On the Neinhaus website there are at least 6 materials aimed directly at understanding and mastery of the basic facts... and that is just addition. As a homeschooling parent, it is not feasible in either space, time, or finances to purchase all of them. I've also found that we don't need all of them.
This is what we have and why.
Addition Strip Board- The addition strip board is the first formal work we do in basic facts. We use it in conjunction with the I Can Make New Numbers Booklet (FREE).
Equation Boxes- This is just a small box with all of the basic fact equations for a given operation. I will give them follow up works or assignments such as, "Do 10 of these on the strip board," or "See how many you know," or "How many can you do in 5 minutes?" They can also tackle the whole board on their own if they are feeling up for a challenge!
Shut The Box Game- Starting with addition this is great practice in making equations up through 12. It can also be made more advance by manipulating the numbers with subtraction, multiplication, and even division provided that the sides are equal. This is also a great way for two children to practice their basic facts together.
Once Aidan had adequately mastered his addition facts, he seemed to quickly understand the reversible nature of subtraction. In fact, the first time I gave him a sheet of 100 subtraction facts (we use math-drills.com), in 10 minutes he finished all of them with only 3 mistakes. I realize that all kids are not and will not be like that, but by focusing on the pairs we can review quickly through to opposites. If the child is stuck you can ask, "8 plus what equals 12?" Not only does this review and apply prior knowledge (critical thinking and problem solving) it is also a great pre algebra concept. I teach multiplication and division in the same way, focusing on mastery of multiplication through the materials and division through the pairs.
Multiplication bead board- This is the first work we do with multiplication. By this age, I prefer to pair with traditional blank tables.
The bead chains (we have the short chains, plus the 1,000 chain) are a good way to practice skip counting and for reciting the multiplication facts. Each chain represents the square of the number (1x1, 2x2, 3x3, etc...)
Remember, that all of the manipulatives (Golden Beads, Stamp Game, Bead Frame) allow for use and understanding without knowing the basic facts. The use of these materials, in fact reinforces basic facts through repetition. Basic fact knowledge is not needed until the child has reached the point of abstraction in his or her work. For more information on that, see my post on teaching addition and subtraction using Montessori materials.