Mathematics 9th Grade
LEARNING UNIT
Extracting information
from our environment:
analysis of tables and
graphs
S/K
LEARNING OBJECT
Reading graphs that describe situations in our
environment
SCO: Identify variables represented by the axes in
measure, expense, consumption and comparison
graphs.
 SKILL 1: Identify the variable represented by the
x-axis.
 SKILL 2: Identify the variable represented by the
y-axis.
SCO: Deduct the meaning of origin in measure,
expense, consumption and comparison graphs.
 SKILL 3: Determine the meaning of zero on the
x-axis for the situation.
 SKILL 4: Determine the meaning of zero on the
y-axis for the situation.
 SKILL 5: Determine the meaning of coordinate
origin for the situation.
SCO: Deduct the meaning of unit on each axis in
measure, expense, consumption and comparison
graphs.
 SKILL 6: Determine what a unit on the x-axis
represents.
 SKILL 7: Determine what a unit on the y-axis
represents.
SCO: Determine the relationship between variables.
 SKILL 8: Determine the value of each variable
with respect to the other.
 SKILL 9: Determine whether or not a given point
belongs to the graph.
Language
Socio cultural context
of the LO
Curricular axis
English
Colombia
Variational thinking and algebraic and analytical
Standard
competencies
Background
knowledge
systems.
Identify relationships between properties of graphs and
properties of algebraic equations.
Real line, ordered pair coordinates, Cartesian plane,
units of measurement.
Basic learning
Rights
Describe characteristics of the relationship between two
variables based on a graph.
English Review topic
Vocabulary box
Type 3 conditional
Bill: A request for payment of money owed, or the
piece of paper on which it is written.
Retrieved from:
http://dictionary.cambridge.org/us/dictionary/english/b
ill
Charge: To ask an amount of money for something,
especially a service or activity.
Retrieved from:
http://dictionary.cambridge.org/us/dictionary/english/c
harge
Expenditure: An amount of money, time, or effort
that is spent. Retrieved from:
http://dictionary.cambridge.org/us/dictionary/english/e
xpenditure
NAME:
_________________________________________________
GRADE:
________________________________________________
Objectives




To recognize variables representing date on each axis of Cartesian
coordinates.
To extract from the graph the meaning of Cartesian coordinate
origin.
To determine the meaning of unit based on the axes of Cartesian
coordinates.
To establish a relationship between variables in order to find the
value of one variable based on the other.
Introduction
What are the benefits of understanding consumption graphs on the
energy bill?
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________________________________________________________
_________
Activity 1. Cartesian coordinates and variables in real contexts.
Introduction
When checking the energy bill, Pablo noticed how consumption bars
increased throughout the year. He worried because he thought that, if
consumption continued increasing at the same rate, it could generate a
very high expense in the future.
Pablo considered that, in order to solve the problem, he should
understand first the meaning of each value and unit in the graph and
the relationship between energy consumption and charges.
Variable of the graph
The graph is a Cartesian plane where each axis (𝑥 and 𝑦) are related to
a variable. In the case of the energy bill, there is a time variable on the
𝑥-axis and an energy consumption variable on the 𝑦-axis.
Units of measurement of variables
A variable represents any magnitude and, therefore, it may have
different units of measurement. For example, the time magnitude may
have the following units of measurement:







Seconds
Hours
Days
Months
Years
Centuries
Lustrums
In the case of Pablo’s energy bill, the following magnitudes and units of
measurement are identified:


