Use scissors, card and pens to make a version of battleships in which all the ships are various sizes of right-angle triangles. Draw out four 20- by 20-inch grids and make a cardboard partition so that the players cannot see the positions of each other's pieces.
Cut out right-angle triangles in different-colored card. Cut one triangle with sides equal to 5, 12 and 13 grid squares in length. Cut two triangles at 6, 8 and 10 squares in length and three at 3, 4 and 5 squares.
Instruct the players to lay out their triangles on their grids with the perpendicular edges of the triangles along the grid lines. Have them take turns guessing the positions using the grid references. If a player scores a hit anywhere on one of the lines, the other player must reveal the grid references of the angles at each end of the line and the number of degrees in each angle as a bearing from North, or straight up.
The player must then "solve" the triangle they have hit by working out the length of each side, the remaining angle and the coordinates of the remaining angle. If they solve the triangle they "sink" it.
Make two sets of cards. Write the letters of the alphabet on one set. On the other set, write objectives related to triangles such as, "Make a triangle with the largest area."
Use the world map as a board. You need one with quite a lot of detail, showing as many cities as possible.
Deal three letter cards to each player each turn. Deal one objective card per turn for all the players to follow.
Instruct the players to pick three cities, each beginning with one of the letters from the cards. Have the students make a triangle between the cities. The aim is to try and make a triangle with a larger surface area than any of the others.
Allow the players to measure two of the sides and two of the angles. Have them calculate the missing triangle information. Award a point to the winner in each round and play until the first person gets seven points.
Use a fast-paced game appropriate to the age group you are teaching. A game with question cards, such as Trivial Pursuit, is a good example.
Modify the game by changing all the question cards to trigonometry questions.
Require the players to roll two dice each turn to decide how far they can move. The values on the dice give them the lengths of two sides of a triangle. They must use these numbers to calculate the third side of a triangle. The distance they move is equal to the third length.