Mathematics Content Standards.
THIRD GRADE 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.
1.2 Compare and order whole numbers to 10,000.
1.3 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.
1.5 Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6).
2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division:
2.1 Find the sum or difference of two whole numbers between 0 and 10,000.
2.2 Memorize to automaticity the multiplication table for numbers between 1 and 10.
2.3 Use the inverse relationship of multiplication and division to compute and check results.
2.4 Solve simple problems involving multiplication of multidigit numbers by one-digit numbers (3,671 x 3 = __).
2.5 Solve division problems in which a multidigit number is evenly divided by a one-digit number (135 ¡Â 5 = __).
2.6 Understand the special properties of 0 and 1 in multiplication and division.
2.7 Determine the unit cost when given the total cost and number of units.
2.8 Solve problems that require two or more of the skills mentioned above.
3.0 Students understand the relationship between whole numbers, simple fractions, and decimals:
fractions represented by drawings or concrete materials to show
equivalency and to add and subtract simple fractions in context (e.g.,
1/2 of a pizza is the same amount as 2/4 of another pizza that is the
same size; show that 3/8 is larger than 1/4).
3.2 Add and subtract simple fractions (e.g., determine that 1/8 + 3/8 is the same as 1/2).
Solve problems involving addition, subtraction, multiplication, and
division of money amounts in decimal notation and multiply and divide
money amounts in decimal notation by using whole-number multipliers and
3.4 Know and understand that fractions and decimals
are two different representations of the same concept (e.g., 50 cents
is 1/2 of a dollar, 75 cents is 3/4 of a dollar).
Algebra and Functions
1.0 Students select
appropriate symbols, operations, and properties to represent, describe,
simplify, and solve simple number relationships:
1.1 Represent relationships of quantities in the form of mathematical expressions, equations, or inequalities.
1.2 Solve problems involving numeric equations or inequalities.
1.3 Select appropriate operational and relational symbols to make an expression true
(e.g., if 4 __ 3 = 12, what operational symbol goes in the blank?).
1.4 Express simple unit conversions in symbolic form
(e.g., __ inches = __ feet x 12).
1.5 Recognize and use the commutative and associative properties of multiplication
(e.g., if 5 x 7 = 35, then what is 7 x 5? and if 5 x 7 x 3 = 105, then what is 7 x 3 x 5?).
2.0 Students represent simple functional relationships:
simple problems involving a functional relationship between two
quantities (e.g., find the total cost of multiple items given the cost
2.2 Extend and recognize a linear pattern by its
rules (e.g., the number of legs on a given number of horses may be
calculated by counting by 4s or by multiplying the number of horses by
Measurement and Geometry
1.0 Students choose and use appropriate units and measurement tools to quantify the properties of objects:
1.1 Choose the
appropriate tools and units (metric and U.S.) and estimate and measure
the length, liquid volume, and weight/mass of given objects.
Estimate or determine the area and volume of solid figures by covering
them with squares or by counting the number of cubes that would fill
1.3 Find the perimeter of a polygon with integer sides.
1.4 Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes).
2.0 Students describe and
compare the attributes of plane and solid geometric figures and use
their understanding to show relationships and solve problems:
2.1 Identify, describe, and classify polygons (including pentagons, hexagons, and octagons).
Identify attributes of triangles (e.g., two equal sides for the
isosceles triangle, three equal sides for the equilateral triangle,
right angle for the right triangle).
2.3 Identify attributes of
quadrilaterals (e.g., parallel sides for the parallelogram, right
angles for the rectangle, equal sides and right angles for the square).
Identify right angles in geometric figures or in appropriate objects
and determine whether other angles are greater or less than a right
2.5 Identify, describe, and classify common
three-dimensional geometric objects (e.g., cube, rectangular solid,
sphere, prism, pyramid, cone, cylinder).
2.6 Identify common solid objects that are the components needed to make a more complex solid object.
Statistics, Data Analysis, and Probability
1.0 Students conduct simple probability experiments by determining the number of possible outcomes and make simple predictions:
1.1 Identify whether common events are certain, likely, unlikely, or improbable.
Record the possible outcomes for a simple event (e.g., tossing a coin)
and systematically keep track of the outcomes when the event is
repeated many times.
