PARABOLA Massimo Marletta

Course11 level (3rd year Liceo Scienze Applicate)

with Computer Aided Design

Non Linguistic Subject Mathematics

Foreign Language (L2) English

CLIL ModelIndividual model: the subject teacher will use the targetlanguage to explore the subject from another point ofview.

General objectives of the CLIL course

The proposed CLIL course aims to conjugate the contentlearning – namely Conic Sections and Parabola – withthe development of English competences and thepromotion of ICT competences such as specific softwareuse, PowerPoint presentation production, the use of theinteractive board and of specific web sites for learningof mathematics.

PREREQUISITES

Subject

• Knowledge of the basic elements of the Cartesian plane: point, line• Ability to perform basic calculations: distance from two points, distance from

a point and a line• Straight line and its equation• Graphic representation of relationships• Ability to solve simple linear equations and systems

Language

• Understanding of words and expressions of common use• Ability to read short texts finding specific information• Ability to communicate in known contexts• Ability to use simple expressions by connecting experiences and events• Ability to take notes and write brief text messages on known topics

Transversal

• Group/pair working. • Internet browsing/searching.• Encourage learning motivation.• Diversity the methods and the models of the educational practice.

SUBJECT OBJECTIVES

Knowledge:

- Classification of Conic Sections - Definition of parabola and related loci (focus, directrix, vertex, etc.)- Classification of parabolas (open upward, open downward)- Equation of parabola

Abilities and Competences:

- Being able to derive the equation of a parabola given any geometric data- Being able to derive geometric characteristics of a parabola given the equation

LANGUAGE OBJECTIVES

Listening

Speaking

Reading

Writing

• Understanding the main elements of a talk of medium length• Reading and understanding written texts of current use, papers and

scientific reports on the topic• Interacting in oral discussions about the topic• Explaining opinions and formulating hypotheses• Producing simple texts about know topics• Improving the physical language in L2• Reading and understanding scientific papers on the topic• Reading web sites on the topic• Being able to understand in L2, without much effort, discussions on the

topic• Being able to understand written texts in the subject’s specific

language (L2), both on paper and on the internet• Being able to interact orally in a discussion about the topic, by

expressing fluently• Being able to clearly present the topic• Being able to produce a guided text on the topic

OTHER OBJECTIVES

ICT

- Being able to use the interactive board and specific software applications- Being able to produce a PowerPoint presentation- Being able to perform a simple data analysis with spreadsheet software- Being able to represent algebraic expressions by means of specific software- Being able to model ideas and concepts by means of a professional CAD tool

and/or a programming language (coding)

Culture - Comprehension of reality- Identification of the concept learned in the real world- Improvement of the interest in a multilingual environment

Methodological StrategiesCode switching, Collaborative learning, Scaffolding, Solving problems in pairs and in group.Use of the interactive board, PowerPoint presentations, internet.

CLIL ActivitiesMatching, labelling, cloze exercises, fill in the gap, information gap, travel game, draw diagrams, rearrange equations

Educational Tools and Materials

Interactive board, web sites, PowerPoint presentations, math/CAD/coding tools, questionnaires (on paper, multimedia), hand-outs, text books.

PlacesClassroom, Computer Lab,Multipurpose classroom

COMMUNICATION

Cognitive Academic Language Proficiency (CALPs)­ Comprehension of the text.­ Understanding the specialized language (symbols, styles, vocabulary).­ Ability to clearly explain the content of the text.­ Understanding an oral presentation.­ Oral interaction.

COGNITION AND THINKING SKILLS

Low-Order Thinking/Cognitive Skills (LOTS)

Describing the content of the text (knowledge).

Memorising the content of the text (knowledge).

Discussing about the text (comprehension).

Generalising the examples provided in the text (comprehension).

Summarising the whole text (comprehension).

Interview other students about the content of the text (application).

COGNITION AND THINKING SKILLSHigh-Order Thinking/Cognitive Skills (HOTS)

Analysing the content of the text (analysis).

Deducing the real meaning of the physical laws (analysis).

Integrating the different parts of the text (synthesis).

Producing an oral presentation (synthesis).

Relating the physics concepts in the text to other physics concepts (evaluation).

Comparing the physical laws to real phenomena (evaluation).

Justifying a real phenomenon by means of the physical laws (evaluation).

Predicting an unknown real phenomenon by means of the physical laws(evaluation).

METACOGNITIVE OBJECTIVESBeing aware of the aim of the task (awareness)

Being able to activate proper strategies to achieve the aim of the task (awareness)

Activate memory and attention (control)

Recall background information (control)

Knowing that part of the knowledge depends on his/her understanding of the textand on his/her ability to relate and discuss with other students (collaborative learningstrategy)

Knowing that part of the knowledge will be provided through other student’sdiscussion (collaborative learning strategy)

METACOGNITIVE OBJECTIVESThinking back to the effectiveness of the strategies adopted (self-evaluation).

Being able to evaluate his/her weakness and strength in the comprehension of the text and discussion with other students (self-evaluation).

Developing appropriate strategies in order to reduce his/her weakness.

In order to stimulate the students’ metacognitive control the teacher will ask students directly what they know or what they do while engaging in particular cognitive activities.

In order to develop self-evaluation abilities and metacognitive awareness, teacher will ask students to think aloud about what they are doing and thinking as they solve a problem or read a text.

