| Mathematics |
Information & Technology
Literacy |
Content Standards:A.
Mathematical Processes
B. Number Operations
and Relationships
C. Geometry
D. Measurement
E. Statistics and Probability
F. Algebraic Relationships |
Content Standards:A. Media and Technology
B. Information and Inquiry
C. Independent Learning
D. The Learning Community |
| A.
Mathematical Processes |
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| By the end of grade 12 students will: |
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| A.12.1 Use reason and logic to |
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- select information clearly related to the problem or question—B.12.4
- evaluate information for stereotyping, prejudice, and misrepresentation—B.12.4
- distinguish among fact, opinion, point of view, and inference—B.12.4
- determine if sources are authoritative, valid, reliable, accurate, relevant, and
comprehensive—B.12.4
- evaluate graphic images for misleading presentation and manipulated data—B.12.4
- determine authorship for all resources and identify points of agreement and disagreement
among sources—B.12.4
- use data-gathering strategies that include summarizing, paraphrasing, comparing, and
quoting—B.12.5
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- analyze and relate information using a variety of relational techniques (e.g., graphic
organizers, database reports, spreadsheet charts, graphs)—B.12.5
- organize information in systematic manner for unity, coherence, clarity, and
emphasis—B.12.5
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- analyze and relate information using a variety of relational techniques (e.g., graphic
organizers, database reports, spreadsheet charts, graphs)—B.12.5
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- formulate questions, pose problems, and make and test conjectures
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- develop specific research questions or a thesis statement based on the nature, purpose,
and scope of project—B.12.1
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- pursue ideas that lead to further understanding and deeper insight
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- synthesize new ideas, evidence, and prior knowledge to address the problem or
question—B.12.6
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| A.12.2 Communicate logical
arguments and clearly show |
B.12.7 Communicate the results
of research and inquiry in an appropriate format |
- why a result does or does not make sense
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- why the reasoning is or is not valid
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- an understanding of the difference between examples that support a conjecture
and a proof of the conjecture
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| 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 |
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| A.12.4 Develop effective oral and written presentations employing correct
mathematical terminology, notation, symbols, and conventions for mathematical arguments
and display of data
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A.12.3 Use a computer and productivity software to organize and create
information
use an integrated program or applications suite to complete a class
assignment—A.12.3
manipulate graphics objects in a word processing program (e.g., select, move, modify,
delete, duplicate, arrange)—A.12.3
use desktop publishing and graphics software to produce page layouts in different
formats (e.g., brochure, tri-fold, newsletter)—A.12.3
analyze data from a database and present conclusions in a document or report—A.12.3
construct a spreadsheet, enter data into cells, use mathematical functions to
manipulate/process data, generate a chart or graph, and interpret the results—A.12.3
use a computer and graphical organizer software to generate modifiable flow charts,
project time lines, organizational charts, or calendars—A.12.3
A.12.4 Use a
computer and communications software to access and transmit information
use desktop conferencing, e-mail, or groupware to communicate with others regarding
assignments or class projects—A.12.4
participate in an on-line discussion group or listserv appropriate to a content
area—A.12.4
A.12.5 Use
media and technology to create and present information
use draw, paint, graphics, or presentation software to visually communicate ideas or
concepts—A.12.5
develop a document or file for inclusion into a website or web page—A.12.5
participate in a desktop conferencing session to present and share information with
others—A.12.5
B.12.7
Communicate the results of research and inquiry in an appropriate format
determine the audience and purpose for communicating the information—B.12.7
compare strengths and weaknesses of possible presentation methods and
products—B.12.7
select the most appropriate format for the product or presentation—B.12.7
develop a product or presentation that utilizes the strengths of the medium and supports
the conclusions drawn in the research effort—B.12.7
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| A.12.5 Organize work and present mathematical procedures and results clearly,
systematically, succinctly, and correctly |
B.12.5 Record and organize information
organize information in systematic manner for unity, coherence, clarity, and
emphasis—B.12.5
B.12.6
Interpret and use information to solve the problem or answer the question
draw conclusions and support them with credible evidence—B.12.6
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| A.12.6 Read and understand |
C.12.3 Develop competence and
selectivity in reading, listening, and viewing |
- mathematical texts and other instructional materials
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- writing about mathematics (e.g., articles in journals)
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- mathematical ideas as they are used in other contexts
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| B.
