So, this may seem simplistic, but the academic goals for a kindergarten student are some beginning reading skills, counting and number recognition and beginning writing. Because we are Catholic, there will always be a component of Religion included, at our house. I've added that to the basic list of goals I found online. I also found web-sites that meet the goals for the Kindergarten student. You need a printer to make worksheets. I'm also including some good read aloud books, just for good measure. Reading aloud to your child everyday is important for their language, grammar, character, virtue and self regulation development. Lastly, work on cutting, pasting and coloring skills to develop fine motor skills for writing later.
I'd like to add the disclaimer that this does not follow any specific "approach". This is only an example of how you could accomplish doing school without purchasing curriculum. There are so many websites out on the Internet that will help you educate your child at home following a specific approach, that I did not take a specific "approach" to creating this list. You can find those by googling things like "free kindergarten charlotte mason". For example, www.materamabilis.org/ has FREE Catholic Charlotte Mason curriculum. You can go there and need not do anything else but visit the library.
Remember, when choosing a curriculum, to look at the needs of the child and their learning style.
Academic Goals for a Kindergartener
Reading Objectives - http://www.starfall.com/
Identify likes and differences in word forms.
Recognizes rhyming words.
Name upper and lower case letters of the alphabet
Name the beginning consonant sounds in spoken words.
Indicate where a sentence starts and ends and use left to right motion when reading.
Make predictions and use picture clues to read.
Sequence a story with beginning middle and end.
Math Objectives - http://www.kidzone.ws/math/kindergarten.htm
Count to 100 by 1’s , 5’s, and 10’s.
Count to 10 by 2’s.
Recognize numbers to 20.
Show sequencing to 20.
Show one to one correspondence to 20.
Correctly write numerals 0—20.
Make patterns and graphs.
Sort and measure simple objects.
Do simple addition and subtraction problems to 20.
Writing Expectations - http://www.first-school.ws/theme/handwriting.htm
Correctly form the capital and lower case letters of the alphabet.
Correctly write first and last name.
Apply letter/sounds as emergent writers.
Write simple sentences.
Catholic Religion Goals - Beginning Catechism, Catholic Read Alouds and Bible Stories
Catechism - http://www.catholiccatechist.org/freeFile_Category.php
Great Catholic Book List - www.hillsideeducation.com/mosaicbooklist.pdf
Bible stories, Saints and Catholic activities - http://www.catholicmom.com/catholic_kids.htm
Unit Study Ideas - http://ebeth.typepad.com/serendipity/2008/08/a-tutorial-for.html
Games and fun activities, thrown in for good measure - http://www.softschools.com/grades/kindergarten.jsp