Zome is a manipulative that is excellent for the upper grades – however it takes time to put away and is fragile. Nevertheless, there is no manipulative so versatile on the market, so it should be considered. I am now equally in favour (especially for younger grades) Space Chips which are indestructible and fast to put away.
As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.
Standards for Mathematical Practice
MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:
MP1 Toughen up!
This is problem solving where our students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.
MP3 Work together!
This is collaborative problem solving in which students discuss their strategies to solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.
MP6 Be precise!
This is where our students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.
MP7 Be observant!
One of the things that the human brain does very well is identify pattern. We sometimes do this too well and identify patterns that don't really exist.