Outcome: F20.2
Demonstrate understanding of inductive and deductive reasoning including:
• analyzing conjectures
• analyzing spatial puzzles and games
• providing conjectures
• solving problems.
Indicators:
Note: It is intended that:
• proofs NOT be limited to the two column proof style
• analysis and conjectures related to spatial puzzles and games be incorporated throughout the course.
a)
b)
c)
d)
e)
Make conjectures by observing patterns and identifying properties, and justify the reasoning.
Provide examples of how inductive reasoning might lead to false conclusions.
Critique the following statement "Decisions can be made and actions taken based upon inductive reasoning".
Identify situations relevant to self, family, or community involving inductive and/or deductive reasoning.
Prove algebraic number relationships, such as divisibility rules, number properties, mental mathematics
strategies, or algebraic number tricks using deductive reasoning.
f) Prove conjectures using deductive reasoning.
g) Analyze an argument for its validity.
h) Identify errors in proofs that lead to incorrect conclusions (e.g., a proof that ends with 2 = 1).
i) Solve situational questions that involve inductive or deductive reasoning.
j) Determine, explain, and verify strategies for solving puzzles or winning games, such as:
• guess and check
• analyze a pattern
• make a systematic list
• create a drawing or model
• eliminate possibilities
• solve simpler problems
• work backward.
k) Create a variation of a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.
Level
Scale
Pre-Requisite
Knowledge
1
B - Beginning
There is a partial
understanding of
some of the simpler
details and
processes.
Prior knowledge is
understood.
2
A – Approaching
No major errors or
omissions regarding
the simpler details or
processes, but
assistance may be
required with the
complex processes.
Descriptor





Indicators
Students who are
not able to be
independently
successful with
level 1 questions
will be given an E.
Recognise and describe
patterns.
Knowledge and
Comprehension
Students who are
successful with
level 1 questions or
those who are
successful with
level 1 or 2
questions with
assistance will be
given a B.
Applying and
Analysing
Students who are
able to be
successful with
level 1 and level 2
questions, or those
who are successful
with higher-level
questions with
assistance, will be
given an A.

Number and geometry facts.




M – Meeting
No major errors or
omissions regarding
any of the
information and/or


Evaluating and
Creating
Students who are
independently
successful with
Identify situations
relevant to self, family,
or community involving
inductive and/or
deductive reasoning.
I understand the meaning of
and difference between
Inductive and Deductive
reasoning.
I can identify examples of
inductive and deductive
reasoning both inside and
outside school.

3
Student-Friendly
Language


Make conjectures by
observing patterns and
identifying properties,
and justify the
reasoning.
Provide examples of how
inductive reasoning
might lead to false
conclusions.
Critique the following
statement "Decisions
can be made and actions
taken based upon
inductive reasoning".
Prove algebraic number
relationships, such as
divisibility rules, number
properties, mental
mathematics strategies,
or algebraic number
tricks using deductive
reasoning.
Prove conjectures using
deductive reasoning.
Analyze an argument for
its validity.
Identify errors in proofs
that lead to incorrect
conclusions (e.g., a proof
Inductive Reasoning:
I can identify and explain
patterns. I can make
conjectures based on those
patterns.
I can find examples where
patterns do not continue
which shows that inductive
reasoning can lead to false
conclusions.
I can critique statements like
statement "Decisions can be
made and actions taken
based upon inductive
reasoning"
Deductive Reasoning:
I can use deductive
reasoning to prove algebraic
number relationships, such
as divisibility rules, number
properties, mental
mathematics strategies, or
algebraic number tricks
I can use deductive
reasoning to prove
conjectures.
I can analyze the statements
of an argument to see if they
are based on correct
reasoning.
processes that were
explicitly taught.
This is the target
level for proficiency.
level 3 or level 4
questions are given
an M.



4
In addition to level 3
performance, indepth inferences and
applications go
beyond what was
explicitly taught.

Students successful
at level 4 will
receive
supplementary
comments specific
to their
achievement in
addition to the M.
that ends with 2 = 1).
Solve situational
questions that involve
inductive or deductive
reasoning.
Determine, explain, and
verify strategies for
solving puzzles or
winning games, such as:
• guess and check
• analyze a pattern
• make a systematic list
• create a drawing or
model
• eliminate possibilities
• solve simpler problems
• work backward.
Create a variation of a
puzzle or a game, and
describe a strategy for
solving the puzzle or
winning the game.
I can identify mistakes in
proofs that lead to incorrect
conclusions (like 2 = 1).
I can solve problems
involving inductive or
deductive reasoning.
I can use reasoning
strategies to solve and
explain the solutions to
puzzles and games.
• guess and check
• analyze a pattern
• make a systematic list
• create a drawing or model
• eliminate possibilities
• solve simpler problems
• work backward
I can create my own puzzles
and games and describe the
strategies needed to solve or
win them.
I can search challenging
puzzles to solve using
inductive and deductive
reasoning strategies.
I can design and produce a
challenging game.
Student-Friendly Rubric
Outcome:
Demonstrate understanding of inductive and deductive reasoning including:
• analyzing conjectures
• analyzing spatial puzzles and games
• providing conjectures
• solving problems.
Meeting
Approaching
Beginning
I understand the meaning
of and difference between
Inductive and Deductive
reasoning.
I can identify examples of
inductive and deductive
reasoning both inside and
outside school.
Inductive Reasoning:
I can identify and explain
patterns. I can make
conjectures based on those
patterns.
I can find examples where
patterns do not continue
which shows that inductive
reasoning can lead to false
conclusions.
I can critique statements
like statement "Decisions
can be made and actions
taken based upon inductive
reasoning"
Deductive Reasoning:
I can use deductive
reasoning to prove
algebraic number
relationships, such as
divisibility rules, number
properties, mental
mathematics strategies, or
algebraic number tricks
I can use deductive
reasoning to prove
conjectures.
I can analyze the
statements of an argument
to see if they are based on
correct reasoning.
I can identify mistakes in
proofs that lead to incorrect
conclusions (like 2 = 1).
I can solve problems
involving inductive or
deductive reasoning.
I can use reasoning
strategies to solve and
explain the solutions to
puzzles and games.
• guess and check
• analyze a pattern
• make a systematic list
• create a drawing or model
• eliminate possibilities
• solve simpler problems
• work backward
I can create my own puzzles
and games and describe the
strategies needed to solve
or win them.
I can search challenging
puzzles to solve using
inductive and deductive
reasoning strategies.
I can design and produce a
challenging game.