Fiona O. at Wilson Middle School began her solution to this week’s Pre-Algebra Problem of the Week by listing all of the possible strategies she thought she might use:

- draw a diagram
- make a table
- list possibilities
- simple computation/logical reasoning

I think Fiona’s list covers almost every single solution submitted. Good call, Fiona! The only other strategy I noticed was that some students used “Solve a Simpler Problem” to help them with their diagrams, tables, possibilities, or logical reasoning.

The problem, *Trick-or-Treat Route*, is about the Anderson children’s plan for trick or treating in their neighborhood (the students also had information about how many minutes it would take to walk between each pair of houses): Reading the solutions, I was really fascinated by thinking about how the strategies Fiona named (plus Solve a Simpler Problem) are interrelated. Here are some things I’m wondering about:

- Would making organized lists help students who jumped right to logical reasoning, but whose answers didn’t match the story?
- What are different ways to organize lists and tables?
- Do some ways of organizing lists and tables make it easier to see patterns and simplify the problem?
- How can you tell if you’ve found all the possibilities?
- How can you tell if you’ve over-counted?
- How do students learn to check their own work on “find all the possibilities” problems?

The first thing I noticed was that of the students who said, “I kept track of all the possibilities” and then over- or under-counted only two submitted their lists. The rest talked *about* their lists but didn’t type them up. I wonder… did those students not make written notes? Were they too hard to read to re-type? Is there a correlation between not wanting to write down the possibilities and not finding the right number?