Game Descriptions Division IV – Grades 6-7


The Mathematics Pentathlon® Program is organized by Grade Level into 4 Divisions. Within each Division there are 5 Problem-Solving Games and related Resources that deal with a broad spectrum of mathematical thought. Division I was designed for Grades K-1, Division II for Grades 2-3, Division III for Grades 4-5, and Division IV for Grades 6-7.

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Game Description Sheet – Division IV (6- 7)
Game Description Sheets – Div I, II, III & IV (K – 7)





The four basic operations, exponentiation, factorials, algebraic thinking, and prime and composite numbers are integrated in this strategy-chance alignment game. The gameboard represents a grid with numerical values that sequentially spiral from the board’s center to the outer band which results in prime numbers that occur along diagonal lines. For each play students form number sentences based on the roll of 3 polyhedra dice and place chips on corresponding numbered spaces of the gameboard. The structural/numerical arrangement of the gameboard relates to one of the games goals: constructing 4 diagonal veins of prime gold. Blocking rules dealing with prime and composite numbers, multiple chip placement based on Goldbach’s conjecture, and a second game goal make this a most challenging computational reasoning game.



Polyhedra dice, pawns, chips and a hexagonal-triangular shaped gameboard are used to play this strategy-chance division game. The goal is to place the greatest number of chips on the board’s six hexagonal-shaped islands. A series of rules related to zero remainders and networking pawns along strategic pathways make this both a conceptual and problem-solving game



This transformational geometry game develops spatial visualization as well as both deductive and inductive reasoning. Each player uses 5 pentominoes (chosen from a set of 12 pieces) and two blocking chips on a 13 by 9 grid to entrap all 5 of the opponent’s pentominoes. In the placement phase players must strategically select and place five pentomino pieces onto the gameboard. In the movement phase players attempt to entrap the opposing player’s five pentominoes by rotating, flipping, or sliding their own pieces.



Equivalence, the four basic operations as well as algebraic principles are investigated in this conceptual and strategic fraction game. A set of 64 fraction bars that pictorially represent various fraction values are used to help students connect symbolic procedures with visual models. On each turn students try to find two bars that when combined through the four basic operations equal one of the answer bars on the specially designed gameboard. Students must use strategic thinking skills when examining all possible combinations of bars and operations as well as setting up moves for future options



The gameboard and game pieces in this fraction-decimal conversion game simulate the ricocheting action of pinballs in a pinball machine. In playing this game students must strategically position and move pawns and blocking chips to land on fraction values of the gameboard which are converted to decimal form and are added to or subtracted from an accumulated score. The goal of the game is to be the first player to reach an accumulated score of between 4.95 and 5.05. Since the gameboard is composed of a network of interconnected fraction circles, students must use both spatial and computational reasoning when making decisions.



The Rule Manual for Mathematics Pentathlon Problem Solving Games DivisionIV (Grades 6-7) is a Full-Color publication that provides the Official Rules for each of the 5 Mathematics Pentathlon Games  including:  Background/History of the Game, Materials, Goal, How to Start the Game, Underlying Math/Science, Basic Rules, and Game Specific Tournament Rules.  This detailed Manual also illustrates and describes the recommended Team Grouping for Cooperative Learning and Good Sportsmanship.  In addition, a detailed Introduction defines Active Problem Solving and the many critical characteristics and philosophy of the Math Pentathlon Program.  A Math Content & Standards Chart for the entire Math Pentathlon Program is outlined on the Inside Back Cover.

The Guide for Teaching and Sequencing the Mathematics Pentathlon Program Division IV (Grades 6-7) is a Full-Color step-by-step Teaching Guide that coordinates the Program’s three key resources:  the Games and Rule Manual, the Adventures in Problem Solving Book II, and the Investigation Exercises Binder II.  Organized into Monthly Lesson Plans each Guide outlines four lessons per month for weekly implementation.  Each lesson describes necessary materials, approximate lesson time, resources with corresponding page numbers, and a summary of each activity with related illustrations.

Adventures in Problem Solving Activity Book II (Grades 4-7) links the Mathematics Pentathlon® series of games with the mathematics curriculum.  The numerous activities and projects described in this book guide teachers/coaches to explore with their students important geometric, numerical, and scientific relationships.  This publication also helps teachers to coordinate the games with mathematics content/process objectives.  In addition, many introductory activities are described that develop prerequisite skills for being successful in playing the Mathematics Pentathlon® games and developing related problem-solving strategies.  Both the Mathematics Pentathlon® Games and Adventures in Problem Solving Book II activities make use of a wide variety of concrete and pictorial models that help students understand and remember important mathematical concepts.

Investigation Exercises Book II (Grades 4-7) is the assessment resource for the Mathematics Pentathlon®Program .  For many years educational leaders have advocated the use of assessment instruments that go beyond the minimal expectancies of standardized testing procedures.  Such conventional instruments evaluate students’ ability to memorize information in unrelated situations.  When teachers “teach to the test” students often use only short-term memory tactics to cope.  The Mathematics Pentathlon®  Games require a dynamic form of thinking that cannot be assessed with conventional instruments.  Investigation Exercises Book II complements the Mathematics Pentathlon® games and Adventures in Problem Solving activities by providing numerous nonconventional paper-pencil ideas for assessing students’ understanding of mathematical relationships/skills that directly relate to the games/activities.  This publication also encourages students to critically examine various game-playing options and choose strategic moves.