Wisconsin State Standards for Mathematics: Grade 9

WI.A. Mathematical Processes: 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 non-routine problems.

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.

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.

A.12.3. Analyze non-routine 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.

A.12.4. Develop effective oral and written presentations employing correct mathematical terminology, notation, symbols, and conventions for mathematical arguments and display of data.

A.12.5. Organize work and present mathematical procedures and results clearly, systematically, succinctly, and correctly.

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.

WI.B. Number Operations and Relationships: Students in Wisconsin will use numbers effectively for various purposes, such as counting, measuring, estimating, and problem solving.

B.12.1. Use complex counting procedures such as union and intersection of sets and arrangements (permutations and combinations) to solve problems.

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.

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).

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).

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.12.6. Routinely assess the acceptable limits of error when evaluating strategies; testing the reasonableness of results; using technology to carry out computations.

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

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.

C.12.2. Use geometric models to solve mathematical and real-world problems.

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).

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.

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

WI.D. Measurement: 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.

D.12.1. Identify, describe, and use derived attributes (e.g., density, speed, acceleration, pressure) to represent and solve problem situations.

D.12.2. Select and use tools with appropriate degree of precision to determine measurements directly within specified degrees of accuracy and error (tolerance).

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.

WI.E. Statistics and Probability: Students in Wisconsin will use data collection and analysis, statistics and probability in problem-solving situations, employing technology where appropriate.

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.

E.12.2. Organize and display data from statistical investigations using frequency distributions; percentiles, quartiles, deciles; line of best fit (estimated regression line); matrices.

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.

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.

WI.F. Algebraic Relationships: 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.

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.

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).

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.

F.12.4. Model and solve a variety of mathematical and real-world problems by using algebraic expressions, equations, and inequalities.