Inventory of “Big Ideas ”
(Vital Understandings ) in Mathematics

Correlated with the Michigan Curriculum Framework for Mathematics (Grade K-8)

For the Teacher

This inventory is work in progress and is written, in part, as a response to the criticism in the TIMSS Report that the mathematics curriculum in the United States is “a mile wide and an inch deep”. It covers too many topics. This inventory is intended as a step towards identifying the few vital concepts that should be taught thoroughly. Hopefully, this inventory will be read, reflected upon, discussed, and provoke responsive comments. Suggestions for improvements are welcome.

The purpose of this inventory is to provide teachers with a checklist of “Big Ideas” (vital understandings) in mathematics. These “Big Ideas” are meant to encompass the most essential concepts and skills addressed in the standards and benchmarks of the Michigan Curriculum Framework. These are the “Big Ideas” that children cannot afford to be without if they are to be successful in mathematics. The list is intended to be “teacher friendly” yet designed to improve the intellectual quality of student performance.

The “Big Ideas” are encountered at many different levels of sophistication. They are experienced in some way at all grade levels. The nature of the activities used to teach the “Big Ideas” vary considerably from grade level to grade level, but the essence of the “Big Ideas” will be present at all levels. These “Big Ideas” are continually developed over the years, but the students’ level of retention, understanding, and use of the knowledge can be observed and assessed at each grade level. 

The “Big Ideas” in this list are meant to be consistent with the Michigan Curriculum Framework for Mathematics.

The “Big Ideas” are aligned with six content strands: 

1. Patterns, Relationships and Functions
2. Geometry and Measurement
3. Data Analysis and Statistics
4. Number Sense and Numeration
5. Numerical and Algebraic Operations and Analytical Thinking
6. Probability and Discrete Mathematics

Each “Big Idea” is illustrated with instructional and assessment examples that are intended to reflect the content in the standards and benchmarks suggested for that level in the Michigan Curriculum Framework for Mathematics. A three digit code under the word “example” indicates the strand, standard, and benchmark addressed. For example: I-1.3 represents Strand I, Standard 1, and Benchmark 3.

This inventory was developed using the following resources:

1. Michigan Curriculum Framework
2. Mathematics Model Curriculum Guide K-8 (provided examples, except where indicated)
   California Department of Education
3. Model Competency-Based Mathematics Program
   Ohio Department of Education
4. New Jersey Guide 8 Early Warning Test for Mathematics