*Making Connections: Foundations for Algebra, Course 1* is the first of a two-year sequence of courses designed to prepare students for a rigorous college preparatory algebra course. It uses a problem-based approach with concrete models. The course helps students to develop multiple strategies to solve problems and to recognize the connections between concepts. The lessons in the course embed the “Mathematical Practices” of the Common Core State Standards released in June 2010. Read More...

Upon completion of this course, students should be able to:

- Collect, organize and display data in multiple ways.
- Represent and compare quantities using manipulatives, diagrams and number expressions.
- Represent multiplication using rectangular arrays.
- Use appropriate tools to model length, area and volume.
- Model integers and their operations.
- Use strategies to estimate calculations.
- Make sense of multiple representations of portions (decimal, fraction, percent) and convert from one form to the other.
- Compare fractions and generate equivalent fractions.
- Recognize proportional relationships using tables and graphs and solve corresponding problems.
- Use models and standard algorithms for computations with fractions and decimals.
- Describe angles, angle pairs and their measures.
- Compute area, surface area and volume of common geometric shapes.
- Use ratios to describe relationships with similar plane figures and other situations.
- Evaluate variable expressions and solve simple equations.
- Solve percent problems including those with discounts, interest and tips.
- Distinguish between dependent and independent events and calculate the probability of independent events.
- Design, conduct and analyze surveys.

The course is structured around problems and investigations that build conceptual understanding of these topics and an awareness of connections between different ideas. Students are encouraged to investigate concepts, communicate their thinking and generalize. Read More...

Lessons are structured for students to collaborate actively by working in study teams. During class time, students work in study teams on challenging problems that introduce new material. The teacher provides guidance as needed and helps to consolidate topics.

The homework in the “Review & Preview” section of each lesson reinforces previously introduced skills and concepts and prepares students for new ones. The homework problems also allow students to apply previously-learned concepts and skills in new contexts and deepen their understanding by solving the same type of problem in different ways. CPM offers open access homework support at the website www.cpm.org/students/homework and also provides teachers with the answers to problems. There are extra practice resources and a parent guide at www.cpm.org and in booklet form. 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 bring the lesson to **closure**. Read More...

Core ideas are synthesized in “Math Notes” boxes. These notes are placed in a purposeful fashion, often falling a couple a 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. “Math Notes” boxes include specific vocabulary definitions and instructions about notation, and occasionally interesting extensions or real-world applications of mathematical concepts.

Technology is used in the course to allow students to see and explore concepts after they have developed some initial conceptual understanding. Ideally, classes would have access to a computer lab with computers for pairs of students. This dynamic tool will provide students with a deeper understanding of the concepts involved. A classroom computer equipped with projection technology would suffice but not allow students to explore individually.

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. Read Less...