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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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Absolute Value
The learner will be able to evaluate expressions, apply the definition of absolute value, recognize absolute value expressions on number lines, and solve equations by finding the solution sets.
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Absolute Value Expressions: Undefined
The learner will be able to determine the value(s) of a variable in the denominator for which an expression containing absolute values is undefined.
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Absolute Value: Equations/Inequalities
The learner will be able to obtain solutions to absolute value equations and inequalities.
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Absolute Value: Graph/Equation
The learner will be able to create graphs of absolute value equations.
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Absolute Value: Graphing Inequalities
The learner will be able to determine solutions for and the graphs of inequalities which involve absolute values.
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Algebraic Concepts: Applying Methods
The learner will be able to apply algebraic methods to solve problems involving rate, work, and percent mixture.
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Algebraic Concepts: Model/Table/Rule
The learner will be able to represent a given algebra problem using a model, table, and number sentence or equation.
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Algebraic Concepts: Problem Solving
The learner will be able to use algebraic methods to solve real-world problems.
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Binomial Expansion: Simplify
The learner will be able to apply the Binomial Theorem to simplify expressions.
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Binomial Theorem: Expanding
The learner will be able to expand powers of binomial expressions by applying the Binomial Theorem.
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Binomials: Applying Basic Operations
The learner will be able to add, subtract, multiply and divide with binomial expressions.
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Binomials: Multiply
The learner will be able to find the product of two binomials which involve square roots.
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Equality/Inequality: One Variable
The learner will be able to solve both equations and inequalities with one variable.
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Equations: Quadratic/Solve
The learner will be able to solve a quadratic equation where a perfect square equals a constant.
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Equations: Second Degree/Factoring
The learner will be able to find solutions for second degree equations by factoring.
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Equations: Solve
The learner will be able to use logarithmic expressions to obtain solutions to equations.
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Equation: Solve/Variable
The learner will be able to solve an equation for one variable in terms of another.
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Equations: Formulas
The learner will be able to solve expressions and equations by applying formulas.
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Equations: Solve/Pairs
The learner will be able to obtain solutions to pairs of equations, when one is quadratic and one is linear, or when both are quadratic.
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Equations: Solve/Radicals
The learner will be able to solve an equation containing a radical.
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Expansion: Pascal's Triangle
The learner will be able to use the properties of Pascal's triangle to determine coefficients of an expansion.
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Exponents: Apply/Rules/Problem Solve
The learner will be able to obtain solutions to problems through the use of the rules of exponents.
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Exponents: Comprehend/Negative
The learner will be able to comprehend negative whole number exponents.
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Exponents: Evaluate Expressions
The learner will be able to evaluate expressions involving powers and/or roots.
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Expressions: Adding Fractions
The learner will be able to add variable fraction expressions with different denominators, simplifying the results.
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Expressions: Distributive Property
The learner will be able to understand and apply the distributive property in expressions that may contain variables.
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Expressions: Properties/Simplify
The learner will be able to use properties of operations with rational numbers to simplify expressions.
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Factorials: Begin Understand
The learner will be able to begin to understand factorial notation.
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Factoring
The learner will be able to factor trinomials, find the difference of two squares, find missing terms which complete perfect square trinomials, find the length and width of a rectangle when given the area (a trinomial), identify deductive arguments based on principles of factoring, describe the inverse relationship between multiplying polynomials and factoring, and use combined types of factoring.
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Factoring: Greatest Common Monomial
The learner will be able to apply the greatest common monomial factor to factor polynomial expressions.
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Factoring: Difference of Squares
The learner will be able to factor the difference between two squares.
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Factoring: Polynomials
The learner will be able to factor trinomials, perfect square trinomials, or the difference between two squares.
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Factoring: Factoring Out Monomials
The learner will be able to factor out a monomial from an expression.
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Factoring: Problem Solving
The learner will be able to obtain problem solutions through factoring.
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Factoring: Quadratic
The learner will be able to solve a quadratic equation by factoring.
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Factors: Factor Theorem/Polynomials
The learner will be able to apply the factor theorem in determining factors of higher degree polynomials.
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Formula: Apply/Distance/Slope/Midpoint
The learner will be able to apply formulas to determine distance, midpoint, and slope.
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Formulas: Apply/Distance/Slope/Midpoint
The learner will be able to apply formulas to determine distance, midpoint, and slope to solve problems.
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Formulas: Write/Equation of Lines
The learner will be able to apply formulas to write equations of lines.
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Graphing/2 Variables
The learner will be able to graph a linear equation in two variables.
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Identify Operation: Single Step
The learner will be able to identify a suitable operation to use in single step problems.
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Inequalities
The learner will be able to solve for the value of a variable given in an inequality and as shown on a graph by manipulating the inequality correctly.
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Inequalities: Algebraic/Solve
The learner will be able to obtain solutions to algebraic inequalities.
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Inequalities: Apply/Linear
The learner will be able to apply linear inequalities.
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Inequalities: Combined/Solution Set
The learner will be able to determine the solution set for a combined inequality.
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Inequalities: Graph/Number Line
The learner will be able to graph inequalities on a number line.
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Inequalities: Graph/Simple/Compound
The learner will be able to graph simple and compound inequalities on a number line.
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Inequalities: Linear/Graph
The learner will be able to create a graph for the solution set of a system of linear inequalities in two variables.
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Inequalities: Solve/Linear/Systems
The learner will be able to obtain solutions to systems of two linear inequalities in two variables and sketch the solution sets.
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Inequalities: Solving
The learner will be able to solve quadratic inequalities.