Number Operations and Relationships |
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| By the end of grade 12 students will: |
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| B.12.1 Use complex counting
procedures such as union and intersection of sets and arrangements (permutations and
combinations) to solve problems. |
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| B.12.2 Compare real numbers
using |
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- order relations (>, <) and transitivity
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- ordinal scales including logarithmic (e.g., Richter, pH rating)
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- ratios, proportions, percents, rates of change
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| 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) |
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| B.12.4 In problem-solving
situations involving the application of different number systems (natural, integers,
rational, real) select and use appropriate |
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- properties (e.g., commutativity, associativity, inverses)
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- modes of representation (e.g., rationals as repeating decimals, indicated roots
as fractional exponents)
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| 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) |
B.12.5 Record and organize information
analyze and relate information using a variety of relational techniques (e.g., graphic
organizers, database reports, spreadsheet charts, graphs)—B.12.5
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- testing the reasonableness of results
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- using technology to carry out computations
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gather and organize statistical or survey data
using e-mail, listservs, or on-line news or discussion groups—A.12.4 |
| C. Geometry |
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| By the end of grade 12 students will: |
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| C.12.1 Identify, describe, and analyze properties of figures, relationships among
figures, and relationships among their parts by |
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- constructing physical models
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- drawing precisely with paper and pencil, hand calculators, and computer software
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- use a computer and graphical organizer software to generate modifiable flow charts,
project time lines, organizational charts, or calendars—A.12.3
- use draw, paint, graphics, or presentation software to visually communicate ideas or
concepts—A.12.5
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- using appropriate transformations (e.g., translations, rotations, reflections,
enlargements)
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- use a computer and graphical organizer software to generate modifiable flow charts,
project time lines, organizational charts, or calendars—A.12.3
- use draw, paint, graphics, or presentation software to visually communicate ideas or
concepts—A.12.5
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| C.12.2 Use geometric models to solve mathematical and real-world problems |
- use draw, paint, graphics, or presentation software to visually communicate ideas or
concepts—A.12.5
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| C.12.3 Present convincing arguments by means of demonstration, informal proof,
counter-examples, or any other logical means to show the truth of |
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- statements (e.g., "these two triangles are not congruent")
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- generalizations (e.g., "the Pythagorean theorem holds for all right
triangles")
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- interpret new information to formulate ideas which address the question or problem using
comparison, evaluation, inference, and generalization skills—B.12.6
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| 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 |
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| C.12.5 Identify and
demonstrate an understanding of the three ratios used in right-triangle trigonometry
(sine, cosine, tangent) |
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| D. Measurement |
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| By the end of grade 12 students will: |
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| D.12.1 Identify, describe, and use derived attributes (e.g., density, speed,
acceleration, pressure) to represent and solve problem situations |
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| D.12.2 Select and use tools
with appropriate degree of precision to determine measurements directly within specified
degrees of accuracy and error (tolerance) |
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| D.12.3 Determine measurements
indirectly, using |
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- proportional reasoning, including those involving squaring and cubing (e.g.,
reasoning that areas of circles are proportional to the squares of their radii)
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- techniques of algebra, geometry, and right triangle trigonometry
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- formulas in applications (e.g., for compound interest, distance formula)
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- geometric formulas to derive lengths, areas, or volumes of shapes and objects
(e.g., cones, parallelograms, cylinders, pyramids)
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- 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)
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| By the end of grade 12 students will: |
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| E.12.1 Work with data in the
context of real-world situations by |
B.12.1 Define the need for
information
B.12.2 Develop information seeking strategies
B.12.3 Locate and access information sources
B.12.4 Evaluate and select information from a variety of print, nonprint, and electronic
formats
B.12.5 Record and organize information
B.12.6 Interpret and use information to solve the problem or answer the question
B.12.7 Communicate the results of research and inquiry in an appropriate format
B.12.8 Evaluate the information product and process |
- formulating hypotheses that lead to collection and analysis of one- and
two-variable data
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- state the information problem or question in clear and concise terms—B.12.1
- relate prior knowledge to the problem or question—B.12.1
- develop specific research questions or a thesis statement based on the nature, purpose,
and scope of project—B.12.1
- conduct a preliminary search to determine if the research questions or thesis statement
is clear and searchable; refine and revise if necessary—B.12.1
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- designing a data collection plan that considers random sampling, control groups,
the role of assumptions, etc.
