"If you don't know where you are going, you're likely to end up somewhere else." (Lawrence J. Peter; educator and author of "Peter's Principles"; 1919–1990.)
The Snail's Trail Homeschool
Our K-12 Understandings:

(What I want my kids to learn)

ART: (taken from http://www.westonschools.org)
  1. We communicate through our images: we articulate through our visual arts vocabulary.
  2. Art is a universal language.   
  3. Skills in criticism are essential for effective communication
  4. Art doesn’t just happen:  it involves a creative process from beginning to end.   
  5. Art can exist on many levels: visual, auditory, and over space and time.
  6. Art involves a determined, reflective, creative process from idea to exhibition
  7. Knowledge of media, materials and techniques empowers us to make choices and to express ourselves.
  8. The human need to make art is met through the development of skill and understanding.   
  9. Understanding and using the elements and principles of design heightens the impact of artistic expression. 
  10. There are commonalities within all forms of art that, once learned, can be incorporated into artwork to communicate effectively. 
  11. There are lots of ways to reach an artistic solution.
  12. We discover ourselves while relating to the world around us through art.
  13.  Understanding art is a doorway to the world. 
  14. Art is the voice and mirror of the world’s people, their history, culture, social context, convictions, triumphs, tragedies, fears, and hopes. 

ENGLISH/LANGUAGE ARTS/DRAMA: (taken from http://www.westonschools.org)
  1. Clarity in spoken language enhances communication.
  2. Thoughtful listening enhances oral communication.
  3. Speakers make decisions based on audience, purpose, and form.
  4. Speaking and listening are life skills that require practice.
  5. Oral communication is a dynamic interaction between speaker and listener.
  6. Reading should be an enjoyable and valuable human experience.
  7. Different forms of print have different functions.
  8. Knowledge about the author’s craft helps a reader construct meaning.
  9. Knowledge about genre characteristics helps a reader construct meaning.
  10. A reader’s experiences influence his/her interpretation of a work of literature.
  11. A writer’s experiences influence his/her work and perspective.
  12. Readers learn to read by reading.
  13. Readers work actively to construct meaning.
  14. Reading is thinking.
  15. Understanding is promoted by a reader’s use of strategies and tools.
  16. Knowledge about literature, language, and the world helps a reader construct meaning. 
  17. Non-fiction is the language of reality while fiction is the language of possibility.
  18. Writing is a powerful vehicle for communicating meaning, sharing information and developing a style.
  19. Reading and writing are reciprocal processes, which support one another.  Readers actively construct meaning and writers actively communicate meaning.
  20. Writers learn to write by writing.
  21. Clarity in writing results in communication of meaning.
  22. Consideration of audience, purpose and form provides focus for writers.
  23. Writing is a process enhanced by the use of strategies and tools.
  24. Knowledge about literature, and of the writer’s craft, helps the writer to write.
  25. Writers shape language for effective communication.
  26. Writers write from a base of knowledge about their subjects.  They use their knowledge to communicate clearly and effectively.
  27. Ideas are made complete by substantiation.
  28. The ability to access and manipulate electronic media is a central skill for communication and scholarship.
  29. Effective use of electronic media requires critical evaluation.
  30. Media presentations reveal multiple intelligences at work.
  31. Media presentations may permit a deeper, more imagistic understanding of a given topic.
  32. Literacy in media productions prepares students for the outside world.
  33. Skillful communication allows someone to be seen and heard.
  34. Portraying a range of characters encourages understanding of self.
  35. Successful communication requires understanding of alternate points of view.
  36. The process of group creation teaches the unique potential of compromise and artistic collaboration.
  37. Employing style or genre in playmaking can shape sharp plots and characterization.
  38. Vocal characterization is its own character.
  39. Characters in drama are defined by physical and vocal characteristics, objectives and actions, and their relationships with other characters.
  40. Dramatic scenes are constructed through the use of discrete units of action or “beats.”
  41. Writers structure the language of their characters’ speeches in order to convey the emotional or mental states of the characters.
  42. Understanding how writers use specific language structures can help actors unlock the emotional depth of the characters they play.
  43. Knowledge of media, materials, and techniques empowers us to make choices and express ourselves.

