Learning Tree

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Elementary Program


Common Core State Standards for Mathematics, Grade 2

Operations and Algebraic Thinking

Represent and solve problems involving addition and subtraction.
1. Addition and subtraction word problems within 100

Add and Subtract within 20.
2. Fluently add and subtract within 20. (memorize by end of Grade 2)

Work with equal groups of objects to gain foundations for multiplication.
3. Odd and even numbers up to 20. (including equation work)
4. Use addition to find total number in a rectangular array. (up to 5 columns and 5 rows)

Number and Operations in Base Ten

Understand Place Value.
1. Hundreds, tens, and ones place in three-digit numbers.
2. Count within 1000 including skip counting by 5’s, 10’s and 100’s.
3. Read and write numbers to 1000 using numerals, number names and expanded form.
4. Compare two three-digit numbers.

Use place value understanding and properties of operations to add and subtract.
5. Fluently add and subtract within 100.
6. Add up to four two-digit number.
7. Add and subtract within 1000, focusing on borrowing and carrying.
8. Mentally add and subtract 10 or 100 to a given number 100-900.
9. Explain how addition and subtraction strategies work.

Measurement and Data

Measure and estimate lengths in standard units.
1. Measure the length of objects using appropriate tools (rulers, yardsticks, meter sticks, measuring tape)
2. Measure objects twice using different units and describe how the two measurements relate.
3. Estimate lengths using inches, feet, centimeters, and meters.
4. Measure to determine how much longer one object is to another.

Relate addition and subtraction to length.
5. Use addition and subtraction within 100 to solve word problems involving lengths with the same units.
6. Represent whole numbers as lengths and represent whole number sums and differences thin 100 on a number line diagram.

Work with time and money.
7. Tell and write time from analog and digital clocks to the nearest five minutes, including a.m. and p.m.
8. Solve word problems involving dollar bills, quarters, dimes, nickels and pennies.

Represent and Interpret data.
9. Generate measurement data by measuring lengths of several objects to the nearest whole unit. Show the measurements by making a line plot.
10. Draw a picture and a bar graph to represent a data set with up to four categories. Solve simple problems using information presented in a bar graph.


Reason with shapes and their attributes.
1. Recognize and draw shapes having specified attributes given angles and faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.
2. Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
3. Partition circles and rectangles into two, three, or four equal shares and describe them using the words halves, thirds, half of, a third of. Recognize that equal shares of identical wholes need not have the same shape.

Common Core State Standards for English Language Arts & Literacy in History/ Social Studies,Science, and Technical Subjects, Grade 2

Reading Standards for Literature

Key Idea and Details
1. Ask and answer who, what, when, where, why, and how questions.
2. Recount stories, including the main message, lesson, or moral from fables and folktales.
3. Describe how characters respond to major events and challenges.

Craft and Structure
4. Describe how words and phrases supply meaning and rhythm in a story, poem, or song.
5. Describe the overall structure of a story, including the beginning and end.
6. Acknowledge differences in the points of view of characters, including speaking in a different voice for each character.

Integration of Knowledge and Ideas
7. Use information gained from the illustrations and words to demonstrate understanding of characters, setting, and plot.
8. (Not applicable in literature.)
9. Compare and contrast two or more versions of the same story.

Range of Reading and Level of Text Complexibility
10. By the end of the year, read and comprehend literature, including stories and poetry in grade 2-3 text complexibility band proficiently.

Reading Standards for Informational Text

Key Idea and Details
1. Ask and answer who, what, when, where, why, and how questions.
2. Identify the main topic of a multiparagraph text as well as the focus of specific paragraphs within texts.
3. Describe the connection between series of historical events, scientific ideas or concepts, or steps in technical procedures in a text.

Craft and Structure
4. Determine the meaning of words and phrases in texts relevant to grade 2.
5. Know and use various text features (captions, bold print, subheadings. glossaries) to locate key information or facts.
6. Identify the main purpose of a text, including what the author wants to answer, explain, or describe.

Integration of Knowledge and Ideas
7. Explain how specific images (a diagram showing how a machine works) contributes to and clarify a text.
8. Describe how reasons support specific points the author makes in a text.
9. Compare and contrast the most important points presented by two texts on the same topic.

Range of Reading and Level of Text Complexibility
10. By the end of the year, read and comprehend informational texts, including history/ social studies, science, and technical texts in grade 2-3 text complexibility band proficiently.

Reading Standards: Foundational Skills

*In Kindergarten, children are expected to demonstrate increasing awareness and competence in the areas that follow. (see Kindergarten and Grade 1 standards)

Phonics and Word Recognition
3. Know and apply grade level phonics and word analysis skills in decoding words.
a. long and short syllable words in one-syllable words
b. spelling sound correspondences for vowel teams
c. two-syllable words with long vowels
d. common prefixes and suffixes
e. inconsistent but common spelling-sound correspondence
f. irregularly spelled words

4. Read with sufficient accuracy and fluency to support comprehension.
a. Read with purpose and understanding.
b. Read orally with accuracy, appropriate rate, and expression.
c. Confirm or self- correct word recognition and understanding, rereading as necessary.

