# Chapter-by-Chapter Resources

You'll notice the image next to some of the resources. This indicates a resource that's especially for people who have a copy of *Powerful Problem Solving*. The first time you access one of these resources, we'll ask you a special question about the book that you'll use to make a free Math Forum account.

### Chapter 1: Introduction

- Learn more about some of the various Math Forum services mentioned on
**page 1**: - Explore Ask Dr. Math® at http://mathforum.org/dr.math/
- Ask questions (about this book or any math teaching topic) and explore the archives of Teacher 2 Teacher at http://mathforum.org/t2t/
- Explore Math Tools, our digital library of technology tools for the math classroom at http://mathforum.org/mathtools/
- Learn more about the Math Forum's Problems of the Week http://mathforum.org/pows/
- Participate in the Math Forum Community at http://mathforum.org/community/
- Read the journal article mentioned on
**page 2**that describes the importance of reflection and revision in supporting students to become problem solvers are http://mathforum.org/articles/Renninger2000.pdf [PDF] - Learn more about the Math Twitter Blogosphere mentioned on
**page 7**by visiting http://mathtwitterblogosphere.weebly.com

### Chapter 2: Communication and Community

- On
**page 17**we mention more mathematical puzzles and challenges for students to work on in groups. Here are some: - Suzanne's Traffic Jam Activity and Resources
- Training for Change's Puzzle Squares
- Suzanne's Quiet Game activities and downloadable Puzzle Templates.
- If you'd like to use tablets or computers to play the Mission Control activity mentioned on
**page 18**, here are some resources: - Pattern blocks applet from the National Library of Virtual Manipulatives.
- Jing allows students to capture 5 minute videos of their computer screens, with audio. The "astronauts" can record their screens with audio of "mission control"'s instructions, and then play it back for mission control!
- Apps like EduCreations and ScreenChomp allow student to record their iPad screens along with audio. While they can't "screen capture" from other apps, "mission control" can make drawings that they then describe for the "astronauts".
- Max wrote a blog post reflecting further on the Making a Peanut Butter and Jelly Sandwich activity on
**page 19**. - And here are some videos of teachers and students carrying out students' instructions for making a PB&J.
- On
**page 21**we refer to Suzanne's Ignite talk, Unsilence Students' Voices.

### Chapter 3: Learning Through Listening

- On
**page 25**we refer to Model-Based Physics. You can learn more about model-based science education at their website. You might also enjoy Frank Noschese's blog describing his model-based physics class. - On
**page 27**we refer to Max's Ignite talk about Why 2 > 4. Watch it here. - On
**page 29**we shared the candidate for the 6th grade $1,000,000 unsolved problem from MathPickle.com. - On
**page 30**we shared a blog post from Bob Lochel about The Take-Away Game. - On
**page 33**the "Clarifying Questions Mingle" is based on this activity from Training for Change. - On
**page 34**we described students working on the Pizza Night PoW. Owners of*Powerful Problem Solving*can access the PoW as well as see possible solutions and student work in the Teacher Packet, and explore the other resources linked in the light blue box. - Here is the Student Handout for the What's the Same? What's Different? activity on
**page 33**. - Here is a link to the
*When Smart Groups Fail*article mentioned on**page 40**.

### Chapter 4: Noticing and Wondering

- On
**page 43**we described students working on the Teresa's Tiles PoW. Owners of*Powerful Problem Solving*can access the PoW as well as see possible solutions and student work in the Teacher Packet, and explore the other resources linked in the light blue box. - Here is the Student Handout for the I Notice, I Wonder Brainstorm activity on
**page 46**. - Here are some of the additional resources for finding prompts to Notice and Wonder about that we mention on
**page 47**: - The Math Forum PoW Blog Free Scenarios
- The Math Forum Video Scenarios
- 101 Questions, a site by Dan Meyer for teachers to share images and videos and ask, "What's the first question that comes to mind?"
- Visual Patterns, a site by Fawn Nguyen that encourages students to predict based on visual patterns.
- Estimation 180, a site by Andrew Stadel that encourages students to make estimations based on images from Mr. Stadel's life.
- On
**page 49**we describe how Suzanne would unfold a Problem of the Week in just five to ten minutes a day. Here's her article called "Think You Don't Have Time to Use the PoWs?" - On
**page 50**we described students working on the Sports Weigh-In PoW. Owners of*Powerful Problem Solving*can access the PoW as well as see possible solutions and student work in the Teacher Packet, and explore the other resources linked in the light blue box.

