Number Sense and Operations:

Standard One:

• Students will understand numbers and ways of representing numbers, relationships among numbers, and number systems and
• understand meanings of operations and how they relate to one another.
• They will compute fluently and make reasonable estimates.

Benchmarks:

• 1.1 Understand numbers, ways of representing numbers, relationships among numbers.
• 1.2 Understand meanings of operations and how they relate to one another.
• 1.3 Compute fluently and make reasonable estimates.
• 1.4 Identify and use the properties of operations on real numbers, including the associative,  commutative, and distributive properties; the existence of the identity and inverse elements for addition and multiplication; the existence of nth roots of positive numbers for any positive integer n;
• 1.5 Express and simplify numerical expressions involving real numbers.
• 1.6 Understand and demonstrate algebraically and graphically the relationship between operations and their inverses, including exponential.
• 1.7 Use estimation to judge the reasonableness of results of computations and of solutions to problems involving real numbers.
• 1.8 Express real numbers in fractional and radical form as well as in exponential form using integral and fractional exponents.
• 1.9 Use logical reasoning as well as estimation and mental computation to determine the validity of a solution in algebraic, and statistical problems.

Data Analysis, Statistics and Probability

Standard Two:

• Students will formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.
• They will select and use appropriate statistical methods to analyze data and
• develop and evaluate inferences and predictions that are based on data and
• understand and apply basic concepts of probability.

Benchmarks:

• 2.1 Formulate questions that can be answered with data and collect, organize and display relevant data to answer them.
• 2.2 Select and use appropriate statistical methods to analyze data.
• 2.3 Develop and evaluate inferences and predictions that are based on data.
• 2.4 Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stem-and-leaf plot, box-and-whisker plot, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data.
• 2.5 Collect and graph data (using graphing calculators and/or computers when appropriate) and express relationships between variables, both verbally and symbolically.
• 2.6 Collect, organize, and analyze data from real problems using graphing calculators and other technology to create tables and graphs.
• 2.7 Approximate a line of best fit (trend line) given a set of data (e.g., scatterplot). Use technology when appropriate.
• 2.8 Use scatter plots of sets of data points to graph a line of best fit.
• 2.9 Use the basic set of operations with the help of Venn diagrams.
• 2.10 Solve counting problems using Venn diagrams.
• 2.11 Describe and explain how the relative sizes of a sample and the population affect the validity of predictions from a set of data.
• 2.12 Understand and apply basic concepts of probability.
• 2.13 Use tree diagrams, tables, organized lists, basic combinaations (“fundamental counting principle”), and area models to compute probabilities for simple compound events, e.g., multiple coin tosses or rolls of dice.
• 2.14 Carry out probability experiments, discuss the results.
• 2.15 Conduct experiments to determine experimental probabilities and construct a table to establish theoretical

Patterns, Relations and Algebra

Standard Three:

• Students will understand patterns, relations, and functions and represent and analyze
•  mathematical situations and structures using algebraic symbols. They will use
• mathematical models to represent and understand quantitative relationships and
• analyze change in various contexts.

Benchmarks:

• 3.1 Represent and analyze mathematical situations and structures using algebraic symbols.
• 3.2 Use mathematical models to represent and understand quantitative relationships.
• 3.3 Analyze change in various contexts.
• 3.4 Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative, recursive (e.g., Fibonacci Numbers), and linear functional relationships.
• 3.5 Use properties of the real number system to judge the validity of equations and inequalities, to prove or disprove statements, and to justify every step in a sequential argument.
• 3.6 Translate between different representations of functions and relations: graphs, equations, point sets, and tabular.
• 3.7 Demonstrate an understanding of the relationship between various representations of a line.
• 3.8 Determine a line’s slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the “slope y-intercept” formulas.
• 3.9 Explain the significance of a positive, negative, zero, or undefined slope.
• 3.10 Find linear equations that represent lines parallel to a given line and through a point, e.g., by using the “point-slope” form of the equation.
• 3.11 Solve equations apply to the solution of everyday problems.

Discussion, Presentation, Composition

• 4.1 Use agreed upon rules to participate in discussions in large and small groups.
• 4.2 Express ideas in an organized way.
• 4.3 Explain their mathematical thinking in writing.
• 4.4 Maintain a system for collecting, referring to, and sharing their work.