UNIDAD DIDÁCTICA AICLE
Teacher: M. Elena Gómez Martín Course/Level: 3º ESO
Subject: Maths DU Title: Maths in your feet. Geometric transformations
Observations
This small unit will be developed in 5 sessions. During them, students will be able to recognize transformation in dance and they will also be able to write and draw transformation in a coordinate plane. They will be moved through a mathematical dance of translation, rotation and reflection. Students will learn to identify congruent figures in order to describe the properties of slides, flip and turns for two-dimensional objects through the use of dance patterns. They will watch some videos and discuss the different movements and steps related to transformation. They will complete related vocabulary exercises and practice and solve some transformation problems. Lastly they will compose, write and perform their own choreography, record it and present it to the rest of the class to be assessed.
In this unit, we can talk about:
Dance is used to demonstrate cultural or ethnic difference, cultural ownership and authenticity of dance idioms, dance as a display of national identity, dance in marketing and tourism, the effects of stylistic hybridity on individual or group identities, how dance practices link to social class, dance as a means of building ideological consensus, and dance as a medium of resistance and social change.
1. Learning outcomes / Evaluation criteria
• Describing transformations quantitatively and recognizing them around us.
• Performing and writing transformation from descriptions and creating their own ones.
• Understanding the importance of symmetry and the transformation of designs through rotation, reflection, and translation. Apart from understanding congruence in tema of rigid motions.
• Developing two different but related skills. Firstly, recognizing and describing symmetries of designs by finding centers of rotation and axes of symmetry. Secondly, making their own design with one or more specified symmetries.
• Performing reflections, translations, and rotations to create geometric - dance patterns to be used in a choreography project. All this supposed, they will have to know the most important movements in a plane and their beauty and use in real life
2. Subject Content
Geometry : Movements in the plane
• Definition of vector. Coordinates
• Definitivos of Transformations
• Types of transformations
⁃ Symmetry
⁃ Transformations
⁃ Translation
⁃ Rotations
• How to perform Transformations
• Connections : dance
3. Language Content / Communication
Vocabulary
Academic Vocabulary:
Nouns: Vector, Transformation, symmetry, rotation, translation, reflection, axis, orientation, clockwise, counterclockwise/ anticlockwise, angle, right angle degree, line of reflection, mirror line, figure, polygon, shape, congruent figures, sequence, quadrant, coordinate plane, origin, axis of symmetry, choreography, design, performance, Ordered pair, x-coordinate, y- coordinate, parallel, pattern, centre, vertical, horizontal, diagonal line, line, graph, equation, properties.point, line, plane, exercise, solution, problem.
Verbs: Recognize, engage, step, choreograph, create, perform, translate, compose, flip, turn, slide
Prepositions/Adverbs: right, left, in front of, opposite, through, but, so, then, because, due to, that's why
Classroom Vocabulary:
Greatings: Good morning/afternoon, Hi!, How are you? How are you doing? Bye, see you tomorrow, see you later, Have a nice day!
Classroom management : sit down, stand up, listen, be quiet, pay attention, hand out, right, wrong, repeat, now, try again, look, turn to page, look at page, open your book/
notebook, close, work in groups, get into groups , wait a minute, First / then / next / after that / finally
Structures
▪ Routines:
⁃ What can you see in this video?
⁃ Do you know typical dances from all over the world? Is there a typical style for each country? What dance styles do
you know?
⁃ Do you think they have something in common? What about choreography?
⁃ What do you think we are going to learn?
⁃ What do you know about transformation? Does it have something to do with dance?
⁃ Do you see any relation between maths and dance?
⁃ Who can tell me what we did / talked about/ learn last lesson?
⁃ Was it ok/ easy/difficult - Did you find it ok/ easy / difficult?
⁃ Do you understand? ⁃ Do you agree with that?
⁃ Where do we see symmetry around us ?
⁃ What are ways we can describe a sequence of transformations ?
⁃ What are Tessellations? Have you ever seen them?
⁃ When is it possible to.. ? How the shape is transformed? ⁃ What's the symbol for ... ?
⁃ How can geometric figures and their properties be described by careful use of geometric language ?
⁃ How are transformations used in various careers and in the real world?
▪ Grammatical Content:
⁃ Present simple and continuous to describe designs and performances Verbs and prepositions of movement : turn, flip, slide, across, toward, up, down, forward, backward, side to side.
⁃ Comparisons to describe, explain and assess figures, activities and their work
⁃ Going to : to explain their intention, ideas..
