Like most people, I begin my lesson on absolute value with a story about distance. I love telling stories in class. Stories are a way to lessen stress in class and provide a way to have some fun. In my story, I drew a number line. I placed the school at zero and told the students that I live 10 blocks from the school. I then asked where if they could determine where I live.
Of, course the first answer was at positive 10. Most students were happy with that answer. When I pressed for another answer, they caught on quick (they know me well).
Absolute Value Stories
This is important for students to understand. Absolute value represents the distance. Distance is always positive. The other story I tell is about my car. My odometer reads 10,000. I travel 100 miles to San Diego (I live in the Inland Empire in Southern California). What does my odometer read when I get to San Diego?
Of course, it now reads 10,100 miles. So when I come home, I am going the other way. Do I now subtract 100 miles? (Students answered only if I am driving backward, lol). Students need concrete models. Telling stories about travel and location that are familiar will help.
Different Teaching Methods
In a recent meeting, the subject of teaching absolute value equations was raised. It was interesting to hear the methods that teachers preferred. Some were convinced that their method was the only one.
This is the way I normally teach this. I explain that the value inside the absolute value bars can either be positive or negative, so we are going to have 2 answers. And I set up both equations as shown.
Connecting Models to Concepts
Another teacher took exception to this. She said it makes no sense to students. Her students need to know why it works. My way does not have an explanation. For her students the why is valuable. She demonstrated that she teaches it this way:
I know what you are thinking. This is a distinction without a difference. But to her eyes, the second method makes sense to her. Because the expression inside the absolute value bars can be positive or negative, then the obvious procedure is to write the expression as positive or negative. This, she insists, can be explained to students.
Using the Number Line
Another teacher did not like either. He is visual. Teachers that love Geometry like pictures and diagrams. He teaches that absolute value is represented on the number line as the distance from zero. Which works fine when there is no number with x between the bars.
When others began asking questions, it got a little confusing. I got confused. Another teacher to the rescue. He shared the following:
This helps students see the equation. It provides some scaffolding for students that need models. This was the way he learned the concept and how he teaches it to students.
I had never seen this version but I tried it, asking students to describe the answer in words and also provide a solution. Students found it easier.
This worksheet formed a great introduction for students. This is the first introduction to