The California Mathematics Content Standards
Grade Six Mathematics Content Standards
By the end of grade six, students have mastered the four
arithmetic operations with whole
numbers, positive fractions, positive decimals, and positive and negative integers; they
accurately compute and solve problems. They apply their knowledge to statistics and
probability. Students understand the concepts of mean, median, and mode of data sets
and how to calculate the range. They analyze data and sampling processes for possible bias
and misleading conclusions; they use addition and multiplication of fractions routinely to
calculate the probabilities for compound events. Students conceptually understand and
work with ratios and proportions; they compute percentages (e.g., tax, tips, interest).
Students know about π and the formulas for the circumference and area of a circle. They
use letters for numbers in formulas involving geometric shapes and in ratios to represent an
unknown part of an expression. They solve one-step linear equations.
compare and order positive and negative fractions, decimals, and
order positive and negative fractions, decimals, and mixed
use ratios in different contexts (e.g., batting averages, miles per
Write the following as ratios:
proportions to solve problems (e.g., determine the value of N if
Find n if:
(This problem also applies to Algebra and Functions Standard 1.1.)
given percentages of quantities and solve problems involving
calculate and solve problems involving addition, subtraction,
2.1 Solve problems involving addition,
subtraction, multiplication, and division
1. If 11/7 is divided by a certain fraction
a/b, the result is 3/8. What is a/b?
addition, subtraction, multiplication, and division problems, including
Simplify to make the calculation as simple as
possible and identify the
least common multiple and the greatest common divisor of
Note: The sample
the standards and
are written to help
clarify them. Some
problems are written
in a form that can be
used directly with
students; others will
need to be modified,
particularly in the
before they are
used with students.
Algebra and Functions
1.0 Students write verbal expressions and sentences as algebraic expressions and
equations; they evaluate algebraic expressions, solve simple linear equations,
and graph and interpret their results:
solve one-step linear equations in one variable.
1.2 Write and evaluate an algebraic expression for
a given situation, using up to
understanding that rate is a measure of one quantity per
Joe can type 9 words in 8 seconds. At this
rate, how many words can he type
3.0 Students investigate geometric patterns and
describe them algebraically:
Measurement and Geometry
1.0 Students deepen their understanding of the measurement of plane and solid
shapes and use this understanding to solve problems:
the concept of a constant such as π; know the formulas for the
1.2 Know common estimates of π (3.14; 22/7)
and use these values to estimate
2.0 Students identify and describe the properties of two-dimensional figures:
2.1 Identify angles as vertical, adjacent, complementary, or supplementary and
provide descriptions of these terms.
properties of complementary and supplementary angles and the sum
Find the missing angles.
2.3 Draw quadrilaterals and triangles from given
information about them (e.g., a
Statistics, Data Analysis, and Probability
1.0 Students compute and analyze statistical measurements for data sets:
1.1 Compute the range, mean, median, and mode of data sets.
1.2 Understand how additional data added to data sets may affect these computations
of measures of central tendency.
1.3 Understand how the inclusion or exclusion of outliers affects measures of
1.4 Know why a specific measure of central tendency (mean, median, mode)
provides the most useful information in a given context.
2.0 Students use data samples of a population and describe the characteristics
and limitations of the samples:
2.1 Compare different samples of a population with the data from the entire
population and identify a situation in which it makes sense to use a sample.
different ways of selecting a sample (e.g., convenience sampling,
displays and explain why the way in which the question was
that represent sampling errors and explain why the sample (and
claims based on statistical data and, in simple cases, evaluate the
3.0 Students determine theoretical and
experimental probabilities and use these
possible outcomes for compound events in an organized way
3.2 Use data to estimate the probability of future
events (e.g., batting averages or
probabilities as ratios, proportions, decimals between 0 and 1, and
1.0 Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from
irrelevant information, identifying missing information, sequencing and
prioritizing information, and observing patterns.
1.2 Formulate and justify mathematical conjectures based on a general description
of the mathematical question or problem posed.
1.3 Determine when and how to break a problem into simpler parts.
2.0 Students use strategies, skills, and concepts
in finding solutions: