• Draw a horizontal rectangle consisting of twenty “one-inch” squares lined up from left to right.

• Draw an “X” on the middle square.

• Make one copy of this “game Strip” for each student.

• Provide each player (or teams of players) with 10 same colored “lizards” (use items such as 1” cubes")

• Provide each player (or teams of players) with 10 different same-colored items to represent “lizards” (again, 1” cubes or other items)

• To switch the positions of all the lizards. Taking turns, add one lizard at a time to the board.

• Each lizard can only move forward on to an open square if it can “leap” forward over one lizard onto an empty space.

• Take turns making moves. As each move is made, players record the sequence of moves and the total number of moves (see Ideas for a Logical Leaping Lizards Table in the next section)

• After completing the table, discuss any patterns observed.

• Suggestion: begin by only adding 4 lizards of the same color to each side of the board….

• As the game progresses, play again using more lizards of each color….

• After completing the table, predict the number and sequence of moves needed to interchange 2 groups of 4 lizards. Repeat as done before…

• Are there any similarities between playing the game with 2 groups of 3 lizards and 2 groups of 4 lizards? What about 2 groups of 5 lizards?

• What do you notice if you continue to add more lizards?

• Extend the game strip so players use two groups of 5, 6 , or 7 or more lizards at a time.

• Compare patterns and similarities between the numbers of groups used.

• This Leaping Lizards puzzle is similar but in the “Tower of Hanoi” a tower of 8 disks is initially stacked in in increasing size of 1 of 3 pegs. The goal is to move all the disks from the left peg to the right peg, using the smallest number of moves possible.

• Print on paper (and later copy for each player) a recording table for this:

• Suggestions:

• make a 3 column table —- in the left column, list the number of Lizards on each side of the game strip.

• In the middle column list the number of moves (by lizard color) — example: for r=red and g=green, a list might look like: r-g-g-r-r-g-g-r

• In the right column write the number of moves — for example: for r-g-r write 3 moves. For r-g-g-r-r-g-g-r, write 8 moves.

This fun activity/game reinforces logical thinking — an essential skill that players can develop through practice. Logic games such as this one engage players and build their appreciation for approaching problems with a plan for solutions. Usually, players begin via trial and error. But as they record data, they notice patterns, and then generalize to more complicated problem solving techniques. These types of activities stimulate and strengthen understanding of special relationships by requiring finding an image and transferring its location. All these thinking processes are important strategies not only for math but for many other subjects as well….