Lesson Plan
Pure Math 1
Wang Peipei
Chapter 11 Arithmetic sequences
Grade: G10
Lesson
Objectives:
Materials:
Date:
Duration: 60mins Coursebook pages: P166
1. Able to proof formulae by direct proof and proof by induction.
2. Use the formulae for the sum of the first n terms to solve
problems involving arithmetic sequence.
PPT, Coursebook, Game cards
Teaching Process
Time
Activities
Descriptions
Method
30mins Prove that Students are sorted into small groups; Groups of 2 to Inquiry
the sum of 3 students of matching ability should do.
learning
the
first n odd
integers is n2 Each group should come up with both a proof based
on Gauss's and a proof by induction. In case of
major issues, one will do. (This can be preceded by
examples prompting the groups to form a
conjecture, thereby reproducing the typical
mathematical discovery process. But the focus of
the activity is proving, not discovering.)
Two people are randomly selected to show and
explain the proof to the class. The proofs are
critiqued regarding logic and presentation. The aim
is to have a decent version of each proof available
for discussion in about half an hour.
1
Lesson Plan
Wang Peipei
10mins Compare the Lead a discussion around the following questions.
proofs
This can be done in a number of ways. One is: five
technically
minutes of discussion within each group, five
minutes of sharing.
Inquiry
learning
1. What are the logical differences between the two
proofs?
2. What are the mathematical differences?
3. What are the mathematical similarities?
10mins Compare the Lead a discussion around the following questions.
This can be done in a number of ways. One is: five
proofs
minutes of discussion within each group, five
cognitively
minutes of sharing.
Inquiry
learning
1. Which proof do you find more appealing?
2. Why do you think that is?
3. What is the role of notation, if any, in making the
proof more appealing?
4. What is the role of logic, if any?
10mins Compare the
proofs in
terms of
their
explanatory
value
5. What would questions involving each kind of
proof look like in an exam paper?
Lead a discussion around the following questions.
This can be done in a number of ways. One is: five
minutes of discussion within each group, five
minutes of sharing.
1. Is there a difference between proving and
explaining?
2. If there is a difference, does a proof have to
explain in addition to proving?
3. If it does, should we always prefer a proof that
does explain to one that doesn't?
4. Do proofs by induction ever have an explanatory
role?
Assignment
Each student should write up a 250-word
presentation including both proofs and their view
after the discussion.
2
Inquiry
learning