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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. Grade 8 Algebra 1 The Massachusetts Mathematics Curriculum Framework provides learning standards for students in grades 7-8. |
| Algebraic Concepts |
| The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. This unit includes studying number systems, operations, and forms. Students explore the symbolic nature of algebraic concepts by identifying and extending patterns in algebra, by following algebraic procedures, and by proving theorems with properties. The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. Students explore the symbolic nature of algebraic concepts by identifying and extending patterns in algebra, by following algebraic procedures, and by proving theorems with properties. |
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Absolute Value: Solve/Linear/Apply
The learner will be able to obtain solutions to equations and inequalities of absolute value of linear expressions and apply them to problem solutions.
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Expressions: Simplify/Numeric/Solve
The learner will be able to simplify numeric expressions, including expressions containing positive integer exponents or absolute value, and obtain problem solutions by applying these simplifications.
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Polynomials: Manipulation
The learner will be able to illustrate facility in symbolic manipulation of polynomial and rational expressions by rearranging and collecting terms, factoring, recognizing and canceling common factors in rational expressions, and using the properties of positive integer exponents.
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Quadratic Equations: Solve/Techniques
The learner will be able to obtain solutions to quadratic equations with real number solutions by factoring, completing the square, or applying the quadratic formula; and illustrate an understanding of the similarities between these techniques.
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Properties: Recognize/Use
The learner will be able to recognize and apply the properties of operations on the 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 real numbers for any positive integer n; the inverse relationship between nth power and nth root of a positive real number; and the denseness of the set of rational numbers in the set of the real numbers.
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Systems of Equations: Solve/Inequalities
The learner will be able to obtain solutions to real world problems (including mixture, rate, and work problems) by applying systems of linear equations or inequalities, using algebraic and graphical techniques.
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Equations: Algebraic/Solve
The learner will be able to obtain solutions to algebraic equations.
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Equations: Problem Solving
The learner will be able to apply equations in obtaining problem solutions.
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Inequalities: Solve
The learner will be able to solve inequalities.
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Polynomials: Subtracting
The learner will be able to subtract polynomials.
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Polynomials: Add
The learner will be able to add polynomials.
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Polynomials: Multiply
The learner will be able to multiply polynomials.
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Polynomials: Divide by Monomial
The learner will be able to divide a polynomial by a monomial.
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Radicals: Determine/Estimate/Solution
The learner will be able to determine the estimated value for the solution to problems involving square roots and cube roots, without the use of a calculator.
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Equality/Inequality: Solving
The learner will be able to use inequalities to solve problems.
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Equality/Inequality: Apply/Real Number
The learner will be able to apply the properties of the real number system to evaluate the validity of equations and inequalities.
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| Functions |
| The Functions Unit includes exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. |
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Functions/Relations: Representations
The learner will be able to translate between the different representations (graphs, equations, point sets, and tabular) of functions and relations.
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Relations: Comprehend
The learner will be able to comprehend relations.
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Functions: Recognize/Domain
The learner will be able to recognize the domain of a given function.
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Functions: Recognize/Range
The learner will be able to recognize the range of a given function.
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Functions: Recognize/Variables
The learner will be able to recognize the dependent and independent variables of a given function.
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Functions: Understand
The learner will be able to understand functions.
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Functions: Solve/Real-World
The learner will be able to use linear functions in order to obtain solutions to real-world problems.
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Functions: Solve/Real-World
The learner will be able to use exponential functions in order to obtain solutions to real-world problems.
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Functions: Solve/Real-World
The learner will be able to use quadratic functions in order to obtain solutions to real-world problems.
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Functions: Solve/Real World
The learner will be able to use reciprocal functions in order to obtain solutions to real world problems.
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| Mathematics Processes |
| The Mathematics Processes Unit focuses on mathematical connections, communication, modeling, concepts and procedures. The Mathematics Processes Unit includes Competencies/Objectives which focus on mathematical connections. Students communicate and model concepts and procedures. |
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Arguments: Apply/Real Number Properties
The learner will be able to apply the properties of the real number system to justify each step in a sequential argument.