1.3 Summarize and display the results of
probability experiments in a clear and organized way (e.g., use a bar
graph or a line plot).
1.4 Use the results of probability
experiments to predict future events (e.g., use a line plot to predict
the temperature forecast for the next day).
1.0 Students make decisions about how to approach problems:
problems by identifying relationships, distinguishing relevant from
irrelevant information, sequencing and prioritizing information, and
1.2 Determine when and how to break a problem into simpler parts.
2.0 Students use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
Use a variety of methods, such as words, numbers, symbols, charts,
graphs, tables, diagrams, and models, to explain mathematical reasoning.
Express the solution clearly and logically by using the appropriate
mathematical notation and terms and clear language; support solutions
with evidence in both verbal and symbolic work.
2.5 Indicate the
relative advantages of exact and approximate solutions to problems and
give answers to a specified degree of accuracy.
2.6 Make precise calculations and check the validity of the results from the context of the problem.
3.0 Students move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original situation.
Note the method of deriving the solution and demonstrate a conceptual
understanding of the derivation by solving similar problems.
READING1.0 Word Analysis, Fluency, and Systematic Vocabulary Development:
understand the basic features of reading. They select letter patterns
and know how to translate them into spoken language by using phonics,
syllabication, and word parts. They apply this knowledge to achieve
fluent oral and silent reading.
Decoding and Word Recognition
1.1 Know and use complex word families when reading (e.g., -ight) to decode unfamiliar words.
1.2 Decode regular multisyllabic words.
1.3 Read aloud narrative and expository text fluently and accurately and with appropriate pacing, intonation, and expression.
Vocabulary and Concept Development
1.4 Use knowledge of antonyms, synonyms, homophones, and homographs to determine the meanings of words.
Demonstrate knowledge of levels of specificity among grade-appropriate
words and explain the importance of these relations (e.g., dog/mammal/animal/living things).
1.6 Use sentence and word context to find the meaning of unknown words.
1.7 Use a dictionary to learn the meaning and other features of unknown words.
1.8 Use knowledge of prefixes (e.g., un-, re-, pre-, bi-, mis-, dis-) and suffixes(e.g., -er, -est, -ful) to determine the meaning of words.
2.0 Reading Comprehension
read and understand grade-level-appropriate material. They draw upon a
variety of comprehension strategies as needed (e.g., generating and
responding to essential questions, making predictions, comparing
information from several sources). In addition to their regular
school reading, by grade four, students read one-half million words
annually, including a good representation of grade-level-appropriate
narrative and expository text (e.g., classic and contemporary
literature, magazines, newspapers, online information). In grade three,
students make substantial progress toward this goal.
Structural Features of Informational Materials
2.1 Use titles, tables of contents, chapter headings, glossaries, and indexes to locate information in text.
Comprehension and Analysis of Grade-Level-Appropriate Text
Ask questions and support answers by connecting prior knowledge with
literal information found in, and inferred from, the text.
2.3 Demonstrate comprehension by identifying answers in the text.
2.4 Recall major points in the text and make and modify predictions about forthcoming information.
2.5 Distinguish the main idea and supporting details in expository text.
2.6 Extract appropriate and significant information from the text, including problems and solutions.
2.7 Follow simple multiple-step written instructions (e.g., how to assemble a product or play a board game).
3.0 Literary Response and Analysis
read and respond to a wide variety of significant works of children's
literature. They distinguish between the structural features of the
text and literary terms or elements (e.g., theme, plot, setting,
Structural Features of Literature
3.1 Distinguish common forms of literature (e.g., poetry, drama, fiction, nonfiction).
Narrative Analysis of Grade-Level-Appropriate Text
3.2 Comprehend basic plots of classic fairy tales, myths, folktales, legends, and fables from around the world.
3.3 Determine what characters are like by what they say or do and by how the author or illustrator portrays them.
3.4 Determine the underlying theme or author¡¯s message in fiction and nonfiction text.
3.5 Recognize the similarities of sounds in words and rhythmic patterns (e.g., alliteration, onomatopoeia) in a selection.
