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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. |
| Algebraic Concepts |
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Algorithms: Create
The learner will be able to create algorithms to solve problems.
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Algorithms: Analyze
The learner will be able to analyze algorithms.
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Algorithms: Exploring/Validation
The learner will be able to explore problems which involve the validation of algorithms using calculators and computers.
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Equality/Inequality/Matrix: Interpreting
The learner will be able to interpret higher order equations, inequalities, and matrices using graphs and tables.
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Systems of Equations: Matrices
The learner will be able to solve systems of linear equations by applying matrix concepts.
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| Calculus and Pre-Calculus |
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Problem Solving: Graphs of Maxima/Minima
The learner will be able to find a maxima and minima of a graph and use it to solve a problem.
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Limiting Processes
The learner will be able to explore the following limiting processes by analyzing them graphically: infinite sequence, infinite series, and area under curves.
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Linear Programming: Problem Solving
The learner will be able to use the concept of linear programming to solve problems.
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Networks: Inductive/Deductive Reasoning
The learner will be able to explore networks using both inductive and deductive reasoning.
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Linear Programming: Represent Problems
The learner will be able to use concepts of linear programming to represent problems.
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Matrices: Variable Quantities/Represent
The learner will be able to use matrices to represent real-world situations where the amounts involved are variable.
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Matrices: Problem Solving
The learner will be able to apply matrix algebra to obtain problem solutions that make use of finite graphs.
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| Functions |
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Representations: Various Problems
The learner will be able to recognize how a function can be a model for a variety of problems.
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Non-Linear Functions: Represent
The learner will be able to model real life processes with logarithmic, exponential, and other non-linear functions.
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Graphing: Analyze/Parameter Changes
The learner will be able to analyze graphs of functions to determine the effects of parameter changes.
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Trigonometric/Circular Functions
The learner will be able to find similarities and differences between trigonometric and circular functions.
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Trigonometric Functions: Graphing
The learner will be able to graph trigonometric functions.
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| Geometry |
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Problem Solving: Transformations
The learner will be able to apply concepts of the different types of transformations in solving problems.
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Properties of Figures
The learner will be able to determine properties and relationships of figures by making assumptions and using given information.
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Problem Solving: Analytic Geometry
The learner will be able to solve both real-world and mathematical problems using concepts of analytic geometry.
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Geometric Concepts: Apply
The learner will be able to apply the concepts of vectors, phase shift, maxima, minima, points of inflection, and/or exact mathematical descriptions of symmetry to find and/or relate objects and their orientation.
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| Number Theory |
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Math Structures: Math Systems
The learner will be able to show that apparently unlike mathematical systems can be similar or identical.
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| Probability/Statistics |
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Statistical Experiments
The learner will be able to study a problem, establish the information needed to solve the problem, devise an experiment, carry it out, collect the data, draw conclusions based on the data, and communicate the results to others.
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Measures of Central Tendency: Applying
The learner will be able to use measures of central tendency to describe data.
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Variability: Applying
The learner will be able to use measures of variability to describe data.
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Correlation: Applying
The learner will be able to use measures of correlation to describe data.
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Measures of Central Tendency: Analyze
The learner will be able to analyze the changes in the measures of central tendency when a data transformation occurs.
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Variability: Analyze
The learner will be able to analyze the changes in the measures of variability when a data transformation occurs.
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Data: Transformation
The learner will be able to perform data transformation and understand how the transformation assists in both interpreting and making predictions with that data.
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Variate: Applying
The learner will be able to use random variable concepts.
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Distributions: Discrete/Create
The learner will be able to construct a discrete probability distribution.
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Distributions: Discrete/Interpret
The learner will be able to interpret a discrete probability distribution.
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Predictions: Curve Fitting
The learner will be able to make predictions from data using curve fitting.
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Uncertainty: Representing/Solving
The learner will be able to represent and solve problems of uncertainty by applying relative frequency and probability concepts.
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Probability Distribution: Normal Curve
The learner will be able to explain (in non-specific terms), the normal curve, and use its attributes in answering questions about data that is assumed to be normally distributed.
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Statistics
The learner will be able to apply appropriate statistics in the verification of hypotheses.
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Probability: Finite
The learner will be able to obtain solutions to problems of enumeration and/or finite probability.
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| Trigonometry |
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Triangles: Problem Solving
The learner will be able to solve real-world triangle problems using trigonometric concepts.
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Periodic Phenomena: Sine/Cosine
The learner will be able to investigate real-world phenomena which is periodic using the sine and cosine functions.
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