School Improvement in Maryland

VSC: Mathematics Grade 8

Document Date: June 2004
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Standard 1.0 Knowledge of Algebra, Patterns, and Functions

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 limits:
    • 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)
  1. Determine the recursive relationship of geometric sequences represented in words, in a table, or in a graph
    Assessment limits:
  1. Determine whether relationships are linear or nonlinear when represented in words, in a table, symbolically, or in a graph
    Assessment limits:
    • Use a graph to determine if a relationsip is linear or nonlinear
  1. 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 limits:
    • Use one unknown and no more than 3 operations and rational numbers (-1000 to 1000)
  1. Evaluate an algebraic expression
    Assessment limits:
    • Use one or two unknowns and up to three operations and rational numbers (-100 to 100)
  1. Evaluate numeric expressions using the order of operations
    Assessment limits:
    • 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)
  1. Simplify algebraic expressions by combining like terms
    Assessment limits:
    • Use no more than 3 variables with integers (-50 to 50), or proper fractions with denominators as factors of 20 (-20 to 20)
  1. 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 limits:
    • Use a variable, the appropriate relational symbols (>, ≥, <, ≤, =) and no more than 3 operational symbols (+, -, ×, ÷) on either side and rational numbers (-1000 to 1000)
  1. Solve for the unknown in a linear equation
    Assessment limits:
    • 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)
  1. Solve for the unknown in an inequality
    Assessment limits:
    • 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)
  1. Identify or graph solutions of inequalities on a number line
    Assessment limits:
    • Use one variable once with a positive whole number coefficient and integers (-100 to 100)
  1. Identify equivalent equations
    Assessment limits:
    • 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)
  1. Apply given formulas to a problem-solving situation
    Assessment limits:
    • Use no more than four variables and up to three operations with rational numbers (-500 to 500)
  1. Write equations and inequalities that describe real-world problems

Topic

C. Numeric and Graphic Representations of Relationships

Indicator

Objectives

  1. Graph linear equations in a coordinate plane
    Assessment limits:
    • 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 limits:
  1. Determine the slope of a linear relationship represented numerically or algebraically

Standard 2.0 Knowledge of Geometry

Topic

A. Properties of Plane Geometric Figures

Indicator

  • 1. Analyze the properties of plane geometric figures

Objectives

  1. Identify and describe geometric relationships between angles formed when parallel lines are cut by a transversal.
    Assessment limits:
    • Use alternate interior, alternate exterior, or corresponding angles
  1. Identify and describe the relationship among the parts of a right triangle
    Assessment limits:
    • Use the hypotenuse or the legs of right triangles

Indicator

  • 2. Analyze geometric relationships

Objectives

  1. Determine the measurements of angles formed by parallel lines cut by a transversal
    Assessment limits:
    • Use alternate interior, alternate exterior, and corresponding angles
  1. Apply right angle concepts to solve real-world problems
    Assessment limits:
  1. Determine whether three given side lengths form a right triangle

Topic

C. Representation of Geometric Figures

Indicator

  • 1. Represent plane geometric figures

Objectives

  1. Draw quadrilaterals
    Assessment limits:
    • Provide given whole number dimensions in inches or centimeters or angle measurements
  1. Construct perpendicular line segments
    Assessment limits:
    • Provide a given point on a given line segment
  1. Construct triangles
    Assessment limits:
    • Construct a triangle congruent to a given triangle

Topic

D. Congruence and Similarity

Indicator

  • 1. Apply the properties of similar polygons

Objectives

  1. Determine similar parts of polygons
    Assessment limits:
    • Use the length of corresponding sides or the measure of corresponding angles and rational numbers with no more than 2 decimal places (0 – 1000)

Topic

E. Transformations

Indicator

Objectives

  1. Identify, describe, and plot the results of multiple transformations on a coordinate plane
    Assessment limits:
    • Identify or plot the result of two transformations on one figure using translations (horizontal or vertical), reflections (horizontal or vertical), or rotations about a given point (90° or 180°)

Standard 3.0 Knowledge of Measurement

Topic

C. Applications in Measurement

Indicator

  • 1. Estimate and apply measurement formulas

Objectives

  1. Estimate and determine the circumference or area of a circle
    Assessment limits:
    • Include circles using rational numbers with no more than 2 decimal places (0 – 10,000)
  1. Estimate and determine area of a composite figure
    Assessment limits:
    • Include composite figures with no more than 6 polygons (triangles, rectangles, or circles) by measuring, partitioning, or using formulas with whole number dimensions (0 - 10,000)
  1. Estimate and determine the volume of a cylinder
    Assessment limits:
    • Use cylinders, given the formula, and whole number dimensions (0-10,000)
  1. Determine the volume of cones, pyramids, and spheres
  1. Determine the surface area of cylinders, prisms, and pyramids

Indicator

  • 2. Analyze measurement relationships

Objectives

  1. Use proportional reasoning to solve measurement problems
    Assessment limits:

Standard 4.0 Knowledge of Statistics

Topic

A. Data Displays

Indicator

  • 1. Organize and display data

Objectives

  1. Organize and display data to make circle graphs
    Assessment limits:
    • Use no more than 5 categories with data in whole number percents
  1. Organize and display data to make box-and-whisker plots
    Assessment limits:
    • Use no more than 12 pieces of data and whole numbers (0 – 1000)
  1. Organize and display data to make a scatter plot
    Assessment limits:

Topic

B. Data Analysis

Indicator

  • 1. Analyze data

Objectives

  1. Interpret tables
    Assessment limits:
    • Use no more than 5 categories having no more than 2 quantities per category and whole numbers or decimals with no more than 2 decimal places (0 – 100)
  1. Interpret box-and-whisker plots
    Assessment limits:
    • Use minimum, first (lower) quartile, median (middle quartile), third (upper) quartile, or maximum and whole numbers (0 – 100)
  1. Interpret scatter plots
    Assessment limits:
    • Use no more than 10 points using whole numbers or decimals with no more than 2 decimal places (0 – 100)
  1. Interpret circle graphs
    Assessment limits:
    • Use no more than 8 categories (0 – 1000)
  1. Analyze multiple box-and-whisker plots using the same scale

Standard 5.0 Knowledge of Probability

Topic

A. Sample Space

Indicator

Objectives

  1. Describe the difference between independent and dependent events
  1. Determine the number of outcomes
    Assessment limits:
    • Use no more than 5 dependent events with no more than 10 outcomes in the first event

Topic

B. Theoretical Probability

Indicator

  • 1. Determine the probability of an event comprised of no more than 2 independent events

Objectives

  1. Express the probability of an event as a fraction, a decimal, or a percent
    Assessment limits:

Indicator

  • 2. Determine the probability of a second event that is dependent on a first event of equally likely outcomes

Objectives

  1. Express the probability as a fraction, a decimal, or a percent
    Assessment limits:

Topic

C. Experimental Probability

Indicator

Objectives

  1. Make predictions and express the probability of the results as a fraction, a decimal with no more than 2 decimal places, or a percent
    Assessment limits:
    • Use 20 to 500 results

Indicator

Objectives

Indicator

Objectives

Indicator

Objectives

Standard 6.0 Knowledge of Number Relationships and Computation/Arithmetic

Topic

A. Knowledge of Number and Place Value

Indicator

Objectives

  1. Read, write, and represent rational numbers
    Assessment limits:
  1. Compare, order, and describe rational numbers with and without relational symbols (<, >, =)
    Assessment limits:
    • Use no more than 4 integers(-100 to 100) or positive rational numbers (0–100) using equivalent forms or absolute value

Topic

C. Number Computation

Indicator

  • 1. Analyze number relations and compute

Objectives

  1. Add, subtract, multiply and divide integers
    Assessment limits:
    • Use one operation (-1000 to 1000)
  1. Calculate powers of integers and square roots of perfect square whole numbers
    Assessment limits:
    • Use powers with bases no more than 12 and exponents no more than 3, or square roots of perfect squares no more than 144
  1. Identify and use the laws of exponents to simplify expressions
    Assessment limits:
  1. Use properties of addition and multiplication to simplify expressions
    Assessment limits:

Indicator

Objectives

  1. Estimate the square roots of whole numbers
    Assessment limits:

Indicator

  • 3. Analyze ratios, proportions, and percents

Objectives

  1. Determine unit rates
    Assessment limits:
    • Use positive rational numbers (0 – 100)
  1. Determine or use percents, rates of increase and decrease, discount, commission, sales tax, and simple interest in the context of a problem
    Assessment limits:
    • Use positive rational numbers (0 - 10,000)
  1. Solve problems using proportional reasoning
    Assessment limits:
    • Use positive rational numbers (0 – 1000)

Standard 7.0 Processes of Mathematics

Topic

A. Problem Solving

Indicator

  • 1. Apply a variety of concepts, processes, and skills to solve problems

Objectives

  1. Identify the question in the problem
  1. Decide if enough information is present to solve the problem
  1. Make a plan to solve a problem
  1. Apply a strategy, i.e., draw a picture, guess and check, finding a pattern, writing an equation
  1. Select a strategy, i.e., draw a picture, guess and check, finding a pattern, writing an equation
  1. Identify alternative ways to solve a problem
  1. Show that a problem might have multiple solutions or no solution
  1. Extend the solution of a problem to a new problem situation

Topic

B. Reasoning

Indicator

  • 1. Justify ideas or solutions with mathematical concepts or proofs

Objectives

  1. Use inductive or deductive reasoning
  1. Make or test generalizations
  1. Support or refute mathematical statements or solutions
  1. Use methods of proof, i.e., direct, indirect, paragraph, or contradiction

Topic

C. Communication

Indicator

  • 1. Present mathematical ideas using words, symbols, visual displays, or technology

Objectives

  1. Use multiple representations to express concepts or solutions
  1. Express mathematical ideas orally
  1. Explain mathematically ideas in written form
  1. Express solutions using concrete materials
  1. Express solutions using pictorial, tabular, graphical, or algebraic methods
  1. Explain solutions in written form
  1. Ask questions about mathematical ideas or problems
  1. Give or use feedback to revise mathematical thinking

Topic

D. Connections

Indicator

  • 1. Relate or apply mathematics within the discipline, to other disciplines, and to life

Objectives

  1. Identify mathematical concepts in relationship to other mathematical concepts
  1. Identify mathematical concepts in relationship to other disciplines
  1. Identify mathematical concepts in relationship to life
  1. Use the relationship among mathematical concepts to learn other mathematical concepts

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