Finally students will be asked to judge how well they learned the given material or how well they answered the comprehension questions.

KWL CHART

What I already know about the topic

What I want to know

What I learned

(to be filled after the module)

ACTIVITIES

INTUITIVE APPROACH & BRAINSTORMING

Make open questions and examplesDiscuss, express ideas, recall previous knowledgeWrite key words in the blackboard

“Have you ever seen a parabola in real life?”

KHAN ACADEMY VIDEOS & ACTIVITIES

KHAN ACADEMY VIDEOS & ACTIVITIES

DURING TASK & SCAFFOLDING

While watching videos

Students are provided with a list of keywords to be checked out as they are pronounced in the video.

The list contains one or more extraneous words that will remain unchecked at the end of the task.

Scaffolding activity

After the first watching students can ask for the transcript of the video.

The teacher can provide a list of difficult word with corresponding Italian translation

NEARPOD ACTIVITY

POLYGRAPH: PARABOLAS

MERLO ITEMS

Target Statement (TS)

Surface Similarity (SS)

Meaning Equivalence (ME)

F. Arzarello et al. (2015) TEACHING AND ASSESSING WITH NEW METHODOLOGICAL TOOLS (MERLO): A NEW PEDAGOGY? IMA International Conference on Barriers and Enablers to Learning Maths: Enhancing Learning and Teaching for All Learners

MASSIMOMARLETTA1.Contrassegnaleaffermazioni(almenodue)checondividonolostessosignificatomatematico.2.Indicaleragionichetihannoguidatonellascelta

rA

!" = $ ∙ (! − ()*" = + ∙ (* − ,)

!" = −!*" = *

* = ! → * = ! + 1 + 4

rB

rC

rD! + * 1 = !1 + 2 ∙ ! ∙ * + *1! + * 3 = !3 + 3 ∙ !1 ∙ * +

+3 ∙ ! ∙ *1 + *3! + * 5 = !5 + (6 ∙ !576 ∙ *

+ ⋯+(576 ∙ ! ∙ *576 + *5

rE

(0,0)

(5,-3)(1,0)

(-5,1)(-1,-2)

(4,-3)

T(x,y)

FILL-IN THE GAP ACTIVITYA conic section is the intersection between a plane and a double-________ cone.By changing the _______ and the location of the intersection a parabola, ellipse, hyperbola, circle point, line or a pair of intersecting _____ is produced.When a plane intersects a double-napped cone and is ______ to the side of the cone, a parabola is formed.

Parabola is the set of all points that are equidistant ________ a point (focus) and a line (directrix)

betweennapped

anglelinesparallel equation

DERIVING EQUATION: LABEL EACH STEP

|" − $| = & − ' ( + " − * (

" − $ ( = & − ' ( + " − * (

"( − 2$" + $( = & − ' ( + "( − 2*" + *(

Equate point to directrix distance andpoint to focus distance

Focus: (a,b); Directrix: y=k

Square both sides of the equation

Work-out the squares of binomials with y

DERIVING EQUATION: LABEL EACH STEP

−2#$ + #& = ( − ) & − 2*$ + *&

2(* − #)$ = ( − ) & + *& −#&

$ = ( − ) &

2(* − #) +* + #2

Simplify like terms

Collect terms in y at LHS

Solve for y

Focus: (a,b); Directrix: y=k

CAD ACTIVITY

Produce a CAD model of a double-napped cone and an intersecting plane (CONE, MIRROR3D, 3DFACE) Describe the procedure you used to realize the modelObserve that by changing the angle of the plane respect to the cone different sections are formed

PARABOLA EQUATION GIVEN 3 POINTSReview of Cramer method for solving linear systems of equationsHow to compute the determinant of a 3x3 matrix

!"#$% + '#$ + ( = *$"#%% + '#% + ( = *%"#+% + '#+ + ( = *+

#$% #$ 1#%% #% 1#+% #+ 1

CODING ACTIVITY: PARABOLA GIVEN 3 POINTS

code.org

PARABOLIC ARCH

Problem:

A building has an entry with the shape of a parabolic arch 8 fthigh and 34 ft wide at the base.

Find an equation for the parabola if the vertex is put at the origin of the coordinate system

Cul

ture

ARCHIMEDESHEAT RAYC

ultu

re

Collaborative learning taskSearch the webGeoGebra activity

ARCHIMEDES HEAT RAY: GEOGEBRA ACTIVITY

Follow the instructions to simulate Archimedes heat ray with GeoGebra:

1. Draw a point (the focus) and a line (the directrix)2. Draw a parabola given the focus and the directrix3. Draw a line perpendicular to the directrix (a “distant ray”)4. Mark the intersection between the parabola and the ray5. Draw the tangent line to parabola in the intersection point6. Draw the perpendicular the the tangent line7. Reflect the incident ray

ARCHIMEDES HEAT RAY: GEOGEBRA ACTIVITY

Observe that as you move the incident ray, the reflected ray is always directed towards the focus of the parabola.

PARABOLA IN REAL WORLD

Cul

ture

Find examples of parabola in everyday life (search the web or take pictures on your own).

Explain why parabola is used in some technical applications (antennas, car headlights).

Explain why when the light from a torch hit the wall a parabola appear (it always do?)