Shape Strategy: A Polygon Game for Sides, Angles and Symmetry
Answer shape questions, then race the computer to claim the shapes that fit the rule.
Getting the game ready...
For grown-ups
This game is for children of about 9 to 12 who are meeting geometry as more than "name the shape". Polygons appear on screen and the player answers questions about them: how many sides, how many vertices, which angles are right, acute or obtuse, which sides are parallel, how many lines of symmetry. Then comes the strategy round. A rule is posted, say "at least one pair of parallel sides", and the player races the computer to claim every shape that fits.
The first part checks vocabulary. The second part is the real thinking, because claiming a shape means testing it against a property, and that is exactly what sorting by properties asks of children in Grades 3 to 6. Many provinces and states introduce angle types and symmetry somewhere in that span, with parallel sides and classifying quadrilaterals usually toward the later end.
The vocabulary that trips kids up
Most wrong answers in this game are word problems, not shape problems. A child can see perfectly well that a shape has five corners and still hesitate because the question said "vertices". Sort these out first, off-screen, in two minutes.
| Word | Plain meaning | Common mix-up |
|---|---|---|
| vertex | a corner where two sides meet | children say "vertexes" or think it means the top only |
| vertices | more than one vertex (say "VER-tih-seez") | treated as a different thing from corners |
| polygon | a flat, closed shape with straight sides | circles get counted; open shapes get counted |
| regular | all sides equal AND all angles equal | a rhombus gets called regular (equal sides, unequal angles) |
| irregular | not regular, any polygon at all that misses one of those | children think "irregular" means "weird looking" |
| acute | an angle smaller than a right angle | confused with "small shape" |
| obtuse | an angle bigger than a right angle but less than a straight line | children call any wide angle obtuse, including straight lines |
| parallel | always the same distance apart, never meeting | children say any two sides that "look nice" are parallel |
The regular and irregular pair deserves extra time. A square is regular. A rectangle is irregular, which surprises almost every child, because a rectangle looks very orderly. Its angles are all equal, but its sides are not. Ask, "Is a rectangle regular?" before playing and let them argue it out.
Playing together
Play the question round together for a few shapes and say your checks out loud. "Sides: one, two, three, four, five. So five vertices too. Is that always true?" (It is, for polygons, and children like discovering it.) For angles, use the corner of a sheet of paper as a right-angle tester. Hold it into each angle on the screen: if the angle hides under the corner it is acute, if it sticks out it is obtuse.
In the strategy round, resist the urge to point. Ask instead: "What is the rule? Does this one have it? How do you know?" If the child claims a shape that does not fit, the game shows the miss. Talk about it: "It had four sides, but were any of them parallel?"
Making it easier
- Play only the question round for the first few sessions.
- Focus on one property per session: sides and vertices one day, angles another.
- Keep a paper corner and a ruler beside the screen.
Making it harder
- Before each strategy rule, have the child predict how many shapes will fit.
- Ask them to invent a rule that fits exactly two of the shapes on screen.
- Add "always, sometimes, never" questions: "A triangle has a right angle: always, sometimes or never?"
The paper sorting activity: Venn diagrams
This is the off-screen version, and it works at a kitchen table or as a classroom station. Cut out about 16 paper polygons: a few triangles (one right-angled, one with all sides equal, one long and thin), a square, a rectangle, a rhombus, a trapezoid, a kite, a regular pentagon, an irregular pentagon, a regular hexagon, an arrow-shaped concave hexagon, an octagon and so on.
Draw two overlapping circles on a big sheet of paper. Label one circle with a property and the other with a second property. The child places each shape in the right region, including the overlap and the outside.
A sample round:
| Circle A | Circle B | In both | Outside both |
|---|---|---|---|
| has a right angle | has at least one pair of parallel sides | square, rectangle | regular pentagon, kite, equilateral triangle |
The outside region is where the learning happens. Children want every shape to go somewhere inside. Leaving a shape outside both circles means saying "it has neither property", which is a sharper statement than it sounds. Change the labels and sort again. Three rounds take about 15 minutes.
Good label pairs to try:
- has four sides / is regular
- has an obtuse angle / has a line of symmetry
- has more than four vertices / has a right angle
Building polygons with straws or toothpicks
Hands make the properties physical. Give a child drinking straws cut to a few lengths (or toothpicks) and small balls of modelling clay for the vertices.
- Build a triangle, then try to squash it. It will not change shape. Build a square and push one corner: it leans into a rhombus. That is a lovely moment, because the side lengths did not change but the angles did, which shows why "equal sides" is not enough to make a shape regular.
- Build a regular hexagon from six equal straws. Count the vertices (six clay balls). Then ask how many straws would make a polygon with ten vertices.
- Build a shape with exactly one pair of parallel sides. Kids often build a trapezoid without knowing its name, then are pleased to learn it.
A bag of 50 straws and a small block of clay covers a whole group. If you are running this as one rotation among several, the Classroom Corner archive has more station ideas.
What to watch for
- Counting sides twice. Have them put a finger on a starting side and keep it there.
- Rotated shapes. A square turned on its point gets called a diamond, and children then doubt it is still a square. Turn the paper together and check the properties again.
- Lines of symmetry guessed, not tested. Fold the paper cut-out. If both halves match exactly, it is a line of symmetry. A rectangle has two, not four, and folding is the only thing that convinces most kids.
- Speed over checking. The strategy round rewards quick claims. If misses pile up, ask for one sentence of proof before each claim.
When the shapes feel easy, switch to number work for a change of pace: the Math War card game is a good companion on another day. For now, fold a paper rectangle along its diagonal and ask whether the halves match. They do not, and that surprise is worth five minutes of talk.