3.6 Identify the speaker or narrator in a selection.
GRADE THREE Writing
WRITING 1.0 Writing Strategies
write clear and coherent sentences and paragraphs that develop a
central idea. Their writing shows they consider the audience and
purpose. Students progress through the stages of the writing process
(e.g., prewriting, drafting, revising, editing successive versions).
Organization and Focus
1.1 Create a single paragraph: a. Develop a topic sentence. b. Include simple supporting facts and details.
Write legibly in cursive or joined italic, allowing margins and correct
spacing between letters in a word and words in a sentence.
Understand the structure and organization of various reference
materials (e.g., dictio-nary, thesaurus, atlas, encyclopedia).
Evaluation and Revision
1.4 Revise drafts to improve the coherence and logical progression of ideas by using an established rubric.
2.0 Writing Applications (Genres and Their Characteristics) Students
write compositions that describe and explain familiar objects, events,
and experiences. Student writing demonstrates a command of standard
American English and the drafting, research, and organizational
strategies outlined in Writing Standard 1.0. Using the writing
strategies of grade three outlined in Writing Standard 1.0, students:
Write narratives: a. Provide a context within which an action takes
place. b. Include well-chosen details to develop the plot. c. Provide
insight into why the selected incident is memorable.
Write descriptions that use concrete sensory details to present and
support unified impressions of people, places, things, or experiences.
Write personal and formal letters, thank-you notes, and invitations: a.
Show awareness of the knowledge and interests of the audience and
establish a purpose and context. b. Include the date, proper
salutation, body, closing, and signature.
Written and Oral English Language Conventions GRADE THREE
WRITTEN AND ORAL ENGLISH LANGUAGE CONVENTIONS
standards for written and oral English language conventions have been
placed between those for writing and for listening and speaking because
these conventions are essential to both sets of skills.
1.0 Written and Oral English Language Conventions Students write and speak with a command of standard English conventions appropriate to this grade level.
Understand and be able to use complete and correct declarative,
interrogative, impera-tive, and exclamatory sentences in writing and
Identify subjects and verbs that are in agreement and identify and use
pronouns, adjec-tives, compound words, and articles correctly in
writing and speaking.
1.3 Identify and use past, present, and future verb tenses properly in writing and speaking.
1.4 Identify and use subjects and verbs correctly in speaking and writing simple sentences.
1.5 Punctuate dates, city and state, and titles of books correctly.
1.6 Use commas in dates, locations, and addresses and for items in a series.
1.7 Capitalize geographical names, holidays, historical periods, and special events correctly.
1.8 Spell correctly one-syllable words that have blends, contractions, compounds, ortho-graphic patterns (e.g., qu, consonant doubling, changing the ending of a word from -y to -ies when forming the plural), and common homophones (e.g., hair-hare).
1.9 Arrange words in alphabetic order.
GRADE THREE Listening and Speaking
LISTENING AND SPEAKING 1.0 Listening and Speaking Strategies
listen critically and respond appropriately to oral communication. They
speak in a manner that guides the listener to understand important
ideas by using proper phrasing, pitch, and modulation.
1.1 Retell, paraphrase, and explain what has been said by a speaker.
1.2 Connect and relate prior experiences, insights, and ideas to those of a speaker.
1.3 Respond to questions with appropriate elaboration.
1.4 Identify the musical elements of literary language (e.g., rhymes, repeated sounds, instances of onomatopoeia).
Organization and Delivery of Oral Communication
1.5 Organize ideas chronologically or around major points of information.
1.6 Provide a beginning, a middle, and an end, including concrete details that develop a central idea.
1.7 Use clear and specific vocabulary to communicate ideas and establish the tone.
1.8 Clarify and enhance oral presentations through the use of appropriate props (e.g., objects, pictures, charts).
Read prose and poetry aloud with fluency, rhythm, and pace, using
appropriate intona-tion and vocal patterns to emphasize important
passages of the text being read.
