Connecticut State Standards for Mathematics: Grade 11

CT.1. Algebraic Reasoning: Patterns And Functions: Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies.

1.1. Students should understand and describe patterns and functional relationships.

1.1.C.a. Core: Describe relationships and make generalizations about patterns and functions.

1.1.E.a. Extended: Model real-world situations and make generalizations about mathematical relationships using a variety of patterns and functions.

1.2. Students should represent and analyze quantitative relationships in a variety of ways.

1.2.C.a. Core: Represent and analyze linear and nonlinear functions and relations symbolically and with tables and graphs.

1.2.E.a. Extended: Relate the behavior of functions and relations to specific parameters and determine functions to model real-world situations.

1.3. Students should use operations, properties and algebraic symbols to determine equivalence and solve problems.

1.3.C.a. Core: Manipulate equations, inequalities and functions to solve problems.

1.3.E.a. Extended: Use and extend algebraic concepts to include real and complex numbers, vectors and matrices.

CT.2. Numerical and Proportional Reasoning: Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.

2.1. Students should understand that a variety of numerical representations can be used to describe quantitative relation-ships.

2.1.C.a. Core: Extend the understanding of number to include integers, rational numbers and real numbers.

2.1.C.b. Core: Interpret and represent large sets of numbers with the aid of technologies.

2.1.E.a. Extended: Extend the understanding of number to include the set of complex numbers.

2.2. Students should use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities.

2.2.C.a. Core: Develop strategies for computation and estimation using properties of number systems to solve problems.

2.2.C.b. Core: Solve proportional reasoning problems.

2.2.E.a. Extended: Investigate mathematical properties and operations related to objects that are not numbers.

CT.3. Geometry and Measurement: Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies.

3.1. Students should use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems.

3.1.C.a. Core: Investigate relationships among plane and solid geometric figures using geometric models, constructions and tools.

3.1.C.b. Core: Develop and evaluate mathematical arguments using reasoning and proof.

3.1.E.a. Extended: Use methods of deductive and inductive reasoning to make, test and validate geometric conjectures.

3.1.E.b. Extended: Explore non-Euclidean geometries.

3.2. Students should use spatial reasoning, location and geometric relationships to solve problems.

3.2.C.a. Core: Verify geometric relationships using algebra, coordinate geometry, and transformations.

3.2.E.a. Extended: Use a variety of coordinate systems and transformations to solve geometric problems in 2 and 3 dimensions using appropriate tools and technologies.

3.3. Students should develop and apply units, systems, formulas and appropriate tools to estimate and measure.

3.3.C.a. Core: Solve a variety of problems involving 1-, 2- and 3-dimensional measurements using geometric relationships and trigonometric ratios.

3.3.E.a. Extended: Approximate measurements that cannot be directly determined with some degree of precision using appropriate tools, techniques and strategies.

CT.4. Working with Data: Probability and Statistics: Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies.

4.1. Students should collect, organize and display data using appropriate statistical and graphical methods.

4.1.C.a. Core: Create the appropriate visual or graphical representation of real data.

4.1.E.a. Extended: Model real data graphically using appropriate tools, technologies and strategies.

4.2. Students should analyze data sets to form hypotheses and make predictions.

4.2.C.a. Core: Analyze real- world problems using statistical techniques.

4.2.E.a. Extended: Describe and analyze sets of data using statistical models.

4.3. Students should understand and apply basic concepts of probability.

4.3.C.a. Core: Understand and apply the principles of probability in a variety of situations.

4.3.E.a. Extended: Solve problems using the methods of discrete mathematics.

4.3.E.b. Extended: Make statistical inferences through the use of probability.