This document provides an overview of a game called "Mayan Mix-Up" that teaches students about geometric representation of functions. The game involves two players each creating a reference map with the locations of four Mayan sites marked by ordered pairs. Players take turns attempting to locate each other's sites, with the goal of being the first to excavate all four sites. Examples are provided of possible site placements and gameplay. The document discusses how ordered pairs are used to specify points on a graph and represent relationships between variables. It includes exploration activities where students practice solving equations and identifying points on a graph.

1. Mark Anthony G. Arrieta BSEd – Math – 4 Math 116A
Mr. Allen C. Barbaso Presentation 2
CHAPTER 3 Functional Relationships
3.3 Geometric Representation
Introduction:
 A student will be asked to lead a prayer.
 Recall the previous topic being discussed by asking a student.
 Introduce the purpose of studying the lesson.
 Ask the students about their idea on the new topic being presented.
Purpose:
1.) Introduce graphs as a method of communicating information geometrically.
2.) Develop the ability to interpret graphs that display relationships between two quantities.
3.) Develop a geometric representation of functions.
Discussion:
 Mayan Mix-Up:
Background: Two archaeologists, Dr. Art Fact and Dr. Barry Treasure, each have acquired
writings describing the location of an ancient Mayan city. Each archaeologist is aware of the
other’s planned search for Mayan treasures. Both Art and Barry have planted spies among
the persons working for the other archaeologist. Each plans to search for the other’s city first,
delaying the excavation of his own site to avoid having the other get both treasures first.
Each man hopes the other will run out of funds, get tired, and leave for home.
Rules:
 Each player begins with a Reference Map (Figure 1) of his or her city by recording the
location of four sites as follows:
The Site of Worship intersects 4 consecutive vertices on the Reference Map,
horizontally, vertically, or diagonally.
The Site of Ancient Secrets intersects 3 consecutive vertices on the Reference Map,
horizontally, vertically, or diagonally.
The Site of Mathematical Writings, each intersecting 2 consecutive vertices on the
Reference Map, horizontally, vertically, or diagonally.
 Vertices are labeled by recording the number of horizontal units from the origin followed
by the number of vertical units. The origin (0, 0) is at the lower left corner, the vertex (10,
10) is at the upper right corner. to mark the vertex (3, 7), we move 3 units to the right
from (0, 0) followed by 7 units up.
 Player 1 names 7 locations where s/he plans to start digging by 7 vertices on the Search
Plan (Figure 1). Player 1 announces the 7 locations by naming the ordered pair
corresponding to the vertices selected.
 Player 2 marks each of Player 1’s locations on the appropriate vertices his/her Reference
Map. After the 7 locations are named, Player 2 announces how many sites were located
and how many times each site was selected, saying “You located the Site of Worship
once” or “You located the Site of Ancient Secrets twice.” Player 2 does not name the
vertex or vertices of the sites discovered by Player 1.

2.  When all the vertices of a given site have been located by a player, the site is considered
excavated and the other player loses location attempts: 3 attempts are lost when the Site
of Worship has been located; 2 attempts when the Site of Ancient Secrets is located, and
1 attempt when each Site of Mathematical Writings is located. For example, if Player 1
has located all 3 vertices of Player 2’s Site of Ancient Secrets, Player 2 gets only 5 rather
than 7 location probes in the next round.
 After Player 1 completes 7 location probes, Player 2 has 7 attempts to locate Player 1’s
sites, unless Player 2 has excavated one or some of Player 1 sites. The game continues
until one player has located all of the opponent’s sites.
Investigation:
1.) Begin the game by creating a Reference Map for your city. Don’t show this to anyone else.
Record the vertices where each site is located.
Site of Worship:
Site of Ancient Secrets:
Math Site 1: Math Site 2:
Play the game. Keep track of all attempts and successful probes in each round, using the Search
Plan and Reference Map. Record vertices in boxes.
Figure 1
Reference Map

3. Search Plan
10
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
Discussion:
 In the Mayan Mix-Up game, a vertex indicating the location of a site is given by supplying
two pieces of information: a horizontal component and a vertical component. Given these
two components, a point on the graph is specified.
 An ordered pair has the form (a, b), where a and b are numbers in which the first number,
a, is called the first component, and the second number, b, is called the second component.
The notation (a, b) implies that order is important. This means that (a, b) and (b, a) are
different unless a = b.
 We have a correspondence between an ordered pair of numbers and a point in the plane. This
is a powerful idea since it allows the application of geometry (a graph) to algebra and vice
versa. The idea of creating a correspondence between pairs of numbers and points in the
plane is credited to the French mathematician Rene Descartes in 1637.
Points to Ponder:
 Point in the plane are indicated by choosing a starting point, called the origin.
 The origin is the point that corresponds to the ordered pair (0, 0).
 We identify a point by listing how far we must travel horizontally and then vertically from
the origin to reach the point.
 For a given ordered pair (a, b):
o The first component, a, indicates a horizontal position of a point in the plane.
o The second component, b, indicates a vertical position of a point in the plane.
 The input axis is the horizontal number line in the plane.
 The output axis is the vertical number line in the plane.
 Consider a possible placement of sites on the Reference Map (Figure 2). The vertices of each
site are identified by ordered pairs, as follows:
 Site of Worship: (3, 3), (4, 3), (5, 3), (6, 3).
 Site of Ancient Secrets: (2, 6), (3, 7), (4, 8).
 Mathematical Writings Site I: (6, 5), (6, 6).
 Mathematical Writings Site II: (7, 9), (8, 9).

4. Figure 2
Reference Map
Explorations:
1.) Given the Reference Map (Figure 3), identify the locations of each site by recording the
ordered pairs of vertices for each site.
Figure 3
Reference Map
2.) Solve for the variable.
a.) 4x = 28
b.) 4t – 9 = 11
c.) y + 5 = 17
d.) 3x + 5 = 5
Math Site II
Site of Ancient Secrets
Math Site I
Site of Worship
Math Site II
Site of Ancient Secrets
Math Site I
Site of Worship

5. 3.) Given the graph in Figure 4, identify the point on the graph where
a.) Input is zero. Write an ordered pair for each point identified.
b.) Output is zero. Write an ordered pair for each point identified.
Figure 4
Explorations: (Answers)
1.) Given the Reference Map (Figure 3), identify the locations of each site by recording the
ordered pairs of vertices for each site.
Site of Worship: (4, 10), (4, 9), (4, 8), (4, 7)
Site of Ancient Secrets: (7, 6), (8, 6), (9, 6)
Math Site I: (5, 1), (6, 1)
Math Site II: (1, 3), (2, 2)
2.) Solve for the variable. (Answers)
a.) 7
b.) 12
c.) 5
d.) 0
3.) Given the graph in Figure 4, identify the point on the graph where
a.) Input is zero. Write an ordered pair for each point identified.
Answer: (0, 2)
b.) Output is zero. Write an ordered pair for each point identified.
Answer: (5, 0) and (8, 0)

6. Reflection:
Using different types of representation help me become more knowledgeable in
mathematical representation as well as it improves my visual analysis. Using them, it is easy for
us to understand graphical representations and problems that are need to be represented
graphically. As a future math teacher in the future it is very important for me to know how to
represent problems using graphical representation because there are problems that easily be
understood when represented graphically.
Reference:
De Marois, Phil; McGowen, Mercedes and Whitkanack, Darlene (2001). “Mathematical
Investigations”. Liceo de Cayagan University, Main Library. Jason Jordan Publishing.