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Board Games: Applications to Mathematics

Prepared by: Cynthia Thomashow, M.S.T and M.Ed.

Executive Director, Center for Environmental Education

Adjunct Faculty @ Unity College, Maine and Antioch University, NE

June 2009

Board Games have multiple uses in the classroom. They are fun and attractive and relatively free of ‘academic stress’, so they are compelling as an activity for students. They are social and convivial with a greater purpose and specific goal. Board Games provide opportunities for ‘safe’ competition among individuals and groups. They teach ‘rule-making’, cause and effect and planning. Abstract games provide a substrate for mathematical operations and logical reasoning. They teach the difference between luck and strategic thinking and critical reasoning. They allow teachers to uncover learning styles and competencies that might not emerge in didactic classroom settings.

The mechanics of Board Games can help teach mathematical reasoning. This paper aligns the different aspects of Board Games with the competencies articulated in the **“National Standards for Mathematics Teaching”** (National Council of Teachers of Mathematics) grades 3 through 5. Math classes at this level lay the foundation for higher order mathematics like Algebra, Geometry and Calculus. The grade-level focal points listed below identify the concepts, major instructional goals and skill expectations within the context of problem-solving, reasoning and critical thinking with the intent of building mathematical competency for all students. Not every student learns at the same rate or acquires concepts and skills at the same time – Board Games provide another venue of practice that is fun and engaging.

Let’s focus on Board Games as a means to support the preparation of students for higher order mathematics. Selected games from the publisher, Gryphon Games (available through the parent company FRED Distribution) including:
“24/7 the Game”,
“Take It Easy”,
“Birds on a Wire”,
“For Sale”,
“Looting London”, and
“Gem Dealer”, (as examples) have the attributes listed below.

Long-term Strategy and Effective Tactics

**The Relationship of Parts to the Whole**

A critical skill for problem solving is successfully employing the tactics that prove instrumental in accomplishing a bigger strategy. Strategy is the overall management of sub-goals to accomplish a long-term goal. Tactics are the small decisions that make up the grand strategy. Sometimes we mistake the sub-goals for the bigger goals…losing our focus on what is really important.

**Assessing Risk, Taking Chances and Using Good Judgment**

There are many ways to accomplish long-term goals. Strategy games can help students learn to accommodate to change, respond to unexpected challenges and overcome obstacles in a fairly non-threatening context. Students learn to recognize the information that is necessary to solve a problem by studying how the parts influence the whole and observing how others are approaching the same problem in different ways.

Playing games can help students learn to focus and hold on to the big picture when solving a problem, not losing oneself in the tactical play. Learning to move in and out from detail to vision, to assess the board for future moves, to know when to let go of a tactic for the sake of the strategy is just good thinking. Students learn to think beyond the present moment, to adjust strategy in response to new challenges.

Game Boards as Mathematical Topography

**Grids and Graphs**

Most Board Games use a grid or graph as a playing surface. Connection games are linked closely with the ‘topography’ of the board surface on which they are played. This is a method to teach students the concept of a graphing grid and to utilize spaces, scale, vertices and their relationship to edges or end-points in play. The board geometry has a profound effect on the play mechanism and the strategies that emerge during play.

**Measurement**

Students recognize area (the board) as a two-dimensional region. They learn to quantify an area by finding the total number of same-sized units of area that cover the shape without gaps or overlaps. Games can further the understanding the properties of two-dimensional shapes by considering congruence and symmetry and by transforming and rotating shapes while laying pieces on a board.

**Fractions and Wholes**

Students develop an understanding of the meaning and use of fractions to represent parts of a whole, parts of a set, or points or distances on a number line. They compare and manage the size of a fractional part relative to the size of the whole board and their pieces. They solve problems that involve comparing and ordering fractions using models like a number line to identify equivalent fractions.

**Connections and Sequences**

Many games involve creating configurations of separate pieces that are linked or become linked as players negotiate the topography of the board grid. Connecting your pieces on a board can have a metric quality or it may lead to making chains that lead to a by-product like the surrounding of territory or the creation of a particular pattern. Pieces may have certain qualities (color, number, shape) that lead to different connection goals. For example, creating advantageous sequences of multiplication or addition is the goal of a game like
“Take It Easy” or
“24/7”.

**Pattern Making**

The connection of pieces on a board grid may lead to a pattern like ‘three-in-a-row’ or a ‘square shape surrounding territory’ – in these cases, the connection is not important, the emerging pattern is. Students learn to keep the ‘big picture’ pattern in mind while manipulated ‘the parts that make up a whole’ with the placement of each piece. Keeping a ‘big idea’ in mind while manipulating the smaller parts of a problem is essential in the development of critical thinking.

Mathematical Reasoning

**Number and Operations**

The properties and operations of number form the basis of many games. Addition and subtraction, multiplication and division are consistently practiced supporting arithmetic skills. The creation and analysis of patterns and relationships that involve multiplication and division are part of readying students for algebra. Students begin to understand the meanings of multiplication and division through the use of representations like equal-sized groups, arrays, area models and ‘jumps’ on the number line through multiplication and successive subtraction, partitioning collections and sequences.

Students begin to use the commutative (involving or relating to exchanges or substitutions), associative (giving the same result regardless of the order taken, thus since a + (b + c) = (a + b) + c) and distributive properties (when two different ways of expanding a collection of pieces produces the same result) as tactics.
(“Take It Easy”,
“24/7”,
“Looting London”)

**Algorithmic Thinking**

The mechanics of a Board Game are algorithmic. The rules create
a logical sequence of steps for solving a problem, often written out as a flow chart of instruction. The process of learning and following rules sets a stage for learning algorithms, the logical step-by-step procedure for solving a mathematical problem in a finite number of steps, often involving repetition of the same basic operation.

**Algebraic Reasoning**

Students may explicitly identify, describe and extend numeric patterns on a Board Game or learn deeply about the growing and repeating of non-numeric patterns. Learning to combine sets of like or different attributes is a basic skill of numeric patterning. Students represent and analyze patterns and functions by using objects and representations (game pieces) in the place of numbers to draw conclusions about relationships. Students develop a strong understanding of the use of a particular rule to describe the operation of numbers or objects in relationship to other numbers and objects.

Data Analysis and Probability

**Analyzing Opportunities**

Board Games give students an opportunity to represent data using a graph-like placement of pieces, the consideration of shape and important attributes of a set of data. During play, students compare related data sets and their distribution and the opportunities for tactical movement. Students gain competence selecting appropriate methods or tactics and applying them accurately to estimate quotients or to calculate them mentally, depending on the context and numbers involved.

Game pieces represent sets of information (a dice, a set of cards, a board with a particular grid, boards with edges and boundaries, sets of numbers and distinctive attributes) that can be manipulated by students toward a desired end. Students can propose and justify conclusions and predictions that are based on available data and design ways to further investigate the conclusions and predictions of movement.

**Probability**

Understanding probability comes with the use of dice and cards that have fixed numerical options. Card counting may be bad in poker but it can serve to exercise the mind and give the student a good chance of predicting an outcome in a game. Dice have only six sides, limiting the number of combinations that will appear on a turn. Predicting the outcome based on reliable probability builds an understanding of bounded possibility over luck.

*Copyright © Cindy Thomashow and FRED Distribution, Inc., 2009, all rights reserved*