Here are some parent friendly resources related to the Math Modules from the New York State Education Department. The Parent Roadmap documents are from The Council of Great City Schools website.  

How to Implement a Story of Units will give you background on how the modules are put together.  Pages 27 to 45 show and explain the math models that students are learning about and using to solve problems.  The vocabulary used in lessons and homework is clearly explained and illustrated.

For an overview of the Pre-K - Grade 5 Math Curriculum, read A Story of Units:

A Story of Units

For specific information on each module, go to:

Kindergarten Math Parent Roadmap
First Grade Math Parent Roadmap
Second Grade Math Parent Roadmap
Third Grade Math Parent Roadmap
Fourth Grade Math Parent Roadmap
Fifth Grade Math Parent Roadmap
How to Implement a Story of Units

Related Link:

Engage NY