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EAST LONGMEADOW PUBLIC SCHOOLS Mathematics The Massachusetts Mathematics Curriculum Framework envisions all students in the Commonwealth achieving mathematical competence through a strong mathematics program that emphasizes problem solving, communicating, reasoning and proof, making connections, and using representations. Acquiring such competence depends in large part on a clear, comprehensive, coherent, and developmentally appropriate set of standards to guide curriculum expectations. |
| Mathematics Processes |
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Inductive Reasoning
The learner will be able to reason using patterns.
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Deductive Reasoning
The learner will be able to reason using facts.
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Number Sequences
The learner will be able to recognize, extend, and interpret patterns in arithmetic and geometric sequences.
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| functions and their graphs |
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Cartesian coordinate System
The learner will be able to graph in the Cartesian Coordinate System.
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Graphing Functions
The learner will be able to graph lines, parabolas, hyperbolas, exponential functions and polynomial functions(to the fourth degree).
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Interpolation and Extrapolation
The learner will be able to interpret graphs, extrapolate and interpolate data from graphs.
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| Number Theory |
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Large Numbers
The learner will be able to write and perform computation of large numbers using exponential form, scientific notation and logarithmic notation in binary and base 10.
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Exponential functions
The learner will be able to graph, recognize and use real-life applications of exponential and logarithmic functions.
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| Symmetry |
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Line and rotational symmetry
The learner will be able to recognize and create examples of line and rotational symmetry.
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Regular Polygons
The learner will be able to recognize, name,and determine the measure of the central angle, individual interior and exterior angles, and the sum of the measures of the interior and exterior angles of regular polygons.
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Tessellations
The learner will be able to create mathematical mosaics by determining which polygons tessellate and knowing properties of and methods of construction of regular and semi-regular mosaics.
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Regular Polyhedra
The learner will be able to recognize the properties of the five regular polyhedra (tetrahedron, octahedron, cube, icosahedron and dodecahedron) and how to construct these polyhedra.
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Pyramids and Prisms
The learner will be able to identify, describe the properties of and construct regular pyramids and prisms.
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| Mathematical Curves |
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Conic Sections
The learner will be able to recognize and interpret graph of circles, hyperbolas, ellipses and parabolas, understand construction of each conic and the relationship of the foci, center, directrix, and asymptotes where appropriate.
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Sine Curve
The learner will be able to graph sine function, using both Cartesian and Polar Coordinate Systems, and determine the amplitude, frequency, and wavelength from the Cartesian graph.
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Spirals
The learner will be able to recognized Archimedean and logarithmic spirals, the relationship of spirals to arithmetic and geometric sequences, and graph spirals using polar coordinates.
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Cycloids
The learner will be able to recognize the graph and properties of a cycloid and construct a cycloid and its variations.
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| Methods of Counting |
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Counting Principle
The learner will be able to apply the basic counting principle.
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Factorial Notation
The learner will be able to use factorial notation and apply it to solve problems.
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Permutations
The learner will be able to use proper notation, compute, and apply permutations, including those with repetition.
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Combinations
The learner will be able to use proper notation and compute and apply combinations.
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| Probability/Statistics |
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Probability
The learner will be able to define and compute the probability of casino games, independent and dependent events, and complementary events.
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Binomial probabilities
The learner will be able to recognize the characteristics and apply binomial probability including the use of Pascal's Triangle.
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Introduction to Statistics
The learner will be able to display data in statistical graphs, including non-numeric data in Bar, Circle and Pictograms, and numerical data in line Graphs and Histograms.
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Apply Statistics
The learner will be able to apply statistics to decoding.
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Statistical Measures
The learner will be able to perform statistical measures of central tendency, including arithmetic mean, median, and mode; measures of variability, including range and standard deviation; and apply variability to graph of the normal curve.
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Collecting Data
The learner will be able to recognize the difference between sample and population and the characteristics of a random sample.
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| Topology |
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Mathematics of Distortion
The learner will be able to recognize closed curves and topological equivalence.
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Networks
The learner will be able to to recognize the degree of a network and Euler Paths, Topological trees, including vertices and diameters; and apply concepts to analyze the Seven Bridges of Konigsberg problem.
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Moebius
The learner will be able to create a Moebius Strip and recognize its properties.
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