### Chapter 5: Change the Representation: Seeing the Big Picture

- On
**page 59**we describe Suzanne's work with a 5th grade class using manipulatives to make sense of and solve a problem. You can watch the videos on Suzanne's blog. - On
**page 59**we described students working on the Wooden Legs PoW. Owners of*Powerful Problem Solving*can access the PoW as well as see possible solutions and student work in the Teacher Packet, and explore the other resources linked in the light blue box. - On
**page 62**, we mentioned a student-friendly handout for Brainstorming Representations. - On
**page 62**we described students working on the Zoo Train PoW. Owners of*Powerful Problem Solving*can access the PoW as well as see possible solutions and student work in the Teacher Packet, and explore the other resources linked in the light blue box. - On
**page 67**, we mentioned a student-friendly handout for comparing and reflecting on representations. - On
**page 68**, we mentioned an activity and student-friendly handout for Paraphrasing.

### Chapter 6: Engaging Students' Number Sense Through Guessing

- On
**page 76**we mentioned an activity and student-friendly handout for PoW IQ. - On
**page 76**we mentioned two blog posts from Dan Meyer: - On
**page 78**we mentioned yet another blog post from Dan Meyer: Teaching With Three-Act Tasks: Act One - Starting on
**page 79**we describe a class that works hard on Guess and Check and gets good at it over time. The teachers made a presentation for NCTM about their students' journey. Check out their presentation, including student work samples! - On
**page 81**, we mentioned a student-friendly handout for Noticing for Guess, Calculate, and Check. - On
**page 82**we mentioned some PoWs that have at least one Guess and Check solution in the Teacher Packet linked from the light blue box: - Ostrich Llama Count PoW
- Charlie's Gumballs PoW
- Eating Grapes PoW
- Congruent Rectangles PoW
- Kaytee's Contest PoW
- On
**page 82**we mentioned the I Get a Kick Out of Soccer PoW. Owners of*Powerful Problem Solving*can access the PoW as well as see possible solutions and student work in the Teacher Packet, and explore the other resources linked in the light blue box. - On
**page 89**we described teachers using Guess and Check to help students get "unstuck". This teacher handout includes the "getting unstuck" diagnosis. - On
**page 91**we mention Bowen Kerns and Al Cuoco's thoughts on why Guess and Check is so vital for success in Algebra. Read more about that here.

### Chapter 7: Getting Organized

- On
**page 92**we described students working on the Integer Images PoW. Owners of*Powerful Problem Solving*can access the PoW as well as see possible solutions and student work in the Teacher Packet, and explore the other resources linked in the light blue box. - On
**page 94**we described students working on the Cupcakes, Cupcakes! PoW. Owners of*Powerful Problem Solving*can access the PoW as well as see possible solutions and student work in the Teacher Packet, and explore the other resources linked in the light blue box. - On
**page 97**we described students and their families working on the Cat Walk PoW. Owners of*Powerful Problem Solving*can access the PoW as well as see possible solutions and student work in the Teacher Packet, and explore the other resources linked in the light blue box. - On
**page 99**, we mentioned a student-friendly handout for Setting Up and Sharing Tables. - On
**page 101**we described students working on the Marble Mayhem PoW. Owners of*Powerful Problem Solving*can access the PoW as well as see possible solutions and student work in the Teacher Packet, and explore the other resources linked in the light blue box. - On
**page 104**, we mentioned an activity and student-friendly handout for Extreme Write It Out. - Since publishing the book, we came across a neat activity that helps students make sense of
*substitution*, a key part of the Write It Out and Extreme Write It Out activities. Check out Elizabeth's blog post about Substitution Stars.

### Chapter 8: Generalizing, Abstracting, and Modeling

- On
**page 110**we described students working on the Frog Farming PoW. Owners of*Powerful Problem Solving*can access the PoW as well as see possible solutions and student work in the Teacher Packet, and explore the other resources linked in the light blue box. - On
**page 116**, we mentioned a student-friendly handout for comparing and reflecting on representations. - On
**page 117**we described students working on the Ostrich Llama Count PoW. Owners of*Powerful Problem Solving*can access the PoW as well as see possible solutions and student work in the Teacher Packet, and explore the other resources linked in the light blue box. - On
**page 118**we described students working on the Trick or Treat Routes PoW. Owners of*Powerful Problem Solving*can access the PoW as well as see possible solutions and student work in the Teacher Packet, and explore the other resources linked in the light blue box. - On
**page 125**we mentioned that Visual Patterns was a great reference for problems to use with the Problem-Solving Bids activity. - This blog post by Fawn Nguyen reminded us a lot of the ideas behind the Problem-Solving Bids and What Would Happen If? activities on
**pages 125 and 127** - On
**page 130**we mention using Twitter to solicit multiple representations for math problems. If you're new to Twitter, Max explains it in 5 minutes in his Ignite video, "Tweet Me, Maybe?" - Here is the Student Handout for helping students compare similarities and differences in their classmates' models and representations, which we mention on
**page 130**. - On
**page 134**we mention Dan Meyer's work on the "Ladder of Abstraction". You can read more on his blog.

