1. TeachingTeaching
ObjectivesObjectives
Unit: GeometryUnit: Geometry
Perseverance and flexibility in the search of solutions to the
problems.
Verbal expression of the procedure continued in the resolution
of problems.
Interpretation of messages that contain information about
quantities and measures or on elements or spatial relations.
The geometry departs integral of the artistic expression of the
humanity on having offered means to describe and to include
the world that surrounds us and to estimate the beauty of the
structures that it has created.
To describe, to analyze properties and relations,
and in classifying and reasoning on forms and
geometric structures.
To construct, to draw, to measure or to classify in
agreement with chosen criteria.
To deepen the competence in the knowledge and
the interaction with the physical world.
To cultivate the sensibility and the creativity, the
divergent thought, the autonomy and the aesthetic
passion.
Area: MathematicsArea: Mathematics Lessons: 4Lessons: 4 Ed. Level: 1st ESOEd. Level: 1st ESO
Final TaskFinal Task
Employment of IT tools to construct, to simulate
and to investigate relations between geometric
elements.
Basic elements of the geometry of the plane: lines,
segments, angles. Utilization of the terminology
adapted to describe accurately situations, forms,
properties and configurations of the physical world.
AssessmentAssessment
CriteriaCriteria
Description of the elementary figures: triangles, quadrilateral, regular
polygons. Measure and angle calculation in flat figures.
To use strategies and simple skills of resolution of problems, such as the
simplest analysis of the terms of reference or the resolution of a problem;
to verify the obtained solution.
To recognize and to describe the elements and properties typical of the
flat figures and her geometric configurations by means of illustrations, of
taken real-life examples, or in the resolution of geometric problems.
Importance the both oral and written expression of the realized
processes and of the consecutive reasonings, since they help to
formalize the thought.
To express, using the mathematical language adapted to their level, the
procedure that has followed in the resolution of a problem. Verbal
expression of the procedure continued in the resolution of problems and
interpretation of messages that contain information about elements or
spatial relations.
Confidence in the own aptitudes to confront problems, to understand the
mathematical relations and to take decisions from them.
The geometry offered means to describe and to include the world that
surrounds us and to estimate the beauty of the structures that it has
created.
Perseverance and flexibility in the search of solutions to the problems.
MaterialsMaterials
ResourcesResources
KeyKey
CompetencesCompetences
Verbal expression of the procedure followed in the resolution of
problems. It consolidates the acquisition of skills involved in the
competence of learning to learn such as the autonomy, the
perseverance, the critical reflection and the skill to communicate
with efficiency the results of the own work.
Interpretation of messages that contain information about
quantities and measures or on elements or spatial relations.
Confidence in the own aptitudes to confront problems, to
understand the mathematical relations and to take decisions from
them.
Perseverance and flexibility in the search of solutions to the
problems. It own process of resolution of problem help from
special form to promote the autonomy and personal initiative
because they are in use for planning strategies, for assuming
challenges and help to coexist with the uncertainty controlling at
the same time the processes of capture of decisions.
Utilization of technological tools to facilitate the calculations of
numerical, algebraic or statistical type, the functional
representations and the comprehension of geometric properties.
Autonomy and personal initiative: developed one's own criteria
and social skills.
Learning to learn: refect on what has been learn and self evaluate
progress.
IT tools to construct, to simulate and to investigate relations
between geometric elements. AUTOCAD program.
To work with the streets map of Valencia city and to study the
configuration of its streets.
CommunicationCommunication
CultureCulture
eses
The learning of the geometry must offer
continuous opportunities to construct, to draw, to
model, to measure or to classify in agreement with
freely chosen criteria. Its study offers excellent
opportunities to establish relations with other
areas, as the nature or the world of the art.
StructuresStructuresVocabularyVocabulary
Language for interactionLanguage for interaction
Formal texts. Using the mathematical language.
Prepositions of place.
Phrasal verbs.
Modals.
The own mathematical language is a vehicle of
communication of ideas that stands out for the
precision in his terms.
To express, using the mathematical language
adapted to their level, the procedure that has
followed in the resolution of a problem.
StudentStudent
LearningLearning
OutcomesOutcomes
CognitionCognition
ContentContent
To identify and to describe the elements and
properties typical of the flat figures and her
geometric configurations by means of
illustrations, of taken real-life examples, or in the
resolution of geometric problems.
To bring together information and to express it,
using the mathematical language adapted to their
level, the procedure that has followed in the
resolution of a problem.
