These strands were chosen to be consistent with international (TIMSS: the Third International Mathematics and Science Study), national (NAEP: the National Assessment of Educational Progress), and state (PSSA: the Pennsylvania System of School Assessment) standards and expectations.
Because teachers need to know material that reaches beyond the level of the geometry and measurement that they themselves are teaching, IMAGES purposefully includes content beyond grades K-5, in support of what students will need to know in subsequent years. How to present the K-5 student expectations posed a dilemma, as the NCTM standards are divided pre-K-2 and 3-5, while most states require assessments at grades 3, 5, and 8. In order to be teacher-friendly, IMAGES clusters content for grades K-3 and
4-5 to help to guide teachers for state benchmark assessments.
Students will best understand this geometry and measurement content when a teacher integrates it within mathematics and also connects it to other disciplines and to what the students already know. A teacher can do this through overlapping and clustering of geometry and measurement content areas, both across strands and within a single strand. Each content strand refers to grade-appropriate activities and lesson plans, which are provided in detail in chapter 4. However, the use of these activities and lessons requires flexibility; the appropriate grade level of each is ultimately the teacher's decision, as in some instances older students would benefit from activities suggested for a younger level, and vice versa. Frequently, activities and lessons will overlap two or more
content strands.
Lessons within this document address the five process standards presented in the NCTM Principles and Standards for School Mathematics: problem solving, reasoning, representation, connections, and communication. The activities included also exemplify assessment strategies and best practices for teaching, which are both outlined in greater detail in other sections. To explore how the IMAGES content strands correlate to the Pennsylvania Academic Standards for Assessment, refer to Appendix A, which lists, by content strand, those standards that apply.
In sum, this content section is meant to be helpful and inspiring as teachers move forward in exploring new and effective ways to reach and support their students. Ideally, it will provide models for teachers to use in creating and adapting their own original lessons that incorporate the content of geometry and measurement and also expand the framework of the state standards and the NCTM Principles and Standards for School Mathematics.
A note on language: While the Pennsylvania Academic Standards seems to use the terms "figure" and "shape" interchangeably, IMAGES consistently uses the term "geometric shape."
