Vermont State Standards for Mathematics: Grade 12
VT.7.6. Mathematical Understanding: Arithmetic, Number, and Operation Concepts: Students understand arithmetic in computation, and they select and use, in appropriate situations, mental arithmetic, pencil and paper, calculator, and computer.
MHS:1. Accurately solves problems involving conceptual understanding and magnitude of real numbers, or simple vectors.
MHS:4. Accurately solves problems involving proportional reasoning or percents involving the effect of changing the base, rate, or percentage (the three cases of percent), or variations on order of finding percentages (10% off followed by 5% off), and compound interest.
MHS:7. Estimates and evaluates the reasonableness of numerical computations and solutions, including those carried out with technology.
MHS:8. Applies properties of numbers (greatest common factor [GCF], least common multiple [LCM], prime factorization, inverses, and identities), or properties of operations to solve problems and to simplify computations.
VT.7.7. Mathematical Understanding: Geometric and Measurement Concepts: Students use geometric and measurement concepts.
MHS:9. Models situations geometrically to solve problems connecting to other areas of mathematics or to other disciplines (i.e., diagrams, coordinate systems, transformations).
MHS:11. Uses the attributes, geometric properties, or theorems involving lines, polygons and circles (e.g., parallel, perpendicular, bisectors, diagonals, radii, diameters, central angles, arc length excluding radians), the Pythagorean Theorem, Triangle Inequality Theorem to solve mathematical situations or problems in context.
MHS:13. Applies concepts of similarity, congruency or right triangle trigonometry to determine length or angle measures and to solve problems involving scale.
MHS:14. Demonstrates conceptual understanding of perimeter, circumference, or area of two-dimensional figures or composites of two-dimensional figures or surface area or volume of three-dimensional figures or composites of three-dimensional figures in problem-solving situations and uses appropriate units of measure and expresses formulas for the perimeter, and area of two-dimensional figures or composites of two-dimensional figures or surface area or volume of three-dimensional figures or composites of three-dimensional figures.
MHS:15. Measures and uses units of measures appropriately and consistently when solving problems across the content strands. Makes conversions within or across systems and makes decisions concerning an appropriate degree of accuracy in problem situations involving measurement. Uses measurement conversion strategies, such as unit/dimensional analysis or uses quotient measures, such as speed and density, that give per unit amounts, or uses product measures, such as person hours to solve problems.
MHS:17. Constructs or accurately represents congruent angles, perpendicular lines, equilateral or isosceles triangles, triangle given the side segments, or inscribe or circumscribe a figure.
VT.7.8. Mathematical Understanding: Function and Algebra Concepts: Students use function and algebra concepts.
MHS:19. Solves and models problems by formulating, extending, or generalizing linear and common nonlinear functions/relations.) And makes connections among representations of functions/relations (equations, tables, graphs, symbolic notation, text).
MHS:20. Demonstrates conceptual understanding of linear relationships and linear and nonlinear functions (including f(x) = ax2, f(x) = ax3, absolute value function, exponential growth) through analysis of intercepts, domain, range and constant and variable rates of change in mathematical and contextual situations.
MHS:21. Demonstrates conceptual understanding of algebraic expressions by evaluating, simplifying, or writing algebraic expressions; and writes equivalent forms of algebraic expressions or formulas (d = rt maps into r = d/t or solves a multivariable equation or formula for one variable in terms of the others).
MHS:22. Demonstrates conceptual understanding of equality by solving linear equations, systems of two linear equations, or problems using tables, graphs, algebraic manipulation, or technology. Demonstrates conceptual understanding of inequality by solving linear inequalities, comparing values of systems of linear functions, using tables, graphs, algebraic manipulation, or technology.
VT.7.9. Mathematical Understanding: Statistics and Probability Concepts: Students use statistics and probability concepts.
MHS:23. Interprets a given representation(s) (box-and-whisker or scatter plots, histograms, frequency charts) to make observations, to answer questions or justify conclusions, to make predictions, or to solve problems.
MHS:24. Analyzes patterns, trends, or distributions in single variable and two variable data in a variety of contexts by determining or using measures of central tendency (mean, median, or mode), dispersion (range or variation), outliers, quartile values, or regression line or correlation (high, low/positive, negative) to analyze situations, or to solve problems; and evaluates the sample from which the statistics were developed (bias, random, or nonrandom).
MHS:25. Organizes and displays data using scatter plots, histograms, or frequency distributions to answer questions related to the data, to analyze the data to formulate or justify conclusions, make predictions, or to solve problems; or Identifies representations or elements of representations that best display a given set of data or situation, consistent with the representations required in MHS:23.
MHS:26. Uses combinations, arrangements or permutations to solve problems or to determine theoretical probability and experimental probability.
MHS:27. For a probability event chooses an appropriate probability model/simulations and uses it to estimate a theoretical probability for a chance event and uses the concept of a probability distribution to determine whether an event is rare or reasonably likely.
MHS:28. In response to a question, designs investigations, considers how data-collection methods affect the nature of the data set (i.e., sample size, bias, randomization, control group), collects data using observations, surveys and experiments, purposes and justifies conclusions and predictions based on the data.
MHS:29. Compares and contrasts theoretical and experimental probabilities of events; and determines and/or interprets the expected outcome of an event.
VT.7.10. Mathematical Problem Solving: Applications: Students use concrete, formal, and informal strategies to solve mathematical problems, apply the process of mathematical modeling, and extend and generalize mathematical concepts. Students apply mathematics as they solve scientific and technological problems or work with technological systems.
MHS:30. Demonstrate understanding of mathematical problem solving and communication by approach and reasoning - the strategies and skills used to solve the problem, and the reasoning that supports the approach.
MHS:31. Demonstrate understanding of mathematical problem solving and communication by execution - the answer and the mathematical work that supports it.
MHS:32. Demonstrate understanding of mathematical problem solving and communication by observations and extensions - demonstration of observation, connections, application, extensions, and generalizations.
MHS:33. Demonstrate understanding of mathematical problem solving and communication by mathematical communication - the use of mathematical vocabulary and representation to communicate the solution.
MHS:34. Demonstrate understanding of mathematical problem solving and communication by presentation - effective communication of how the problem was solved, and of the reasoning used.