The purpose of this game is to motivate students to examine
relationships among geometric properties. From the perspective of the
Van Hiele model of geometry, the students move from recognition or
description to analysis (Fuys 1988). Often, when asked to describe
geometric figures, middle school students mention the sides ("The
opposite sides are equal") or the angles ("It has four right angles"),
but they rarely use more than one property or describe how two
properties are related. For example, is it possible to have a
four-sided figure with opposite sides not equal and four right angles?
Or a triangle with three right angles? What geometric relationships
make such figures possible or impossible? By having to choose figures
according to a pair of properties, players go beyond simple recognition
to an analysis of the properties and how they interrelate.
Polygon Capture Game Polygons
Choosing all figures in the Polygon Capture Game Polygons Activity Sheet that have parallel opposite sides is relatively easy. Choosing all figures with parallel opposite sides and at least one obtuse angle requires reasoning, and a good analysis of such figures leads to the inference
that all non-rectangular parallelograms have these two properties, as does the regular hexagon.
Another purpose of the game is to give students a format for
using important geometric vocabulary-parallel, perpendicular,
quadrilateral, acute, obtuse, and right angle-in a playful situation.
The basic game is described below and is followed by warm-ups and
Polygon Capture Game Rules
Polygon Capture Game Cards
To get ready for the game, distribute copies of Polygon Capture Game Rules, Polygon Capture Game Cards, and Polygon Capture Game Polygons.
You will need only one copy of each master for every two students.
Before introducing the game, have the students cut out the polygons and
the cards. They should also mark each card on the back to designate it
as an "angle" or "side" card. The eight cards from the top of Polygon Capture Game Cards sheet should be marked with an "A" for angle property; the eight cards from the bottom should be marked with an "S" for side
Before the game, assess the students' familiarity with the vocabulary used in this game, such as parallel, perpendicular, polygon, and acute angle by engaging students in a class discussion in which they define, illustrate, or find examples of the geometry terms.
Basic Rules of the Game
Have the students read the rules on Polygon Capture Game Rules sheet.
Teachers have found it helpful to begin by playing the game
together, the teacher against the class. You may want to do so a few
times until the class is confident about the rules. For the first game,
remove the Steal Card to simplify the game.
To introduce the game as a whole-class activity, lay all
twenty polygons in the center of the overhead projector. Students may
lay out their shapes and follow along. An introductory game observed in
one of the classrooms (as shown in step 4, below) proceeded as follows.
- The teacher draws the cards All angles have the same measure and All sides have the same measure. She takes figures D, G, Q, and S, placing them in her pile and out of play.
- Students then pick the cards At least two angles are acute and It is a quadrilateral. They choose figures I, J, K, M, N, O, and R.
- On her second turn, the teacher picks the cards There is at least one right angle and No sides are parallel.
She chooses figures A and C and then asks students to find a figure
that she could have taken but forgot. One student points out that
figure H has a right angle and no parallel sides. Other students are
not sure that this polygon has a right angle, which leads to a
discussion of how they might check.
- The students then proceed to take two new cards
| || |
|(a) Teacher selects cards. |
Angle card: All angles have the same measure.
Side card: All sides have the same measure.
|(b) Students select cards. |
Angle card: At least
two angles are acute.
Side card: It is a quadrilateral.
| || |
Sample Steps in a
|(c) Teacher selects cards. |
Angle card: There is at least one right
Side card: No sides are parallel.
|(d) Students capture piece that teacher missed.|
When no polygons remain in play that match the two cards chosen,
the player may turn over one additional card-either an angle or a side
card. This move calls for some planning and analysis to determine
whether an angle card or a side card is most likely to be useful in
capturing the most polygons. If the player still cannot capture any
polygons, play moves to the opponent. When all cards in a deck are used
up before the end of the game, they are reshuffled. Play continues
until two or fewer polygons remain. The player with the most polygons
is the winner.
When the "Wild Card" is selected, the player may name whatever
side property he or she wishes; it need not be one of the properties
listed on the cards. Again, a good strategy to capture the largest
number of polygons requires an analysis of the figures that are still
When the "Steal Card" comes up, a card from the deck is not
drawn. Instead, the player has the opportunity to capture some of the
opponent's polygons. The person who has chosen the Steal Card names two
properties (one side and one angle) and "steals" the polygons with
those properties from the opponent. The students may select their own
properties, not necessarily those on the game cards. If the opponent
has no polygons yet, the Steal Card is put back in the deck and a new
One interesting aspect of the game is the various strategies
that students use. Some students go through the figures one at a time,
using a trial-and-error method to match them to properties on the
cards. Some students perform two sorts; they find the polygons that
match the first card and, of this group, those that also match the
second card. Others seem to analyze the properties and mentally
visualize the polygons that are possible. In analyzing properties ("Is
this angle acute?"), students quickly learn to use angles and sides in
other figures as benchmarks, for example, using the right angle in a
rectangle to check whether a triangle has a right angle. Generally
classes play with no time limits, although students could choose a
limit as an option.
In the Classroom
"I first played the game against the students and then had them play against each other. They were arguing about whether they could take certain polygons—it allowed them to solidify their understanding by explaining their reasoning to someone else." -Ava T. Parnes, MS Math/Science Teacher (New York, NY)
- Carroll, William. "Polygon Capture: A Geometry Game." Mathematics Teaching in the Middle School, Volume 4 (Ocober 1998), pp. 90‑94.
- Fuys, David, Dorothy Geddes, and Rosamond Tischler. The Van Hiele Model of Thinking in Geometry Among Adolescents. Journal for Research in Mathematics Education Monograph Series, no. 3. Reston, Va.: National Council of Teachers of Mathematics, 1988.