We will explore the content standards using what I call the Vertical Articulation of the standards. In other words, instead of grouping them by grade level they are grouped by content standard to that students can see the progression of the content; a critical element when trying to differentiate instruction.
For the practice standards I have added an additional two practices which I believe to be central to the study of mathematics and which have been totally neglected by the authors of the Common Core. Here they are:
9. Enjoy and celebrate mathematics
Mathematically proficient students enjoy and appreciate the aesthetics of quantitative and spatial relationships. They are captivated by the challenges of resolving mathematical problems and are able to use their mathematical understanding in creative and novel ways. They will demonstrate genuine curiosity when faced with novel mathematical situations. Younger students will share their excitement about finding several different ways of making 6, of understanding why a square number is so called and that pi is a ratio between the circumference and diameter of a circle and not just a number that goes on forever. Older students will recognize and celebrate the artistic elements associated with fractals and the aesthetic characteristics of algebraic relationships.
10. Recognize linguistic and cultural diversity in mathematics
Mathematically proficient students will recognize that math is not the same the world over. Living in diverse communities students will recognize that there are differences in mathematics and the ways we learn mathematics based on local and global cultural differences. As they work with students from different cultures they will be aware of the ways language development, as well as the language used in mathematics, are major factors in learning math for all students as well as those who are English Learners.