Utilization of technological tools to facilitate the
comprehension of the geometric properties and to
realize a work of group.
Language for the topicLanguage for the topic
To guess different gassings given understanding
the vocabulary appeared in the unit.
To write familiar objects useful to survive
attending the correct spelling.
To make a presentation using adjectives.
2. Unit:Unit: GeometryGeometry
Assessment/Assessment/
ReflectionReflection
Want to know/Want to know/
Reinforcement/Reinforcement/
ExtensionExtension
MainMain
ActivitiesActivities
Introduction/
RevisionRevision
Warm up
Activities
Read the text and complete the exercises.
Understand the main points of a conversation or short presentation in clear standard speech on
matters regularly encountered.
Inside the plane we distinguish two fundamental elements the point and the straight line. It
defines point and straight line.
The straight lines, points, symmetries, angles and other geometric elements are the base of the
game of the billiards. It investigates this game.
Utilization of technological tools to facilitate the comprehension of the geometric properties
and to realize a work of group.
Divides a circle in 8 equal parts and verifies with the carrier the measure of each one of the
angles. Repeats the exercise dividing the circle in several parts and verifies in every case the
measure of the extent of the angles.
Indicate on the figure if these angles are sharp, straight, obtuse or flat.
To work in pairs with the streets map of Valencia city and to study the configuration of its
streets (lines, segments and angles).
Bisectrix of an angle.
Explain the steps that you will have to follow to add two or more angles analytical and
graphically.
Explain the steps that you will have to follow to reduce two or more angles analytical and
graphically.
Practice doing the exercises.
Geometric elements
System Sexagesimal and Operations with angles
Geometric constructions
Learning OutcomesLearning Outcomes
Euclides, great mathematician
of the history, defined: the point
and the straight line.
Utilization of the
terminology adapted
to describe forms.
Straight lines and angles. The plane.
Points and straight lines.
Straight line and segment.
Properties of the straight line.
Parallelism.
To apply the surface calculation
of lines, segments and angles to
real-life situations.
CommunicationCommunication CognitionCognition CultureCultureContentContent
The billiards are a game in which they control many of the elements of the flat geometry (points,
straight lines, angles, symmetries ...). Observe the video of since the correct path can be
calculated to give to the red ball bouncing before in one or two bands.
http://actividadesyrecursos.jimdo.com/actividades/matem%C3%A1ticas/
Pupil's book.
Materials/Materials/
ResourcesResources
Lesson: 1. Basic elements: lines, segments and angles.Lesson: 1. Basic elements: lines, segments and angles.
Material creat i adaptat de diversos autors pel Servici d’Ensenyaments en Valencià - Conselleria d’Educació. (2010)
Unit:Unit: GeometryGeometry Lesson:Lesson: 2. Flat elementary figures: triangles, quadrilateral and regular polygons.2. Flat elementary figures: triangles, quadrilateral and regular polygons.
3. Assessment/Assessment/
ReflectionReflection
Want to know/Want to know/
Reinforcement/Reinforcement/
ExtensionExtension
MainMain
ActivitiesActivities
Introduction/
RevisionRevision
Warm up
Activities
ANSWERS THESE QUESTIONS
What is a polygonal line? How is it called the surface contained by a polygonal closed line?
When do we say that a polygon is concave?
Draw a polygonal opened line, a concave polygon and a convex polygon.
TANGRAM OF FIVE PIECES
With the pieces that appear in the scene you tries to construct other figures.
Investigate: What another tangram is based on the division of a square? How many pieces it has?
Individual work.
Draw a base and the corresponding height in each of the following triangles.
Select classification according to the angles and according to the sides.
In the triangle of the figure, draw a mediatriz, a bisectrix, a median and a height. (Each of
the straight lines draws of a different color)
To work in pairs with the streets map of Valencia city and to study the configuration of its
streets (triangles, quadrilateral and regular polygons).
There has come the moment to verify everything what you have learned. Realize the following
exercises without the computer. As soon as you them have the teacher made he(she) will say to
you if you can verify them with the computer.
Draw a triangle which sides measure 6, 7 and 8 centimeters. How is it the triangle according to
his sides and according to his angles? Plan all the straight lines and notable points. Where are
notable points placed?
Learning OutcomesLearning Outcomes
Tangram of five pieces.Utilization of the
terminology adapted to
describe forms.
Represent and to identify the geometric elements
that they characterize to different polygons.
Construct triangles.
Recognize and to draw different types of
quadrilateral.
