The document outlines key concepts in number and operations, algebra, and geometry. For number and operations, it discusses understanding numbers, representations of numbers, relationships between numbers, and number systems. It also mentions computing fluently and making reasonable estimates. For algebra, it discusses patterns, relations, functions, using algebraic symbols to represent mathematical situations, and analyzing change. For geometry, it discusses analyzing properties of 2D and 3D shapes, specifying locations and spatial relationships, applying transformations and symmetry, and using visualization to solve problems.

1. Number and Operations
Understand numbers, ways of
representing numbers, relationships
among numbers, and number systems.
Understand meanings of operations
and how they relate to one another.
Compute fluently and make reasonable
estimates.

2. Algebra
Understand patterns, relations, and
functions
Represent and analyze mathematical
situations and structures using algebraic
symbols
Use mathematical models to represent
and understand quantitative relationships
Analyze change in various contexts

3. Geometry
Analyze characteristics and properties of two- and
three-dimensional geometric shapes and develop
mathematical arguments about geometric
relationships
Specify locations and describe spatial relationships
using coordinate geometry and other
representational systems
Apply transformations and use symmetry to
analyze mathematical situations
Use visualization, spatial reasoning, and geometric
modeling to solve problems

4. Understand patterns,
relations, and functions

5. Algebra
Understand patterns,
relations, and functions

6. Use visualization, spatial
reasoning, and geometric
modeling to solve
problems

7. Geometry
Use visualization, spatial
reasoning, and geometric
modeling to solve
problems

8. Apply transformations
and use symmetry to
analyze mathematical
situations

9. Geometry
Apply transformations
and use symmetry to
analyze mathematical
situations

10. Compute fluently and
make reasonable
estimates

11. Number and Operations
Compute fluently and
make reasonable
estimates

12. Represent and analyze
mathematical situations
and structures using
algebraic symbols

13. Algebra
Represent and analyze
mathematical situations
and structures using
algebraic symbols

14. Understand meanings of
operations and how they
relate to one another

15. Number and Operations
Understand meanings of
operations and how they
relate to one another

16. Analyze characteristics and
properties of two- and three-
dimensional geometric
shapes and develop
mathematical arguments
about geometric relationships

17. Geometry
Analyze characteristics and
properties of two- and three-
dimensional geometric
shapes and develop
mathematical arguments
about geometric relationships

18. Understand numbers,
ways of representing
numbers, relationships
among numbers, and
number systems

19. Number and Operations
Understand numbers,
ways of representing
numbers, relationships
among numbers, and
number systems

20. Use mathematical models
to represent and
understand quantitative
relationships

21. Algebra
Use mathematical models
to represent and
understand quantitative
relationships

22. Specify locations and
describe spatial
relationships using
coordinate geometry and
other representational
systems

23. Geometry
Specify locations and
describe spatial
relationships using
coordinate geometry and
other representational
systems

24. Analyze change in various
contexts

25. Algebra
Analyze change in various
contexts