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MAKING A DIFFERENCE ONE GAME AT A TIME.

Are there family board games that you enjoy? Do you ever wish you could take some of those games and make them academically challenging for your learners? How do you go about doing that?

These are just some of the questions that teachers might ask themselves when planning high-impact lessons for the classroom setting. Yet, finding the time to change up an existing game can be a daunting feat. Nevertheless, Cicchino (2015) points out the importance of game-based learning as a style that enables learners to make meaningful choices and utilize critical thinking while accessing their visual, spatial and aural learning capacities. The question remains, how?

The blue orange[TM] game company has thirty-three versions of their ever-popular game, Spot It![TM], on the market today. The Spot It![TM] game is one that requires quick thinking and a focused eye to spot one, and only one, match between any two given cards. There is always a match, and only one match. Through the use of game-based learning, learners can enjoy this game using a variety of themed symbols as well as Basic English, Basic French, numbers and shapes, and the alphabet. However, what is stopping teachers from making this game their own by changing up the formulas and adding in symbols they need to connect to a particular learning unit or standard?

To ensure academic content goals are being met, educators must find a way to make strong connections.

What is Spot It!?

Spot It![TM] is a fast-paced matching game where one depends on laser-focus and a trained eye. However, critical thinking is at work in the game as well because players must determine what symbols, which may or may not look identical, are considered a match. After all, all cards have one, and only one, match. Each game of Spot It![TM] is made up of a deck of 55 cards with 8 symbols on each. The goal of the game is to be the first person to find the match between the two cards in play. Keep in mind that the nature of the game allows for success, frustration, and lots and lots of good fun.

What are Classroom-Friendly Options?

To make this game classroom-friendly, consider your content standards. In math, you could use patterns, time, measurement, place value, computation, fractions, and so much more. Are you focusing on reading skills? If so, why not make up your own Spot It![TM] game for rhyming words, vocabulary, syllabication, or sight words. Science even lends itself well to this game through the life cycle, solar system, or geology. The possibilities are limitless. All you need is a little bit of creativity mixed with your content standards and the math behind the game. Stay tuned for the math ...

What is the Math Behind Spot It![TM]?

For a game of Spot It![TM] you would need to create 55 cards, each with 8 different objects on them, such that any two cards have exactly one match. Geometrically speaking, this would be 55 lines, each with 8 points, where any two lines intersect exactly once. Can you try to draw them? They do not have to be straight, of course. There is an article in Math Horizons describing this method.

Considering the problem algebraically, we need to come up with 55 sets of 8 elements each, with the property that any two sets have exactly one element in common. For example, consider the sets:

A = {1,2,3,4,5,6,7,8}

B = {8,9,10,11,12,13,14,15}

C = {1,9,16,17,18,19,20,21}

Notice that:

A [intersection] B = {8}

A [intersection] C = {1}

B [intersection] C = {9}

What could D be? Now, you have to find 51 more! This would get a bit tricky.

Here we present a way to construct sets that have the property that any two have an intersection with exactly one element. The number of 'cards', 'objects', and 'objects' on each 'card' will depend on your choice of a prime number, p. The following construction will result in a total of [p.sup.2] + p + 1 cards and objects, with p + 1 objects on each card. We will construct three different types of sets based on the prime number p that you have chosen. The following paragraph contains the mathematics for defining the sets. An example follows this.

Before we begin, we must define congruence modulo p. We will say that x and y are congruent modulo p, written x [congruent to] y (mod p) if x and y have the same remainder when x is divided by p. For example, 7 [congruent to] 2 (mod 5) and 1 [congruent to] 13 (mod 3) Define sets, [R.sub.a,b] consisting of ordered pairs and a singleton defined by:

[R.sub.a,b] = {[infinity]} [union] {(x,y): x [member of] {0,1,2, ..., p - 1} y [congruent to] ax + h (mod p)}

where a and b cycle through all the numbers from 0 to p - 1. There will be p x p = [p.sup.2] of these sets. Next, define sets [S.sub.c], consisting of ordered pairs and a singleton defined by:

[S.sub.c] = {[infinity]} [union] {(c,d):d [member of] {0,1,2, ..., p - 1}}

where c goes from 0 to [p.sub.-1], so there are p of these types of sets. Lastly, define a set:

T = {[infinity], 0,1,2, ... ,p - 1}.

Now we are ready to make our cards. Assign each ordered pair and singleton an object. Here are the [3.sup.3] + 3 + 1 = 13 sets (cards) for p = 3. Creating a chart for the 13 objects can simplify things. I have filled in a chart with an example for a shape Spot It![TM] game. Your cards are labeled with the set names, and your objects are placed, in any order, on their respective cards.

[R.sub.0,0 = {0,(0,0),(1,0),(2,0)}

[R.sub.0,l] = {0,(0,1),(1,1),(2,1)}

[R.sub.0,2] = {0,(0,2),(1,2),(2,2)}

[R.sub.1,0] = {1,(0,0),(1,1),(2,2)}

[R.sub.1,1] = {l,(0,l),(l,2),(2,0)}

[R.sub.1,2] = {1,(0,2),(l,0),(2,l)}

R.sub.2,0] = {2,(0,0),(1,2),(2,1)}

[R.sub.2,1] = {2,(0,1),(1,0),(2,2)}

[R.sub.2,2] = {2,(0,2), (1,1), (2,0)}

[S.sub.0] = {[infinity], (0,0),(0,1),(0,2)}

[S.sub.1] = {[infinity], (1,0),(1,1),(1,2)}

[S.sub.2] = {[infinity], (2,0), (2,1), (2,2)}

T = {[infinity], 0,1,2}

The objects do not have to be identical. Notice that the circle appears on four cards. We could have used pictures (a frisbee, a plate, a swimming pool, and a pizza) to represent the four different circles. How about four objects that all have the same first letter sound? How about four different ways to make the same sum?
c     0     1      2

     1+4   1+5    1+6
0    2+3   2+4    2+5
     3+2   3+3    3+4
     4+1   4+2    5+2

     1+7   1+8    2+8
1    2+6   2+7    3+7
     3+5   3+6    4+6
     4+4   4+5    5+5

     2+9   10+2   10+3
2    3+8   9+3    7+6
     4+7   4+8    8+5
     5+6   6+6    4+9

[infinity]   0      1      2

10+4         10+5   10+6   7+10
7+7          8+7    9+7    9+8
2+12         9+6    8+8    11+6
8+6          4+11   12+4   15+2


Students can easily participate in the making of the cards by filling out the table themselves. For example, with first letter sounds they can draw or cut out four objects that begin with their assigned letter. This gives the entire class the opportunity to engage in their own learning. Comprehension and understanding can then be facilitated both in the creation and the playing of the game.

References

Albright. Brian, "The Mathematics of Spot It![TM]" Presented at the April 17, 2015 MAA section meeting at Wayne State College.

Cicchino, M. I. (2015). Using game-based learning to foster critical thinking in student discourse. Interdisciplinary Journal of Problem-Based Learning 9(2), 57-74. doi: dx.doi.org/10/7771/1541-5015.1481

Hsieh, Y.H., Lin, Y.C., & Hou, H.T. (2015). Exploring elementary-school students' engagement patterns in a game-based learning environment. Educational Technology & Society 18(2), 336-348. doi:10.7771/1541-5015.1481

Gina L. Bittner

Peru State College

Laura McCauley

Peru State College
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Author:Bittner, Gina L.; McCauley, Laura
Publication:Education
Geographic Code:1USA
Date:Mar 22, 2018
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