At
each grade level, with respect to content
appropriate
for that grade level, students will:
Standard 4.5
(Mathematical
Processes) All students will use mathematical
processes of problem solving, communication,
connections, reasoning, representations,
and technology to solve problems and communicate
mathematical ideas.
Standard 4.5.1.A
Problem
Solving
Standard 4.5.1.A.1
Learn
mathematics through problem solving, inquiry,
and discovery.
Standard 4.5.1.A.2
Solve
problems that arise in mathematics and in other
contexts (cf. workplace readiness standard
8.3).
· Open-ended problems
· Non-routine problems
· Problems with multiple solutions
· Problems that can be solved in several ways
Standard 4.5.1.A.3
Select
and apply a variety of appropriate problem-solving
strategies (e.g., "try a simpler problem" or "make
a diagram") to solve problems.
Standard 4.5.1.A.4
Pose
problems of various types and levels of difficulty.
Standard 4.5.1.A.5
Monitor
their progress and reflect on the process of
their problem solving activity.
Standard 4.5.1.B
Communication
Standard 4.5.1.B.1
Use
communication to organize and clarify their
mathematical thinking.
· Reading and writing
· Discussion, listening, and questioning
Standard 4.5.1.B.2
Communicate
their mathematical thinking coherently and
clearly to peers, teachers, and others, both
orally and in writing.
Standard 4.5.1.B.3
Analyze
and evaluate the mathematical thinking and
strategies of others.
Standard 4.5.1.B.4
Use
the language of mathematics to express mathematical
ideas precisely.
Standard 4.5.1.C
Connections
Standard 4.5.1.C.1
Recognize
recurring themes across mathematical domains
(e.g., patterns in number, algebra, and geometry).
Standard 4.5.1.C.2
Use
connections among mathematical ideas to explain
concepts (e.g., two linear equations have a
unique solution because the lines they represent
intersect at a single point).
Standard 4.5.1.C.3
Recognize
that mathematics is used in a variety of contexts
outside of mathematics.
Standard 4.5.1.C.4
Apply
mathematics in practical situations and in
other disciplines.
Standard 4.5.1.C.5
Trace
the development of mathematical concepts over
time and across cultures (cf. world languages
and social studies standards).
Standard 4.5.1.C.6
Understand
how mathematical ideas interconnect and build
on one another to produce a coherent whole.
Standard 4.5.1.D
Reasoning
Standard 4.5.1.D.1
Recognize
that mathematical facts, procedures, and claims
must be justified.
Standard 4.5.1.D.2
Use
reasoning to support their mathematical conclusions
and problem solutions.
Standard 4.5.1.D.3
Select
and use various types of reasoning and methods
of proof.
Standard 4.5.1.D.4
Rely
on reasoning, rather than answer keys, teachers,
or peers, to check the correctness of their
problem solutions.
Standard 4.5.1.D.5
Make
and investigate mathematical conjectures.
· Counterexamples as a means of disproving conjectures
· Verifying conjectures using informal reasoning or proofs.
Standard 4.5.1.D.6
Evaluate
examples of mathematical reasoning and determine
whether they are valid.
Standard 4.5.1.E
Representations
Standard 4.5.1.E.1
Create
and use representations to organize, record,
and communicate mathematical ideas.
· Concrete representations (e.g., base-ten blocks or algebra tiles)
· Pictorial representations (e.g., diagrams, charts, or tables)
· Symbolic representations (e.g., a formula)
· Graphical representations (e.g., a line graph)
Standard 4.5.1.E.2
Select,
apply, and translate among mathematical representations
to solve problems.
Standard 4.5.1.E.3
Use
representations to model and interpret physical,
social, and mathematical phenomena.
Standard 4.5.1.F
Technology
Standard 4.5.1.F.1
Use
technology to gather, analyze, and communicate
mathematical information.
Standard 4.5.1.F.2
Use
computer spreadsheets, software, and graphing
utilities to organize and display quantitative
information (cf. workplace readiness standard
8.4-D).
Standard 4.5.1.F.3
Use
graphing calculators and computer software
to investigate properties of functions and
their graphs.
Standard 4.5.1.F.4
Use
calculators as problem-solving tools (e.g.,
to explore patterns, to validate solutions).
Standard 4.5.1.F.5
Use
computer software to make and verify conjectures
about geometric objects.
Standard 4.5.1.F.6
Use
computer-based laboratory technology for mathematical
applications in the sciences (cf. science standards).
