Today I received another such email. Here is my reply. It is general enough that hopefully someone (parent or teacher or both) will find it useful.
As a dad of three elementary school students myself, I truly understand and appreciate your concern. It is an expectation that teachers differentiate their instruction in order to meet the needs of ALL students. Clearly, some teachers do this better than others.
Coaching teachers on the concept of differentiated instruction is a far bigger topic than I can fit in an email, but I will try to hit the main points:
For a particular lesson or topic, when a student has demonstrated understanding and is in need of enrichment, it is important that this enrichment activity SHOULD NOT merely look like extra work. "More of the same" is not what should happen. Instead, best practice calls for the teacher to provide the student with mathematics that is inherently engaging and does more than just give the student more "drill" work of simple concepts.
One online resource that does this phenomenally well is NRich. http://nrich.maths.org/
Specifically, since you have a 4th grader, go here...
...and then click on any of the "Collections" or "Upper Primary Live Problems".
This is an AWESOME source of engaging problems that really give a high-flying student to opportunity to think like a mathematician. These are NOT your typical worksheet full of boring problems.
Here is a curated list of other excellent resources for the type of enrichment you are seeking for your son:
Another particularly excellent resource is Open Middle. ( http://www.openmiddle.com/ )
Common Core was not designed to make it easier for students to go at their own pace. However, Common Core is designed to have fewer topics taught each year to allow students to dig deeper into the current grade level mathematics. Essentially "going deeper" with 4th grade content is preferable - and better for your son - than "going faster" with superficial 5th grade content.
Ideally, your son's teacher would print an engaging problem from one of these two sites and give it to your son to work on (possibly over the course of several days) whenever he needs the extra challenge. A good problem is one that takes more than just a couple of minutes to solve. It requires thinking, problem solving, struggle, etc.
My experience is students LOVE this sort of challenge and become more engaged with mathematics.
I hope this gets you started! Please feel free to email me with any additional questions or concerns you might have.