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- 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. On a daily basis, students in Core Connections Integrated II use problem-solving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments justifying their thinking.
- Under teacher guidance, 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. Key concepts addressed in this course are: Geometric transformations reflection, rotation, translation, and 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 investigate patterns to make conjectures, and formally prove them. 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, and trigonometric ratios.
- Probability independence and conditional probability, compound events, expected value, and permutations and combinations. Investigation of a variety of functions including square root, cube root, absolute value, piecewise-defined, step, and simple inverse functions. Representations of quadratic functions with a graphs, tables, equations, and contexts. Solve quadratic equations using a variety of methods such as the zero product property, completing the square, and the quadratic formula. Symbolic manipulation of expressions in order to solve problems, such as factoring, distributing, multiplying polynomials, expanding exponential expressions, etc. Using algebra to write and solve equations arising from geometric situations. 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 about the lesson structure. 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. 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.
- 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. Checkpoints offer examples with detailed explanations, in addition to practice problems with answers. 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 Guidebook 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 about the course structure.
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