| LESSON Arithmetic and geometric progressions
Timing 2 weeks Course / Level 3º ESO Subject: Mathematics for academic studies
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| CONTENTS | DIDACTIC OBJECTIVES | KEY COMPETENCES
| SKILLS |
| Lesson Contents: 1.Sequences 2. Series 3. Arithmetic progressions 4. The sum of an arithmetic series 5. Geometric progressions 6. The sum of a geometric series
Linguistic Contents: -Syntactic-discursive aspects: . To express probability: I think it has to be / It's I got the same number because … . To describe the term in a sequence I think you are wrong because … Don't you think there are more options? I do because … This way we won't get anything useful because… We have to consider How do you calculate/ estimate/ define... this? Why do you think that? - Vocabulary: Sequence. (General) term. Length of a sequence. Increasing or (decreasing) sequence. Limit (of a sequence). Arithmetic/geometric progression. Common difference. Common ratio.
Cultural Contents: -Study of sequences in ancient civilizations: Babylon and Ancient Egypt -Fibonacci sequence
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1. Find regularities in numerical sequences.
2. Find some of the relationships between regularities and sequences Numbers.
3. Find the general term of an arithmetic or geometric progression.
4. Identify and use sequences.
5. Find the sum of n consecutive terms of an arithmetic progression.
6. Find the sum of n consecutive terms of a geometric progression
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Language communication (CCL)
Mathematical competence and basic competences in science and technology (FCTC)
Learning to Learn (CAA)
Sense of initiative and entrepreneurship (SIEP)
Digital Competence (CD)
Awareness and cultural expressions (CEC)
| To know, to acquire, to extend and to apply the vocabulary of the subject Make a comprehensive reading of the statements
To know the basic notions about probability To use adequately the strategies of the basic calculation of probabilities Solve situations using learned mathematical notions
Organize ideas, ideas and arguments in an orderly and constructive way
Be autonomous to carry out individual activities Express own ideas in an argumentative way
Update the use of new technologies to improve work and facilitate daily life.
Study how different cultures have contributed over time to develop the concept of progression and what is its application current utility.
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| LEARNING STANDARDS | EVALUATION CRITERIA | RESOURCES / MATERIALS | ACTIVITIES/ ASSESSMENT |
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1. Write a concrete term of a given sequence by its general term, or recurrently. 2. It obtains the general term of a sequence given by its first terms (very simple cases). 3. He recognizes the arithmetic progressions and calculates their difference, their general term, and obtains any term. 4. Calculate the sum of the first terms of an arithmetic progression. 5. He recognizes the geometric progressions, calculates his reason, his general term and obtains any term. 6. Calculate the sum of the first terms of a geometric progression. 7. Calculate the sum of the infinite terms of a geometric progression with | R | <1. 8. Solve problems, with statement, of arithmetic progressions. 9. Solve problems, with statement, of geometric progressions.
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- Relate concepts to solve practical situations and answer questions on successions
- Calculate the general term of a sequence, an arithmetic progression, or a Geometric progression
- Calculate determinate terms of successions or progressions
- Calculate the sum of the first terms of an arithmetic or geometric progression |
Didactic material in PDF format
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- Activities to write the general term of a sequence given its first terms. - Activities to recognize an arithmetic progression and calculate its different elements. - Activities to calculate the sum of the n first terms of an arithmetic progression. - Activities to recognize a geometric progression and calculate its different elements. - Activities to calculate the sum of the n first terms of a geometric progression. - Activities to calculate the sum of the infinite terms of a geometric progression when | R | <1. - Activities to solve problems involving arithmetic progressions. - Activities to solve problems involving geometric progressions.
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