The California Mathematics Content Standards
Grade Three Mathematics Content Standards
By the end of grade three, students deepen their
understanding of place value and their
understanding of and skill with addition, subtraction, multiplication, and division of whole
numbers. Students estimate, measure, and describe objects in space. They use patterns to
help solve problems. They represent number relationships and conduct simple probability
1.0 Students understand the place value of whole numbers:
1.1 Count, read, and write whole numbers to 10,000.
What is the smallest whole number you can make
using the digits 4, 3, 9,
1.2 Compare and order whole numbers to 10,000.
Identify the place value for each digit in numbers to 10,000.
1.4 Round off numbers to 10,000 to the nearest ten, hundred, and thousand.
Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6).
True or false?
2.0 Students calculate and solve problems
involving addition, subtraction,
1. 591 + 87 = ?
To prepare for recycling on Monday, Michael
collected all the bottles in
automaticity the multiplication table for numbers between
inverse relationship of multiplication and division to compute
problems involving multiplication of multidigit numbers by
2.5 Solve division problems in which a multidigit
number is evenly divided by
2.6 Understand the special properties of 0 and 1 in multiplication and division.
True or false?
2.7 Determine the unit cost when given the total
cost and number of units.
3.0 Students understand the relationship
between whole numbers, simple fractions,
3.1 Compare fractions represented by drawings or
concrete materials to show
Which is longer: 1/3 of a foot or 5 inches? 2/3
of a foot or 9 inches?
subtract simple fractions (e.g., determine that 1/8 + 3/8 is the same
Find the values:
problems involving addition, subtraction, multiplication, and division
Pedro bought 5 pens, 2 erasers and 2 boxes of
crayons. The pens cost
3.4 Know and understand that fractions and
decimals are two different representations
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
Algebra and Functions
select appropriate symbols, operations, and properties to represent,
relationships of quantities in the form of mathematical expressions,
1.2 Solve problems involving numeric equations or
2.0 Students represent simple functional relationships:
problems involving a functional relationship between two
John wants to buy a dozen pencils. One store
offers pencils at 6 for $1.
2.2 Extend and recognize a linear pattern by its
rules (e.g., the number of legs on
Here is the beginning of a pattern of tiles.
Assuming that the pattern
Measurement and Geometry
1.0 Students choose and use appropriate units and
measurement tools to quantify
1.1 Choose the appropriate tools and units (metric
and U.S.) and estimate and
determine the area and volume of solid figures by covering them
Find the perimeter of a polygon with integer sides.
1.4 Carry out simple unit conversions within a
system of measurement
2.0 Students describe and compare the
attributes of plane and solid geometric
describe, and classify polygons (including pentagons, hexagons, and
attributes of triangles (e.g., two equal sides for the isosceles
attributes of quadrilaterals (e.g., parallel sides for the
2.4 Identify right angles in geometric figures or
in appropriate objects and
2.5 Identify, describe, and classify common
three-dimensional geometric objects
Statistics, Data Analysis, and Probability
1.0 Students conduct simple probability experiments
by determining the number
1.1 Identify whether common events are certain,
likely, unlikely , or improbable.
possible outcomes for a simple event (e.g., tossing a coin) and
display the results of probability experiments in a clear and
1.4 Use the results of probability experiments to
predict future events (e.g., use a
make decisions about how to approach problems:
2.2 Apply strategies and results from simpler
problems to more complex