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 onestep linear equations.
Number Sense
Students
compare and order positive and negative fractions, decimals, and
Compare and
order positive and negative fractions, decimals, and mixed
Interpret and
use ratios in different contexts (e.g., batting averages, miles per Write the following as ratios:
Use
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.)
Calculate
given percentages of quantities and solve problems involving
Students
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?
Solve
addition, subtraction, multiplication, and division problems, including Simplify to make the calculation as simple as
possible and identify the
Determine the
least common multiple and the greatest common divisor of 
Note: The sample problems illustrate 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 primary grades, before they are used with students. The symbol


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:
Write and
solve onestep linear equations in one variable. 1.2 Write and evaluate an algebraic expression for
a given situation, using up to
Demonstrate an
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:
Understand
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 twodimensional figures: 2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.
Use the
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 central tendency. 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.
Identify
different ways of selecting a sample (e.g., convenience sampling,
Analyze data
displays and explain why the way in which the question was
Identify data
that represent sampling errors and explain why the sample (and
Identify
claims based on statistical data and, in simple cases, evaluate the 3.0 Students determine theoretical and
experimental probabilities and use these
Represent all
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
Represent
probabilities as ratios, proportions, decimals between 0 and 1, and 

Mathematical Reasoning 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: 