Exploration Stations Descriptions/Instructions
Paper Pool: In this investigation, students are asked to play a game called Paper Pool to identify the number of
hits and the pocket the ball will land in for any size table. The game is played on rectangular grids made of
congruent squares. An imaginary ball is hit from the lower left-hand corner (labeled A) at a 45° angle. A ball
hit in this way will bounce off each side it hits at a 45° angle. The ball continues to roll until it reaches a pocket
located at one of the corners. The number of hits for each table and the pocket at which the ball will stop
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Instructions and Exploration. Create the tables on the handout by drawing the path of the ball and recording the
pocket, number of hits and dimensions. Complete the sheet “Paper Pool Record Sheet” to look for patterns.
Lining up Dominoes: One person shuffles the dominoes and deals an equal number to each player. Find
the piece says “Start” or “Begin”. The other half of the domino will have a problem to be solved. Connect
the dominoes together by finding a solution. Another problem will be on the second part of that domino.
Continue play until all pieces are connected.
Polynomial Four in a Row: Play begins by the first player placing the two paper clips on any pair of factors
along the bottom edge of the game board. The player then places a marker on the square, which is the product
of the two factors. The next player is allowed to move exactly ONE clip and cover the square, which is the
product of the two indicated factors. (Both clips can be placed on the same factor to square that factor.) Play
alternates until someone gets four markers in a row, horizontally, vertically, or diagonally.
Integer Logic: Integers are given to fill in the top row and left column so the numbers add or multiply to give
the number in the corresponding inner square. Each given number must be used once in the top row and once
again in the left column. Once border numbers are placed, complete the other inner squares with the correct
sum or product.
Matching Representations: Separate the cards into groups of graphs, tables, equations and slope/y-intercept.
Choose two of the representations and match the corresponding representations. Continue adding an additional
representation until all cards in one group represent the same linear function.
The Power of Fun: “The Power of Fun” is an investigation where three puzzles are used to support several
important mathematical concepts. As with any such puzzle, students learn from talking through their
experiences, trying to see what sorts of moves lead to dead ends, and why certain forms make it impossible to
move further. In each case, the object is to accomplish the task in the least number of moves.
Interpreting Distance/Time: Separate the cards into groups of graphs, tables and verbal descriptions. Choose
two of the representations and match the corresponding representations. Continue adding an additional
representation until all cards in one group represent the same distance/time scenario.
24 Game – Integers: The object of this game is to make 24 with the integers on the card. See the direction
sheet with the card for a detailed explanation and examples.
24 Game – Algebra/Exponents: The object of this game is to make 24 using the numbers and algebraic
expressions on the card. See the direction sheet with the card for a detailed explanation and examples.