Health/PE:(taken from http://www.westonschools.org)
  1. Application of knowledge is necessary to increase the likelihood of leading a healthy lifestyle.
  2. Understanding how your body works is important in maintaining optimal health.
  3. Good nutrition is an essential component of good health.
  4. The better you eat, the better you feel.
  5. You are what you eat.
  6. People need interaction to be happy and healthy.
  7. We are all parts of a whole.
  8. Knowledge of mental health concepts provides a background for dealing with personal crisis or difficult situations.
  9. Understanding oneself leads to self-acceptance.
  10. Communication is a key component of good mental health.
  11. Personal hygiene is the foundation for disease prevention.
  12. Identifying illness and seeking treatment is an essential life skill. 
  13. Each citizen is responsible for personal and public safety.
  14. Part of being a good citizen is being prepared to assist others in times of need.
  15. Use of substances can positively and negatively impact our lives.
  16. Abuse of substances will always lead to negative outcomes.
  17. You alone are responsible for your actions.
  18. Every action has some reaction.
  19. Movement is the core of kinesthetic awareness.
  20. Mastery is the result of thoughtful practice.
  21. Fitness does not just happen.  You must understand it and practice regularly.
  22. Physical fitness is a journey, not a destination.
  23. Safe cooking means safe eating.
  24. Skillfully prepared food satisfies the senses.
  25. Careful cooking procedures create good food. 
  26. Wise choices promote healthy and enjoyable eating practices.
  27. Food is a common thread between cultures.
  28. Culinary traditions reflect geography and cultural heritage.

History & Social Studies: (taken from http://www.westonschools.org)
  1. Sociology, anthropology, psychology, and other social sciences teach us that human and societal development is a complex process.
  2. Cultural exchange and human interactions impact the way societies and individuals develop.  Understanding cultural interaction enables us to appreciate and respect the enormous variety of human experience.
  3. For a variety of motives, nations and individuals seek to expand their influence, which has intended and unintended consequences.
  4. Historical events are not isolated; they are complex and have consequences.
  5. Knowing about the past helps us understand the present.
  6. Research is a skill for life-long learning.
  7. Competent historical research requires the location and interpretation of documentary evidence.
  8. Good research combines effective use of multiple resources  and student persistence.
  9. Questioning is a critical aspect of learning.  
  10. Throughout history, individuals from all walks of life have influenced the course of events.
  11. When ideas motivate and unify individuals to act as a group, change occurs.  
  12. Understanding concepts in geography such as exact location, relative location, and cardinal directions provide a fundamental understanding of the world.
  13. Connecting different peoples with their geographic locations throughout the world develops a deeper cultural awareness.
  14. The ability to create and interpret maps allows us to move through the world effectively. 
  15. Physical geography is a major factor in the emergence and development of different political systems, economies and cultures.
  16. Geography has a continual effect on groups of people and their cultures.
  17. Throughout history, humans have struggled to fit the environment to their needs – sometimes successfully, sometimes not.
  18. Individuals make choices as producers, investors, and consumers.
  19. Individuals, businesses and governments interact in creating an economy. 
  20. Economic systems are determined by decisions about production and distribution, property ownership, and individual freedom.
  21. Economic systems have a political dimension.
  22. Economic systems are dynamic.  They have and will continue to change according to time and place. 
  23. The form of a community’s government has a strong influence on its history and economics.
  24. A national and global citizen must understand how political power is used and shared around the world.
  25. A national and global citizen must understand that communities organize and govern themselves in a variety of ways.
  26. A national and global citizen must be able to assess the most appropriate form of government for a community.
  27. Analysis of the history and function of American government provides students with an understanding of the complex genius inherent in our fluid system of government.
  28. A successful democracy depends on the participation of its citizens.
  29. Understanding the privileges and duties of citizenship promotes active, responsible participation, locally, nationally, and globally.
  30. Active, responsible participation can lead to a more tolerant and peaceful world. 

