I came across Excel Math at a conference for traditional schools, but this is a product that should do as well or better in the homeschool market for teaching math to students in kindergarten through sixth grade. It is very reasonably priced, easy to use, uses an incremental/spiral approach with plenty of review, addresses the math standards, and also stresses conceptual understanding and practical application. The entire program is also available in Spanish.
You need to purchase a student book (called Individual Student Set) and a Teacher's Edition. (For classrooms, pages are not bound and come in sets of 10, 15, 22, 30 or 35. Pages arrive stacked in the order they will be used.) Student pages, printed in black-and-white, are 8.5" x 14"—wider than normal page size as you can tell from the images to the right.
While the program is designed for the classroom and requires presentation by a teacher, it easily adapts for homeschool use. Manipulatives are used in many lessons, but these are items like play money or items to be used for regrouping. Masters for manipulatives that you can print, cut out, and use are in the Teacher's Edition if you do not have other options. You do not need to purchase any manipulatives.
Lessons are divided into three main sections: the "classroom lesson," guided practice, and homework. Lessons begin with the teacher stating the objective of the lesson and teaching one new concept using the "classroom lesson." As directed and taught by the teacher, students work through demonstrations and applications of the new concept, and complete a few practice problems. (See the left side of the image above.) A "Basic Fact Practice" section is at the bottom of this section for students first grade level and above. Guided practice on the reverse side of this page then works on previously taught concepts and skills. Students work through each boxed group of problems. (See image below.) Students self-check as they go along using Excel Math's unique "Checkanswer" system. Each box has 2 to 4 problems. Students add the answers to those problems and compare that answer to the number in the top right corner of the box. If they match, their answers are likely to all be correct. If not, the student goes back to try to discover the error. If a student is stumped, the teacher then assists him or her in locating and correcting the error. This allows children to work independently, while simultaneously getting immediate feedback as to whether their answers are correct. Concepts taught in the "classroom lesson" will show up a number of times scattered over months so that students master and remember them. The homework section that appears to the right of the classroom lesson covers concepts that students should be able to handle without difficulty on their own.
Student problems in Guided Practice and Homework are a varied mix of previously taught concepts rather than rows of similar problems to drill a single skill. Students have to stop and think about how to tackle each type of problem rather than zipping through their work. In addition, many of these are word problems or applications. These features requires students to apply higher level thinking skills than do some other math programs.
Tests assess student mastery of material introduced 3 to 4 weeks prior to the test but do not test concepts introduced during the week preceding the test. Kindergarten level has only 6 tests; first grade has 16; all other grades have weekly tests. Quarterly and year-end tests offer students the opportunity to complete a "bubble" answer sheet as they do on standardized tests.
On the reverse side of test pages for grade 2 and up are "Create A Problem Stories." These need not be used as part of the test; they probably work better as an interactive project. A brief story provides data. Students are then asked to create one or two word problems of their own based on the story. This unusual technique should be both challenging and fun for students.
Teacher's editions provide brief lesson plans for each lesson. Although these are not scripted, they are quite easy to follow and require minimal preparation other than gathering manipulatives when needed. You don't have to buy manipulatives since teacher's editions include reproducible patterns for many different manipulatives; you might copy these on to card stock. TE's also have brain teasers called "Stretches" for second grade and above. These might be oral problems or they might require a visual illustration. They are not in student books and need to be written down on a whiteboard, paper or some other media when necessary. Answer keys are included in the form of student pages with overprinted answers for easy reference.
Excel Math is a challenging, but even more so at the fifth and sixth grade levels. It comes close to Singapore Math with advanced thinking and conceptual skills.
Excel Math is used as either a supplement or a core program in traditional schools. While homeschoolers can use it as a supplement, there's no reason not to make this your core program since it offers complete coverage. Correlation to state standards is available on the website along with sample lessons, placement tests, and other helpful information.