⁃ Passive : To talk about transformation ( this is rotated…)
⁃ Zero and first conditional: Logical mathematical arguments
⁃ Expressing opinions : I think that…, The design/performance is like a..., From my point of view…
⁃ Connectors, linkers, giving opinion.. On one hand… on the other hand..., I (don't) agree with you.
▪ Classroom management:
⁃ Fill the gaps
⁃ Let's move on to the next point
⁃ ( Put your ) hands up if you know / can say / can tell me ..
⁃ The next point / question is
⁃ Solve the following problems
⁃ What does this expression mean?
⁃ I think this is a solution. I don't think so. I agree. What's the symbol for ...?
⁃ How do you read this? What's the next step?
Discourse Type
• Dialogue: To develop social interaction and work in groups
• Descriptive: To describe the topic to discuss or the activity they must perform.
• Argument: To express valid logic and, through correct reasoning, try to motivate or convince the class
• Exposition: To Define and analyze different ideas and activities
Language Skills
• Writing; It is expressed clearly, legibly and without spelling errors, showing an effective use of mathematical terminology and notation.
• Reading; Recognize basic grammatical features and vocabulary appropriate involving geometric problems.
• Listening; Show understanding by responding appropriately to questions and requests.
• Speaking: Communicate with peers and teacher demonstrating skills of group interaction and using vocabulary accurately and appropriately
4. Contextual (cultural) elements
Dance is used to demonstrate cultural or ethnic difference, cultural ownership and authenticity of dance idioms, dance as a display of national identity, dance in marketing and tourism, the effects of stylistic hybridity on individual or group identities, how dance practices link to social class, dance as a means of building ideological consensus, and dance as a medium of resistance and social change, and overall the presence and use of maths patterns in dance and culture.
5. Cognitive (thinking) processes
To Know, understand, recognize, apply, analyze, share, create and assess, Thinking skills, creativity, justifying choices, applying new learning in different contexts.
6a. Task/s
• Lesson Introduction
• Understanding Transformations and dance patterns: present a mind map with the different transformations to the class
• Vocabulary
• Small Project : Create a genially presentation in which a Graph Choreography composition with at least 12 steps, a description of a choreography and a video with the choreography performance should be included. Present it to the class.
6b. Activities
▪ ACT. 1: Video + open questions to work in groups to set previous knowledge, introduce the topic and discuss the different movements and steps related to transformation.
▪ ACT. 2: Brainstorming + Video: Names, verbs, steps or movements related to transformation. While they are brainstorming, some terms related are explained for them to know. And at the end, A video will be watched to better understand the terms ( setting the needed vocabulary). Use of
TICS ( Mentimeter )
▪ ACT. 3: Warming-up : Game. stand up, face the teacher and follow the instructions to move and find out the different transformations we are developing by moving our feet and bodies
▪ ACT. 4: Identify the learning outcomes . Explanation
▪ ACT. 5: Jigsaw Investigation : watch a presentation, discuss the main points and make a graphic organizer (Mind map) with the different transformations and the most important elements and characteristics. Present it and explain it to the class. Use of TICS ( Powerpoint and Mentimeter )
▪ ACT. 6: Worksheet I. Directions: Match the vocabulary word on the left with the figures and definitions on the right. Use of TICS. ( Learning app)
▪ ACT. 7: Worksheet II. Filling the gap to see if the concept is got. Look up in a dictionary those words that are not understood. When finished, pass the activity to a partner to get the assessment ( Online dictionary)
▪ ACT. 8: Worksheet III. Writing patterns. compose a choreography
▪ ACT. 9: Worksheet IV. Racing Transformation. Competition game. Draw transformations and name axes and points
7. Methodology
The methodology will be active and participative and enable students to make connections between their own knowledge and experiences, and the new information being taught.
The unit is developed to cover communication, cognition, content and culture. It is designed by scaffolding the content and integrating the four skills. Starting with activities that promote receptive skill to give students the chance to learn faster using them before working on productive ones.
It is based on bloom taxonomy and there are different ways to approach the content so different intelligences are covered, not only mathematical or linguistic ones but also kinesthetic or visual, trying to make all the lessons interactive. Apart from this, the unit is designed taking into account the key competences and that is reflected on all its activities .
Organization and class distribution / timing.
The unit is divided into 5 lessons.
