Many homeschoolers feel unprepared to teach math. The following information should solve that problem.
First, all children need to memorize the addition, subtraction, multiplication, and division tables. Without those facts ready in the mind, children can not progress. The basics are necessary. It may sound old fashioned, but flashcards work. That is why they have been used by so many people over the years. The best flashcards I have found are sold by Veritas Press. Also, what you sing you will remember. Both Christian Book Distributors and Veritas Press sell the Math Memory Songs by Kathy Troxel.
SAXON Math by Nancy Larson is an extremely user-friendly math program designed to be used either by teachers or homeschoolers. You are told exactly what to do and what to say at every step. You are told exactly what materials you will need for each lesson. SAXON Math is available either from Christian Book Distributors or Veritas Press. For the K-3 levels, you will need a set of manipulatives (linking cubes, teddy bear counters, dominoes, color tiles, geoboards, tangrams, plastic clocks, a balance, etc.) which are available through Christian Book Distributors. Note: Even the author of the program says that SAXON Math I can be used at the Kindergarten Level. It follows that Saxon Math 2 would be used in First Grade and so on.
My recommendations are as follows:
Kindergarten Saxon I
First Grade Saxon 2
Second Grade Saxon 3
Third Grade Saxon 54
Fourth Grade Saxon 65
Fifth Grade Saxon 76
Sixth Grade Saxon Algebra 1/2
Seventh Grade Elementary Algebra by Harold Jacobs
Eighth Grade Geometry by Harold Jacobs
Ninth Grade Algebra II and Trigonometry by
Paul A. Foerster and Saxon Algebra 2
Tenth - Twelfth Calculus: Early Transcendental
Functions by Larson, Howard, Edwards
Daily Math Practice (Grade 1, Grade 2, Grade 3, etc.) by Jo Ellen Moore and Marilyn Evans gives students additional practice and it coordinates with Saxon math quite well. Drill is important in math. This is available from Veritas Press or from Evan-Moor Publications.
If you want your children to understand that some money we can spend, some money we give to the church, and some money we must save, I suggest "My Giving Bank" by Larry Burkett. It has three appropriately decorated sections and is available from Christian Book Distributors.
Games are an excellent way to teach math concepts. Start with simple counting games for very young children. Examples include: Dominoes, Candyland, and Chutes and Ladders. Christian Book Distributors has a something called "Math Smart Addition Gard Game" (Talicor Inc.) which is played like dominoes, but using addition facts. They also have subtraction, multiplication, and division versions of the card game. Cribbage can be taught to even very young children, if you teach one rule at a time. It is excellent practice for addition. Yahtzee requires both addition and multiplication. Monopoly has been updated so that no money is used! It uses "electronic" transactions. You can still buy the classic Monopoly we played as children, but check the box carefully. Chess can also be taught to young children. It is excellent at building strategy and thinking skills.
Don't overlook the importance of jigsaw puzzles in preparing children for math. Analyzing the shapes of the various pieces is an important step in preparing to do math. I am particularly fond of the very large floor puzzles from Melissa and Doug. The pieces are quite big and few in number so these puzzles are excellent for pre-schoolers.
If you have progressed beyond the basics and are looking for materials to teach algebra, geometry, and calculus, I suggest that you check Veritas Press.
Algebra: Elementary Algebra by Harold Jacobs as well as Saxon Algebra I and The Usborne Illustrated Dictionary of Math by Tori Large.
Geometry: Geometry (3rd ed.) by Harold Jacobs, Thirteen Books of Euclid's Elements (Volume I has books I & II, Volume II has books III through IX, and Volume III has books X to XIII.), as well as Flatland: A Romance of Many Dimensions by Edwin A. Abbott and Sphereland by Dionys Burger (a sequel to Flatland). You can but the last two as one volume.
Algebra II and Trigonometry: Algebra II and Trigonometry by Paul A. Foerster as well as Saxon Algebra 2.
Calculus: Calculus Early Transcendental Functions by Larson, Howard, and Edwards.