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| Numeration |
| The Numeration Unit focuses on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships. The Numeration Unit includes Competencies/Objectives which focus on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships. |
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Patterns: Linear/Quadratic/Exponential
The learner will be able to explain, complete, continue, examine, generalize, and construct a wide variety of patterns, including iterative, recursive, linear, quadratic, and exponential relationships.
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Direct Variation: Apply/Problem Solve
The learner will be able to apply direct variation to obtain solutions to real world problems.
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Inverse Variation: Apply/Problem Solve
The learner will be able to apply inverse variation to obtain solutions to real world problems.
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| Perspective/Role in Society |
| The Perspective/Role in Society Unit focuses on real-world mathematics. This units includes mathematics in society and the role of mathematics in personal finance and careers. |
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Interest: Apply/Compound/Real World
The learner will be able to apply compound interest to obtain solutions to real world problems.
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| Probability/Statistics |
| The Probability/Statistics Unit focuses on data analysis and probability concepts. This unit includes collecting, analyzing, and making sense of real-world data (including overlapping data, inconclusive data, etc.). The Probability/Statistics Unit includes Competencies/Objectives which focus on data analysis and probability concepts. Students collect, analyze, and make sense of real world data (including overlapping data, inconclusive data, etc.). |
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Data Analysis: Choose/Create/Interpret
The learner will be able to choose, create, and interpret a suitable graphical display for data sets and apply suitable statistics to communicate information about the data, applying these concepts in comparing different data sets.
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Data: Estimate/Line of Best Fit
The learner will be able to estimate a line of best fit for a given set of data.
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Sampling: Explain/Size/Validity/Predict
The learner will be able to explain how the relative sizes of a sample and the population affect the validity of predictions made based on a data set.
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| Real Numbers and the Coordinate Plane |
| The Real Numbers and the Coordinate Plane Unit includes graphing equations, and making connections between algebraic concepts and their geometric correspondences. The Real Numbers and the Coordinate Plane Unit includes Competencies/Objectives which focus on graphing concepts. Students graph equations and make connections between algebraic concepts and their geometric correspondences. |
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Slope: Describe/Significance
The learner will be able to describe the significance of a positive, negative, zero, or undefined slope.
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Slope: Determine From Graph
The learner will be able to use the graph of a linear equation to determine the slope.
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Linear Equations: Graph
The learner will be able to find the equation of a line when given its graph.
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Linear Equations: Understand/Forms
The learner will be able to illustrate an understanding of the relationships between the various presentation forms of lines.
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Linear Equations: Intercepts
The learner will be able to find the intercepts of a linear equation.
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Linear Equations: Slope
The learner will be able to find the slope of a linear equation.
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Linear Equations: Geometric Explanation
The learner will be able to determine the linear equation when presented with a geometric description of the line.
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Linear Equations: Determine/Equation
The learner will be able to determine the equation of the line through a point that is either perpendicular or parallel to a particular line.
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Linear Equations: X-/Y-Intercepts
The learner will be able to find the x- and y-intercepts of a line when given the graph of a linear relationship.
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Real Numbers: Approximate/Computation
The learner will be able to judge the reasonableness of computation results involving real numbers using approximations.
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Real Numbers: Approximate/Solutions
The learner will be able to judge the reasonableness of problem solutions involving real numbers using approximations.
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Real Number Properties: Apply/Proofs
The learner will be able to apply the properties of the real number system to prove or contradict statements.
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| Technology |
| The Technology Unit includes studying computer hardware and software, uses for calculators, and applications of technology in problem solving. The Technology Unit includes Competencies/Objectives which focus on studying computer hardware and software, uses for calculators, and applications of technology in problem solving. |
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Technology as a Tool: Suitable
The learner will be able to apply technology as appropriate.
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