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Standards of Learning
Grade Six
The sixthgrade standards place continued emphasis on the study of
whole numbers, decimals, and fractions. Students will use ratios
to compare data sets, make conversions within a given measurement
system, make geometric constructions and classify threedimensional
figures, and solve linear equations in one variable. 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. Students also will identify reallife applications
of the mathematical principles they are learning that can be
applied to science and other disciplines they are studying.
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 problemsolving 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
6.1 The student will identify representations of a given percent
and describe orally and in writing the equivalence
relationship between fractions, decimals, and percents.
6.2 The student will describe and compare two sets of data using
ratios and will use appropriate notations such as a/b, a to
b, and a:b.
6.3 The student will explain orally and in writing the concepts
of prime and composite numbers.
6.4 The student will compare and order whole numbers, fractions,
and decimals, using concrete materials, drawings or pictures,
and mathematical symbols.
6.5 The student will identify and represent integers on a number
line.
Computation and Estimation
6.6 The student will
* solve problems that involve addition, subtraction, and/or
multiplication with fractions and mixed numbers, with and
without regrouping, that include like and unlike
denominators of 12 or less and express their answers in
simplest form; and
* find the quotient, given a dividend expressed as a decimal
through thousandths and a divisor expressed as a decimal
to thousandths with exactly one nonzero digit. For
divisors with more than one nonzero digit, estimation and
calculators will be used.
6.7 The student will use estimation strategies to solve multistep
practical problems involving whole numbers, decimals, and
fractions.
6.8 The student will solve multistep consumer application
problems involving fractions and decimals and present data
and conclusions in paragraphs, tables, or graphs.
Measurement
6.9 The student will compare and convert units of measures for
length, weight/mass, and volume within the U.S. Customary
system and within the metric system and estimate conversions
between units in each system:*
* lengthpart of an inch (1/2, 1/4, and 1/8), inches, feet,
yards, miles, millimeters, centimeters, meters, and
kilometers;
* weight/massounces, pounds, tons, grams, and kilograms;
* liquid volumecups, pints, quarts, gallons, milliliters,
and liters; and
* areasquare units.
* The intent of this standard is for students to make
"ballpark" comparisons and not to memorize conversion factors
between U.S. and metric units.
6.10 The student will estimate and then determine length,
weight/mass, area, and liquid volume/capacity, using standard
and nonstandard units of measure.
6.11 The student will determine if a problem situation involving
polygons of four sides or less represents the application of
perimeter or area and apply the appropriate formula.
6.12 The student will create and solve problems by finding the
circumference and/or area of a circle when given the diameter
or radius. Using concrete materials or computer models, the
student will derive approximations for pi from measurements
for circumference and diameter.
6.13 The student will estimate angle measures using 45 degrees,
90 degrees, and 180 degrees as referents and use the appropriate
tools to measure the given angles.
Geometry
6.14 The student will identify, classify, and describe the
characteristics of plane figures including similarities and
differences.
6.15 The student will determine congruence of segments, angles,
and polygons by direct comparison, given their attributes.
Examples of noncongruent and congruent figures will be
included.
6.16 The student will construct the perpendicular bisector of a
line segment and an angle bisector, using a compass and
straightedge.
6.17 The student will sketch, construct models, and classify
rectangular prisms, cones, cylinders, and pyramids.
Probability and Statistics
6.18 The student, given a problem situation, will collect,
analyze, display, and interpret data in a variety of
graphical methods, including line, bar, and circle graphs and
stemandleaf and boxandwhisker plots. Circle graphs will
be limited to halves, fourths, and eighths.
6.19 The student will describe the mean, median, and mode as
measures of central tendency and determine their meaning for
a set of data.
6.20 The student will determine and interpret the probability of
an event occurring from a given sample space.
Patterns, Functions, and Algebra
6.21 The student will recognize, describe, and extend a variety of
numerical and geometric patterns.
6.22 The student will investigate and describe concepts of
exponents, perfect squares, and square roots, using
calculators to develop the exponential patterns. Patterns
will include zero and negative exponents, which lead to the
idea of scientific notation. Investigations will include the
binary number system as an application of exponents and
patterns.
6.23 The student will
* model and solve algebraic equations, using concrete
materials; and
* solve onestep linear equations in one variable, involving
whole number coefficients and positive rational solutions.
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