Following is a list of topics that are part of a well-rounded kindergarten (K5) classroom. Use this list as a starting point for a customized course of study for your 5 or 6 year old.

Language Arts
Phonics (single sounds, common blends, ch-, sh-, th-)
Recognition of lower and upper-case letters
Recognition of name when written
Understanding letter placement in words
Introduction to music, poetry, literature (nursery rhymes, stories, etc.)
Following and giving directions
Narrating in own words, clearly expressing an idea, storytelling
Reading-readiness skills (moving left to right, fine motor skills, etc.)
Singing
Listening in various environments
Role-playing (puppet shows, etc.)
Beginning writing process
Writing name and age
Writing alphabet and numbers to 9
Recognition of Dolch sight words
Introduction to foreign language
“Reading” a wordless picture book

Math
Counting to 20
Concept of zero
One-to-one relationship
More, less, equal
Sequence of events
Meaning of addition and subtraction
Introduction to number line
Simple estimation
Shapes
Calendar
Days of week
Time telling to the hour
Introduction to monetary denominations
Simple problem solving
Recognition of numbers 0-9
Begin to place single numbers together to make double digit numbers
Basic cooking and measuring
Single digit addition to 9

Science/Health/Safety
Observation of common items and occurrences
Common animals and plants
Relationship between animals and plants
Classification of living things
Care of pets
Plant care
Weather and seasons
Temperature
Light
Colors
Senses
Earth, moon, stars, planets
Clouds and rain
Conservation and environmentalism
Experimentation and observation
Building skills
Personal hygiene
Good eating habits
Good exercise habits
Major body parts
Basic bodily functions
Body structure
Safety rules and symbols

Social Studies
Meaning of holidays, traditions and customs
Understanding and appreciating other cultures
Role in family and community
Work and jobs
Basic human needs
Self-respect and awareness
Awareness of others
Address and phone number
City, state, country
Cause and effect
Kindness to animals
Social skills and expectations
Manners

Art/Music
Hand-on practice with various methods and media
Colors and color blends
Warm and cold colors
Basic artistic concepts
Symmetry
Exposure to art museums
Exposure to theater
Role-playing
Puppet shows
Exposure and identifying of musical genres
Identifying instruments
Singing and pronunciation
Rhythm

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Homeschooling With Confidence: A Plain English Guide to Homeschooling in the United States