Subtraction Games – Butterfly
Gulugufe is a Subtraction game that combines strategic thinking with the learning of basic facts. The game encourages players to practice solving subtraction algorithms using their knowledge of Addition.
About the Game:
Gulugufe means butterfly in the African nation of Mozambique. It is a two-player strategy game played on a board made in the shape of a butterfly. Gulugufe is a very social game. It’s like a sport. Spectators cheer good moves and from time to time heckle the players, ‘All in good fun’. This version of the game has been modified to teach Mathematics concepts.
What You Need:
– 9 counters of one color
– 9 counters of another color
How to Play:
1. Set up the board so counters are covering each of the algorithms. One color covering all the algorithms on the left and one color covering all the algorithms on the right.
2. The person with the shortest hair goes first.
3. Players slide their pieces to empty spots and say the answer to the algorithm aloud for the opponent to hear.
4. Pieces are captured by jumping over them (the same as in Checkers)
Rules for Capturing Pieces:
Printable Subtraction Games – Printer Friendly
– If a piece can jump over an opposition piece and land on an empty space the opposition piece is captured and taken from the board.
– Players can only move and capture along the lines marked on the board.
– Multiple captures – if a piece can jump over an opposition piece, land on a vacant space then jump over another piece and on a vacant space then both opposition pieces can be removed from the board.
– Captures are compulsory
– If more than one capture is available the player may choose which option they wish to take.
Ways to Win:
1. Capture all your opponent’s pieces.
2. The person with the most pieces left when there are no more legal moves to be played.
3. Stalemate – is when one player has trapped the other so they cannot capture or make a legal move. The trapped player loses.
4. If no more pieces can be captured, the player with the most pieces remaining wins.
– If no more pieces can be captured and both players have the same amount of pieces, the game is a draw.
This game can be played in the sand or dirt. Draw the board with a stick and use stones as markers. I’ve played this game in the sand at the beach with shells and stones.
Before the Game:
– Explore the inverse relationship between Addition and Subtraction.
– Do plenty of modeling of using Addition to solve Subtraction algorithms. Counting backward is an inefficient strategy. Use what you know and manipulate the numbers. Play with the numbers.
– Be sure the students have a thorough understanding that Subtraction algorithms like these are efficiently solved by using know Doubles Facts e.g. 14-7=… becomes 7 plus what equals 14.
– Make sure students can use concrete materials to demonstrate what the algorithms mean. Research shows rote learning these facts without a thorough understanding of what they represent is pointless.
– As a teacher be aware of ‘pseudo-context’ in the creation of word problems. How can you avoid this? Why is it important?
– Discuss you can use one process to solve the other i.e. Once you know the Addition Facts you also know the Subtraction Facts if you manipulate the numbers.
During the Game:
– Monitor the gameplay looking for teachable moments.
– Have a set of materials with you where you can model and ask students to model algorithms for you.
– Use a calculator to model patterns. Have the students predict the answer before you press the equal’s button.
After the Game:
– Have your students teach this game to another class.
– Students reflect on their journey towards mastery and automaticity.
Included in the Download:
3 High Color Boards
3 Low Color Boards
1 PowerPoint file to make the introduction and discussion of the game easier.