The variable on the 𝑥-axis represents time measured in months.
The variable on the 𝑦-axis represents energy consumption
measured in watts per hour (kwh).
Learning activity
Solve items 1, 2, 3 and 4 based on Pablo’s energy bill.
1) At
a)
b)
c)
d)
point P (3, 70), the time variable is:
𝑦=3
𝑦 = 70
𝑥=3
𝑥 = 70
2) State which relationship does not correspond to Pablo’s
consumption graph.
a. In the fourth month, consumption of 73.33 kwh was
charged.
b. In the ninth month, consumption of 90 kwh was charged.
c. In the first month, consumption of 60 kwh was charged.
d. In the last month of the year, consumption of 100 kwh was
charged.
3) In the ______ month, 80 watts per hour were consumed.
third
sixth
fifth
4) If the energy company wants to adjust the basic rate to 50 kwh,
the coordinates of the first bar in the consumption graph would be
located at:
a. (0, 50)
b. (0, 0)
c. (50, 0)
d. (50, 50)
Summary
Homework
1) Identify the variable related to the x-axis and the variable related
to the y-axis in each of the following situations:
a. A vehicle travels from Bogotá to
changes speed depending on how long
b. The Rodriguez want to control
expenditure. For this, they will keep
expenses during a year.
Choachí. The driver
the travel takes.
the family basket
a monthly record of
2) Pablo observes the consumption graph in the water bill, which
summarizes the consumption in the first six months.
Remember that water consumption is measured in m3.
a. Identify variables of the situation.
b. What is the basic rate and what are its coordinates in the
graph?
c. What was the consumption in the fourth month?
Evaluation
Test your knowledge
1) The units of measurement cm3, liter, m3 and milliliters correspond
to the _______ variable.
time
temperature
volume
length
2) Coordinates are located in the Cartesian plane in the form ______.
(𝑥, 𝑦)
(𝑦, 𝑥)
(𝑥, 𝑥)
(𝑦, 𝑦)
3) In a water consumption graph, the coordinates
correspond to:
a. Maximum water consumption.
b. Minimum water consumption.
c. Total water consumption.
d. Consumption of 0 m3 in the eighth month.
(0,
800)
4) Decide whether the following statements are true (T) or false (F).
a. If both variables in a given situation are zero, the coordinate
is located at the point (0, 1). (F)___ or (T)___
b. It is possible to identify a coordinate in the graph knowing
one of the two variables. (F)___ or (T)___
5) Based on the following graph, identify with "X" the coordinates
matching the description.
Description
In the third month, 1875 m3 were
consumed.
2250 m3 were consumed in the
sixth month.
Minimum water consumption is
1500 m3
Coordinate
(1875, 3) (_)
(3, 1875) (_)
(6, 2250) (_)
(2250, 6) (_)
(0, 1500) (_)
(1500, 0) (_)
Glossary
Cartesian plane: Composed of two perpendicular number lines that
cross at a point called origin or coordinate (0, 0). The horizontal line is
referred to as x and the vertical as y.
Variable: Symbolic expression representing what is subject to some
change.
Vocabulary box
Bill: A request for payment of money owed, or the piece of paper on
which it is written.
Retrieved from:
http://dictionary.cambridge.org/us/dictionary/english/bill
Charge: To ask an amount of money for something, especially a service
or activity.
Retrieved from:
http://dictionary.cambridge.org/us/dictionary/english/charge
Expenditure: An amount of money, time, or effort that is spent.
Retrieved from:
http://dictionary.cambridge.org/us/dictionary/english/expenditure
Bibliography
El Plano Cartesiano, Unidad 4: Plano cartesiano, relaciones y funciones.
Retrieved on May 14, 2016 from:
https://ensmafisica2011.wikispaces.com/file/view/plano+cartesiano.PDF
Dolores. (2006). Lectura e interpretación de gráficas socialmente
compartidas, Revista latinoamericana de investigación en matemática
educativa. Retrieved on May 13, 2016 from:
http://www.scielo.org.mx/scielo.php?pid=S166524362007000100004&s
cript=sci_arttext
Iturbe. (2014). Funciones. Interpretación de gráficos. Retrieved on May
13, 2016 from:
http://unrn.edu.ar/blogs/RRP-Roca/files/2014/04/TP-FuncionesInterpretacion.pdf