MATH: (taken from http://www.westonschools.org)
  1. Successful problem solvers possess a set of core beliefs that support their work: problem solving is important, takes significant time and repeated efforts, and reflection.
  2. Specific strategies have wide application in attacking problems and can help in problem solving: consider simpler cases, make analogies to other problems, work backwards, etc.
  3. Different ways of representing selected parts of the available information (algebra, geometric diagrams, programming languages, models and manipulatives) are important tools in problem solving.
  4. Practice in using representational schemes, shifting among representations, and creating new representations improves problem-solving skills.
  5. Specific examples can be organized to reveal patterns or generalizations that may be applicable to new situations; practice in organizing and generalizing improves problem solving.
  6. Rules of logic can assist in determining the truth of statements constructed from other statements whose truth is known.
  7. Problems can be solved by dealing with a finite set of cases that  covers all possibilities.
  8. Mathematical proof requires the application of the rules of deduction to already proven statements and/or clearly stated postulates.
  9. For an argument to be convincing it must be supported by reasoning and statements which the listener finds understandable and with which the listener will agree.
  10. A numeral is different from a number: a given number has multiple equivalent representations.
  11. Numbers are used for purposes beyond counting or measuring objects- e.g. for representing a position or as a label.
  12. Some numerals represent the exact desired value; others represent only an approximation of the desired value.
  13. Our system is base ten- the position of a digit influences the value represented, zero is needed as a number, and regrouping is possible.
  14. Counting numbers can be uniquely decomposed into prime factors. Integers can be classified.
  15. The set of numbers expands, as new numbers are invented/discovered to meet new needs.
  16. If two real numbers are unequal, one is larger and there are infinitely many real numbers between them. 
  17. There is a 1 to 1 match between real numbers and points on a line.
  18. The decimal system cannot represent an exact irrational value whereas radicals and certain symbols such as π do represent the exact value.
  19. Fractions have two uses:  to measure a quantity or point on a number line (convertible to a decimal) and to represent a ratio (convertible to a percentage).
  20. Basic number facts are the building blocks for most computations.
  21. Multiple strategies and tools exist for completing a calculation.
  22. Some strategies are more “efficient” than others.
  23. Some computations will predictably produce a more significant change in value than others.
  24. Computational patterns can be used to check results.
  25. Operations have useful properties.
  26. The order in which operations are done determines the result; there is a default order for performing operations.
  27. Operations can be reversed using their inverses.
  28. Estimation prior to performing a computation helps insure reasonable answers.
  29. Why an algorithm works can be explained logically; this understanding can assist in recalling and applying the algorithm.
  30. Any measurement other than counting produces an approximate rather than an exact value.
  31. A measurement can be estimated and some estimates are better than others.
  32. A measurement consists of a number, a unit, and an implied precision.
  33. Many different units may measure the same attribute; the unit identifies the attribute and only units for the same attribute may be converted.  Some units are more appropriate for a specific task than others.
  34. There are many different tools for measuring an attribute; some are more appropriate for a specific task than others.
  35. Objects/phenomena of the same type have the same measurable attributes.
  36. Some attributes are commonly measured and their units and the approximate sizes of those units are common knowledge.
  37. Some measurements may be calculated from the measures of other attributes.
  38. Rates can be measured as a ratio of two quantities.
  39. Some measures are maintained when an object is broken into parts and the parts rearranged.
  40. Geometric/spatial visualization improves with practice
  41. Vocabulary and terminology should reflect acquisition of concepts and their relationships
  42. Properties are maintained under transformations: a square is still a square when rotated; perpendicular segments need not be horizontal and vertical
  43. Congruent objects are “the same.”
  44. Scaling objects up or down preserves some properties and has predictable effects on measures
  45. Shapes can be quantified in useful ways: dimensionality, measures, count of vertices, faces, edges; number of intersection points.
  46. Relations between shapes are powerful analytic tools (e.g. congruence-isometries; similarity-size transformations; symmetries; topological equivalence; projections).
  47. Some quantifications imply others such as the Pythagorean theorem.
  48. Some relations imply others.  
  49. Shapes can represent and be represented by some aspects of other things.
  50. Shapes can usefully be viewed statically and dynamically.
  51. Shapes are classified.
  52. Different useful geometries develop from different sets of assumptions; different geometries have different results for 1-7 above.
  53. Since it is often impossible to gather data from an entire population so a subset is used.  The more representative of the population the subset (sample) is, the more likely that the data will be valid.
  54. Graphics and statistical measures may represent raw data and can assist in understanding the data and its distribution.  Different representations of the same data can however give different impressions to the reader.
  55. Graphics and statistics for paired data can disclose possible correlations, describe the strength of the possible correlation, and assist in interpolating/extrapolating new data pairs.
  56. Mathematical measures can indicate how likely it is that results from a sample will apply to the population at large.
  57. How data is gathered impacts its validity.
  58. People make important decisions based on information conveyed by statistics.  
  59. Statistics are frequently used to support a point of view.
  60. Probability is a measure of the relative likelihood that an event will happen.
  61. The probability of an event can be predicted based on the outcomes of many identical or similar events.
  62. The probability of a simple event can be predicted by compiling an exhaustive set of equally likely outcomes.
  63. The probability of a complex event can sometimes be predicted from calculations using the probability of simpler events.
  64. Mathematical models, representations, and simulations are used to approximate probabilities.
  65. Some events are independent of one another; the occurrence of one doesn’t alter the probability of the other happening.
  66. A binomial probability distribution can model many real world distributions.
  67. Algebraic symbols can efficiently represent mathematical processes and algorithms, both explicitly and recursively.
  68. Algebraic symbols can efficiently represent claims of properties and/or identities (a+b = b+a).  
  69. Algebraic symbols can efficiently represent subsets of space (e.g. the plane x+y+z = 6).
  70. Algebraic symbols can efficiently represent desired results or solution sets (x+y>8).
  71. Manipulation of algebraic expressions by applying properties, using technology, or graphing can produce useful new information.
  72. Sequences of shapes or numbers can represent a variety of patterns, simple and complex.
  73. Functions and relations can accurately model real world relationships between variables.
  74. Functions may be combined or decomposed using composition to obtain new functions and inverses.
  75. Relationships between two or more varying quantities can be represented in many ways.
  76. Switching from one representation to another can reveal new information about a relationship.
  77. Changing the inputs to a function systematically and observing the relative rate of change of the output and the cumulative value of the output can provide useful information about situations being modeled by the function.
  78. Mathematics has a rich human history and is still growing today.
  79. Mathematics develops representations and manipulates abstractions independent of their application.
  80. The application of mathematical abstractions can lead to new abstractions to study.
  81. Mathematics uses numbers and other symbols to describe abstractions of real world phenomena.
  82. Both mathematical abstractions and mathematical applications can be beautiful.