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- develop a plan to obtain needed information using a variety of research and
investigative strategies (e.g., interviews, questionnaires, experiments,
surveys)—B.12.2
- establish goals, plans, budgets, and timelines for completing a project—C.12.4
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- conducting an investigation based on that plan
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- identify a full range of appropriate and available information from local, national, and
global sources—B.12.2
- determine and apply evaluative criteria to prioritizing potential sources—B.12.2
- pursue a variety of resources reflecting differing points of view, cultures, and
disciplines—B.12.2
- identify and evaluate keywords, concepts, subject headings, and descriptors for each
information source—B.12.2
- locate information using the classification system and catalog in use at a variety of
libraries and resource agencies—B.12.3
- construct effective electronic and manual searches using keywords, phrases, Boolean
logic, and limiters—B.12.3
- determine when to use general or specialized print and electronic reference
tools—B.12.3
- compare, evaluate, and select appropriate Internet search engines and
directories—B.12.3
- select information clearly related to the problem or question—B.12.4
- evaluate information for stereotyping, prejudice, and misrepresentation—B.12.4
- distinguish among fact, opinion, point of view, and inference—B.12.4
- determine if sources are authoritative, valid, reliable, accurate, relevant, and
comprehensive—B.12.4
- determine authorship for all resources and identify points of agreement and disagreement
among sources—B.12.4
- use data-gathering strategies that include summarizing, paraphrasing, comparing, and
quoting—B.12.5
- credit sources for all quotations, visuals, major ideas, and specific facts or data
using accepted citation formats—B.12.5
- analyze and relate information using a variety of relational techniques (e.g., graphic
organizers, database reports, spreadsheet charts, graphs)—B.12.5
- organize information in systematic manner for unity, coherence, clarity, and
emphasis—B.12.5
- compile a bibliography in a format stipulated by an accepted manual of style—B.12.5
- interpret new information to formulate ideas which address the question or problem using
comparison, evaluation, inference, and generalization skills—B.12.6
- synthesize new ideas, evidence, and prior knowledge to address the problem or
question—B.12.6
- draw conclusions and support them with credible evidence—B.12.6
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- using technology to generate displays, summary statistics, and presentations
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- use desktop publishing and graphics software to produce page layouts in different
formats (e.g., brochure, tri-fold, newsletter)—A.12.3
- analyze data from a database and present conclusions in a document or report—A.12.3
- construct a spreadsheet, enter data into cells, use mathematical functions to
manipulate/process data, generate a chart or graph, and interpret the results—A.12.3
- use a computer and graphical organizer software to generate modifiable flow charts,
project time lines, organizational charts, or calendars—A.12.3
- gather and organize statistical or survey data using e-mail, listservs, or on-line news
or discussion groups—A.12.4
- use draw, paint, graphics, or presentation software to visually communicate ideas or
concepts—A.12.5
- produce a multimedia program using text, graphics, moving images, and sound—A.12.5
- develop a document or file for inclusion into a website or web page—A.12.5
- participate in a desktop conferencing session to present and share information with
others—A.12.5
- select the most appropriate format for the product or presentation—B.12.7
- develop a product or presentation that utilizes the strengths of the medium and supports
the conclusions drawn in the research effort—B.12.7
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| E.12.2 Organize and display data from statistical investigations using |
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- percentiles, quartiles, deciles
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- line of best fit (estimated regression line)
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- construct a spreadsheet, enter data into cells, use mathematical functions to
manipulate/process data, generate a chart or graph, and interpret the results—A.12.3
- use a computer and graphical organizer software to generate modifiable flow charts,
project time lines, organizational charts, or calendars—A.12.3
- use draw, paint, graphics, or presentation software to visually communicate ideas or
concepts—A.12.5
- analyze and relate information using a variety of relational techniques (e.g., graphic
organizers, database reports, spreadsheet charts, graphs)—B.12.5
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| E.12.3 Interpret and analyze information from organized and displayed data when
