POLYNOMIALS

Teacher: María Soledad Salomón Plata      

Course/Level: 3º E.S.O. Matemáticas Orientadas a las Enseñanzas Académicas

Subject: Mathematics          

DU Title: Polynomials

 

 

https://docs.google.com/document/d/1NMyTuiwuq5PyuCvltZWqzTlplXqtKclblmBcrDW6m3w/edit

 

1. LEARNING OUTCOMES/EVALUATION CRITERIA

1. Translating statements expressed in everyday language into algebraic language

2. Identify monomies, polynomials, and their elements. Calculate the numerical value.

3. Perform basic arithmetic operations with monomies and polynomials: addition, subtraction, multiplication and division.

4. Identify and apply remarkable identities correctly.

5. Factorize fourth grade polynomials using Ruffini Rule, remarkable identities and the extraction of common factors.

6. Evaluate and use algebraic language to solve different situations of everyday life and the scientific method.

7. Appreciate perseverance and effort in the search for solutions to problems.

 

2. SUBJECT CONTENT

-       Investigation of regularities, relations and properties that appear in sets of numbers. Expression using algebraic language.

-       Translation of algebraic expressions. Remarkable equality. Elementary operations with polynomials.

 

 

 

3. LANGUAGE CONTENT / COMMUNICATION

 

3.1 VOCABULARY

Essential Vocabulary:

Polynomial, coefficient, independent term, degree of a polynomial, exponent, variable, monomy, binomial, trinomial, addition and subtraction of polynomials, multiplication of polynomials, Polynomial factoring, monic polynomial, Ruffini Rule, remarkable identities, square of an addition, square of a subtraction, addition multiplied by sustraction.

 

Re-use vocabulary:

Solve, reduce, calculate, simplify, add, subtract, multiply, divide,…

 

Classroom routines:

Exercise revision, task correction, explanation periods, joint examples implementation, doubts resolutions

 

3.2 STRUCTURES

Routines: Some examples of routine expressions are:

-       Let's go over what we learned in the last lesson about notable identities.

-       ¿How do we add monomies?

-       ¿What is the grade of this polynomial?

-       ¿What are the numbers by which we can divide with Ruffine Rule?

 

Grammar contents: Present Simple, Present Continuous, Future simple, First conditional, Second Conditional, Third conditional, comparative sentences

 

Classroom management: Some examples of classroom management expressions are:

-       Now, let's correct the task.

-       Any questions?

-       We are going to do this exercise together.

-       Quiet, please.

 

 

3.3 DISCOURSE TYPE

The discourse to be used focuses on the description and sequencing of procedures. There will also be frequent dialogues in shared teaching with the teacher specialist in L2 and with the students in order to encourage greater participation.

 

3.4 LANGUAGE SKILLS

Language skills to be used are: writing, reading, speaking, social interaction.

 

 

4. CONTEXTUAL (CULTURAL) ELEMENTS

The importance of this didactic unit lie in the use of algebraic notation and polynomial, which will be needed in other didactic units of this course and in subsequent courses. It is important to show students the multiple applications of polynomial, which are useful in representing and solving problems of geometric, economic, physical and many other aspects of everyday life.

 

5. COGNITIVE (THINKING) PROCESSES

Traduce, Recognize, Carry out operations, Apply remarkable identities, Factorize.

 

6a. TASK/S

Read and answer the questions.

Identify elements by using L2

Explain concepts by using L2

Solve exercises

 

6b. ACTIVITIES

Introductory videos.

