School Improvement in Maryland

Using the State Curriculum: Mathematics, Grade 8

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Algebra:

Mathematics:

State Curriculum Toolkit

Tools aligned to State Curriculum indicators and/or objectives.

  • Clarification of Indicator and/or Objective
    Explanation and/or examples of indicator and/or objective
  • Lesson Seeds
    Ideas/seeds for an objective-aligned activity
  • Higher Order
    Thinking Skills

    Examples of questions at various levels of cognitive demand
  • Sample Assessments
    Items and annotated student responses as appropriate
  • Public Release Items
    Actual MSA items and annotated student responses as appropriate

Standard 1.0 Knowledge of Algebra, Patterns, and Functions

Students will algebraically represent, model, analyze, or solve mathematical or real-world problems involving patterns or functional relationships.

Topic

A. Patterns and Functions

Indicator

  • 1. Identify, describe, extend, and create patterns, functions and sequences
Objectives
  1. Determine the recursive relationship of arithmetic sequences represented in words, in a table or in a graph
    Assessment limit: Provide the nth term no more than 10 terms beyond the last given term using common differences no more than 10 with integers (-100 to 5000)
  2. Determine the recursive relationship of geometric sequences represented in words, in a table, or in a graph
    Assessment limit: Provide the nth term no more than 5 terms beyond the last given term using the recursive relationship of geometric sequences with whole numbers and a common ratio of no more than 5:1 (0 – 10,000)
  3. Determine whether relationships are linear or nonlinear when represented in words, in a table, symbolically, or in a graph
    Assessment limit: Use a graph to determine if a relationsip is linear or nonlinear
  4. Determine whether relationships are linear or nonlinear when represented symbolically

Topic

B. Expressions, Equations, and Inequalities

Indicator

  • 1. Write, simplify, and evaluate expressions
Objectives
  1. Write an algebraic expression to represent unknown quantities
    Assessment limit: Use one unknown and no more than 3 operations and rational numbers (-1000 to 1000)
  2. Evaluate an algebraic expression
    Assessment limit: Use one or two unknowns and up to three operations and rational numbers (-100 to 100)
  3. Evaluate numeric expressions using the order of operations
    Assessment limit: Use no more than 5 operations including exponents of no more than 3 and 2 sets of parentheses, brackets, a division bar, or absolute value with rational numbers (-100 to 100)
  4. Simplify algebraic expressions by combining like terms
    Assessment limit: Use no more than 3 variables with integers (-50 to 50), or proper fractions with denominators as factors of 20 (-20 to 20)
  5. Describe a real-world situation represented by an algebraic expression

Indicator

  • 2. Identify, write, solve, and apply equations and inequalities
Objectives
  1. Write equations or inequalities to represent relationships
    Assessment limit: Use a variable, the appropriate relational symbols (>, ≥, <, ≤, =) and no more than 3 operational symbols (+, -, ×, ÷) on either side and rational numbers (-1000 to 1000)
  2. Solve for the unknown in a linear equation
    Assessment limit: Use one unknown no more than 3 times on one side and up to three operations (same or different but only one division) and rational numbers (-2000 to 2000)
  3. Solve for the unknown in an inequality
    Assessment limit: Use a one- or two-operation inequality with one variable on one side no more than 3 times whose result after combining coefficients is a positive whole number coefficient with integers (-100 to 100)
  4. Identify or graph solutions of inequalities on a number line
    Assessment limit: Use one variable once with a positive whole number coefficient and integers (-100 to 100)
  5. Identify equivalent equations
    Assessment limit: Use one unknown no more than 3 times on one side and up to three operations (same or different but only one division) and integers (-2000 to 2000)
  6. Apply given formulas to a problem-solving situation
    Assessment limit: Use no more than four variables and up to three operations with rational numbers (-500 to 500)
  7. Write equations and inequalities that describe real-world problems

Topic

C. Numeric and Graphic Representations of Relationships

Indicator

Objective
  1. Graph linear equations in a coordinate plane
    Assessment limit: Use two unknowns having integer coefficients (-9 to 9) and integer constants (-20 to 20)

Indicator

  • 2. Analyze linear relationships
Objectives
  1. Determine the slope of a graph in a linear relationship
    Assessment limit: Use an equation with integer coefficients (-9 to 9) and integer constants (-20 to 20) and a given graph of the relationship
  2. Determine the slope of a linear relationship represented numerically or algebraically

Note: Highlighted assessment limits will be tested in the no calculator section of MSA. In the assessment limit, (0-10) or (-10 to 10) means all numbers in the problem or the answer will fall within the range of 0 to 10 (including endpoints) or -10 to 10 (including endpoints), respectively. All content standards are tested in MSA but not all objectives. Objectives that have an assessment limit are tested on MSA. Objectives without an assessment limit are not tested on MSA.

June 2004