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*Core Connections Geometry* is the second course in a five-year sequence of college preparatory mathematics courses that starts with Algebra I and continues through Calculus. It aims to formalize and extend the geometry that students have learned in previous courses. It does this by focusing on establishing triangle congruence criteria using rigid motions and formal constructions and building a formal understanding of similarity based on dilations and proportional reasoning. It also helps students develop the concepts of formal proof, explore the properties of two- and three-dimensional objects, work within the rectangular coordinate system to verify geometric relationships and prove basic theorems about circles. Students also use the language of set theory to compute and interpret probabilities for compound events. Read More...

On a daily basis, students in *Core Connections Geometry* use problem-solving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments justifying their thinking. Students learn in collaboration with others while sharing information, expertise, and ideas.

The course is well balanced between procedural fluency (algorithms and basic skills), deep conceptual understanding, strategic competence (problem solving), and adaptive reasoning (extension and transference). The lessons in the course meet all of the content standards, including the “plus” standards, of Appendix A of the *Common Core State Standards for Mathematics*. The course embeds the CCSS Standards for Mathematical Practice as an integral part of the lessons in the course.

**Key concepts addressed in this course are:**

- Geometric transformations (reflection, rotation, translation, dilation) and symmetry
- Relationships between figures (such as similarity and congruence) in terms of rigid motions and similarity transformations
- Properties of plane figures
- Proofs of geometric theorems (investigating patterns to make conjectures, and formally proving them)
- Using coordinates to prove geometric theorems
- Modeling with geometry
- Measurements of plane figures (such as area, perimeter, and angle measure)
- Theorems about circles, including arc lengths and areas of sectors
- Measurements of three-dimensional solids (such as volume and surface area)
- Tools for analyzing and measuring right triangles, general triangles, and complex shapes (such as the Pythagorean Theorem, trigonometric ratios, and the Laws of Sines and Cosines)
- Geometric constructions (with compass and straightedge)
- Using algebra to formulate and solve equations arising from geometric situations.
- Probability (independence and conditional probability, compound events, expected value, and permutations and combinations) Read Less...

The *Core Connections* courses are built on rich, meaningful problems and investigations that develop conceptual understanding of the mathematics and establish connections among different concepts. The lesson problems are non-routine and team-worthy, requiring strategic problem solving and collaboration. Throughout the course, students are encouraged to justify their reasoning, communicate their thinking, and generalize patterns. Read More...

In each lesson students work collaboratively in study teams on challenging problems. The teacher is continuously providing structure and direction to teams by asking questions and giving clarifying instructions. The teacher gives targeted lectures or holds whole-class discussions when appropriate. The teacher has the freedom to decide the level of structure or open-endedness of each lesson. While students are in teams, the teacher checks for understanding by questioning students’ thinking and asking students to justify their solutions. Questioning is informative to both the teacher and the student as it guides the students to the learning target. At the close of each lesson, the teacher ensures that the students understand the big mathematical ideas of the lesson.

The homework in the “Review & Preview” section of each lesson includes mixed, spaced practice, and prepares students for new topics. The homework problems give students the opportunity to apply previously-learned concepts to new contexts. By solving the same types of problems in different ways, students deepen their understanding. CPM offers open access homework support at homework.cpm.org. Read Less...

Chapters are divided into sections that are organized around core topics. Within each section, lessons include activities, challenging problems, investigations and practice problems. Teacher notes for each lesson include a “suggested lesson activity” section with ideas for lesson introduction, specific tips and strategies for lesson implementation to clearly convey core ideas, and a means for bringing the lesson to closure. Read More...

Core ideas are synthesized in “Math Notes” boxes throughout the text. These notes are placed in a purposeful fashion, often falling one or more lessons after the initial introduction of a concept. This approach allows students time to explore and build conceptual understanding of an idea before they are presented with a formal definition or an algorithm or a summary of a mathematical concept. “Math Notes” boxes include specific vocabulary, definitions and instructions about notation, and occasionally interesting extensions or real-world applications of mathematical concepts.

Learning Log reflections appear periodically at the end of lessons to allow students to synthesize what they know and identify areas that need additional explanation. Toolkits are provided as working documents in which students write Learning Logs, interact with Math Notes and create other personal reference tools.

Each chapter offers review problems in the chapter closure: typical problems that students can expect on an assessment, answers, and support for where to get help with the problem. Chapter closure also includes lists of Math Notes and Learning Logs, key vocabulary in the chapter, and an opportunity to create structured graphic organizers.

The books include “Checkpoints” that indicate to students where fluency with a skill should occur. Checkpoints offer examples with detailed explanations, in addition to practice problems with answers.

In addition, CPM provides a *Parent Guide with Extra Practice* available for free download cpm.org of in booklet form for purchase. In addition to practice problems with answers, the *Parent Guide with Extra Practice* provides examples with detailed explanations and guidance for parents and tutors.

Each chapter comes with an assessment plan to guide teachers into choosing appropriate assessment problems. CPM provides a secure online test generator and sample tests. The Assessment Handbook contains guidance for a wide variety of assessment strategies.

Technology is used in the course to allow students to see and explore concepts after they have developed some initial conceptual understanding. The course assumes that classes have access to at least one of these three technology setups: a set of graphing calculators and whole-class display technology for the teacher, a full computer lab with computers that have graphing software for each student, or a classroom computer with graphing software equipped with projection technology. Read Less...