The book I have is aligned with the National Council of Teachers of Mathematics (NCTM) standards. Lessons are divided into five categories: Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability.
The skills taught are addition, reading bar graphs, using a calendar, capacity, coins, counting, fractions, language, length, likelihood, matching, number line, odd/even, order, pattern, real world problems (word problems), shapes, subtraction, time, weight, whole numbers.
The topics spiral throughout the book. For example, the first eleven pages of the book are organized like this:
1 page of Geometry
1 page of Algebra
5 pages of Number and Operations
3 pages of Algebra
1 page of Number and Operations
A topic is dealt with, followed by a different topic or two, and then the topic comes back up later. The idea behind this is that a child will have time to let concepts sink in "before dealing with more complex aspects of the skill/concept" (from the Introduction). Because I teach full time, my job informs the way I teach my own child (and parent her), and my experience as a parent informs how I do my public school job. As a public school 4th grade teacher who uses a curriculum that does not spiral, I see a great value in spiraling.
The authors suggest that the buyer proceed page by page through the book. However, they also say that "if your child is interested in a given topic and seems to want more, it would not be unreasonable for you to skip to the next level of that topic and do more of it." This is what we've done. My three-year-old has done 87 pages in order. But she's also bounced around the book because she saw pages that caught her eye and wanted to do them.
The Mathematical Reasoning series offers books from Level A through Level G (kindergarten through 6th grade). There is also a Beginning 1 book (for 3 year olds) and a Beginning 2 book (for 4 year olds). I bought Beginning 1 when my daughter was 2. It was as wonderful as Level A, but Beginning 1 focuses only on numbers 1 through 5, and my daughter outgrew it by 2 1/2. (She's got a mind of her own, this one. Mommy was thinking, Oh how lovely, we're following Charlotte Mason, so I have years before I have to think about teaching you addition. Years? Try nanoseconds.) Though Beginning 1 is designed for age 3, I would recommend it for children as young as 2. I would recommend Level A for children as young as 3 and 4.
The authors also suggest that you "keep learning fun and avoid frustrating your child. Work around your child's attention span." Hello, Charlotte Mason. If your child has a three minute attention span, work for three minutes. If your child has a twenty minute attention span, work for twenty.
The authors advise finding ways to relate the skills to your child's daily life. One way we did this was with the idea of even numbers. We talked about shoes, and how a shoe has a partner. One pair of shoes has two shoes, and when all the items in a set have partners, it's an even number, so two is even. What happens if you put Mommy's shoes with your shoes? Now you have four shoes. All the shoes have partners, so four is an even number. (It's all hands-on right now.) The authors also say that if your child has difficulty with a page, come back to it later or recreate the lesson with manipulatives. I also love the suggestion of making a number line that your child can walk on. We haven't tried this yet, but I plan to soon.
The book is available for $31.99 and does not require the additional cost of a Teacher's Manual. I have not used Saxon Math, but I have relatives who have and loved it, but the Saxon Math 1 Homeschool: Complete Kit is $107.35. I really, really, truly believe you should not need a Teacher's Manual for math in kindergarten or first grade. Arithmetic just isn't that complicated. The price difference is $75 I would rather spend on things like science kits. Your child does not have to write in Mathematical Reasoning (but certainly can), as many of the activities can be done by saying the answer or pointing to the answer; this means that the book can be reused with a second child. For activities involving tracing numbers, you can practice tracing with a finger, writing numbers on a whiteboard or a separate piece of paper, writing with chalk on the sidewalk, writing with bathtub crayon in the tub, printing handwriting pages off the internet, or - if you intend to only use the book once - writing in the book.
The book is full color and inviting. It has shapes, animals, clowns, fruit, sports equipment, dominoes, happy faces, etc. To view sample pages, click here and then click the tab that says "Sample Pages."
My daughter doesn't have the fine motor skills or the desire to trace numbers, so I don't force her to do this. Being able to write and being able to compute are separate skills, just as being able to write and being able to read are separate skills. A child learns to compute and read before being able to write. Charlotte Mason knew this, and that's why children gave answers orally and narrated orally instead of writing. Just because a child is a pre-writer doesn't mean you should put off teaching ideas. (My plan - which I reserve the right to change as needed - is to teach cursive when my daughter is six, earlier if she's interested.)
When my daughter finishes Level A, I will be buying Level B.
Not an affiliate link; I just think this book is awesome.