Gizmos for New York - Mathematics: High School (New York City: Performance Standards adopted )

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

1.1.1: M1. Number and Operation Concepts

1.1.1.1: M1a. Use addition, subtraction, multiplication, division, exponentiation, and root-extraction.

1.1.1.1: M1b. Understand and use opposite, reciprocal, raising to a power, taking a root, and taking a logarithm.

1.1.1.1: M1c. Have facility with the mechanics of operations as well as understanding of their typical meaning and uses in applications.

1.1.1.1: M1d. Understand and use number systems.

1.1.1.1: M1e. Represent numbers in various forms and graph them.

1.1.1.1: M1f. Compare numbers using order relations, differences, ratios, proportions, percents, and proportional change.

1.1.1.1: M1g. Carry out proportional reasoning.

1.1.1.1: M1h. Understand dimensionless numbers as well as numbers with specific units of measure.

1.1.1.1: M1i. Carry out counting procedures such as those involving sets and arrangements.

1.1.1.1: M1j. Use concepts in solving problems involving integers.

1.1.1.1: M1l. Recognize and represent basic number patterns.

1.1.1: M2. Geometry and Measurement Concepts

1.1.1.1: M2b. Work with two- and three- dimensional figures and their properties.

1.1.1.1: M2c. Use congruence and similarity in describing relationships between figures.

1.1.1.1: M2d. Visualize objects, paths, and regions in space and describe these using geometric language.

1.1.1.1: M2e. Know, use, and derive formulas for perimeter, circumference, area, surface area, and volume.

1.1.1.1: M2f. Use the Pythagorean Theorem in many types of situations.

1.1.1.1: M2g. Work with similar triangles and use the three basic trigonometric functions.

1.1.1.1: M2h. Analyze figures in terms of their symmetries.

1.1.1.1: M2i. Compare slope and angle of elevation as measures of steepness.

1.1.1.1: M2j. Investigate geometric patterns.

1.1.1.1: M2k. Work with geometric and non-geometric measures.

1.1.1.1: M2l. Use quotient measures and product measures.

1.1.1.1: M2o. Represent geometric curves and graphs of functions in standard coordinate systems.

1.1.1.1: M2p. Analyze geometric figures and prove simple things about them using deductive methods.

1.1.1: M3. Function and Algebra Concepts

1.1.1.1: M3b. Describes, generalizes, and uses basic types of functions: linear, exponential, power, rational, square and square root, and cube and cube root.

1.1.1.1: M3c. Utilizes the concepts of slope, evaluation, and inverse in working with functions.

1.1.1.1: M3d. Works with rates of many kinds, expressed numerically, symbolically, and graphically.

1.1.1.1: M3e. Represents constant rates as the slope of a straight line graph, and interprets slope as the amount of one quantity (y) per unit amount of another (x).

1.1.1.1: M3f. Understands and uses linear functions as a mathematical representation of proportional relationships.

1.1.1.1: M3g. Uses arithmetic sequences and geometric sequences and their sums, and sees these as the discrete forms of linear and exponential functions, respectively.

1.1.1.1: M3h. Defines, uses, and manipulates expressions involving variables, parameters, constants, and unknowns in work with formulas, functions, equations, and inequalities.

1.1.1.1: M3i. Represents functional relationships in formulas, tables, and graphs, and translates between pairs of these.

1.1.1.1: M3j. Solves equations symbolically, graphically, and numerically, especially linear, quadratic, and exponential equations; and knows how to use the quadratic formula for solving quadratic equations.

1.1.1.1: M3k. Makes predictions by interpolating or extrapolating from given data or a given graph.

1.1.1.1: M3l. Understands the basic algebraic structure of number systems.

1.1.1.1: M3m. Uses equations to represent curves such as lines, circles, and parabolas.

1.1.1.1: M3o. Uses functions to analyze patterns and represent their structure.

1.1.1: M4. Statistics and Probability Concepts

1.1.1.1: M4a. Organizes, analyzes, and displays single-variable data, choosing appropriate frequency distribution, circle graphs, line plots, histograms, and summary statistics.

1.1.1.1: M4b. Organizes, analyzes, and displays two-variable data using scatter plots, estimated regression lines, and computer generated regression lines and correlation coefficients.

1.1.1.1: M4c. Uses sampling techniques to draw inferences about large populations.

1.1.1.1: M4d. Understands that making an inference about a population from a sample always involves uncertainty and that the role of statistics is to estimate the size of that uncertainty.

1.1.1.1: M4e. Formulates hypotheses to answer a question and uses data to test hypotheses.

1.1.1.1: M4f. Interprets representations of data, compares distributions of data, and critiques conclusions and the use of statistics, both in school materials and in public documents.

1.1.1.1: M4h. Creates and uses models of probabilistic situations and understands the role of assumptions in this process.

1.1.1.1: M4i. Uses concepts such as equally likely, sample space, outcome, and event in analyzing situations involving chance.

1.1.1.1: M4j. Constructs appropriate sample spaces, and applies the addition and multiplication principles for probabilities.

1.1.1.1: M4k. Uses the concept of a probability distribution to discuss whether an event is rare or reasonably likely.

1.1.1.1: M4l. Chooses an appropriate probability model and uses it to arrive at a theoretical probability for a chance event.

1.1.1.1: M4m. Uses relative frequencies based on empirical data to arrive at an experimental probability for a chance event.

1.1.1.1: M4n. Designs simulations including Monte Carlo simulations to estimate probabilities.

1.1.1.1: M4o. Works with the normal distribution in some of its basic applications.

1.1.1: M6. Mathematical Skills and Tools

1.1.1.1: M6b. Use a variety of methods to estimate the values, in appropriate units, to an appropriate degree of accuracy.

1.1.1.1: M6f. Use the number line and Cartesian coordinates in the plane and in space.

1.1.1.1: M6h. Set up and solve equations symbolically and graphically.

1.1.1.1: M6l. Use tools in solving problems.

Correlation last revised: 9/5/2008

New York - Mathematics: High School

New York City: Performance Standards | Adopted:

1.1.1: M1. Number and Operation Concepts

1.1.1: M2. Geometry and Measurement Concepts

1.1.1: M3. Function and Algebra Concepts

1.1.1: M4. Statistics and Probability Concepts

1.1.1: M6. Mathematical Skills and Tools