Grade 5

Overview

This overview provides only the highlights of the new learning that should take place at the fifth-grade level. The specific skills and subject matter that fifth graders should be taught in each of the five mathematical strands are set forth in the formal standards and indicators for these strands. To alert educators as to when the progression in learning should occur for students in this grade, specific language is used with certain indicators:

· An indicator beginning with the phrase “Generate strategies” addresses a concept that is being formally introduced for the first time, and students must therefore be given experiences that foster conceptual understanding.

· An indicator beginning with the phrase “Apply an algorithm,” “Apply a procedure,” “Apply procedures,” or “Apply formulas” addresses a concept that has been introduced in a previous grade: students should already have the conceptual understanding, and the goal must now be fluency.

· An indicator beginning with the phrase “Apply strategies and formulas” or “Apply strategies and procedures” addresses a concept that is being formally introduced for the first time, yet the goal must nonetheless be that students progress to fluency.

Highlights of the new learning for grade-five students are

· applying an algorithm to divide whole numbers fluently,

· understanding the concept of prime and composite numbers,

· generating strategies to add and subtract fractions,

· applying an algorithm to add and subtract decimals through thousandths,

· classifying shapes as congruent,

· translating between two-dimensional representations and three-dimensional objects,

· predicting results of combined multiple transformations,

· analyzing shapes for line and/or rotational symmetry,

· using a protractor to measure angles,

· using equivalencies to convert units of measure within the metric system,

· applying formulas to determine perimeter and area,

· applying strategies and formulas to determine volume,

· applying procedures to determine elapsed time within a 24-hour period,

· applying procedures to calculate the measures of central tendency, and

· concluding why the sum of the probabilities of the outcomes of an experiment must equal 1.

Grade 5

Mathematical Processes

The mathematical processes provide the framework for teaching, learning, and assessing in mathematics at all grade levels. Instructional programs should be built around these processes.

Standard 5-1: The student will understand and utilize the mathematical processes of problem solving, reasoning and proof, communication, connections, and representation.

The indicators for this standard, which are appropriate for grades three through five, are adapted from Principles and Standards for School Mathematics (NCTM 2000). Classroom application should be based on the standard and its indicators; the mathematical goals for the class; and the skills, needs, and understandings of the particular students.

Indicators

5-1.1 Analyze information to solve increasingly more sophisticated problems.

5-1.2 Construct arguments that lead to conclusions about general mathematical properties and relationships.

5-1.3 Explain and justify answers based on mathematical properties, structures, and relationships.

5-1.4 Generate descriptions and mathematical statements about relationships between and among classes of objects.

5-1.5 Use correct, clear, and complete oral and written mathematical language to pose questions, communicate ideas, and extend problem situations.

5-1.6 Generalize connections between new mathematical ideas and related concepts and subjects that have been previously considered.

5-1.7 Use flexibility in mathematical representations.

5-1.8 Recognize the limitations of various forms of mathematical representations.

Grade 5

Number and Operations

Standard 5-2: The student will demonstrate through the mathematical processes an understanding of the place value system; the division of whole numbers; the addition and subtraction of decimals; the relationships among whole numbers, fractions, and decimals; and accurate, efficient, and generalizable methods of adding and subtracting fractions.

Indicators

5-2.1 Analyze the magnitude of a digit on the basis of its place value, using whole numbers and decimal numbers through thousandths.

5-2.2 Apply an algorithm to divide whole numbers fluently.

5-2.3 Understand the relationship among the divisor, dividend, and quotient.

5-2.4 Compare whole numbers, decimals, and fractions by using the symbols <, >, and =.

5-2.5 Apply an algorithm to add and subtract decimals through thousandths.

5-2.6 Classify numbers as prime, composite, or neither.

5-2.7 Generate strategies to find the greatest common factor and the least common multiple of two whole numbers.

5-2.8 Generate strategies to add and subtract fractions with like and unlike denominators.

5-2.9 Apply divisibility rules for 3, 6, and 9.

Grade 5

Algebra

Standard 5-3: The student will demonstrate through the mathematical processes an understanding of the use of patterns, relations, functions, models, structures, and algebraic symbols to represent quantitative relationships and will analyze change in various contexts.

Indicators

5-3.1 Represent numeric, algebraic, and geometric patterns in words, symbols, algebraic expressions, and algebraic equations.

5-3.2 Analyze patterns and functions with words, tables, and graphs.

5-3.3 Match tables, graphs, expressions, equations, and verbal descriptions of the same problem situation.

5-3.4 Identify applications of commutative, associative, and distributive properties with whole numbers.

5-3.5 Analyze situations that show change over time.

Grade 5

Geometry

Standard 5-4: The student will demonstrate through the mathematical processes an understanding of congruency, spatial relationships, and relationships among the properties of quadrilaterals.

Indicators

5-4.1 Apply the relationships of quadrilaterals to make logical arguments about their properties.

5-4.2 Compare the angles, side lengths, and perimeters of congruent shapes.

5-4.3 Classify shapes as congruent.

5-4.4 Translate between two-dimensional representations and three-dimensional objects.

5-4.5 Predict the results of multiple transformations on a geometric shape when combinations of translation, reflection, and rotation are used.

5-4.6 Analyze shapes to determine line symmetry and/or rotational symmetry.

Grade 5

Measurement

Standard 5-5: The student will demonstrate through the mathematical processes an understanding of the units and systems of measurement and the application of tools and formulas to determine measurements.

Indicators

5-5.1 Use appropriate tools and units to measure objects to the precision of one-eighth inch.

5-5.2 Use a protractor to measure angles from 0 to 180 degrees.

5-5.3 Use equivalencies to convert units of measure within the metric system: converting length in millimeters, centimeters, meters, and kilometers; converting liquid volume in milliliters, centiliters, liters, and kiloliters; and converting mass in milligrams, centigrams, grams, and kilograms.

5-5.4 Apply formulas to determine the perimeters and areas of triangles, rectangles, and parallelograms.

5-5.5 Apply strategies and formulas to determine the volume of rectangular prisms.

5-5.6 Apply procedures to determine the amount of elapsed time in hours, minutes, and seconds within a 24-hour period.

5-5.7 Understand the relationship between the Celsius and Fahrenheit temperature scales.

5-5.8 Recall equivalencies associated with length, liquid volume, and mass:

10 millimeters = 1 centimeter, 100 centimeters = 1 meter, 1000 meters = 1 kilometer;

10 milliliters = 1 centiliter, 100 centiliters = 1 liter, 1000 liters = 1 kiloliter; and

10 milligrams = 1 centigram, 100 centigrams = 1 gram, 1000 grams = 1 kilogram.