School Improvement in Maryland

VSC: Mathematics Grade 5

Document Date: June 2004
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The objectives assessed on MSA at each grade level are embedded in the Voluntary State Curriculum (VSC). They are identified with the notation, Assessment limit. Assessment limits provide clarification about the specific skills and content that students are expected to have learned for each assessed objective. Even though some objectives in the VSC may not have an Assessment limit at a given grade-level, these non-assessed objectives still must be included in instruction. They introduce important concepts in preparation for assessed skills and content at subsequent grade levels.

The 'VSC Toolkit' provides additional resources for understanding and teaching the content standards.

Standard 1.0 Knowledge of Algebra, Patterns, and Functions

Topic

A. Patterns and Functions

Indicator

  • 1. Identify, describe, extend, and create numeric patterns and functions

Objectives

  1. Interpret and write a rule for a one-operation (+, -, x, ÷ with no remainders) function table
    Assessment limits:
    • Use whole numbers or decimals with no more than 2 decimal places (0 – 1000)
  1. Create a one-operation (x, ÷ with no remainders) function table to solve a real world problem
  1. Complete a one-operation function table
    Assessment limits:
    • Use whole numbers with +, -, x, ÷ (with no remainders) or use decimals with no more than two decimal places with +, - (0 – 200)
  1. Apply a given two operation rule for a pattern
    Assessment limits:

Topic

B. Expressions, Equations, and Inequalities

Indicator

  • 1. Write and identify expressions

Objectives

  1. Represent unknown quantities with one unknown and one operation (+, -, ×, ÷ with no remainders)
    Assessment limits:
  1. Determine the value of algebraic expressions with one unknown and one operation
    Assessment limits:
    • Use +, - with whole numbers (0-1000) or ×, ÷ (with no remainders) with whole numbers (0-100) and the number for the unknown is no more than 9
  1. Use parenthesis to evaluate a numeric expression

Indicator

  • 2. Identify, write, solve, and apply equations and inequalities

Objectives

  1. Represent relationships by using the appropriate relational symbols (>, <, =) and one operational symbol (+, -, ×, ÷ with no remainders) on either side
    Assessment limits:
  1. Find the unknown in an equation use one operation (+, -, ×, ÷ with no remainders)
    Assessment limits:

Topic

C. Numeric and Graphic Representations of Relationships

Indicator

  • 1. Locate points on a number line and in a coordinate grid

Objectives

  1. Represent decimals and mixed numbers on a number line
    Assessment limits:
    • Use decimals with no more than two decimal places (0 – 100) or mixed numbers with denominators of 2, 3, 4, 5, 6, 8, or 10 (0 - 10)
  1. Create a graph in a coordinate plane
    Assessment limits:
    • Use the first quadrant and ordered pairs of whole numbers (0 – 50)

Standard 2.0 Knowledge of Geometry

Topic

A. Plane Geometric Figures

Indicator

  • 1. Analyze the properties of plane geometric figures

Objectives

  1. Identify and describe relationships of lines and line segments in geometric figures or pictures
    Assessment limits:
    • Use parallel or perpendicular lines and line segments
  1. Identify polygons within a composite figure
    Assessment limits:
    • Use polygons with no more than 8 sides as part of a composite figure comprised of triangles or quadrilaterals
  1. Identify and describe the radius and diameter of a circle

Indicator

  • 2. Analyze geometric relationships

Objectives

  1. Compare and classify quadrilaterals by length of sides and types of angles (Include the angle symbol <ABC)
    Assessment limits:
    • Use squares, rectangles, rhombi, parallelograms, and trapezoids
  1. Compare triangles by sides

Topic

B. Solid Geometric Figures

Indicator

  • 1. Analyze the properties of solid geometric figures

Objectives

  1. Identify and classify pyramids and prisms by the number of edges, faces, or vertices
    Assessment limits:
    • Use triangular pyramids, rectangular pyramids, triangular prisms, or rectangular prisms
  1. Identify and classify pyramids and prisms by the base
    Assessment limits:
    • Use triangular prisms and pyramids or rectangular prisms and pyramids

Indicator

  • 2. Analyze the relationship between plane geometric figures and faces of solid geometric figures

Objectives

  1. Compare a plane figure to faces of solid geometric figure
    Assessment limits:
    • Analyze and identify the number or arrangement of rectangles needed to make a rectangular prism, number of triangles/rectangles needed to make a triangular prism, and the number of circles/rectangles needed to make a cylinder.

