Notice and Wonder® Here is the quote, direct from the website:
We believe that when students become active doers rather than passive consumers of mathematics the greatest gains of their mathematical thinking can be realized. The process of sense-making truly begins when we create questioning, curious classrooms full of students’ own thoughts and ideas. By asking What do you notice? What do you wonder? we give students opportunities to see problems in big-picture ways, and discover multiple strategies for tackling a problem. Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be “over and done,” but to realize the many different ways to approach problems.
I love anything out of Math Forum. I am a rabid fan of Max Ray-Riek and Annie Fetter. I *may* even cross into groupie-dom.
Estimation 180.com Most of our real-life math is all about estimation, so here is a great and FUN place to practice that skill. There is a task for every day of the school year, plus a bunch more! All of the tasks can be adjusted to meet the needs of the students at your grade level.
OpenMiddle.com problems. These are some of my favorite. They have a beginning and end point, but students can follow a number of paths to find the solution in the “middle”. For example: Use the digits 1-4, no more than once each to multiply a two digit number by a one digit number and make the largest product.
3-Act Math Tasks: There are a couple of great resources for these. Act 1 introduces the problem. Act 2 asks the students to make a plan and solve the problem, and Act 3 offers a solution. The magic happens with all of the math talk that happens in all three acts, especially students are justifying their solutions.
Dan Meyers 3 Act Tasks: http://blog.mrmeyer.com/category/3acts/
And more 3 Act Tasks: https://whenmathhappens.com/3-act-math/
Numberless Word Problems: Start with a word problem, but replace the numbers with “some” or “more/less than”. Talk all the way through the problem. What do you notice? What questions could you ask? What numbers would be reasonable? (or unreasonable?) Start giving students numbers and continue the conversation. What do we know now? What kind of problem could this be? What do you expect the other number(s) to be? Continue adding numbers until all numbers are present. Ask the students to generate their own questions, based on the problem and share them with the class, then invite them to solve or answer any two questions. They will usually ask if they can answer all of them—because they want to solve their own or their friend’s questions! Brian Bushart has many resources for numberless problems on his blog. https://bstockus.wordpress.com/numberless-word-problems/