given |
- analyze data from a database and present conclusions in a document or report—A.12.3
- construct a spreadsheet, enter data into cells, use mathematical functions to
manipulate/process data, generate a chart or graph, and interpret the results—A.12.3
- use a computer and graphical organizer software to generate modifiable flow charts,
project time lines, organizational charts, or calendars—A.12.3
- analyze and relate information using a variety of relational techniques (e.g., graphic
organizers, database reports, spreadsheet charts, graphs)—B.12.5
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- measures of dispersion, including standard deviation and variance
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| E.12.4 Analyze, evaluate, and critique the methods and conclusions of statistical
experiments reported in journals, magazines, news media, advertising, etc. |
B.12.4 Evaluate and select information from a variety of print, nonprint, and
electronic formats
evaluate information for stereotyping, prejudice, and misrepresentation—B.12.4
distinguish among fact, opinion, point of view, and inference—B.12.4
determine if sources are authoritative, valid, reliable, accurate, relevant, and
comprehensive—B.12.4
evaluate graphic images for misleading presentation and manipulated data—B.12.4
determine authorship for all resources and identify points of agreement and disagreement
among sources—B.12.4
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| E.12.5 Determine the likelihood of occurrence of complex events by |
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- using a variety of strategies (e.g., combinations) to identify possible outcomes
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- develop a plan to obtain needed information using a variety of research and
investigative strategies (e.g., interviews, questionnaires, experiments,
surveys)—B.12.2
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- designing and conducting simulations
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- applying theoretical probability
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| F. Algebraic
Relationships |
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| By the end of grade 12 students will: |
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| 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 |
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| F.12.2
Use mathematical functions (e.g., linear, exponential, quadratic, power) in a variety of
ways, including |
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- recognizing that a variety of mathematical and real-world phenomena can be modeled by
the same type of function
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- translating different forms of representing them (e.g., tables, graphs, functional
notation, formulas)
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- demonstrate how to import and export text, graphic, and sound files—A.12.2
- manipulate graphics objects in a word processing program (e.g., select, move, modify,
delete, duplicate, arrange)—A.12.3
- construct a spreadsheet, enter data into cells, use mathematical functions to
manipulate/process data, generate a chart or graph, and interpret the results—A.12.3
- use draw, paint, graphics, or presentation software to visually communicate ideas or
concepts—A.12.5
- analyze and relate information using a variety of relational techniques (e.g., graphic
organizers, database reports, spreadsheet charts, graphs)—B.12.5
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- describing the relationships among variable quantities in a problem
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- using appropriate technology to interpret properties of their graphical representations
(e.g., intercepts, slopes, rates of change, changes in rates of change, maximum, minimum)
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- construct a spreadsheet, enter data into cells, use mathematical functions to
manipulate/process data, generate a chart or graph, and interpret the results—A.12.3
- use draw, paint, graphics, or presentation software to visually communicate ideas or
concepts—A.12.5
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| F.12.3 Solve linear and
quadratic equations, linear inequalities, and systems of linear equations and inequalities |
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- graphically, including use of appropriate technology
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- use draw, paint, graphics, or presentation software to visually communicate ideas or
concepts—A.12.5
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- symbolically, including use of the quadratic formula
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| F.12.4 Model and solve a variety of mathematical and real-world
problems by using algebraic expressions, equations, and inequalities |
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Matrix developed by Wisconsin Department of Public Instruction |