Topic

C. Representation of Geometric Figures

Indicator

  • 1. Represent plane geometric figures

Objectives

  1. Identify, describe, and draw angles, parallel line segments, and perpendicular line segments
    Assessment limits:
    • Provide their dimensions as whole numbers (0 - 20) or angle measurements (0° - 179°)

Topic

D. Congruence and Similarity

Indicator

  • 1. Analyze similar figures to

Objectives

  1. Identify or describe geometric figures as similar
    Assessment limits:
    • Use same shape and different size

Topic

E. Transformations

Indicator

Objectives

  1. Identify and describe the results of translations, reflections, and rotations of geometric figures
    Assessment limits:
    • Use translation along a vertical line, reflection over a horizontal line, or rotation 90° or 180° around a given point

Standard 3.0 Knowledge of Measurement

Topic

A. Measurement Units

Indicator

  • 1. Read customary and metric measurement units

Objectives

  1. Estimate and determine weight or mass
    Assessment limits:
    • Use the nearest ounce for weight and the nearest gram for mass
  1. Estimate and determine capacity
    Assessment limits:
    • Use the nearest ounce

Topic

B. Measurement Tools

Indicator

  • 1. Measure in customary and metric units

Objectives

  1. Select and use appropriate tools and units
    Assessment limits:
    • Measure length to 1/8 inch with a ruler

Indicator

  • 2. Measure angles

Objectives

  1. Measure a single angle and angles in regular polygons
    Assessment limits:
    • Measure an angle between 0 and 180 to the nearest degree

Topic

C. Applications in Measurement

Indicator

  • 1. Estimate and apply measurement formulas

Objectives

  1. Determine perimeter
    Assessment limits:
    • Use polygons with no more than 8 sides and whole numbers (0 –500)
  1. Determine area
    Assessment limits:
  1. Find the area and the perimeter of any closed figure on a grid
    Assessment limits:
    • Use whole and partial units (0-50)
  1. Estimate and determine volume by counting

Indicator

Objectives

  1. Determine start, elapsed, and end time
    Assessment limits:
    • Use the nearest minute
  1. Determine equivalent units of measurement
    Assessment limits:
    • Use seconds, minutes, and hours or pints, quarts, and gallons

Standard 4.0 Knowledge of Statistics

Topic

A. Data Displays

Indicator

  • 1. Collect, organize, and display data

Objectives

  1. Collect data by conducting surveys to answer a question
  1. Organize and display data in stem-and-leaf plots
    Assessment limits:
  1. Organize and display data in line plots
    Assessment limits:
    • Use no more than 20 pieces of data with a range of no more than 20 and whole numbers (0 – 200)
  1. Organize and display data in double bar graphs
    Assessment limits:
    • Use no more than 4 categories and intervals of 1, 2, 5, or 10 and whole numbers (0 – 100)
  1. Organize and display data in line graphs
    Assessment limits:
    • Use y-axis with intervals of 1, 2, 4, 5, or 10 and x-axis with no more than 10 time intervals and whole numbers (0 – 100)
  1. Determine the appropriate type of graph to effectively display data

Topic

B. Data Analysis

Indicator

  • 1. Analyze data

Objectives

  1. Interpret and compare data in stem & leaf plot
    Assessment limits:
  1. Interpret and compare data in line plots
    Assessment limits:
    • Use no more than 20 pieces of data with a range of no more than 20 and whole numbers (0 – 100)
  1. Interpret and compare data in double bar graphs
    Assessment limits:
    • Use no more than 4 categories and intervals of 1, 2, 5, or 10 and whole numbers (0 – 1000)
  1. Interpret and compare data in double line graphs
    Assessment limits:
    • Use y-axis with intervals of 1, 2, 5, or 10 and x-axis with no more than 10 time intervals and whole numbers (0 – 100)
  1. Read circle graphs
    Assessment limits:

Indicator

Objectives

  1. Determine the mean of a given data set or data display
    Assessment limits:
    • Use no more than 8 pieces of data and whole numbers without remainders (0 – 1000)
  1. Apply the range and measures of central tendency to solve a problem or answer a question

Standard 5.0 Knowledge of Probability

Topic

A. Sample Space

Indicator

  • 1. Identify possible outcomes

Objectives

  1. Determine possible outcomes of independent events
    Assessment limits:
    • Use two independent events with no more than 4 outcomes each and an organized list or tree diagram

Topic

B. Theoretical Probability

Indicator

  • 1. Determine the probability of one simple event comprised of equally likely outcomes

Objectives

  1. Make predictions and express the probability as a fraction
    Assessment limits:

Standard 6.0 Knowledge of Number Relationships and Computation/Arithmetic

Topic

A. Knowledge of Number and Place Value

Indicator

  • 1. Apply knowledge of fractions, decimals, and place value

Objectives

  1. Read, write, or represent fractions or mixed numbers using symbols, models, and words
    Assessment limits:
    • Use denominators that are factors of 24 and numbers (0 – 200)
  1. Read, write, or represent decimals using symbols, words, or models
    Assessment limits:
    • Use no more than 3 decimal places (0 – 100)
  1. Identify and determine equivalent forms of proper fractions
    Assessment limits:
    • Use denominators that are factors of 100, decimals, or percents (0 – 200)
  1. Compare or order fractions with or without using the symbols (<, >, or =)
    Assessment limits:
    • Use no more than 4 fractions or mixed numbers with denominators that are factors of 100 and numbers (0 – 100)
  1. Compare, order, and describe decimals with or without using the symbols (<, >, or =)
    Assessment limits:
    • Use no more than 4 decimals with no more than 3 decimal places and numbers (0 – 100)

Topic

B. Number Theory

Indicator

  • 1. Apply number relationships

Objectives

  1. Identify or describe numbers as prime or composite
    Assessment limits:
  1. Identify and use rules of divisibility
    Assessment limits:
  1. Identify the greatest common factor
    Assessment limits:
    • Use 2 numbers whose GCF is no more than 10 and whole numbers (0 – 100)
  1. Identify a common multiple and the least common multiple
    Assessment limits:

Topic

C. Number Computation

Indicator

  • 1. Analyze number relations and compute

Objectives

  1. Multiply whole numbers
    Assessment limits:
  1. Divide whole numbers
    Assessment limits:
    • Use a dividend with no more than a 4-digits by a 2-digit divisor and whole numbers (0 - 9,999)
  1. Interpret quotients and remainders mathematically and in the context of a problem
    Assessment limits:
    • Use dividend with no more than a 3-digits by a 1 or 2 digit divisor and whole numbers (0 – 999)
  1. Add and subtract proper fractions and mixed numbers with answers in simplest form
    Assessment limits:
    • Use denominators as factors of 24 and numbers (0 – 20)
  1. Add decimals including money
    Assessment limits:
    • Use no more than 4 addends and no more than 3 decimal places in each addend and numbers (0 – 1000)
  1. Subtract decimals including money
    Assessment limits:
    • Use a minuend and subtrahend with no more than 3 decimal places and numbers (0 – 1000)
  1. Multiply decimals
    Assessment limits:
    • Use a decimal in monetary notation by a single digit whole number and numbers (0 – 100)
  1. Divide decimals by whole numbers

Indicator

Objectives

  1. Determine the approximate sum and difference of decimals
    Assessment limits:
    • Use no more than 3 addends with no more than 3 decimal places in each addend or the difference of a minuend and subtrahend with no more than 3 decimal places and numbers (0 – 1000)
  1. Determine approximate product and quotient of whole numbers
    Assessment limits:
    • Use a 1-digit factor with the other factor having no more than 3 digits or a dividend having no more than 3 digits and a 1-digit divisor and whole numbers (0 – 5000)
  1. Determine the approximate product of decimals
    Assessment limits:
    • Use a decimal in monetary notation and a single digit whole number (0 – 100)

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