Download MathematicalProofsLP

Mathematical Proof
Learning Target:
Materials:
Learning Target:
Prerequisites:
Learning Target:
Familiarity with informal
argumentation, basic
understanding of the
language of logic.
Learning Target:
Learning Target:
To disprove a
b statement, one must
find only one
instance for which
the statement is
false.
Success Criteria:
I can… use a
counterexample to disprove
a statement.
Formative assessment:
Quick discussion disproving
a statement about our
workshop.
Evidence of specific
instances may be
used to build a
conjecture in
mathematics, but is
not sufficient to
constitute a proof.
Success Criteria:
I can use specific instances
of mathematical
phenomena occurring to
build a conjecture.
Formative Assessment:
Ongoing throughout the
week. Gallery walk –
integer conjectures.
To prove a
statement, one must
use generalizations to
show the statement
holds for all instances
satisfying the
property.
Success Criteria:
I can use generalizations to
prove a statement. I can
determine when a proof is
sufficient to show a
statement holds for all
cases.
Formative Assessment:
Ongoing throughout the
week. Initial activity: T/F do
these count as proofs?
An alternative form of
counterproof is to
assume a statement is
true, build an argument
from that assumption,
and arrive at a logically
unsound conclusion,
proving the initial
assumption false.
Success Criteria:
I can… disprove a
conjecture using proof by
contradiction.
Formative Assessment:
Exit ticket – proof by
contradiction in nonmathematical context.
Mathematical proof
depends on building
arguments from
known statements
which lead logically
to other statements.
Big Idea:
Mathematical proof builds
arguments from purposefully
sequenced, logically sound
statements to show that a
particular statement holds
under all instances of a given
condition.
Success Criteria:
I can… construct a multistep mathematical proof
and evaluate the quality of
others’ mathematical
proofs.
Formative Assessment:
Writing assignment, peer
review proofs of integer
properties.
Later big ideas that
build on this big idea
include:
All mathematical
communication