Writing Standards

Text Types and Purposes
1. Write opinion pieces, introducing the topic, stating an opinion, supplying reasons using linking words, and providing a concluding statement.
2. Write informative/ explanatory texts in which they introduce a topic, use facts and definitions, and provide a concluding statement.
3. Write narratives in which they recount a well-elaborated event or short sequence of events including details to explain actions, thoughts, and feelings, use temporal words to signal event order, and provide a sense of closure.

Production and Distribution of Writing
4. (begins in Grade 3)
5. With guidance, focus on a topic and strengthen writing as needed by revising and editing.
6. With guidance, use a variety of digital tools to produce and publish writing, including in collaboration with peers.

Research to Build and Represent Knowledge
7. Participate in shared research and writing projects.
8. Recall information from experiences or gather information from provided sources to answer a question.
9. (begins in Grade 4)

Range of Writing
10. (begins in Grade 3)

Speaking and Listening Standards

Comprehension and Collaboration
1. Participate in collaborative conversations with diverse partners about grade 2 topics and texts.
a. Follow agreed upon rules for discussions.
b. Build on others’ talk in conversation by linking their comments to the remarks of others.
c. Ask for clarification and further explanation as needed.
2. Recount or describe key ideas or ideas from a text read aloud or information presented orally or through media.
3. Ask and answer questions about what a speaker says.

Presentation of Knowledge and Ideas
4. Tell a story or recount an experience with appropriate facts,descriptive details,speaking in audibly coherent sentences.
5. Create audio recordings of stories or poems; add drawings or other visual displays to clarify ideas, thoughts, and feelings.
6. Produce complete sentences to provide requested detail or clarification.

Language Standards

Conventions of Standard English
1. Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
a. nouns
b. irregular plural nouns
c. reflexive pronouns
d. past tense of irregular verbs
e. adjectives and adverbs
f. complete simple and compound sentences
2. Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
a. capitalization of holidays, product names and geographic nouns
b. commas
c. apostrophe
d. seling patterns
e.consult reference materials, including dictionaries

Knowledge of Language
3. Use knowledge of language and its conventions when writing, speaking, reading or listening.
a. Compare formal and informal use of English.

Vocabulary Acquisition and Use
4. Determine or clarify the meaning of unknown and multi-meaning words and phrases.
a. Use sentence- level context as a clue.
b. Determine the meaning of the new word formed when a known prefix is added.
c. Use a known root word as a clue to the meaning of an unknown word.
d. Use knowledge of the meaning of individual words to predict the meaning of compound words.
e. Use glossaries and beginning dictionaries to determine or clarify the meaning of words and phrases.
5. Demonstrate understanding of word relationships and nuances in word meanings.
a. Identify real-life connections between words and their use.
b. Distinguish shades of meaning among closely related verbs.
6. Use words and phrases acquired through conversations, reading, and being read to, and responding to texts, including using adjectives and adverbs to describe.

CommonNational Science Education Standards(Grade K-4)

The new common core standards integrate Science into reading and it doesn’t officially start as an independent subject until Grade 6. However, Learning Tree believes that science is important enough to receive individual focus, so we will follow the national science education standards.


Science As Inquiry Standards

1. Abilities necessary to do scientific inquiry

  1. Students answering questions using scientific resources combined with observations.

  2. Plan and conduct a simple systematic observation or investigation.

  3. Use simple instruments such as ruler, thermometer, watch, balance, magnifier, microscope, computer, or calculator to gather data and extend the senses.

  1. Use knowledge and evidence (data) to formulate explanation.

  2. Communicate or analyze investigations and explanations that might be drawn or spoken as well as written.

2. Understandings about scientific inquiry

  1. Recognizing that all of the above are things scientists do.


Physical Science Standards

1. Properties of objects and materials

  1. Objects have measurable and observable properties, which use tools.

  2. Objects can be described by their properties and classified accordingly.

  3. Materials can exist in different states (solid, liquid, gas).


2. Position and motion of objects

  1. Position of an object can be described relative to other objects.

  2. Object’s motion can be described by observing its position over time.

  3. Position or motion of object can be changed by pushing or pulling.

  4. Sound is produced by vibration of objects and pitch can be varied.


3. Light, heat, electricity, and magnetism

  1. Light travels in a straight line and can be reflected, refracted, and absorbed by objects.

  1. Heat can be produced and conducted.

  2. Electricity in circuits can produce light, heat, sound, and magnetic effects.

  1. Magnets attract and repel.


Life Science Standards

1. Characteristics of organisms

  1. All organisms have different needs.

  2. The environment must supply the needs of organisms.

  3. Each organism has different structures for different functions.

  4. Behavior is influenced by internal cues (hunger) and external cues(change in environment).

2. Life cycles of organisms

  1. Plants and animals have life cycles.

  2. A life cycle includes: birth, development, adulthood, reproduction, and death.

  3. Offspring resemble parents.

  4. Some characteristics of organisms are inherited while others result

    from interactions.

