What is Intop Card Game?

Answer 1

Mnemonics in Teaching Operations of Integers

Are you having trouble with signed numbers? If yes, then you are not alone. Many of my students confessed that they were confused with operating integers (natural numbers, their negatives, and zero) although they had memorized or studied the following rules of operation:

1. Addition. In adding two numbers having like signs, add their absolute values and prefix the common sign to the result. If the two numbers have unlike signs, find the difference in their absolute values and prefix the sign of the number with greater absolute value to the result.

2. Subtraction. In subtracting two numbers, change the sign of the subtrahend and proceed to the rules in addition.

3. Multiplication/Division. If two given numbers have like signs, their product or quotient is positive; if unlike, negative.

With the aforesaid problem in mind, I decided to make Mnemonic Devices or memory aids that would make the access of principles underlying operations of integers from memory easier. I shortened the above rules of operation, respectively, into the following letter strategies:

1. + LA US or + LA CS, US SONGAV which stands for "like (L) signs, add (A); unlike (U) signs, subtract (S)" or "like (L) signs, add (A): common sign (CS); unlike (U) signs, subtract (S): sign of the number with greater absolute value (SONGAV)."

2. - CTSOTS LA US which stands for "change the sign of the subtrahend (CTSOTS) and proceed to the rules of addition (LA US)."

3. ÷x LP UN which stands for "like (L) signs, positive (P); unlike (U) signs, negative (N)."

The use of mnemonic devices is supported by the primacy effect theory of memory and was proven to be effective in instruction by Scruggs and Mastropieri (1999). The above devices were also used in my mathematics classes, and they gained satisfactory feedback from students. I also conducted a master's thesis on these devices as used in a card game called Intop. And it was found out that mnemonic instruction was more effective in building learner's mastery of skills in operating signed numbers than the traditional teaching method.

Mnemonics and Intop Card Game

Young people find games fun; so do the old ones. Yes, mnemonics are effective memory aids; but, do they motivate the learners? That is why I created a card game to serve the purpose of motivating them while learning the mnemonic devices. This card game comes from the words "Integer Operations," that is why it is abbreviated as Intop.

This card game is composed of three sets of cards: int cards, op cards, and selop cards. Each int card contains any of the integers ranging from -10 to 10 (negative numbers written in red and whole numbers in black). An op card contains any of the mnemonic devices for the four fundamental operations of integers. Selop cards contain all of the four symbols of operations from which a player may choose his desired operation if he does not want the op card sent by his opponent.

Number of cards per int card

Int card

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

Pcs.

2

2

2

2

2

3

3

4

4

4

0

1

2

3

4

5

6

7

8

9

10

4

4

4

4

3

3

2

2

2

2

2

Samples of int cards

Op cards

Selop card

How to Play Intop Card Game

1. Intop cards are divided into two groups: int cards and op cards (including selop cards).

2. Intop cards are shuffled separately before the game starts.

3. Intop cards are distributed to players separately; that is, int cards are distributed first before op cards.

4. The number of players shall be 2, 3, or 5 - since the number of int cards (60) and op cards (30) with a total of 90 is divisible by those numbers (regardless of the additional 6 selop cards).

5. The first player shall be determined by throwing a die. Turns shall be done in counterclockwise direction.

6. The first player shall send to the next player one int card and one op card.

7. The next player selects an int card from his acquired Intop cards to complete the int-op-int card combination, avoiding negative result as much as possible. If the current player does not want to use the op card sent by the previous player, he/she may use a selop card (if he/she has) which gives him/her a chance to use a desired operation that will give him/her a positive result or a relatively higher score. In case of division, the divisor shall be a factor of the dividend (including ±1). In case the current player has no available int cards which are factors of the previously sent int card, he/she may use any number as a divisor, giving him/her a fractional or decimal score. Division by zero is prohibited.

8. Passing cards and completing card combinations continue in rounds until all Intop cards are used.

9. To determine the winner in the game, scores in rounds shall be added. Any player who gets the highest total score shall be adjudged as the winner.

The teaching of operations with integers should not be confined in the letter strategies alone. Students should discover the link between these concepts and the real world so that students can find them meaningful. Through this connection and the use of mnemonics and Intop card game in instruction, the learning of mathematics will be full of meaning, fun, and effectiveness.