"Algebra: the universal language"

"Algebra: the universal language"

Unidad didáctica de la asignatura de Matemáticas, dirigida al segundo curso de la E.S.O.

1. Learning outcomes / evaluation criteria:

• Get to know the main concepts of algebra.

• Find the degree of a monomial or polynomial.

• Write an algebraic expression from a real situation by reading or listening to it.

• Write or produce accurate sentences from a specific algebraic expression. 

• Get the numerical value of an algebraic expression.

• Add, subtract, multiply and divide monomials.

• Add, subtract and multiply polynomials.

• Know the remarkable identities.

2. Subject content:

• Main algebraic concepts: monomial, polynomial, degree, similar monomials, coefficient, literal part.

• Algebraic expressions: translation between natural language and algebraic language.

• Operations with monomials: addition, subtraction, multiplication and division.

• Operations with polynomials: addition, subtraction and multiplication.

3. Language Content / Communication:

• Vocabulary: 

• Verbs: add, subtract, multiply, divide, reduce,  square, cube, translate, replace.

• Names: degree, monomial, polynomial, coefficient, unknown, square, cube. 

• Adjectives: algebraic, positive, negative, half, third, double, triple, quadruple, twice.

• Prepositions: minus, plus, by.

• Structures:

• Routines: practising listening and speaking thanks to mental calculation. At the beginning of the sesion the teacher says some operations with monomials in order for the pupils to calculate them the fastest as possible.

• Grammar contents: comparatives, conditionals, present simple. Expressions: "half/double/triple/quadruple a number", "the square, cube of a number" "a number squared/cubed is...", "a third of...".

• Classroom management: "work in pairs", "translate into...", "classify and group the monomials", "replace the unknown by ...", "order the polynomial".

• Discourse type: exposition, transactional discourse.

• Language skills: 

• Writing: when translating into natural language or copying exercises.

• Speaking: dialogues with partners or teacher and mental calculation.

• Reading: statement of the exercises, algebraic sentences.

• Listening: mental calculation, teacher expositions. 

4. Contextual elements:

Students already know how to operate with Z numbers and fractions. In this unit, they will get to know the concept of algebraic expression and its utility. They will discover how to use the unknowns by exploring with everyday situations (money, clothes, video-games, ages...) and practicing activities.

5. Cognitive processes:

• Remembering. They will remember how to operate with negative numbers.

• Understanding. They will understand each new concept and the way we operate with unknowns.

• Applying. They will apply their knowledge by doing activities and solving problems.

• Evaluating. They will evaluate some of their own jobs (as well as their own learning process).

• Creating. They will write algebraic sentences for their mates to translate them.

6. Tasks and activities:

• Tasks:

• Relating algebraic expressions with sentences.

• Identifying the parts of an algebraic expression (degree, coefficient, unknown,...)

• Operating monomials and polynomials.

• Getting the numerical value for an algebraic expression depending on the unknown's value.

• Finding the correct algebraic expression for a real situation.

• Creating word phrases for a certain algebraic expression.

• Activities:

• Finding eXpressions: relate each sentence with the correct algebraic expression.

• Hieroglyph: create a hieroglyph from monomials and polynomials.

• Quick brain: mental math contest with recordings of algebraic expressions.

• Little everyday problems: build and classify algebraic expressions from word phrases.

• Exam creators: make up a sentence or short text for each algebraic expression.

• Operations: sum, subtract or multiply polynomials.

• Remarkable identities: Remarkable identities

• Basketball math test: basketball game

Hieroglyph activity examples.

7. Methodology:

• Organization and class distribution / timing:

7 class sessions (50' each session):

• First 10 minutes: speaking practice by mental calculation (operating with monomials or polynomials, finding the correct algebraic expression, …).

• Teacher's explanation of the content (15').

• Activity/ies from 6b: individual or collective (25').

The last session will be dedicated to the final test, in order to evaluate the acquired knowledge.

• Resources / materials:

• Conventional materials: blackboard, notebook, pencil, teacher notes.

• Audiovisual materials: digital board, recordings, videos.

• New technologies: laptops, online dictionary.

• Key Competences:

• Mathematical competence and basic competences in science and technology.

• Communication in foreign languages.

• Learning to learn.

• Digital competence.

• Social and civil competences.

8. Evaluation:

• Notebook: clean, complete, ordered, corrected, ...

• Class notes: from the development of the activities (not understood, almost understood, mostly understood, perfectly understood).

• Final test: individual activities, similar to the tasks carried out in class.

Enlace a la plantilla de la unidad: https://drive.google.com/file/d/1Qs63pN_HoGMkpmbOMEh2IXh11gCMSHFN/view?usp=sharing

Alicia Casado de las Heras