MUSIC: (taken from http://www.westonschools.org)
  1. Singing is a fundamental form of expression that connects all human beings socially and emotionally in every culture.
  2. Music literacy fosters musical independence
  3. Playing an instrument communicates thoughts, images, and emotions without words.
  4. Improvisation and composition create musical ideas.
  5. Critical Response raises the level of understanding and expression in music
  6. Historical and Cultural connections in the arts lead to understanding of all peoples.

SCIENCE & Technology :(taken from http://www.westonschools.org)
  1. Good evidence is characterized by accurate observations and measurements made during an investigation.
  2. Scientific explanations must be based on credible evidence.
  3. Communicating results of scientific investigations requires specificity and clarity.
  4. Science is an ongoing process of questioning and knowledge acquisition.
  5. Our ability to predict is limited by our current knowledge and technology.
  6. Building and testing models is a useful process to understand and predict the behavior of systems.
  7. Structure and properties are interdependent.
  8. Systems behave in an orderly and predictable way.
  9. There is observable change over different scales of time. It occurs in a predictable, repeatable pattern with consequences.
  10. Heat transfer drives geological and meteorological activity.
  11. Gravity is an underlying force that structures the universe and the earth’s motion as a part of a solar system.
  12. Systems behave in an orderly and predictable way.
  13. There is constant tension between change and balance over time.
  14. Energy and matter are conserved.
  15. Forces cause change.
  16. Change leads to equilibrium.
  17. All matter has a basic structure that determines its properties and its interactions with other matter.
  18. Living things rearrange matter.   
  19. Living things transform energy.   
  20. Structure is related to function.
  21. Life is characterized by continuity and diversity.
  22. Living systems either maintain balance or change.  
  23. Engineering designs are created through a cyclical  process 
  24. Engineers and designers communicate their designs through technical drawings and specifications.
  25. Complex designs are often best understood as systems, which perform a function which cannot be accomplished by their component parts acting individually.