### Chapter 9: Looking for Structure

- On
**page 136**we mentioned "The World's Hardest Simple Math Problem". Good luck and have fun! - On
**page 117**we described students working on the Counting Shells PoW. Owners of*Powerful Problem Solving*can access the PoW as well as see possible solutions and student work in the Teacher Packet, and explore the other resources linked in the light blue box. - Here is a Student Handout that might help students with the activity being modeled on
**page 139**. - On
**page 142**, we mentioned a student-friendly handout for the Sticky Notes Strategies activity. - In the strategy table
**page 145**we mentioned that there are PoWs to accompany each strategy. Here are a selection: - Change the Representation
- Elementary: How Many Berries Did I Eat?
- Pre-Algebra: Frog Farming
- Algebra: Crossed Wires
- Guess and Check
- Elementary: Eating Grapes
- Pre-Algebra: Shopping at the School Store
- Algebra: Eating Contest
- Make a Table
- Elementary: How Far Will Taylor Run?
- Pre-Algebra: So Many Salmon
- Algebra: To B or Not To B
- Use Logical Reasoning
- Elementary: Counting Shells
- Pre-Algebra: Movie Seating
- Algebra: Symbol Logic
- Solve a Simpler Problem v. 1
- Elementary: The Arm-Wrestling Match
- Pre-Algebra: Lillian's Lines
- Algebra: Plane and Simple
- Solve a Simpler Problem v. 2
- Elementary: All Aboard!
- Pre-Algebra: Women's Walkway
- Algebra: Don't Be Square
- Look at Cases
- Elementary: Emmy's Action Figures
- Pre-Algebra: Forming Triangles from a Folding Ruler
- Algebra: Arranging Rectangles
- Work Backwards v. 1
- Elementary: Charlie's Gumballs
- Pre-Algebra: Sharing Smelt
- Algebra: Flying Off the Shelves
- On
**page 149**, we mentioned an example of modeling a strategy using the Where's Juanita Walking PoW. And here is Max's story of modeling Solve a Simpler Problem using Where's Juanita Walking. - On
**page 149**, we mentioned the activity Same Math Idea, Different Math Story activity, which can be found on the linked handout. - On
**page 150**we mention Math Teachers' Circles. Click here to learn more about them. - Click here if you'd like links for the books and web resources that we listed starting on
**page 150**.

### Chapter 10: The Problem-Solving Process and Metacognition

- On
**page 153**we described students working on the Wooden Legs PoW. Owners of*Powerful Problem Solving*can access the PoW as well as see possible solutions and student work in the Teacher Packet, and explore the other resources linked in the light blue box. - On
**page 158**we described students working on the Charlie's Gumballs PoW. Owners of*Powerful Problem Solving*can access the PoW as well as see possible solutions and student work in the Teacher Packet, and explore the other resources linked in the light blue box. - Jing allows students to capture 5 minute videos of their computer screens, with audio. Students can use this to capture (and review) their best problem solving!
- Here is the Wonderama Reproducible for the Wonderama activity on
**page 165**. - Here are the Getting Unstuck and I Don't Know What to Do Reproducibles mentioned on
**page 167**.

### Chapter 11: Reflecting, Revising, Justifying, and Extending

- Here are links to the four blog posts mentioned (and linked with a QR code) on
**page 169**: - “Watch Students Watch the Answer to Their Math Problem” -- Sadie Estrella
- “Barbie Bungee iMovies—Line of Best Fit” -- Julie Reulbach
- Super Mario Bros. Results” -- Nora Oswald
- Voter Turnout Video -- Laurel Pollard's Students at Hanover Street School
- Read the journal article mentioned on
**page 170**that describes the importance of reflection and revision in supporting students to become problem solvers are http://mathforum.org/articles/Renninger2000.pdf [PDF] Note: this is the same article that was mentioned way back on page 2. - Watch this great debate among elementary students on whether 6 is even or odd (or both!) facilitated by Deborah Ball.
- Here are the handouts and description for the supplementary constraints activities:
- Read more about the ideas behind Face-to-Face and Elbow-to-Elbow revisions, mentioned on
**page 176**. - Here is the Student Handout for the Face to Face Revision activity on
**page 176**. - Here is the Student Handout for the Elbow to Elbow Revision activity on
**page 177**. - Here is the Student Handout for the Testing 1, 2, 3, 4 activity on
**page 178**. - Here are a few "reputable math sources" for your math debates: