Number Systems
Learning Target:
Materials:
Learning Target:
Prerequisites:
Familiarity with arithmetic
operations, prime numbers,
and roots of algebraic
equations.
Learning Target:
Learning Target:
Learning Target:
The natural numbers
are closed under
addition and
multiplication
Success Criteria:
I can… determine if an
infinite subset of the natural
numbers is closed under an
operation and justify my
conclusion.
Formative assessment:
Whiteboard gallery walk
investigating closure of
subsets under various
properties.
The integers are
closed under
addition, subtraction,
and multiplication
Success Criteria:
I can determine if a finite or
infinite subset of the
integers is closed under an
operation and justify my
conclusion. I can create a
symbolic generalization for
a subset of the integers
based on the subset’s
properties.
Formative Assessment:
Groups will be assigned
subsets to generalize
symbolically, devise two
closure questions, and swap
with another group to
investigate closure.
The rational numbers
are closed under
addition, subtraction,
multiplication, and
division.
Success Criteria:
I can… determine if a
number is rational. I can
determine if an infinite
subset of the rationals is
closed under an operation
and justify my conclusion.
Formative Assessment:
Group presentations
proving closure of one
subset of rational under an
operation, non-closure of
the set under a different
operation.
The irrational numbers
are included in the real
numbers to allow for
non-repeating and nonterminating decimals,
constructible (but nonrational) lengths, and
solutions to algebraic
equations, among other
numbers.
Success Criteria:
I can…determine if a
number is irrational and
generate irrational
numbers. I can determine
if a finite subset of
irrational numbers is closed
under an operation. I can
approximate an irrational
number with a rational
number.
Formative Assessment:
Writing activity – formal
proof that a given number
is irrational and
approximation of that
quantity by a rational
number.
The real numbers are
either algebraic or
transcendental.
Big Idea:
Each level of number in the
real number system is closed
under more operations than
the previous level, or
incorporates numbers which
are needed to represent
phenomena which cannot be
represented by lower-level
numbers.
Success Criteria:
I can… determine if a
number is algebraic or
transcendental. I can sketch
a proof of the existence of
transcendental numbers. I
can determine if a subset of
the reals is algebraic or
transcendental.
Formative Assessment:
Gallery walk – proving
subsets are algebraic or
transcendental. Venn
diagram of the real
numbers.
Later big ideas that
build on this big idea
include:
Everything in
mathematics???
Algebra, calculus,
analysis, topology …