**General Information**

Table of Contents

Correlations

**Student/Parents (English)**

eTools/Videos

Homework Help

Parent Guide with Extra Practice

Resource Pages

**Estudiantes/Padres (Español)**

Páginas de Recursos

Guía para padres con práctica adicional

*Core Connections Integrated III* is the third course in a five-year sequence of rigorous college preparatory mathematics courses that starts with Algebra I and continues through Calculus. It aims to apply and extend what students have learned in previous courses by focusing on finding connections between multiple representations of functions, transformations of different function families, finding zeros of polynomials and connecting them to graphs and equations of polynomials, modeling periodic phenomena with trigonometry, and understanding the role of randomness and the normal distribution in making statistical conclusions. Read More...

On a daily basis, students in *Core Connections Integrated III* 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 imbeds the CCSS Standards for Mathematical Practice as an integral part of the lessons in the course.

Key concepts addressed in this course are:

- Visualize, express, interpret and describe, and graph functions (and their inverses, in many cases). Given a graph, students will be able to represent the function with an equation, and vice-versa, and transform the graph, including the following function families:
- absolute value
- exponential
- linear
- logarithmic
- piecewise-defined
- polynomial
- quadratic
- square root
- trigonometric

- Use of variables and functions to represent relationships given in tables, graphs, situations, and geometric diagrams, and recognize the connections among these multiple representations.
- Application of multiple algebraic representations to model and solve problems presented as real world situations or simulations.
- Solving linear or quadratic equations in one variable, systems of equations in two variables, and linear systems of equations in three or more variables.
- Use of algebra to rewrite complicated algebraic expressions and equations in more useful forms.
- Rewriting rational expressions and arithmetic operations on polynomials.
- The relationship between zeros and factors of polynomials.
- Operations with complex numbers, and solving quadratics with complex solutions.
- Applications of the Law of Sines and Law of Cosines.
- Modeling periodic phenomena with trigonometric functions.
- Calculating the sums of arithmetic and geometric series, including infinite geometric series.
- Concepts of randomness and bias in survey design and interpretation of the results.
- Use of a normal distribution to model outcomes and to make inferences as appropriate.
- Use of computers to simulate and determine complex probabilities.
- Use of margin of error and sample-to-sample variability to evaluate statistical decisions.
- Solving trigonometric equations and proving trigonometric identities

The *Core Connections* 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...