Mathematics Standards Grade 12

Content Standard: Students in Wisconsin will draw on a broad body of mathematical knowledge and apply a variety of mathematical skills and strategies, including reasoning, oral and written communication, and the use of appropriate technology, when solving mathematical, real-world* and nonroutine* problems.

• 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

• 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

• mathematical texts and other instructional materials
• writing about mathematics (e.g., articles in journals)
• mathematical ideas as they are used in other contexts

Content Standard: Students in Wisconsin will use numbers effectively for various purposes, such as counting, measuring, estimating, and problem solving.

• order relations (>, <) and transitivity*
• ordinal scales including logarithmic (e.g., Richter, pH rating)
• arithmetic differences
• ratios, proportions, percents, rates of change

Content Standard:  Students in Wisconsin will be able to use geometric concepts, relationships and procedures to interpret, represent, and solve problems.

• 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

• statements (e.g., "these two triangles are not congruent")
• generalizations (e.g., "the Pythagorean* theorem holds for all right triangles")

C.12.5 Identify and demonstrate an understanding of the three ratios used in right-triangle trigonometry (sine, cosine, tangent)

Content Standard:  Students in Wisconsin will select and use appropriate tools (including technology) and techniques to measure things to a specified degree of accuracy. They will use measurements in problem-solving situations.

• 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)

E. STATISTICS AND PROBABILITY

 Content Standard: Students in Wisconsin will use data collection and analysis, statistics and probability in problem-solving situations, employing technology where appropriate.

• 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

• frequency distributions
• percentiles*, quartiles, deciles
• line of best fit* (estimated regression line)
• matrices

• measures of dispersion*, including standard deviation and variance
• measures of reliability
• measures of correlation*

• using a variety of strategies (e.g., combinations*) to identify possible outcomes
• conducting an experiment
• designing and conducting simulations*
• applying theoretical probability

Content Standard: Students in Wisconsin will discover, describe, and generalize simple and complex patterns and relationships. In the context of real-world problem situations, the student will use algebraic techniques to define and describe the problem to determine and justify appropriate solutions.

• 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*)

• numerically
• graphically, including use of appropriate technology
• symbolically, including use of the quadratic formula

Standards developed by Wisconsin Department of Public Instruction