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STEM.M.MATHEMATICS: National Council of Teachers of Mathematics (NCTM)
MATHEMATICS: National Council of Teachers of Mathematics (NCTM)
NCTM.1. Number and Operations 1.1. Understand numbers, ways of representing numbers, relationships among numbers, and number systems. 1.1.1. Develop a deeper understanding of very large and very small numbers and of various representations of them.
1.1.2. Compare and contrast the properties of numbers and number systems, including the rational and real numbers, and understand complex numbers as solutions to quadratic equations that do not have real solutions.
1.2. Understand meanings of operations and how they relate to one another. 1.2.1. Judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities.
1.2.3. Develop an understanding of permutations and combinations as counting techniques.
1.3. Compute fluently and make reasonable estimates. 1.3.1. Develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases.
1.3.2. Judge the reasonableness of numerical computations and their results.
NCTM.2. Algebra 2.1. Understand patterns, relations, and functions. 2.1.2. Understand relations and functions and select, convert flexibly among, and use various representations for them. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
2.1.3. Analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior.
2.1.5. Understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
2.2. Represent and analyze mathematical situations and structures using algebraic symbols. 2.2.2. Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency - mentally or with paper and pencil in simple cases and using technology in all cases.
2.2.3. Use symbolic algebra to represent and explain mathematical relationships.
2.3. Use mathematical models to represent and understand quantitative relationships. 2.3.2. Use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts.
2.3.3. Draw reasonable conclusions about a situation being modeled.
NCTM.3. Geometry 3.1. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. 3.1.1. Analyze properties and determine attributes of two- and three-dimensional objects.
3.1.2. Explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them.
3.2. Specify locations and describe spatial relationships using coordinate geometry and other representational systems. 3.2.1. Use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations.
3.2.2. Investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian coordinates.
3.3. Apply transformations and use symmetry to analyze mathematical situations. 3.3.1. Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices.
3.3.2. Use various representations to help understand the effects of simple transformations and their compositions.
NCTM.4. Measurement 4.2. Apply appropriate techniques, tools, and formulas to determine measurements. 4.2.2. Understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders.
NCTM.5. Data Analysis and Probability 5.1. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them. 5.1.2. Know the characteristics of well-designed studies, including the role of randomization in surveys and experiments.
5.1.4. Understand histograms, parallel box plots, and scatterplots and use them to display data.
5.1.5. Compute basic statistics and understand the distinction between a statistic and a parameter.
5.2. Select and use appropriate statistical methods to analyze data. 5.2.1. For univariate measurement data, students should be able to display the distribution, describe its shape, and select and calculate summary statistics.
5.2.2. For bivariate measurement data, students should be able to display a scatterplot, describe its shape, and determine regression coefficients, regression equations, and correlation coefficients using technological tools.
5.3. Develop and evaluate inferences and predictions that are based on data. 5.3.2. Understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference.
5.3.3. Evaluate published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions.
5.4. Understand and apply basic concepts of probability 5.4.4. Understand the concepts of conditional probability and independent events.
NCTM.6. Problem Solving 6.1. Build new mathematical knowledge through problem solving.
6.2. Solve problems that arise in mathematics and in other contexts.
6.3. Apply and adapt a variety of appropriate strategies to solve problems.
NCTM.7. Reasoning and Proof 7.1. Recognize reasoning and proof as fundamental aspects of mathematics.
7.2. Make and investigate mathematical conjectures.
7.3. Develop and evaluate mathematical arguments and proofs.
7.4. Select and use various types of reasoning and methods of proof.
NCTM.9. Connections 9.2. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.