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Inverse Operations: Apply/Square/Root
The learner will be able to apply the inverse relationship between squaring and taking the square root to simplify computation and obtain problem solutions.
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Linear Equation: Graph/2-Variables
The learner will be able to graph linear equations in two variables, including vertical and horizontal lines.
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Linear Equations: Differentiate
The learner will be able to differentiate between linear and non-linear equations.
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Linear Equations: Solve
The learner will be able to obtain solutions to linear equations.
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Logarithmic Equations
The learner will be able to solve equations involving logarithms.
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Logarithmic Equations: Exponents
The learner will be able to express logarithmic equations using exponents.
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Logarithmic: Evaluate/Expressions
The learner will be able to evaluate logarithmic expressions.
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Logarithms: Express as Exponents
The learner will be able to transform logarithmic equations into exponential equations and vice versa.
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Logarithms: Solving/Variable
The learner will be able to solve a logarithmic equation for the value of a variable.
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Logarithms: Solving/Variable Exponent
The learner will be able to solve an expression in the form a X b to the x power = c for x using logarithms.
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Logarithms: Use/Change of Base Rule
The learner will be able to use the change of base rule.
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Monomial: Rules Exponents
The learner will be able to apply the rules of exponents to multiply and divide monomials.
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Monomial: Rules Exponents
The learner will be able to multiply monomials by polynomials using the rules of exponents.
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Monomials: Add/Subtract
The learner will be able to add and subtract monomials.
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Monomials: Multiplying
The learner will be able to multiply monomials.
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Multiple Step Story Problems
The learner will be able to solve a story problem requiring multiple calculations.
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Operations: Division by Zero
The learner will be able to describe how division by zero is impossible.
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Order of Operations
The learner will be able to demonstrate an understanding of the standard algebraic order of operations.
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Order of Operations: Apply
The learner will be able to apply the order of operations.
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Pascal's Triangle: Explore/Patterns
The learner will be able to investigate patterns in Pascal's Triangle.
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Polynomial Equations: Solving
The learner will be able to solve polynomial equations using the appropriate method.
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Polynomial: Identify/Degree
The learner will be able to identify the degree of polynomials.
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Polynomials: Problem Solving
The learner will be able to apply polynomial equations up to fourth degree to obtain solutions to problems by factoring.
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Polynomials: Solve/Factoring
The learner will be able to solve polynomial equations by factoring.
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Polynomials: Synthetic Division
The learner will be able to solve polynomials which involve synthetic division.
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Polynomials: Writing/Using Roots
The learner will be able to given its roots, write a polynomial equation.
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Quadratic Equation: Factoring
The learner will be able to solve quadratic equations by factoring.
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Quadratic Equation: Quadratic Formula
The learner will be able to solve quadratic equations by applying the quadratic formula.
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Quadratic Equations: Complete the Square
The learner will be able to determine the roots and solution of a quadratic equation by completing the square and factoring.
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Quadratic Equations: Equation/Roots
The learner will be able to determine a quadratic equation when its roots are given.
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Quadratic Equations: Graphing
The learner will be able to graph a quadratic equation on the coordinate plane.
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Quadratic Equations: Solve
The learner will be able to apply a method for obtaining solutions to quadratic equations over the set of complex numbers.
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Quadratic Equations: Solving/Calculator
The learner will be able to solve quadratic equations to the nearest decimal approximation by using the quadratic formula and a calculator.
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Quadratic Inequalities: Solve/Factoring
The learner will be able to solve quadratic inequalities by factoring.
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Radical Equations: Solve
The learner will be able to obtain solutions to radical equations using appropriate strategies.
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Radical: Graph/Equations
The learner will be able to graph radical equations.
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Radicals: Equations/Basic/Solve
The learner will be able to solve basic radical equations.
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Radicals: Square Roots/Simplify
The learner will be able to simplify radical expressions with square roots.
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Radicals: Simplify
The learner will be able to simplify the sums, differences, products, and quotients of radical expressions.
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Remainder/Factor Theorems
The learner will be able to apply the remainder and factor theorems.
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System of Equations: Solve
The learner will be able to obtain solutions (if they exist) to a linear system of equations.
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System of Equations: Solve Problems
The learner will be able to apply a system of linear equations to obtain problem solutions.
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Systems of Equations
The learner will be able to calculate solutions to systems of linear equations.
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Systems of Equations: Cramer's Rule
The learner will be able to apply Cramer's Rule to obtain solutions to systems of equations in two or three variables.
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Systems of Equations: Describe/Solution
The learner will be able to solve and describe the solutions of systems of equations found by substitution.
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Systems of Equations: Describe/Solution
The learner will be able to solve and describe the solution of systems of equations found by graphing.
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Systems of Equations: Describe/Solution
The learner will be able to solve and describe the solutions of systems of equations found by addition or subtraction.
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Systems of Equations: Elimination
The learner will be able to solve a system of linear equations by addition.
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Systems of Equations: Graphing
The learner will be able to graph systems of equations.
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Systems of Equations: Graphing
The learner will be able to solve a system of linear equations by graphing.
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Systems of Equations: Identify
The learner will be able to identify inconsistent systems of equations.
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Systems of Equations: Interpret
The learner will be able to make comparisons and interpretations of graphs of linear systems of equations.
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Systems of Equations: Quadratic
The learner will be able to solve a system of equations involving quadratic equations.
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Translate Problems: Determine/Solution
The learner will be able to translate a problem scenario into a basic mathematical equation and determine the solution.
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Variable: Identify/Unknown Quantity
The learner will be able to identify that a variable is used to illustrate an unknown quantity.
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