Here’s a math problem I thought of when I was driving today.

There are three points and two lines on a plane. All we know is that one or both lines go through each point. Discuss the possible ways this might occur.

I think this would be an interesting exploration. I would encourage students to use a tool like Desmos or paper and pencil as they think it through in groups/pairs or individually. The students could ask all kinds of questions such as (with some possible responses in parentheses):

- What are the points? (
*Does it matter? Can we try different points to see if it matters? Maybe this is a good thing to discuss in your response*) - Where are the lines? (
*That’s what we are trying to think about.*) - Can I graph this? (
*Sure, how do you do that if the points are unnamed?*) - Are the points collinear? (
*Good question, no one knows, so maybe we should account for different possibilities*.)

Solving this question would encourage students to graph and think about points and lines as they try to generalize relationships. Though there are particular answers, there are many ways to explore and students could easily work together. I like that students would need to consider multiple situations and have to articulate them in their response. I also think it would also provide a great basis for discussion to have as a whole class as you compare strategies and discuss whether everyone has considered all of the possibilities.

Thoughts on this task? Add them to the comments. 🙂