NRICH: Sealed Solution

I used this task from NRICH at a teacher workshop several years ago to give teachers an opportunity to practice making conjectures, reasoning, and justifying. It caught my attention again today as I visited the NRICH website in search of rich tasks. I think it's held up quite well over the years and after reading about Alan Parr's implementation with students, I'm impressed with the multiple opportunities for extension this task provides.

Start with a few key questions:

• Which envelope shall we try first? Why?
• What could be in this envelope?
• Are there any numbers which you know definitely aren't in this envelope? Why?
• Are there any other solutions?

Provide students with number cards to try out their ideas. As they work together, ask questions about what they are noticing and wondering. You might find that this recording sheet can assist with keeping track of student observations. These resources from Max Ray of the Math Forum can help guide students toward more productive problem solving.

When students have found and shared some methods and solutions, give them an opportunity to make up some of their own problems. Alan Parr shares some student-generated problems that might be a good starting point.