Calculate perimeters and areas of polygons.
To apply the surface calculation
of polygons to real-life
situations.
CommunicationCommunication CognitionCognition CultureCultureContentContent
Tangram of five pieces.
http://actividadesyrecursos.jimdo.com/actividades/matem%C3%A1ticas/
Pupil's book.
Materials/Materials/
ResourcesResources
Material creat i adaptat de diversos autors pel Servici d’Ensenyaments en Valencià - Conselleria d’Educació. (2010)
Unit:Unit: GeometryGeometry Lesson: 3. The circumference and the circle.Lesson: 3. The circumference and the circle.
4. Assessment/Assessment/
ReflectionReflection
Want to know/Want to know/
Reinforcement/Reinforcement/
ExtensionExtension
MainMain
ActivitiesActivities
Introduction/
RevisionRevision
Warm up
Activities
Look in the dictionary for the definition of circumference.
With your compass a circumference draws 2 cm of radio. Verifie that the distance of the center
to any point is equal to 2 cm.
Investigate:
Construct a circle of carton and measures the distance of the center to the edge. Coil a chunk of cord about
the contour of the circle. Unroll it later and measure it also. Divide the second quantity between the first one
and annotates the result. You can repeat the experiment with circles of different sizes.
What can you say of the results that are obtained?
In pairs, to elaborate a table with the definitions of the different elements that we can distinguish
in a circumference.
To draw a circumference and represents on it a radius, a diameter, an arch, a string and a
semicircumference.
To work in pairs with the streets map of Valencia city and to study the configuration of its streets
(The circumference and the circle).
Calculate the distance between both centers. Compare this value with the sum of both radiuses.
Draw two tangent foreign circumferences.
Draw two foreign circumferences.
Draw two concentric circumferences.
Indicate which of the points are to equal distance of the center, which think to a distance of the major
center that the radius, which are distantly minor that the radius and which are to a distance equivalent to
the double of the radius.
Learning OutcomesLearning Outcomes
The world of the
art.
Utilization of the terminology
adapted to describe forms.
The circumference. Elements of the
circumference.
Point and circumference.
Straight line and circumference.
Two circumferences.
To identify the different present
elements in the circumference and the
circle.
To know the relative positions of
points, straight lines and
circumferences.
CommunicationCommunication CognitionCognition CultureCultureContentContent
Construct a circle of carton and measures the distance of the center to the edge.
http://actividadesyrecursos.jimdo.com/actividades/matem%C3%A1ticas/
Pupil's book.
Materials/Materials/
ResourcesResources
Material creat i adaptat de diversos autors pel Servici d’Ensenyaments en Valencià - Conselleria d’Educació. (2010)
Unit:Unit: GeometryGeometry
Learning OutcomesLearning Outcomes
Lesson:Lesson: 4. Circle and circular figures.4. Circle and circular figures.
5. Assessment/Assessment/
ReflectionReflection
Want to know/Want to know/
Reinforcement/Reinforcement/
ExtensionExtension
MainMain
ActivitiesActivities
Introduction/
RevisionRevision
Warm up
Activities
To know the picture: "Los Relojes Blandos" by Salvador Dali.
To look for painters who draw circles or circular figures.
To read the text and completes the definition: Circle and circular figures.
How do you calculate the length of the circumference?
Areas in the circle.
To work in pairs with the streets map of Valencia city and to study the configuration of its
streets (Circle and circular figures).
Finally, to study all the geometry figures of the streets map of Valencia city.
Now, To practise solving different exercises:
The Circumference and its Elements.
Relative positions of Points, Straight lines and Circumferences.
Angles in the Circumference.
Lengths and Areas of the Circular Figures.
The circumference and its elements.
The circle and its elements.
Lengths and areas.
Angles in the circumference.
The world of the art.
To know the picture:
"Los Relojes Blandos"
Utilization of the terminology
adapted to describe forms.
The circle.
Circular figures.
Lengths in the circumference.
Areas in the circle.
To know the properties of the angles
constructed in the circumference.
To measure lengths and areas of
circular figures.
CommunicationCommunication CognitionCognition CultureCultureContentContent
http://actividadesyrecursos.jimdo.com/actividades/matem%C3%A1ticas/
To know the picture: "Los Relojes Blandos" by Salvador Dali.
Pupil's book.
Materials/Materials/
ResourcesResources
Material creat i adaptat de diversos autors pel Servici d’Ensenyaments en Valencià - Conselleria d’Educació. (2010)
