Revised lesson plan 3
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Paramvir Singh
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LESSON
PLAN 3
Exploring
sequence and series ( Open -ended questions)
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Mathematics
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EDCP 342A
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Date : Feb.12, 2017
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Room 1213
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Topic/learning
objectives: After completing this lesson, students will explore their deep
understanding of the topics of the arithmetic and geometric sequences. Open
ended questions will allow the students to get extra information such as
demographic information. Many solutions and many ways of solving the questions
would be found.
Textbook Pre -Calculus 11
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HOOK
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Teacher will
invite the whole class to the white board and ask them to
place
the digits 1, 2, 3, 4, and 5 in the small circles on the board so that the
sums across and vertically are the same. Describe the strategy you used to
find your solution(s)
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Whole class will
participate actively and find the sum by placing different digits in
different circles and will tell what way they got the solutions.
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A sample video
will be played of a question which has many possible approaches to solve it.
Lesson
content/activities:
Teacher will divide the whole class in two groups and ask them to solve some questions
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Consider the
following sequence 1,4,7,10,13….
Is 35 a member
of this sequence?
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Explain why the
sequence 4,5,7,10, 14, Is not arithmetic
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Write an
arithmetic sequence with common difference -1/2
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Write a
geometric series for which r = 0.5, n=5
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Write a
geometric sequence with a common ratio of 2/3
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Students will
attempt to solve these questions individually and if they need help, they can
take help from their group members.
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Teacher will
observe them and ask some questions for extensions
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The students who did not get all the questions
will be helped by group members
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A brief
discussion would take place in the class. Teacher gives four advanced
questions to four groups. Each group will choose one question according to
their seating plan. For example, group A will choose question number 1, B
will choose second, group C will choose 3 and group D will choose 4. When a
group solved the sum, would move to the next question.
Teacher will move around the groups, provide them scaffolding if they
needed. Questions are here:
1.
You work in a
grocery store and are stacking apples in the shape of a square pyramid with 7
layers. Write a rule for the number of apples in each layer. Then graph the
sequence.
2.
For a display at
sports store, you are stacking soccer balls in a pyramid whose base is
equilateral triangle. Tn represents balls per layer which is given
by Tn= n(n+1) ÷2, where n=1 represents the first layer. How many balls would be in
the fifth layer? How many balls are in stack with five layers? Compare the
number of balls in a layer of a triangular pyramid with the number of balls
in the same layer of square pyramid?
3.
What are the possibilities of handshakes if
6 people meet where everyone shakes hand with everyone else
only once.
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What are the
ways to represent it geometrically?
·
Describe a
similar situation in which the method of determining the handshakes may apply
and could be represented geometrically
4.
If a ball is dropped from a height of 3.0 m.
After each bounce, it rises to 75% of its previous height. After how many
bounces the ball will reach a height of approximately 40 cm?
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Does the height
affect the bounces? If yes then how if not then why?
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Students in
small groups will discuss about the situation.
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They will have
an opportunity to showcase or discuss their findings and patterns
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To draw or to
calculate they can use GeoGebra or calculator
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Teacher will
briefly review the lesson.
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Time
15 minutes
20 minutes
35 minutes
5 minutes
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Homework/assessment
They will
be assigned some other open-ended problems so that they can develop their
thinking process and unanticipated findings can be discovered
Learning outcomes
All
pupils will be involved in problem solving and. They can recognize the problem
whether it is related with arithmetic sequence or geometric sequence and they
proceed according to that.
Most
pupils participate in finding unanticipated findings. They use their creativity
and their self-expressions in solving problems.
Some
pupils may try some advanced open- ended problems.
Comments/evaluation
As in
open- ended question we expect many approaches, so rubric would be the best
technique for evaluation.
Good to have a class devoted to open-ended problem solving around sequences and series. Question #2 is a bit confusing to me -- you are suggesting a 3D triangular-based pyramid stack of tennis balls. How does Tn= n(n+1)/2 work with this construction? How could the first layer be equal to 1? (You would need to have the first layer be the largest!) Do make sure you try out all your examples first to check that they work well.
ReplyDeleteIn terms of timings, you might want to organize it so that the groups switch at the same time -- or if not, just to work out how the groups will work independently without overhearing each other's solution techniques.