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Grade Five
The fifth-grade standards place emphasis on developing
proficiency in using whole numbers, fractions, and decimals
to solve problems. Students will collect, display, and
analyze data in a variety of ways and solve probability
problems, using a sample space or tree diagram. Students
also will solve problems involving volume, area, and
perimeter. Students will be introduced to variable
expressions and open sentences.
While learning mathematics, students will be actively
engaged, using concrete materials and appropriate
technologies such as calculators and computers. However,
facility in the use of technology shall not be regarded
as a substitute for a student's understanding of
quantitative concepts and relationships or for proficiency
in basic computations.
Mathematics has its own language, and the acquisition of
specialized vocabulary and language patterns is crucial
to a student's understanding and appreciation of the
subject. Students should be encouraged to use correctly
the concepts, skills, symbols, and vocabulary identified
in the following set of standards.
Problem solving has been integrated throughout the six
content strands. The development of problem-solving
skills should be a major goal of the mathematics program
at every grade level. Instruction in the process of
problem solving will need to be integrated early and
continuously into each student's mathematics education.
Students must be helped to develop a wide range of skills
and strategies for solving a variety of problem types.
Number and Number Sense SOL STATEMENT
- 5.1 The student will
- read, write, and identify the place values
of decimals through thousandths;
- round decimal numbers to the nearest tenth or
hundredth; and
- compare the values of two decimals through
thousandths, using the symbols >, <, or =.
- 5.2 The student will
- recognize and name commonly used fractions
(halves, fourths, fifths, eighths, and tenths)
in their equivalent decimal form and vice versa;
and
- order a given set of fractions and decimals from
least to greatest. Fractions will include like
and unlike denominators limited to 12 or less,
and mixed numbers.
Computation and Estimation
- 5.3 The student will create and solve problems
involving addition, subtraction, multiplication,
and division of whole numbers, using paper and
pencil, estimation, mental computation, and
calculators.
- 5.4 The student will find the sum, difference, and
product of two numbers expressed as decimals
through thousandths, using an appropriate method
of calculation, including paper and pencil,
estimation, mental computation, and calculators.
- 5.5 The student, given a dividend of four digits or
fewer and a divisor of two digits or fewer, will
find the quotient and remainder.
- 5.6 The student, given a dividend expressed as a
decimal through thousandths and a single-digit
divisor, will find the quotient.
- 5.7 The student will add and subtract with fractions
and mixed numbers, with and without regrouping,
and express answers in simplest form. Problems
will include like and unlike denominators limited
to 12 or less.
Measurement
- 5.8 The student will describe and determine the
perimeter of a polygon and the area of a square,
rectangle, and right triangle, given the appropriate
measures.
- 5.9 The student will identify and describe the diameter,
radius, chord, and circumference of a circle.
- 5.10 The student will differentiate between perimeter,
area, and volume and identify whether the application
of the concept of perimeter, area, or volume is
appropriate for a given situation.
- 5.11 The student will choose an appropriate measuring
device and unit of measure to solve problems
involving measurement of
- length - part of an inch (1/2, 1/4, and 1/8),
inches, feet, yards, miles, millimeters, centimeters,
meters, and kilometers;
- weight/mass - ounces, pounds, tons, grams, and
kilograms;
- liquid volume - cups, pints, quarts, gallons,
milliliters, and liters;
- area - square units; and
- temperature - Celsius and Fahrenheit units.
Problems also will include estimating the conversion
of Celsius and Fahrenheit units relative to familiar
situations (water freezes at 0°C and 32°F, water
boils at 100°C and 212°F, normal body temperature
is about 37°C and 98.6°F).
- 5.12 The student will determine an amount of elapsed
time in hours and minutes within a 24-hour period.
- 5.13 The student will measure and draw right, acute,
and obtuse angles and triangles, using appropriate
tools.
Geometry
- 5.14 The student will classify angles and triangles
as right, acute, or obtuse.
- 5.15 The student, using two-dimensional (plane) figures
(square, rectangle, triangle, parallelogram, rhombus,
kite, and trapezoid) will
- recognize, identify, describe, and analyze their
properties in order to develop definitions of these
figures;
- identify and explore congruent, noncongruent, and
similar figures;
- investigate and describe the results of combining
and subdividing shapes;
- identify and describe a line of symmetry; and
- recognize the images of figures resulting from
geometric transformations such as translation (slide),
reflection (flip), or rotation (turn).
- 5.16 The student will identify, compare, and analyze
properties of three-dimensional (solid) geometric
shapes (cylinder, cone, cube, square pyramid, and
rectangular prism).
Probability and Statistics
- 5.17 The student will
- solve problems involving the probability of a
single event by using tree diagrams or by
constructing a sample space representing all
possible results;
- predict the probability of outcomes of simple
experiments, representing it with fractions or
decimals from 0 to 1, and test the prediction; and
- create a problem statement involving probability
and based on information from a given problem
situation. Students will not be required to solve
the created problem statement.
- 5.18 The student will, given a problem situation,
collect, organize, and display a set of numerical
data in a variety of forms, using bar graphs,
stem-and-leaf plots, and line graphs, to draw
conclusions and make predictions.
- 5.19 The student will find the mean, median, mode,
and range of a set of data.
Patterns, Functions, and Algebra
- 5.20 The student will analyze the structure of
numerical and geometric patterns (how they change
or grow) and express the relationship, using words,
tables, graphs, or a mathematical sentence.
Concrete materials and calculators will be used.
- 5.21 The student will
- investigate and describe the concept of variable;
- use a variable expression to represent a given
verbal quantitative expression involving one
operation ; and
- write an open sentence to represent a given
mathematical relationship, using a variable.
- 5.22 The student will create a problem situation based
on a given open sentence using a single variable.
(from
Standards of Learning Currently in Effect for Virginia
Public Schools )
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