Brainstorming

Interactive exercises

Problem solving

Written evidence

 

7. METHODOLOGY

 

ORGANIZATION AND CLASS DISTRIBUTION / TIMING

Methodology will be active and participative, taking advantages from the discussion periods between students. We will use different groupings such as individual, by pairs or trios, homogenous group and heterogeneous group.  This unit is supposed to be 11 sessions long, although this is an initial planning which depends on the student learning:   All the materials and links listed below are available on my Symbaloo webmix: https://www.symbaloo.com/home/mix/13eP2ERB5Y   SESSION 1: It will be visualize the following introductory video: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:multiply-monomial-polynomial/v/polynomials-intro     SESSION 2: With a brainstorming, we will define concepts relating to algebraic expressions, monomials, polynomials and their elements, and their English denominations. Later we will review both the mathematical contents and the vocabulary associated with the following activity that encourages scaffolding: https://math.libretexts.org/Bookshelves/PreAlgebra/Book%3A_Prealgebra_(OpenStax)/10%3A_Polynomials/10.0E%3A_10.E%3A_Polynomials_(Exercises)   SESSION 3: Students will perform the following activity named "Polynomials and free fall" by pairs, which show the relationship of the contents to the nearest context. After reading an English text describing a real situation they will answer some questions and perform exercises related to the numerical value of a polynomial.   SESSION 4: We will perform a flipped classroom activity in which two ramdomly chosen students will explain polynomial product to their classmates. We will try to create a classroom atmosphere in which students feel comfortable so that they are not afraid to make a grammatical mistake during the explanation.   SESSION 5: After explaining Remarkable Identities, students will perform the following online exercises:  http://www.mathspadilla.com/3ESO/Unit5-AlgebraicLanguage/remarkable_identities.html SESSION 6: In this session, after explaining dividing polynomials, student will perfom the following interactive activity: https://tutorial.math.lamar.edu/problems/alg/dividingpolynomials.aspx     SESSION 7: In this session, after explaining factorization of algebraic expressions, student will perform the following interactive activity:  https://www.solumaths.com/en/math-games-online/play/factoring-game-remarkable-identities   SESSION 8: In this session after explaining algebraic fractions and solving several examples, students will practice by performing the following activities by pairs: https://www.superprof.co.uk/resources/academic/maths/algebra/polynomials/algebraic-fractions-worksheet.html   SESSION 9: In this session, students will perform refresher activities available in the following links. Student will be grouped in heterogeneous groups: https://es.liveworksheets.com/oc1866309fe https://es.liveworksheets.com/qt1261321kf https://es.liveworksheets.com/yo2330407bu   SESSION 10:  This session will be dedicated to the realization of the written evidence. All statements will be in English.   SESSION 11: In this session we will correct the test together and solve all the doubts arose in its realization.

In this unit will be used the following resources: textbook, digital blackboard, computers.

 

 

 

RESOURCES / MATERIALS

In this unit will be used the following resources: textbook, digital blackboard, computers.

 

KEY COMPETENCES

Competence in Mathematics, Science and Technology

Competence in Linguistic Communication

Digital Competence

Learning to Learn

Social and Civic Competences

 

8. EVALUATION (CRITERIA AND INSTRUMENTS)

It will be implemented a formative evaluation during the learning process which a continuous assessment of each student.

 

Evaluation Criteria:

-       Use algebraic language to express a given property or relationship through a statement, extracting relevant information and transforming it.

 

 

Evaluation Instruments

-       Written evidence

-       Oral questions

-       Task performance

-       Notebook revision

 

 

 

MARÍA SOLEDAD SALOMÓN PLATA

 

 

 

Notas bibliográficas y créditos:

 

Un primer modelo de esta plantilla ha sido publicado en:

Pérez Torres, I. 2009. Apuntes sobre los principios y características de la metodología AICLE, en V. Pavón, J. Ávila (eds.), Aplicaciones didácticas para la enseñanza integrada de lengua y contenidos. Sevilla: Consejería de Educación de la Junta de Andalucía-Universidad de Córdoba.171-180.

 

Está basada sobre todo en la experiencia práctica a la hora de diseñar unidades y conversaciones con expertos y compañeros. También he tenido en cuenta la teoría de las 4 Cs de Do Coyle, expuesta en numerosas publicaciones, como por ejemplo: Coyle, D., Hood, P. and Marsh, D., 2010. Content and Language Integrated Learning. Cambridge University Press.