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 [16003]
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:

Problems #2, #3, #4, #5: Proportional Reasoning / Distance = Rate • Time
Cork Costs [3524]
Buying Cola [1982]
Downloading Duel [4724]
Apple Picking [4544]

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 [3560]
Peeling Potatoes [5264]

Problems #8, #9, #10, #11: Using a single variable to find unknown amounts
A Cranberry Craving [3284]
Eight Squares on a Table [17049]
A Snowy Driveway [3308]
Which Coupon Is Better [3656]

Problems #12, #13, #14: Extending patterns and finding rules or shortcuts
Anjelica’s Very Odd Magic Sweater [4052]
Gearing Up [1898]
Shortcut Savings [16984]

Problems #15, #16, #17: Using variables to solve situations with multiple unknowns
Boxes of Stationery [2078]
Ostrich Llama Count [5156]
Kaytee’s Contest [16004]

Problems #18, #19, #20: Algebraic proof and justification
Accounting for Age [3056]
Divisible by a Dozen [2960]
Suli’s Sense [5300]

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:

Try Annie’s Phone in the Pocket idea. Read:

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+

Tips on encouraging student discussions. Read:
Keeping Quiet:
Unsilence Students’ Voices:

If you have questions, please ask and I’ll be happy to respond. Have stories to share? Please do!