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DOUBLE BAG MATH SCRATCH

A Math Showcase Presented to the
Faculty of Camarines Norte State College
Laboratory High School

In Partial Fulfillment of the Requirements for the First Grading Period

MICHAEL ALEXIS G. ASUNCION
KENNETH JAMES L. BORILE
SADAM RICHARD C. CANUTO
KARL JOSEL M. CASTILLO
ELDRIN PAUL R. GARCIA

August 2006
ACKNOWLEDGEMENT

No words can express our deepest appreciation and gratitude to our dear Lord for giving us the strengths and abilities to make this project possible.

There also people who extended their supports and efforts for the completion of this math showcase, to our parents, for giving us moral supports and helping us financially, to our ever beautiful Mathematics teacher, Mrs. Jennifer Rubio, for her dedication in teaching us, to Kuya Jaycee, for sharing his ideas and concept of the game, and to our classmates, our competitors, for a healthy competition.

THE PROPONENTS

ABSTRACT

Arithmetic is the oldest and simplest branch of mathematics, used by almost everyone, for tasks ranging from simple daily counting to advanced science and business calculations. In common usage, the word refers to a branch of mathematics which records elementary properties of certain operations on numbers.

Scrabble is a popular word game and board game in which 2-4 players score points by forming words from individual lettered tiles on a 15×15 game board.

The showcase was made to help those students having difficulties in arithmetic like solving simple problems and computing sign numbers.

The game is entitled “Double Bag Math Scratch”. It is inspired by the game double bag scrabble with a twist of mathematics. We use the word scratch because it is synonymous to scrabble.

CHAPTER I – INTRODUCTION

Scrabble is a popular word game and board game in which 2-4 players score points by forming words from individual lettered tiles on a 15×15 game board. Arithmetic is the oldest and simplest branch of mathematics, used by almost everyone, for tasks ranging from simple daily counting to advanced science and business calculations. In common usage, the word refers to a branch of mathematics which records elementary properties of certain operations on numbers.

The showcase is entitled “Double Bag Math Scratch”. It is inspired by the game double bag scrabble with a twist of mathematics. We use the word scratch because it is synonymous to scrabble.

A. Review of related literature

The game Scrabble was created by architect Alfred Mosher Butts in 1938, as a variation on an earlier word game he invented called Lexiko. The two games had the same set of letter tiles, whose distributions and point values Butts worked out meticulously by counting letter usage from the New York Times and other sources. The new game, which he called “Criss-Crosswords”, added the 15-by-15 game board and the crossword-style game play.

B. Significance of the game

This game can help those students having difficulties in arithmetic like solving simple problems and computing sign numbers.

C. Scope and Limitation

Double Bag Math Scratch was tested several times by the proponents to make the new rules and twist from the game “scrabble”.

This showcase was designed for students who wanted to get in a new board game with an exciting twist from the game “scrabble”. This is applicable for ages 10 year of age and above.

E. Definition of terms

1. Meticulously - me·tic[pic]u·lous·ly adv. Synonyms: meticulous, painstaking, careful, scrupulous, fastidious, punctilious These adjectives mean showing or marked by attentiveness to all aspects or details.

2. Equation - e·qua·tion ([pic]-kw[pic][pic]zh[pic]n, -sh[pic]n) n. The act or process of equating or of being equated.

3. Subsequent - sub·se·quent (s[pic]b[pic]s[pic]-kw[pic]nt[pic], -kw[pic]nt) adj. Following in time or order; succeeding.

4. Innovation - in·no·va·tion ([pic]n[pic][pic]-v[pic][pic]sh[pic]n) n. a. The act of introducing something new. b. Something newly introduced.

5. Thrilling - thrill (thr[pic]l) v. thrilled, thrill·ing, thrills v.tr. a. To cause to feel a sudden intense sensation; excite greatly. b. To give great pleasure to; delight. c. To cause to quiver, tremble, or vibrate.

CHAPTER II - METHODOLOGY

A. Materials and Tools used

The proponents use recycled scrabble board for this game.

The game have 100 Tiles: 70 tiles with NUMBERS from 0 to 9 and 30 OPERATION SIGN tiles. Each of the number tiles has score values (the small number to the bottom right of the number). Two racks: Each player takes a rack at the beginning of the game allowing them to arrange their seven tiles. Two tile bags: all the tiles are placed in the bags at the beginning of the game.