Analysis and Evaluation of Oral and Media Communications
1.10 Compare ideas and points of view expressed in broadcast and print media.
1.11 Distinguish between the speaker¡¯s opinions and verifiable facts.
2.0 Speaking Applications (Genres and Their Characteristics) Students
deliver brief recitations and oral presentations about familiar
experiences or interests that are organized around a coherent thesis
statement. Student speaking dem-onstrates a command of standard
American English and the organizational and delivery strategies
outlined in Listening and Speaking Standard 1.0. Using the speaking
strategies of grade three outlined in Listening and Speaking Standard
Make brief narrative presentations: a. Provide a context for an
incident that is the subject of the presentation. b. Provide insight
into why the selected incident is memorable. c. Include well-chosen
details to develop character, setting, and plot.
Plan and present dramatic interpretations of experiences, stories,
poems, or plays with clear diction, pitch, tempo, and tone.
Make descriptive presentations that use concrete sensory details to set
forth and support unified impressions of people, places, things, or
Continuity and Change
Students in grade three learn more about our
connections to the past and the ways in which particularly local, but
also regional and national, government and traditions have developed
and left their marks on current society, providing common memories.
Emphasis is on the physical and cultural landscape of California,
including the study of American Indians, the subsequent arrival of
immigrants, and the impact they have had in forming the character of
our contemporary society.
3.1 Students describe the physical and human
geography and use maps, tables, graphs, photographs, and charts to
organize information about people, places, and environments in a
geographical features in their local region (e.g., deserts, mountains,
valleys, hills, coastal areas, oceans, lakes).
2. Trace the
ways in which people have used the resources of the local region and
modified the physical environment (e.g., a dam constructed upstream
changed a river or coastline).
3.2 Students describe the American Indian nations in their local region long ago and in the recent past.
1. Describe national identities, religious beliefs, customs, and various folklore traditions.
2. Discuss the
ways in which physical geography, including climate, influenced how the
local Indian nations adapted to their natural environment (e.g., how
they obtained food, clothing, tools).
3. Describe the
economy and systems of government, particularly those with tribal
constitutions, and their relationship to federal and state governments.
4. Discuss the interaction of new settlers with the already established Indians of the region.
3.3 Students draw from historical and community resources to
organize the sequence of local historical events and describe how each
period of settlement left its mark on the land.
1. Research the explorers who
visited here, the newcomers who settled here, and the people who
continue to come to the region, including their cultural and religious
traditions and contributions.
2. Describe the economies
established by settlers and their influence on the present-day economy,
with emphasis on the importance of private property and
3. Trace why their community
was established, how individuals and families contributed to its
founding and development, and how the community has changed over time,
drawing on maps, photographs, oral histories, letters, newspapers, and
other primary sources.
3.4 Students understand the role of rules and laws in our daily lives and the basic structure of the U.S. government.
1. Determine the reasons for
rules, laws, and the U.S. Constitution; the role of citizenship in the
promotion of rules and laws; and the consequences for people who
violate rules and laws.
2. Discuss the importance of
public virtue and the role of citizens, including how to participate in
a classroom, in the community, and in civic life.
3. Know the histories of
important local and national landmarks, symbols, and essential
documents that create a sense of community among citizens and exemplify
cherished ideals (e.g., the U.S. flag, the bald eagle, the Statue of
Liberty, the U.S. Constitution, the Declaration of Independence, the
4. Understand the three branches of government, with an emphasis on local government.
5. Describe the ways in which
California, the other states, and sovereign American Indian tribes
contribute to the making of our nation and participate in the federal
system of government.
6. Describe the lives of
American heroes who took risks to secure our freedoms (e.g., Anne
Hutchinson, Benjamin Franklin, Thomas Jefferson, Abraham Lincoln,
Frederick Douglass, Harriet Tubman, Martin Luther King, Jr.).
3.5 Students demonstrate basic economic reasoning skills and an understanding of the economy of the local region.
1. Describe the ways in which
local producers have used and are using natural resources, human
resources, and capital resources to produce goods and services in the
past and the present.
