1. Module 7

1.41. Page 3

Mathematics 10-3 Module 7 Lesson 8

Module 7: Trigonometry

 

Explore

 

spatial reasoning: the reasoning used to work through a problem involving geometric figures

You have just investigated the tangram puzzle. That puzzle did not require numbers or equations. Rather, it involved spatial reasoning.

 

Another popular game and puzzle that involves spatial reasoning is pentominoes. The word pentominoes was coined by Solomon Golomb more than 50 years ago during a speech he delivered to a mathematics club at Harvard University. The word pentomino describes a shape formed by joining five identical squares. Each square in the set of five shares at least one side with another square. There are 12 such arrangements.

 

This illustration shows the 12 possible pentomino arrangements.

 

Because these pentominoes can be flipped over and rotated during play, the following arrangements, for example, would all be considered the same!

 

This illustration shows four rotations of the T-shaped pentomino. The examples are shown with the T upright, upside down, lying on its left side, and lying on its right side.

 

Try This

 

In this activity you will play games and solve puzzles based on pentonimoes. You will also analyze your strategy. But first, you will need to construct the pieces and the board.

 

You have a choice. You can play an “Online Game of Pentominoes,” or you can download the Paper Version of Pentomino Game Pieces and Pentomino Game Board. If you choose to play an online game, try searching the Internet using the term “Scholastic Play Pentominoes.”

 

If you are using the paper version, follow these instructions to prepare the game pieces and board.

  • Glue the pentomino pieces onto a card, such as an old file folder, and then cut out the pieces.

  • Since the game pieces can be flipped over, you may wish to use your coloured markers to make the back of each piece match the front.

  • Draw the black grid lines on the back as well of the pieces as well.

  • Glue the game board to a cardboard file folder or other cardstock.

Rules of Play

 

This is a game for 2, 3, or 4 players.

  • Players take turns placing a piece of their choice anywhere on the game board. The pentonimoes may be rotated or flipped over, but they must be placed on unoccupied squares on the board.

  • Pieces may touch or be placed side-by-side. However, the pieces must not overlap!

  • If there are two players, the first player who cannot place a piece on the board loses.

  • If three or more players begin, the first player who cannot place a piece on the board is eliminated. The board is cleared, and the remaining players play a second round. Players are eliminated until a winner is declared!

Play several games until you are comfortable that you can share your game strategy with other students.

 

Now answer these questions.

 

TT 1. Look at these drawings.

 

 

This illustration shows two drawings of pentominoes. The first is two squares in a horizontal row with three squares in a horizontal row extending to the right from below the right square. The second graphic is three squares in a vertical column with two squares in a vertical column extending below the right side of the bottom square.

 

Do these drawings represent the same pentomino piece? Why or why not?

 

TT 2. Look at these drawings.

 

 

This illustration shows two drawings of pentominoes. The first one is three squares in a horizontal row with one square below the middle square and one square above the right square. The second is three squares in a vertical column with one square to the left of the middle square and one square to the right of the top square.

 

Do these drawings represent the same pentomino piece? Why or why not?

 

TT 3. If you were coaching a younger brother or sister to play the pentomino game, what strategies would you recommend your sibling use to win the game?

 

Share

 

Share the strategies you recommended in TT 3 with a partner or group.

 

What new strategies did you learn from others? Which strategies are most likely to help you win a game of pentonimoes? Which strategies do you think will have no effect on your success?

 

Summarize your favourite strategy and your least-favourite strategy in a paragraph, and save this information in your course folder.