Open Ended Questions Yield "Teachable Moments"

I always start class with some sort of question to get students' brains thinking about math again. In Algebra 1, we were talking about equations the previous day. Some are true, like 3 + 2 = 5. Some are false, like 3 + 2 = 6. Some are open, like x + 2 = 6. This means they might be true or they might be false, depending on the value of x.

So, today's opening question was 1) Write an open equation. 2) Find the value(s) that make your open equation true. Most students wrote fairly straightforward equations involving one variable. However, one girl was excited to share hers with the class, because it was so different. It was x = 2y. This led to talking about the fact that there an infinite number of solutions and we quickly went around the room naming solutions. It was even pointed out by the students that it was best to pick out y and use that to find x.

I wasn't expecting to talk about equations with 2 unknowns or an infinite number of solutions, but it happened. The reason it happened was because I used an open ended question.

On an unrelated note, I have published my second TI-NSpire Quick tip. It can be found at mathteacher24 on YouTube. Also, my video lesson is now live at TED-Ed. It can be viewed at Ted-Ed and is labeled Leigh Nataro:What Happens If You Guess?