LESSON 1. Introducing the topic. (1 Session of 55 minutes): Working on linguistic and cultural contents
A video to connect them to culture and real life to activate the schemata that let us know what they do know about this subject and how we scaffold the content. (Symmetry, rotation, reflection and translation)
- Task 1. Video ( 10 min)
The first video is related to an African dance where we can see a lot of types of transformations so after watching it, students will be asked some questions to link content and culture and to develop listening and speaking apart from some competences such as communication, social and civic competences.
- Task 2 Brainstorming + video ( 10 min)
The second task is a brainstorming in which students will be asked to tell all the terms they know and have listened related to transformations as well as, important concepts will be explained in a clear and short way for them to understand future activities. They will watch a new video related to practical dance in which they can see and read different transformations related to different steps and movements. In this lesson the activities are quite similar because they have to develop the same skills and competences but set the basis of the concept they need to have clear to be able to develop the rest of lessons
- Task 3. Learning outcomes ( 5 min)
The third task will be an explanation of the learning outcomes so they also have clear the aim and expectations of the unit.
- Task 4. Jigsaw Investigation ( 30 min)
The last task will be in groups. They will be given a presentation with different concepts, explanations and terms related to transformations. A type of transformation will be assigned to each group so they will have to investigate it, meaning and how to draw it on the coordinate plane, preparing a mind map to explain to the rest of the class. At the end of the class they must have the four concepts (Symmetry, rotation, reflection and translation) clear.
LESSON 2. Content Development (1 session of 55 minutes).
- Task 1. Warming - up. Mirror game ( 15 min).
TPR or kinesthetic activity in with they must follow the teacher and perform different steps and movements related to transformations, that are previously drawn on the board for them to learn and remembered
- Task 2. Matching activity (5 min) and Task 3. Filling the gaps (10 min)
are related to vocabulary. In both, students must read, understand and also write a bit, being allowed to use a dictionary in case they need some help. They will have peer to peer assessment, swapping papers to check them.
- Task 4. Writing patterns (25min).
Students will learn how to design a choreography based on basic squares. They must recognize all transformations and then, they must write and describe different transformations that appear in all the squares. Peer assessment
- Task 5. Racing transformation by groups. ( 10 min)
Students are given some activities they must develop in a short time competing with the other groups. Peer assessment
LESSON 3 AND 4. SMALL PROJECT. (3 sessions of 55 minutes)
Content Consolidation
Design, compose, draw the different steps in a dance graphic, write and describe the development and aim of the project and finally, record a video with the choreography
performance. They have to create a genially presentation with all these things mentioned and present it to the class.
FINAL SESSION (55 minutes). Presentation and Assessment
They will be assessed by a rubric
Resources / Materials
▪ Digital Board. Computer, projector
▪ YOUTUBE: ⁃ VIDEO 1. https://www.youtube.com/watch?v=UH6yC7GjqZk
⁃ VIDEO 2. https://www.youtube.com/watch?v=X1xPZjItmDk
▪ POWERPOINT : https://www.slideserve.com/graham-harding/transformations
Jigsaw Investigation
▪ MENTIMETER: https://www.menti.com/i67vvvxyh7
Brainstorm
Warming-up. Game
Filling the gaps
Writing patterns
Competition. Racing Transformation
Small Project. Final Task
▪ LEARNING APPS : https://learningapps.org/watch?v=pnc45g3cj21
Match
▪ DICTIONARY: https://www.wordreference.com/es/
▪ GENIALLY: https://genial.ly/es/
Key Competences
• Communication
• Digital competence (ICT)
• Math competence
• Learning to learn
• Initiative and Entrepreneurship
• Social competence.
• Cultural awareness and expression
• Interpersonal and civic competence
8. Evaluation (criteria and instruments)
Evaluation Criteria:
• Describing transformations quantitatively and recognizing them around us.
• Performing and writing transformation from descriptions and creating their own ones.
• Understanding the importance of symmetry and the transformation of designs through rotation, reflection, and translation. Understanding congruence in terms of rigid motions.
• Knowing the most important movements in a plane
Evaluation instruments
• Continuous assessment of each student with different oral and written activities
• Peer to peer assessment
• Rubric
Elena Gómez Martín
Muy buen trabajo, ELena. Me gusta mucho tu unidad. ¡Muy completa!
ResponderEliminarEnhorabuena por tu unidad. Sin duda, un gran trabajo. Espero que pronto puedas llevarla a la práctica.
ResponderEliminarUn saludo
Gracias!
ResponderEliminar