The Mathematical Practice Standards are integrated throughout the text. From the Exploration through the Exercises, students see where the Mathematical Practice Standards can be applied. In the Explorations, there is always a callout in the minor column that relates to the Practice Standards. Students can tell from the title of the callout which Practice Standard it refers to, and forces students to look at the math and make connections to the Practice Standards. The same is true during the Lessons. These callouts appear in the minor column of the Lesson pages as well. Then during the Exercises, students and teachers will notice inline heads relating directly to the Practice Standards. Inline heads such as Making an Argument, Attending to Precision, Structure, Modeling with Mathematics, Abstract Reasoning, and Using Tools all allow for students and teachers to easily make connections to the Practice Standards.
Mathematical Practice Standards are called out In Laurie’s Notes in the Teaching Edition as well. Author Laurie Boswell has provided teachers with an invaluable resource to use on a daily basis. She provides ways to motivate the students each day, questions during the lesson, common errors students might make, various connections, tips for teachers, and suggestions for closure. Throughout these notes, teachers will see the Mathematical Practices in boldface text, so they will quickly see when and where the standards are being used each day.
Students also must persevere through the Explorations while working with a partner and without direct instruction. Students develop their own mathematical thinking through the explorations, and frequently critique the reasoning of others in the class. Students are repeatedly required to explain their reasoning and communicate mathematical ideas precisely. Students must make sense of real-life application and modeling exercises. They must plan a solution pathway and model the mathematics while justifying their reasoning. Students learn when to create diagrams, tables, and graphs, and know when these tools are useful. Students are continually exposed to the Mathematical Practices throughout each course and the entire program. For instance:
Make sense of problems and persevere in solving them.
• Essential Questions help students focus on core concepts as they analyze and work through each Exploration.
• Section opening Explorations allow students to struggle with new mathematical concepts and explain their reasoning in the Communicate Your Answer questions.
Reason abstractly and quantitatively.
• Reasoning, Critical Thinking, