I face this year will make me a better teacher. In the end, I am excited and eager to begin establishing myself in a new learning community.