2. Understand that some goods are made locally, some elsewhere in the United States, and some abroad.
3. Understand that individual economic choices involve trade-offs and the evaluation of benefits and costs.
4. Discuss the relationship of students "work" in school and their personal human capital.
Students demonstrate the motor skills and movement patterns needed to perform a variety of physical activities.
1.1 Chase, flee, and move away from others in a constantly changing environment.
1.2 Perform an inverted balance (tripod) by evenly distributing weight on body parts.
1.3 Perform a forward roll.
1.4 Perform a straddle roll.
1.5 Jump continuously a forward-turning rope and a backward-turning rope.
1.6 Balance while traveling and manipulating an object on a ground-level balance beam.
1.7 Catch, while traveling, an object thrown by a stationary partner.
1.8 Roll a ball for accuracy toward a target.
1.9 Throw a ball, using the overhand movement pattern with increasing accuracy.
1.10 Throw and
catch an object with a partner, increasing the distance from the
partner and maintaining an accurate throw that can be easily caught.
1.11 Kick a ball to a stationary partner, using the inside of the foot.
1.12 Strike a ball continuously upward, using a paddle or racket.
1.13 Hand-dribble a ball continuously while moving around obstacles.
1.14 Foot-dribble a ball continuously while traveling and changing direction.
1.15 Perform a line dance, a circle dance, and a folk dance with a partner.
Students demonstrate knowledge of movement concepts,
principles, and strategies that apply to the learning and performance
of physical activities.
2.1 Describe how changing speed and changing direction can allow one person to move away from another.
and demonstrate the correct hand position when catching a ball above
the head, below the waist, near the middle of the body, and away from
2.3 Explain the difference between throwing to a stationary partner and throwing to a moving partner.
2.4 Identify the key elements for increasing accuracy in rolling a ball and throwing a ball.
the differences between dribbling a ball (with the hand and the foot,
separately) while moving forward and when changing direction.
2.6 Define the terms
folk dance, line dance, and circle dance.
2.7 Compare and contrast folk dances, line dances, and circle dances.
Students assess and maintain a level of physical fitness to improve health and performance.
3.1 Demonstrate warm-up and cool-down exercises.
3.2 Demonstrate how to lift and carry objects correctly.
3.3 Participate three to four days each week, for
increasing periods of time, in continuous moderate to vigorous physical
activities that require sustained movement of the large-muscle groups
to increase breathing and heart rate.
increasing numbers of each: abdominal curl-ups, oblique curl-ups on
each side, modified push-ups or traditional push-ups with hands on a
bench, forward lunges, side lunges, and triceps push-ups from a chair.
3.5 Climb a vertical pole or rope.
3.6 Hold for an increasing period of time basic
stretches for hips, shoulders, hamstrings, quadriceps, triceps, biceps,
back, and neck.
3.7 Sustain continuous movement for increasing periods of time while participating in moderate to vigorous physical activity.
3.8 Measure and record improvement in individual fitness activities.
Students demonstrate knowledge of physical fitness concepts, principles, and strategies to improve health and performance.
4.1 Identify the body¡¯s normal reactions to moderate to vigorous physical activity.
4.2 List and define the components of physical fitness.
4.3 Explain the purpose of warming up before physical activity and cooling down after physical activity.
4.4 Recognize that the body will adapt to increased workloads.
4.5 Explain that fluid needs are linked to energy expenditure.
the need for oxygen and fuel to be available during ongoing muscle
contraction so that heat and waste products are removed.
4.7 Describe the relationship between the heart, lungs, muscles, blood, and oxygen during physical activity.
4.8 Describe and record the changes in heart rate before, during, and after physical activity.
4.9 Explain that a stronger heart muscle can pump more blood with each beat.
4.10 Identify which muscles are used in performing muscular endurance activities.
4.11 Name and locate the major muscles of the body.
4.12 Describe and demonstrate how to relieve a muscle cramp.
4.13 Describe the role of muscle strength and proper lifting in the prevention of back injuries.
4.14 Identify flexibility exercises that are not safe for the joints and should be avoided.
4.15 Explain why a particular stretch is appropriate preparation for a particular physical activity.
4.16 Differentiate the body¡¯s ability to consume
calories and burn fat during periods of inactivity and during long
periods of moderate physical activity.
