SUBJECT
GRADE
MATHEMATICS
9th
LEARNING UNIT
A Special Set of Numbers: The
Complex Numbers
TITLE OF LEARNING
IDENTIFICATION OF THE SETS OF RATIONAL AND
IRRATIONAL NUMBERS
CURRICULAR AXIS
STANDARD
COMPETENCIES
Numerical thinking, and numerical systems.
1. To use real numbers in their different representations and in
different contexts.
2. To solve problems and simplify calculations using properties,
relations of the real numbers and operations between them.
3. To produce simple texts with different functions (descriptive,
narrative, argumentative) about personal topics, and topics
related to other subjects.
4. Use plans represented in maps or diagrams to develop my
written pieces.
Identification of the sets of intergers, rational and irrational
numbers.
1. To identify the elements of the set of integer numbers.
2. To classify the natural numbers as the positive extension of
the set of integer numbers.
3. To recognize the properties of the integer numbers.
4. To establish the usual operations of the set of integer
numbers.
5. To interpret the properties of operations on the set of integer
numbers.
6. To identify the elements of the set of the rational numbers.
7. To recognize the different representations of the rational
numbers.
8. To interpret each of the representations of the rational
numbers.
9. To determine the usual operations on the set of the rational
numbers.
10. To characterize the properties of the operations on the set of
the rational numbers.
11. To characterize the irrational numbers as those having a nonperiodic infinite decimal representation.
12. To set the characteristics of the irrational numbers.
13. To recognize the most representative irrational numbers.
14. To locate on the number line the irrational numbers
associated to square roots.
15. To identify the set of real numbers, as the union of the sets
of rational numbers and irrational numbers.
LEARNING OBJECTIVES
SKILLS/ KNOWLEDGE
LEARNING FLOW
16. To determine to which numerical sets belong a certain real
number.
17. To locate real numbers on the number line.
18. To recognize the properties of real numbers with respect to
addition and multiplication.
19. To add, subtract, multiply and divide real numbers.
20. To produce simple argumentative texts about topics related
to math.
21.
To use diagrams to exemplify written information.
Introduction: The Numbers and Their Uses
Objetives
Activities
Activity
Activity
Activity
Activity
1:
2:
3:
4:
The
The
The
The
Integer Numbers
Rational Numbers
Irrational Numbers
Real Numbers
Abstract
Homework
Evaluation
ASSESSMENT
GUIDELINE
Glossary
By working on this LO, the student will be better able to identify,
classify and operate the elements of the set of real numbers.
The student will be able to develop problems related to the set of
integer numbers and its subsets.
Stage
Learning flow
Teaching/Learning Activities
Recommended
Resources
Introduction
Introduction
Present an animated resource in which Animation Resource
the uses of the numbers in different
contexts are mentioned.
Development
The teacher
Activity 1: The Integer Numbers
The teacher presents
presents the
topic
Activity 1
the topic
Show a video that presents a card game
and some conceptualization questions to
complete a diagram of content and a
conceptual map with the basic structure
of the set of integers.
Present a practice activity to practice the
use of the Conditional 0 while
investigating the properties and identify
them from arithmetic polynomials and
equalities.
Conceptualize on the set of integers and
the hierarchy of operations. There are
some proposed exercises, a recreational
activity and a section of problems.
Activity 2
Activity 2: The Rational Numbers
Present
an
interactive
resource
introducing the conceptualization of the
rational numbers, the representation on
the number line and operations.
Set an inquiry activity about the rational
numbers.
Propose a filling out activity of a diagram
of content of subsets, and a concept map
with its structure.
Pose the practice activity in which the
student must determine the property
used, complete some sentences that are
true
about
the
rational
numbers’
properties using the Conditional 0, and
resolve some arithmetic polynomials.
Activity 3
Activity 3: The Irrational Numbers
Present an introductory animation and a
table
with
examples
for
its
characterization. From there, an activity
with the same structure starts.
Propose an inquiry activity around the
following questions:
What are the most representative
irrational numbers?
What is the usefulness of irrational
numbers?
How are they graphed on the number
line?
Then, present the most representative
numbers and set the activity to
corroborate with the calculator. Also,
suggest the student to watch the
explanatory
videos
about
irrational
numbers:
Numbers Pi and e
 [Derivando].
(2015,
November
th
18 ). ¿Qué es el numero e? [Video
File].
Retrieved
from:
https://www.youtube.com/watch?v
=Z5czpA-fyMU

The Golden Mean:
 [Pato Donald Dibujos Animados].
(2014, December, 29th). El pato
Donald Dibujos Animados y la
proporción aurea en español.
[Video
File].
Retrieved
from
https://www.youtube.com/watch?v
=q8P5FEtz5ms
Then make the explanation about
drawing numbers on a number line and
work on the construction activity.
Activity 4
Activity 4: The Real Numbers
Present an introductory animation, along
with a conceptual map of the general
structure of real numbers.
Indicate the elements about their
representation on the number line and
propose a matching activity for the
students to reinforce the identification of
each subset.
Also, present the diagram of content for
the student to complete.
Propose the student an inquiry about the
properties of real numbers from the web:

Lección
7:
http://www.conevyt.org.mx/colabo
racion/colabora/objetivos/libros_pd
f/sma3_u1lecc7.pdf
Additionally, propose a practice activity to
complete the properties in a box.
Then, explain the development of
problems in context using real numbers,
using usual operations. Also, give a few
tips to solve problems from the
postulates of George Polya. Propose two
problems for the student to analyze
them, and other two to solve them.
Abstract
Look annexed in this file.
Interactive Resource
Printable Material
Homework
Propose the following task:
Propose the following
1. In groups of 2 or 3 students, create, task:
as they like, a building proposal (may
be
buildings,
faces,
structures,
landscapes) with segments of different
sizes from a pattern, but the measures
should be calculated in different
numerical sets (integers, rational and
irrational).
2. Individually,
propose
a
problem
activity
related
to
income
and
expenses in their family circle. They
must consider the use of the usual
operations.
Evaluation
Glossary
Annexed 1.
Pose an assessment with three types of
questions: the first, match; the second,
true-false; and the last, a section of
multiple-choice problems with a single
answer.
Define the following concepts:
Element of a set
Neutral Element
Inverse Element
Dense Set
Commeasurable
Incommensurable
Interactive Resource
Printable Material
Printable Material