lesson plan 1
Paramvir Singh
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LESSON
PLAN 1
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Mathematics
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EDCP 342A
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Date : December 14, 2017
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Room 1213
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Topic/learning
objectives:
After completing this lesson students will be
able to know about the history of arithmetic and geometric sequences and their
inventors. They will also know about the origin of the formulas which we often
use in sequences and series.
Resources: Textbook Pre -Calculus 11, and internet
HOOK
Could
you find the sum of first 10 natural numbers, without using calculator?
How
about 20?
Lesson
content/activities:
An arithmetic progression is simply a
sequence of numbers that are separated by the same amount. Even though we are
not sure about the specific history of arithmetic sequences, it was developed
by Egyptian mathematicians. The formula of sum of arithmetic sequences is
given by Carl Friedrich Gauss. He was born in Braunschweig, Germany. He
contributed significantly to many fields including number theory, Algebra,
Differential, Statistics and Geometry. When he was just 10 years old when his
teacher gave him a question to find the sum of 1+2+3+4+5+6+7+……….100. Gauss solved this sum in different way and
responded quickly that answer is 5050. He used his technique 100 (101)÷2. The general
sum of natural numbers is n(n+1) ÷2.
Similarly,
geometric series which are patterned by common ratio, like 1,3,9,27,81……
This
given sequence shows common ratio is 2. This type of geometric sequences was
invented by Greek mathematician Euclid. First these geometric sequences were
described in 300BC in his book 1X of Elements. Geometric sequences played a
significant role in developing Calculus. As these are intrinsic part of
mathematics, also played a significant role in Physics, Engineering, Biology,
Computer Science and Finance.
The
Greeks introduced the sequence of triangular numbers 1,3,6,10…
They
also found the geometric technique to solve 12+22+32+……….+n2=
n(n+1)(2n+1)÷6
They
used mathematical induction to get the proof of this geometric progression.
They also invented the technique to solve
the sum of 13+23+33+……………. n3=
square of n(n+1) ÷2
When
we talk about the infinite series, contribution of Greek mathematicians could
be seen in a first glance. Archimedes produced the first known summation of
infinite series with a method which is still used in the area of Calculus
today. He found the area under the curve of parabola with the help of
infinite series. After him James, Brook Taylor, Leonard Euler, Cauchy and
many more mathematicians did great work in this field.
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Time
10 minutes
50 minutes
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Homework/assessment
They
will search about the real-world applications of sequence and series and will
try to explore more. They will also collect some important information of history
of these topics.
Learning outcomes
All pupils
will listen carefully and they will get some knowledge of the history of
sequences and series
Most pupils
should understand the arithmetic and geometric interpretations of formulas
Some pupils
may try to know about the history of further topics and would share with their
classmates.
Comments/evaluation
Teacher
will ask general questions about the history of sequence and series. It will
help him to know about the understanding of topic discussed in the class
Lesson plans: #1: This is not an adequate lesson plan, Paramvir.
ReplyDelete• You have only scripted out what YOU will say. This is a completely teacher-centred, lecture
-centred lesson plan, with no consideration of what the students will be doing (other than listening to you talk). That is not adequate. All lessons need to include active learning and participation on the part of the students.
•The lesson has you telling things that the students could be working out for themselves. For example, an excellent participatory lesson can be designed around Gauss’ summation of an arithmetic series and the derivation of the summation formula from that memorable story and participatory experience. However you are planning to just quickly tell everything, and you have missed an opportunity to have students think mathematically!
•There are mathematical errors in the lesson. For example, you write: “Similarly, geometric series which are patterned by common ratio, like 1,3,9,27,81……This given sequence shows common ratio is 2." No, it is not 2 -- it is 3.
•It is NOT enough to just say some words (that the students may not have any understanding of -- like differentiation, calculus, infinite series,..) and then count that as teaching the history of mathematics. You are planning to more or less read an encyclopedia entry aloud, but that is not really teaching; students may easily tune out and ignore what you are reading, or simply not understand, and they will not have learned anything about the mathematics.
•The timing is not at all clear. You have listed 10 minutes and 50 minutes in the margin, but there is no sense which activities go with those timings. Most schools now have 70 - 75 minute class blocks too -- is your school really operating with 60 minute blocks? You have not taken any consideration of timing, and this was something you identified as needing work in your micro teaching reflections.