I’ve pondered this challenge for a couple of days. So many options! But a tweet from @mathymeg07 led me to a post from @MrAKHaines blog Math Pun Pending.

The post was celebrating a variety of strategies his students had use to answer the question:

He wrote: *When I wrote the question, I had anticipated that students would use a couple of different strategies. What I didn’t know was that my 25 students would use a combined seven correct solution strategies to solve this problem.*

Two parts to my post: 1. How can I make this an open question and 2. How can I use student samples to develop a better lesson in the future?

**How can I make this an open question?**

A. Name a point that is NOT on this line.

B. Name a point that this line passes through.

Thanks to @PIspeak‘s TMC14 session in Jenks, I urge students to “Support your claim with evidence/reasoning. I want to see your thinking!”

**How can I use student samples to develop a better lesson in the future for my classroom?**

I appreciated the fact that he never explicitly taught “the teacher’s efficient strategy” but allowed group discussions and support to drive the lesson. Students shared ideas. The last paragraph in his post says, *“My students are acting like mathematicians, y’all. They’re using their toolkit of math ideas to solve problems flexibly. I couldn’t be happier.”*

In the end, that’s what we all want – students thinking on their own, making sense and being confident enough to explore a problem with their own ideas. So, how does this tie in with the Better Questions prompt? My outline of the lesson feels a bit like those I’ve used from Formative Assessment Lessons, but I feel it lends itself to students doing the thinking, talking – I only provide the materials and support to make desired connections that will lead to the learning goal.

I’ve been following the #T3Learns chat from Wiliam’s book. In chapter 3 of Embedding Formative Assessment, it suggests using **student sample work**. How might I structure a lesson, utilizing student samples of this question? In Principles to Actions, MTP3 states E**ffective teaching engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.**

- Begin with the same question. Allow students to write a response. (3-5 min)
- Place students into small groups and allow them to share their approaches. (5-7)
- Allow groups to explore student samples, making note of different ideas, what they like/ways to improve, questions they’d like to ask the student. *maybe as a gallery walk? (15-20)
- Discuss their findings as a whole group. (10 in)
- Connections to/between the different mathematical representations. (5-10 min)
- Written reflection: (3-5 min. possibly use as a start up / bell ringer to begin class with following day – providing an opportunity for retrieval of previous days information?)
- my strategy was most like:____
- the strategy I liked most was ____ because ___
- the strategy I found most difficult to understand was ___ because ___
- Which approach was most efficient? Why?
- What do you think was the BIG IDEA your teacher intended for you to learn/understand?

- Transfer…provide a few, different contextual problems that allow students to connect the mathematics to something tangible, maybe in a problem posing situation (should this be small group? individual? ) (5-15, would this be better as follow-up the following day?)

Timing is often an issue for me. I want to provide students with enough time to make sense/discuss, but not so much time it feels long and drawn out. Are the times I have listed appropriate?

Please offer suggestions. How have you used a similar approach successfully in your own classroom?