3. Organisms andenvironments  

  1. Plants are the base of an ecosystem.

  2. All animals depend on plants.

  1. Organisms’ patterns of behavior relate directly to the environment (kinds and numbers of other organisms, the availability of food and resources, and physical characteristics of the environment).

  1. Organisms can cause changes.

  2. Humans depend on environments.


Earth And Space Science Standards 地球科学、宇宙科学

1. Properties of earth materials

  1. Earth materials have different physical and chemical properties.

  2. Soils have different properties and abilities to support plants.

  3. Fossils provide evidence about the environment, plants, and animals of the past.


2. Objects in the sky

  1. The sun, moon, stars, birds, clouds, airplanes, all have characteristics that can be observed and described.

  1. The sun provides light and heat necessary to maintain Earth’s temperature.


3. Changes in earth and sky

  1. The surface of the Earth changes.

  2. Weather changes from day to day and over the seasons.

  3. Objects in the sky have patterns of movement.


Science And Technology Standards

1. Abilities of technological design

  1. Identify a simple problem.

  2. Propose a solution.

  3. Implement a proposed solution.

  4. Evaluate a product of design.

  5. Communicate a problem, design, and solution.


2. Understandings about science and technology

  1. Identify a simple problem.

  2. Propose a solution.

  3. Implement a proposed solution.

  4. Evaluate a product of design.

  5. Communicate a problem, design, and solution.


3. Abilities to distinguish between natural objects and objects made by humans

  1. Some objects occur in nature; others have been designed and made by

  2. people to solve human problems and enhance the quality of life.

  3. Objects can be categorized into two groups, natural and designed.


Science In Personal And Social Perspectives

1. Personal health

  1. Safety and security are basic needs of humans.

  2. Individuals have some responsibility for their own health.

  3. Nutrition is essential to health.

  4. Different substances can damage the body and how it functions.


2. Characteristics and changes in populations

  1. Human populations include groups of individuals living in a particular location. Population density refers to the number of people of a particular population that live in a given amount of space.

  1. The size of human populations can increase or decrease.


3. Types of resources

  1. Resources are things we get from the living and nonliving environment to meet the needs and wants of a population.

  1. Some resources are basic materials (air, water, soil).

  2. Some resources are produced (food, fuel, building materials).

  3. Some resources are nonmaterial (quiet places, beauty, security, safety).


4. Changes in environments

  1. Environments are the space, conditions, and factors that affect an individual’s and a population’s ability to survive and their quality of life.

  1. Changes in environments can be natural or influenced by humans.

  2. Some environmental changes occur slowly, and others occur rapidly.


5. Science and technology in local chalennges  

  1. People continue inventing new ways of doing things. It is helpful to try to determine in advance how ideas and inventions will affect other people.

  1. Science and technology have greatly improved food quality and quantity, transportation, health, sanitation, and communication. These benefits are not available worldwide.


History And Nature Of Science Standards

3. Science as a human endeavor

  1. Science has a rich history.

  2. Many contributions have been made to science and technology.

  3. Science will never be finished.

  4. Science can be a life-long career.

  5. Many people derive great pleasure from doing science.


National Standards for Social Studies (Grade K-4)

The new common core standards integrate Social Science into reading and it doesn’t officially start as an independent subject until Grade 6. However, Learning Tree believes that social science is important enough to receive individual focus, so we will follow the national social science education standards.


Civics, Government, and Human Rights 公民、政府、人権

1. How do citizens, civic ideals, and government institutions interact to balance the needs of individuals and the common good?

2. How have economic, political, and cultural decisions promoted or prevented the growth of personal freedom, individual responsibility, equality, and respect for human dignity?


Geography, People, and the Environment 地理、市民、環境

1. How do physical geography, human geography, and the human environment interact to influence or determine the development of cultures, societies, and nations? 


Economics, Innovation, and Technology 経済、改革、技術

1. How can individuals, groups, and societies apply economic reasoning to make difficult choices about scarce resources? What are the possible consequences of these decisions for individuals, groups, and societies?

2. How have scientific and technological developments over the course of history changed the way people live and economies and governments function?


History, Culture, and Perspectives 歴史、文化、これからの展望

1. How do our interpretations of past events inform our understanding of cause and effect, and continuity and change, and how do they influence our beliefs and decisions about current public policy issues?

2. How can the study of multiple perspectives, beliefs systems, and cultures provide a context for understanding and challenging public actions and decisions in a diverse and interdependent world?

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