MATHEMATICS
Grade 12 Standards Met
A.12.1
Use reason and logic to
evaluate
information
perceive
patterns
identify
relationships
formulate
questions, pose problems, and make and test conjectures
pursue
ideas that lead to further understanding and deeper insight
[ALNC*; BHNC+; CM*+; ICF+; MKE*; OBG+; UWA*]
A.12.2
Communicate logical arguments and clearly show
why
a result does or does not make sense
why
the reasoning is or is not valid
an
understanding of the difference between examples that support a conjecture and a
proof of the conjecture
[ALNC*; BHNC*; CM*+; ICF+; MKE*; OBG+]
A.12.3
Analyze nonroutine* problems and arrive at solutions by various means,
including models* and simulations, often starting with provisional conjectures
and progressing, directly or indirectly, to a solution, justification, or
counter-example
[ALNC*; CM*+; ICF+; UWA+]
A.12.4
Develop effective oral and written presentations employing correct
mathematical terminology, notation, symbols, and conventions for mathematical
arguments and display of data
[ALNC*; ICF+]
A.12.5
Organize work and present mathematical procedures and results clearly,
systematically, succinctly, and correctly
[ICF+]
A.12.6
Read and understand
mathematical
texts and other instructional materials
writing
about mathematics (e.g., articles in journals)
mathematical
ideas as they are used in other contexts
[BHNC*]
B.12.1
Use complex counting procedures such as union and intersection of sets
and arrangements (permutations* and combinations*) to solve problems.
[UWA+]
B.12.2
Compare real numbers using
order
relations (>, <) and transitivity*
ordinal
scales including logarithmic (e.g., Richter, pH rating)
arithmetic differences
ratios,
proportions, percents, rates of change
[ALNC*; CM*; ICF+]
B.12.3
Perform and explain operations on real numbers (add, subtract, multiply,
divide, raise to a power, extract a root, take opposites and reciprocals,
determine absolute value)
[ALNC*; ICF+]
B.12.4
In problem-solving situations involving the application of different
number systems (natural, integers, rational*, real*) select and use appropriate
computational
procedures
properties
(e.g., commutativity*, associativity*, inverses*)
modes
of representation (e.g., rationals as repeating decimals, indicated roots as
fractional exponents)
[ALNC*; CM*]
B.12.5
Create and critically evaluate numerical arguments presented in a variety
of classroom and real-world situations (e.g., political, economic, scientific,
social)
[ALNC*; BHNC*; CM*; ICF+; MKE*; UWA+]
B.12.6
Routinely assess the acceptable limits of error when
evaluating
strategies
testing
the reasonableness of results
using
technology to carry out computations
[ALNC*; UWA+]
C.12.1
Identify, describe, and analyze properties of figures, relationships
among figures, and relationships among their parts by
constructing
physical models
drawing
precisely with paper and pencil, hand calculators, and computer software
using
appropriate transformations* (e.g., translations, rotations, reflections,
enlargements)
using
reason and logic
[ALNC*]
C.12.2
Use geometric models* to solve mathematical and real-world problems
[ALNC*]
C.12.3
Present convincing arguments by means of demonstration, informal proof,
counter-examples, or any other logical means to show the truth of
·
statements (e.g., these two triangles are not
congruent)
generalizations
(e.g., the Pythagorean* theorem holds for all right triangles)
[ALNC*]
C.12.4
Use the two-dimensional rectangular coordinate system* and algebraic
procedures to describe and characterize geometric properties and relationships
such as slope*, intercepts*, parallelism, and perpendicularity
[ALNC*; CM*]
C.12.5
Identify and demonstrate an understanding of the three ratios used in
right-triangle trigonometry (sine, cosine, tangent)
D.12.1
Identify, describe, and use derived attributes* (e.g., density, speed,
acceleration, pressure) to represent and solve problem situations
[ALNC*; CM¨]
D.12.2
Select and use tools with appropriate degree of precision to determine
measurements directly* within specified degrees of accuracy and error
(tolerance)
[ALNC*]
D.12.3
Determine measurements indirectly*, using
estimation
proportional
reasoning, including those involving squaring and cubing (e.g., reasoning that
areas of circles are proportional to the squares of their radii)
techniques
of algebra, geometry, and right triangle trigonometry
formulas
in applications (e.g., for compound interest, distance formula)
geometric
formulas to derive lengths, areas, or volumes of shapes and objects (e.g.,
cones, parallelograms, cylinders, pyramids)
geometric
relationships and properties of circles and polygons (e.g., size of central
angles, area of a sector of a circle)
conversion
constants to relate measures in one system to another (e.g., meters to feet,
dollars to Deutschmarks)
[ALNC*; BHNC*; CM*; UWA*]
E.12.1
Work with data in the context of real-world situations by
formulating
hypotheses that lead to collection and analysis of one- and two-variable data
designing
a data collection plan that considers random sampling, control groups, the role
of assumptions, etc.
conducting
an investigation based on that plan
using
technology to generate displays, summary statistics*, and presentations
[ALNC*; BHNC*; CM*+; ICF+; OBG+; UWA+]
E.12.2
Organize and display data from statistical investigations using
frequency distributions
percentiles*,
quartiles, deciles
line of
best fit* (estimated regression line)
matrices
[ALNC*; CM+]
E.12.3
Interpret and analyze information from organized and displayed data when
given
measures
of dispersion*, including standard deviation and variance
measures
of reliability
measures
of correlation*
[ALNC*; CM+; ICF+]
E.12.4
Analyze, evaluate, and critique the methods and conclusions of
statistical experiments reported in journals, magazines, news media,
advertising, etc.
E.12.5
Determine the likelihood of occurrence of complex events by
using
a variety of strategies (e.g., combinations*) to identify possible outcomes
conducting an experiment
designing
and conducting simulations*
applying
theoretical probability
[ALNC*; CM+]
F.12.1
Analyze and generalize patterns of change (e.g., direct and inverse
variation) and numerical sequences, and then represent them with algebraic
expressions and equations
[ICF+]
F.12.2
Use mathematical functions* (e.g., linear*, exponential*, quadratic*,
power) in a variety of ways, including
recognizing
that a variety of mathematical and real-world phenomena can be modeled* by the
same type of function
translating
different forms of representing them (e.g., tables, graphs, functional
notation*, formulas)
describing
the relationships among variable quantities in a problem
using
appropriate technology to interpret properties of their graphical
representations (e.g., intercepts, slopes, rates of change, changes in rates of
change, maximum*, minimum*)
[ALNC*; CM*+; ICF+]
F.12.3
Solve linear and quadratic equations, linear inequalities, and systems of
linear equations and inequalities
numerically
graphically,
including use of appropriate technology
symbolically,
including use of the quadratic formula
[ALNC*]
F.12.4
Model and solve a variety of mathematical and real-world problems by
using algebraic expressions, equations, and inequalities
[ALNC*; BHNC]