We use Shiller Math and I have been very happy with it. The K-3 grade math consists of three math workbooks (teacher and student) that cover the math curriculum for the four year period, though I have been told it is typical to be finished at the end of second grade.
It is a Montessori based program that builds on itself. The spiraling of activities is well done throughout the guides. Each time a topic/skill is re-introduced, a little more depth is added to it.
It isn't like anything I have seen so it is difficult to gauge a "math level", but that really doesn't matter, does it? We continue to work at K's (age 6) pace and I think we have finally caught up to her actual level at this point so we might have to go a bit slower.
We completed Book One last week and she took the final test. I am giving her the rest of 2008 "off" from math as she is well ahead of her "grade level".
Skills covered in Book One and some notes on them for myself:
1. Comparing numbers. We have compared numbers from day one in this book. We have used unit cubes, dominoes, and the bucket balance to do so. I love this because it establish a great foundation in number sense. I am quite confident in K's (age 6) ability in this area.
2. Equations in adding up to the sum of three and subtracting with the highest number used being 3. (whew...I think that is the best way to say it...LOL) K is doing great with adding and subtracting, including writing equations to represent word problems. The numbers have remained small, but they have already introduced missing addends, multi-step word problems and equations, as well as having the empty "answer box" on the left and the equation on the right. The only thing that threw her off a bit was seeing the equations written "backwards", meaning having the blank space for the answer on the left and the problem to solve on the right.
The final test also included a word problem that I thought was a bit tough for her, as well as "above" most of the practice problems we had completed. She was supposed to write an equation to represent, "Mrs. Peacock has one more seat in her car than Mr. Marley and Mr. Marley has two seats in his car." I had to walk her through this one.
3. Patterns. There has been a lot of emphasis on patterns through numbers and pictures. Kayleigh is doing well and on her test recognized very easily the pattern, "a quarter turn". She recognizes skip counting patterns quickly as well, though the "skip counting 2, starting with 1" through her off. (1, 3, 5, 7...) She can complete patterns pretty easily so far.
4. Geometry. We have gone over equilateral and isosceles triangles. WE have also had to do a lot of "which doesn't belong" with a group of shapes. They have emphasised number of sides or curved only, etc. She does well with Geometry.
4. Random Stuff.
Solo. Duet. Trio. This book includes the names of groupings like this. She is still a bit confused on duet. We need to use the terms more during the day. She was also asked to name things that come in a trio. That one is tough! (examples were stoplight lights, tricycle wheels) We are just incorporating these terms into our school day as I remember to keep reviewing them.
Roman Numerals. We have accomplished the numerals up to III.
Odd vs. Even. We need to keep reviewing these terms. She hadn't seen them in awhile. She was given the numbers, "2, 4, 6, 8" and asked to name the type of numbers. Her answer was "skip counting 2's" so I then asked if they were odd or even because her answer was correct. I wanted to see if she knew odd or even. She got it right, but I suspect it was a guess.
Ordinal Numbers. Book one went over these up to "Fourth". She knows these terms well.
Function Machines. There were a few basic lessons on function machines, though that is not what they call them yet. The book refers to them as "magic boxes" which have a rule. Something is put in, the rule is applied, and the answer comes out. She likes these and does well with them.
Overall, I am really happy with this curriculum. I was a bit scared to teach my own children math because that is my background. I wasn't sure how I would like the curriculum's out there. But I love this one.
It is like NOTHING I have ever seen and it isn't the way I taught (or was taught). I find it strange that we have only done addition up to 3, yet have learned equilateral and isosceles triangles. But it makes a lot of sense to me. She is really learning the basics is ALL areas of math.
I also think this guide uses a variety of manipulatives and gives an excellent basis in number sense. I saw WAY too many older elementary students and middle school students who lacked basic number sense, so this is really important to me. I know how important it is for success in mathematics.
In January, we will begin Book 2. I have a feeling we will move a bit slower through this book and I have no problem with that. There is no reason to rush any subject! I look forward to beginning the next book to see how this curriculum keeps developing.
*side note - If you are "new" to homeschooling and have young kids like I do. This curriculum is a great investment because you can purchase 5 years of free downloads for $50. You can download the current guides at anytime and print a copy for the next child. So while the initial investment was a bit expensive. That is it. I won't have to buy anything else for any child in this house. The guides are saved in my email and we can just print them as we need them!