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New for 2008-2009 The Problem Solving and Communication Activity Series
This new Math Forum program is designed to help students expand their repertoire of ways to approach challenging problems. Over the course of the year, we'll cover many of the fundamental problem solving strategies in conjunction with the Problems of the Week. Each problem will focus on a particular strategy, and we'll provide a document that describes activities to do with your students and examples of typical student responses to the problem. The problem-specific documents both provide illustrations of the activities and help you anticipate ideas that might come up in your class. We will also cycle through the strategies multiple times during the year so that students can get better at problem solving over the course of the Activity Series and the school year. The documents below are all in PDF format. To see all of the supporting documents for this year's Current PoWs, including links to the problems, visit the PoW Teacher Resources Page, also known as the Teacher Support pages. [Jump to Current Round]
Round 0: Introducing the Activity Series
	The introductory document contains a series of activities designed to get students thinking about what good problem solvers do, and how to communicate their thinking by writing (or talking) mathematically. Problem Solving and Communication Activity Series: Program Description & Introduction
Round 1: Understanding the Problem
	What does it mean to fully understand a problem, and how does it help students find solution paths and build confidence? Included in these documents are several activities that support students to develop strategies for understanding challenging math problems, along with facilitation suggestions for teachers.
	August 18 to August 31		August 25 to September 7
	FunPoW	AlgPoW	PreAlgPoW	GeoPoW
	Subway Tokens	Operation Warm Up	Cadence	Points, Lines, & Planes
Round 2: Understanding the Problem II
	We will continue to explore how to understand what the problem is asking by providing a second week's worth of activities for each of the four new PoWs.
	September 1 to September 14		September 8 to September 21
	FunPoW	AlgPoW	PreAlgPoW	GeoPoW
	Zelma's ZIP Code	Filling Glasses	Tiling Triangles	Divided Rectangle
Round 3: Guess and Check
	Guess and check is an important (and popular) problem-solving strategy, though it often gets a bad rap and may not be developed into the strong and powerful resource it could be. The guess and check strategy has at least three purposes: (1) to understand a problem thoroughly, (2) to home in on a solution, and (3) to discover efficient ways to jump to a solution by noticing patterns and developing related algebraic representations.
	September 15 to September 28		September 22 to October 5
	FunPoW	AlgPoW	PreAlgPoW	GeoPoW
	You Think Your Teacher is Tough!	Eating Contest	Caliyah's Cart	Dilating a Quadrilateral
Round 4: Solve a Simpler Problem
	Solve a Simpler Problem is a technique that can be used in several ways to solve challenging problems. In some situations you can see how to work the problem with easier numbers. This may show you an approach that you can try with the more difficult numbers. Second, you can choose to break the original problem into smaller steps, finding answers for parts of the problem, and then putting those together for the whole solution. Finally, students may see a way to change this hard problem into one that they have solved before.
	September 29 to October 12		October 6 to October 19
	FunPoW	AlgPoW	PreAlgPoW	GeoPoW
	Order in the Court	Sierpinski Stages	Women's Walkway	Where's Juanita Walking?
Round 5: Making a Table
	The Tables and Patterns strategy is a way to organize your problem solving that makes it easier to explore patterns in the calculations and results. It is often used after some initial work on the problem using Understanding the Problem or Guess and Check strategies. Tables can be used to efficiently home in on answers, or you can use tables to organize the logic of your calculations and make explicit the relationships between quantities in the problem. As you may have seen in the Simpler Problem strategy, tables can help put different iterations in order and compare them. Tables can take the form of simple t-tables to very complex spreadsheets. Spreadsheets and other related software are especially efficient because they can be used to rearrange your work for different comparisons without having to write it all over again.
	October 13 to October 26		October 20 to November 2
	FunPoW	AlgPoW	PreAlgPoW	GeoPoW
	Growing Worms	To Be or Not To Be	Measuring Melons	The Shortest Possible Side
Round 6: Understanding the Problem (Revisited)
	What does it mean to fully understand a problem, and how does it help students find solution paths and build confidence? This time around we have expanded activities to elicit relevant knowledge, recognize implications, and make drawings that focus on the key mathematical information.
	October 27 to November 9		November 3 to November 16
	FunPoW	AlgPoW	PreAlgPoW	GeoPoW
	Wooden Legs	Voter Turnout	Ostrich Llama Count	A Minor Problem
Round 7: Guess and Check (Revisited)
	In our previous round of Guess and Check, we focused on using guess and check to understand the problem and to home in on a solution. In this round we delve deeper into the uses of guess and check and present activities that help students: Test their solutions in a variety of ways. Use guess and check to ask good questions and get "unstuck." Figure out good guesses or problem approaches.
	November 10 to November 23		November 17 to November 30
	FunPoW	AlgPoW	PreAlgPoW	GeoPoW
	Nuts in a Bowl	A Championship Season	Two Heads Are Better Than One	Triple Tango
Round 8: Solve a Simpler Problem (Revisited)
	Solve a Simpler Problem is a technique that can be used in several ways to solve challenging problems. In some situations you can see how to work the problem with easier numbers. This may show you an approach that you can try with the more difficult numbers. Second, you can choose to break the original problem into smaller steps, finding answers for parts of the problem, and then putting those together for the whole solution. Finally, students may see a way to change this hard problem into one that they have solved before.
	November 24 to December 7		December 1 to December 14
	FunPoW	AlgPoW	PreAlgPoW	GeoPoW
	Building Barns	How Many Ties?	Lillian's Lines	Pythagorean Circles
Round 9: Making a Table (Revisited)
	The Tables and Patterns strategy is a way to organize your problem solving that makes it easier to explore patterns in the calculations and results. It is often used after some initial work on the problem using Understanding the Problem or Guess and Check strategies. Tables can be used to efficiently home in on answers, or you can use tables to organize the logic of your calculations and make explicit the relationships between quantities in the problem. As you may have seen in the Simpler Problem strategy, tables can help put different iterations in order and compare them. Tables can take the form of simple t-tables to very complex spreadsheets. Spreadsheets and other related software are especially efficient because they can be used to rearrange your work for different comparisons without having to write it all over again.
	December 8 to December 28		December 15 to January 4
	FunPoW	AlgPoW	PreAlgPoW	GeoPoW
	Rugby Rules!	Two By Canoe	Gas Guzzlers	Circle Derby

Round 10: Cases   Case-based reasoning helps problem solvers to understand the problem, work towards a solution, surface interesting mathematics, and verify the robustness of their solutions. To understand the problem, problem solvers might test interesting or representative cases and think about the different outcomes they see. When solving the problem, they might use cases to consider when certain outcomes will occur, or to narrow down the possibilities they have to investigate. Some problems have different answers for different cases. Exploring different cases can lead to questions that problem solvers might explore further, like, "what would happen if I used a negative number?" or, "would this work for obtuse triangles, too?" Finally, when determining whether a possible solution is correct, good problem solvers test their solution using multiple cases, especially cases that they know behave differently.   December 29 to January 11 January 5 to January 18   FunPoW AlgPoW PreAlgPoW GeoPoW    Change You Can't Count On   A Slippery Slope   Unknown Numbers   Making the Biggest Triangle

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