Students demonstrate and utilize knowledge of
psychological and sociological concepts, principles, and strategies
that apply to the learning and performance of physical activity.
5.1 Set a personal goal to improve a motor skill and work toward that goal in nonschool time.
5.2 Collect data and record progress toward mastery of a motor skill.
5.3 List the
benefits of following and the risks of not following safety procedures
and rules associated with physical activity.
5.4 Use appropriate cues for movement and positive words of encouragement while coaching others in physical activities.
5.5 Demonstrate respect for individual differences in physical abilities.
5.6 Work in pairs or small groups to achieve an agreed-upon goal
1. Energy and matter have multiple forms and can be changed from one form to another. As a basis for understanding this concept:
a. Students know energy comes from the Sun to Earth in the form of light. b. Students know sources of stored energy take many forms, such as food, fuel, and batteries.
c. Students know machines and living things convert stored energy to motion and heat.
d.Students know energy
can be carried from one place to another by waves, such as water waves
and sound waves, by electric current, and by moving objects.
e. Students know matter has three forms: solid, liquid, and gas.
f. Students know evaporation and melting are changes that occur when the objects are heated.
g. Students know that
when two or more substances are combined, a new substance may be formed
with properties that are different from those of the original
h. Students know all matter is made of small particles called atoms, too small to see with the naked eye.
i. Students know people
once thought that earth, wind, fire, and water were the basic elements
that made up all matter. Science experiments show that there are
more than 100 different types of atoms, which are presented on the periodic table of the elements.
2. Light has a source and travels in a direction. As a basis for understanding this concept:
- Students know
- sunlight can be blocked to create shadows.
- Students know
- light is reflected from mirrors and other surfaces.
- the color of light striking an object affects the way the object is seen.
- Students know
- an object is seen when light traveling from the object enters the eye.
in physical structure or behavior may improve an organism's chance for
survival. As a basis for understanding this concept:
a. Students know plants and animals have structures that serve different functions in growth, survival, and reproduction.
b. Students know examples of diverse life forms in different environments, such as oceans, deserts, tundra, forests, grasslands, and wetlands.
c. Students know living
things cause changes in the environment in which they live: some of
these changes are detrimental to the organism or other organisms, and
some are beneficial.
d. Students know when the environment changes, some plants and animals survive and reproduce; others die or move to new locations. e.«Â Students know that
some kinds of organisms that once lived on Earth have completely
disappeared and that some of those resembled others that are alive
4. Objects in the sky move in regular and predictable patterns. As a basis for understanding this concept:
a. Students know the
patterns of stars stay the same, although they appear to move across
the sky nightly, and different stars can be seen in different seasons.
b. Students know the way in which the Moon¡¯s appearance changes during the four-week lunar cycle.
c. Students know telescopes
magnify the appearance of some distant objects in the sky, including
the Moon and the planets. The number of stars that can be seen through
telescopes is dramatically greater than the number that can be seen by
the unaided eye.
d. Students know that Earth is one of several planets that orbit the Sun and that the Moon orbits Earth.
e. Students know the position of the Sun in the sky changes during the course of the day and from season to season.
Investigation and Experimentation
progress is made by asking meaningful questions and conducting careful
investigations. As a basis for understanding this concept and
addressing the content in the other three strands, students should
develop their own questions and perform investigations. Students will:
observations to improve accuracy and know that the results of similar
scientific investigations seldom turn out exactly the same because of
differences in the things being investigated, methods being used, or
uncertainty in the observation.
evidence from opinion and know that scientists do not rely on claims or
conclusions unless they are backed by observations that can be
c. Use numerical data in describing and comparing objects, events, and measurements.
d. Predict the outcome of a simple investigation and compare the result with the prediction.
e. Collect data in an investigation and analyze those data to develop a logical conclusion.
Last Modified on 7/27/2008 9:53:40 PM