Max (@maxmathforum) and I have thought deeply about what helps students transition from an arithmetic lens on the world to an algebraic lens. For the 2017-2018 PoW season, we have been deliberate in our selection for the twenty PoWs to offer in Pre-Algebra. Here’s what we’ve chosen and why!
Problem #1: Getting your problem-solving year off to a good start!
At Least a Mile 
This problem aligns to 4th, 5th, and 6th grade CCSStandards and provides opportunities to revisit the idea of Notice and Wonder® or introduce it to students who have not yet been exposed to the idea. If it’s new for you, check this page for ideas: http://mathforum.org/pow/noticewonder/
Problems #2, #3, #4, #5: Proportional Reasoning / Distance = Rate • Time
Cork Costs 
Buying Cola 
Downloading Duel 
Apple Picking 
Problems #6, #7: The success that students can feel using a non-threatening strategy can build their confidence to use these strategies along with an algebraic approach.
Pumpkin Carving for Charity 
Peeling Potatoes 
Problems #8, #9, #10, #11: Using a single variable to find unknown amounts
A Cranberry Craving 
Eight Squares on a Table 
A Snowy Driveway 
Which Coupon Is Better 
Problems #12, #13, #14: Extending patterns and finding rules or shortcuts
Anjelica’s Very Odd Magic Sweater 
Gearing Up 
Shortcut Savings 
Problems #15, #16, #17: Using variables to solve situations with multiple unknowns
Boxes of Stationery 
Ostrich Llama Count 
Kaytee’s Contest 
Problems #18, #19, #20: Algebraic proof and justification
Accounting for Age 
Divisible by a Dozen 
Suli’s Sense 
Access to these 20 PoWs (and the other 20 in each of the other 5 services on the Calendar for the Current Problems) costs just $25 (or just $20 if you are an NCTM member!). Read the details of a Current PoW subscription here: http://mathforum.org/pow/productinfo.html
Try Annie’s Phone in the Pocket idea. Read: http://mathforum.org/blogs/suzanne/2014/08/10/listening-to-yourself/
Help your students add to their problem-solving toolbox. Read: “Examining Solution Methods” activity. Just use the Teacher Packet [pdf] that we provide for each PoW and you can create a similar activity for any of the PoWs you’re using with your students.
Are you wondering how to give feedback to all of your students. Read:
Feedback for 140+ http://mathforum.org/blogs/suzanne/2014/08/09/feedback-for-140/
Tips on encouraging student discussions. Read:
Keeping Quiet: http://mathforum.org/blogs/suzanne/2015/02/25/keeping-quiet/
Unsilence Students’ Voices: http://mathforum.org/articles/communicator.article.sep.2012.pdf
If you have questions, please ask and I’ll be happy to respond. Have stories to share? Please do!