Tile Scoring Values

|Number/ |Value |Distribution |
|Operation | |(no. of tiles) |
|0 |5 |6 |
|1 |-1 |8 |
|2 |2 |10 |
|3 |-3 |3 |
|4 |4 |9 |
|5 |-5 |6 |
|6 |6 |8 |
|7 |-7 |3 |
|8 |8 |10 |
|9 |-9 |7 |
|+ |-2 |8 |
|- |5 |5 |
|X |1 |8 |
|÷ |5 |5 |
|= |0 |4 |

The Playing Board

The playing board consists of 15 x 15 squares in the playing area with gridlines to separate the squares. There are special premium squares on the board with bonus score values:

a. Double Number Score, a light blue square doubles the score of a number placed on it. b. Triple Number Score, a dark blue square triples the score of a number placed on it.

c. Double Equation Score, the score for the entire equation is doubled when one of its tiles is place on a light red square.

d. Triple Equation Score, the score for the entire equation is tripled when a tile is placed on a dark red square.

If an equation crosses both premium number and equation squares, all the bonus number values are added up before the complete score is doubled or tripled.

The bonus scores of the premium squares only apply to the turn in which the tiles are placed on them.

B. Playing the Game

One player is elected as scorekeeper. They may also take part in the game. The scorekeeper keeps tally of each player’s score, entering it after each player’s turn.

To Begin Playing, all the tiles are placed in the bags. Each player takes a tile out to find out who players first. The player who has the lowest numbered tile plays first. The exposed tiles are put back into the bag and the bag is shaken to shuffle them.

Each player, in turn, then draws four new tiles from the numbers bag, three tiles from the operations bag and places them on their rack without disclosing them to his/her opponent.

Play continues clockwise and on each subsequent turn, players then have the choice of exchanging tiles, passing, or placing an equation on the board.

Remember that each player should place one operation each time on his/her turn, then one digit number must be placed only in between the operation (ex. 2+9)

Exchanging Tiles: any player may use their turn to replace any or all of the tiles on their rack. They do so by discarding them face down, drawing the same number of new tiles, then mixing the discarded tiles with those remaining in the bag. They then wait for their next turn to play.

Passing (Missing a Turn): instead of placing tiles on the board, or exchanging tiles, a player may also decide to pass, whether or not they do not want to make an equation. However, should all players pass twice in succession, the game ends.

Placing the First Equation: the first player combines two number tiles and one operation tile to form an equation on the board to read either across or down with one tile on the centre square (star). Diagonal equations are not permitted.

All tiles played in this and subsequent turns must be placed in one continuous line horizontally or vertically.

Scoring the First Equation: a player completes their turn by counting and announcing their score, which is recorded by the scorekeeper. The score for the turn is calculated by adding up all the values of the numbers on the tiles and summing up the equation values of the tiles separately, plus the premium values resulting from placing tiles on premium squares. The tile value will be multiplied in the premium squares containing double number score and triple number score only, while the equation will be multiplied in the premium tiles containing triple equation score and double equation only.

Ending a Turn: at the end of every turn, the player draws a maximum two number tiles and one operation tile, thus always keeping seven tiles on their rack.

Next Players Turn: The second player and then each player in turn, has the choice of exchanging tiles, passing or adding one or more tiles to those already played so as to form new equation. Adding of tiles to the placed equation of the recent turn of the other player must be one number tile and operation tile only.

All tiles played in any one turn must be placed in one row only across, or one column only down the board.

The player gets full score for all equations formed or modified by their play. They include the bonus scores of any premium squares on which they have placed the tiles.

Sometimes an equation may cross two premium squares. The equation score is doubled then redoubled – 4 times the complete equation score; or tripled and then re-tripled – 9 times the complete word score.

WINNING DOUBLE BAG MATH SCRATCH

The game ends when all the tiles have been drawn and one of the players has used all the tiles in their rack. The game also ends when all possible plays have been made or all players passed twice in consecutive turns.

After all the scores are added up, each player’s score is reduced by the sum of their unplayed tiles, and if one player has used all their tiles, their score is increased by the some of the unplayed tiles of all the other players.

Remember – the game can be won or lost on the last number or operation in the bags.
CHAPTER III – CONCLUSION

The showcase was designed for a new exciting game, for which almost of the students both from the intermediate grades of the elementary and secondary can easily draw a level of expectations from an old board game. This is a new bend of fun that can be derived by the students.

This is also intended to create a thrilling game out of the boring subject that they called “Mathematics”.

CHAPTER IV – RECOMMENDATION

The showcase should be criticized, for more innovations for the game. New ideas can be set by the students with the permission of the proponents, for its more functional value as a new form of a mathematical tool.

TABLE OF CONTENTS

ACKNOWLEDGEMENT

ABSTRACT

CHAPTER I – INTRODUCTION 1-2

A. REVIEW OF RELATED LITERATURE

B. BACKGROUND OF THE STUDY

C. SIGNIFICANCE OF THE GAME

D. SCOPE AND LIMITATION

E. DEFINITION OF TERMS

CHAPTER II – METHODOLOGY 2-6

A. MATERIALS AND TOOLS USED

B. PLAYING THE GAME

CHAPTER III – FINDINGS

CHAPTER IV – CONCLUSIONS 6

CHAPTER V – RECOMMENDATION 6

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