Unit Plan Pre-calculus 11 Sequence and Series
EDCP 342A Unit planning: Rationale and
overview for planning a 3 to 4-week unit of work in secondary school
mathematics
Your name: Paramvir Singh
School, grade & course: Fraser Heights Secondary School Surrey
School, grade & course: Fraser Heights Secondary School Surrey
Topic of Unit: Sequence and Series (Pre-Calculus
11)
Preplanning questions:
(1)
Why do we teach this unit to
secondary school students? Research and talk
about the following: Why is this topic included in the curriculum? Why is it
important that students learn it? What learning do you hope they will take
with them from this? What is intrinsically interesting, useful, beautiful
about this topic? (150 words)
The
main objective of this topic to make students familiar with different
patterns and sequences so that they would be able in recognizing these different
patterns in nature and human body. The pattern of the logistic spiral is
found in the chambered nautilus. Patterns of seed growth, petals on flowers
and rabbit reproduction are in our surrounding. These bring them near to the
realistic experiences of life. Infinite terms of sequences and series would
tend to the infiniteness of nature that might be in stars, forests or in
oceans. Similarly, the web of a spider represents the geometric sequence.
Students
will be able to distinguish between geometric sequence and series. They will
be able to find common difference in ordered list of terms. Even they will
generate their sequences by recognizing repeated common difference and number
of terms. By using their inductive
reasoning, they will learn to find the sum of finite and infinite series and
their nature whether these are convergent or divergent.
When
the terms of sequences are added, it becomes series. Some series increase
without bound as n increases, some approach to a limit. There are certain
formulas for calculating the limits of series, which is a part of Calculus,
would be discussed and its real -life applications would be found.
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(2)
A mathematics project connected to this unit: Plan
and describe a student
mathematics project that will form part
of this unit. Describe the topic, aims, process and timing, and what the
students will be asked to produce, and how you will assess the project. (250
words)
Math project:
The main aim of this project is to involve all the
students in problem solving project so that they have some real -life
experience. They can recognize arithmetic and geometric patterns in their
surroundings. They will be divided into small groups of 4-5 students. They
will divide their work and start working on the project. This project will
increase their abstract thinking about the content and they would have real
experience of sequence and series. They will learn the relevance of studied
topic in the class that they can use it somewhere.
Students would be free to choose the topics from
their unit according to their interest, which are associated with real- life
experiences. If they need help, the teacher can help them in choosing topic
or any other help of resources can be provided. For example, they can work on
the petals of sunflower and they can record their findings. They can also
find the patterns of Fibonacci sequence in other flowers. They can also work
on project which is based on triangular number. It can help them in arranging
boxes in the grocery store. In this way, they will learn the use of
arithmetic sequences in real world applications. They can also work on
squared spiral, by calculating and recording lengths they can make
relationship of arithmetic series and its application. The students who would
be interested in geometric progression they can also choose such type of
topic. As a spider’s orb web is an impressive architectural feat. Usually it
makes the geometric sequence.
10 minutes would be assigned for every group to
present their findings in the class. They will discuss their experiences.
They will describe the topic at first and then how it is related with real
world and which patterns of sequences and series they found in it. All
presentations should be finished within the block.
After the presentations, students would be asked to
write their reflections about the project. That should be brief so that they
can talk about main findings, their weaknesses and how they would improve it
next time. It would help to understand their positions and their abilities as
well. Obviously, it would be helpful in their evaluation
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(3) Assessment
and evaluation: How will you build a
fair and well-rounded assessment and evaluation plan for this unit? Include
formative and summative, informal/ observational and more formal assessment
modes. (100 words)
Many things I would involve in this evaluation. The
very first thing, I believe is, the content knowledge. How much do they have
knowledge of sequence and series? Problem solving skills and strategies are
also equally important. Do they distinguish between sequence and series,
finite series and infinite series? Multiple choice quizzes and class tests
would be also part of evaluation. Informal interviews can also help to judge
their ability. Besides this, homework is also a tool. A full written test
would also be taken so that their total understanding can be checked
properly. Grades or rubric can be used to express their understanding of the
unit.
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Elements of your unit plan:
a) Give a numbered list of the topics of the
10-12 lessons in this unit in the order you would teach them.
Lesson
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Topic
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1
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Arithmetic
Sequences
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2
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Determine
the Sum of Arithmetic Series
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3
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Determine
the terms of an Arithmetic Series
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4
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Geometric
Sequences
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5
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Determine
the Sum of a Geometric Series
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6
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Sum
of an infinite Geometric Series
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7
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8
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9
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10
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(11)
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(12)
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Thanks for this thoughtful unit plan outline, Paramvir.
ReplyDeleteRationale: Very nice to include these beautiful natural examples of sequences that can be analyzed mathematically! I think there is a typo though: the chambered nautilus is in the form of a logarithmic spiral (not ‘logistic’).
Project: This sounds like an interesting project! I would give the students quite a bit more guidance at the start though. Rather than saying they will be free to choose any topic, I think that it will be important for you to offer a suggested topic list of mathematical sequences in nature and culture that groups can choose from — with the option of suggesting something not on the list if they wish.
Similarly, they will need more guidance on your expectations for the products of this project. What are they responsible for making, doing and understanding? What format should it take? What is the nature of their presentations? Do they involve making a poster, slides, a model, or leading the class in an interactive activity or game, etc.?
They will also need to know how their work will be assessed and evaluated, so that they are clear about what you are looking for.
With these provisos, I think this is a very good project idea!
Assessment plan: Sounds good!
Unit elements: This is not adequate, Paramvir. First, you only list 6 lessons, but the unit ought to have 10-12 lessons. You have omitted some important topics including sequences and series in nature and culture (see your own rationale for the unit!) and an emphasis on problem-solving using sequences and series. You could also offer a lesson or two on sequences and series that are neither arithmetic nor geometric (Fibonacci sequence, triangular numbers, etc.)
Secondly, the sequencing of the six lessons you have listed does not make sense. Normally students would learn about finding the terms of an arithmetic sequence (not series!) before they took on the sum of an arithmetic series. You mention summing an infinite geometric series, but not finite geometric series, although perhaps that is what you mean by lesson 5?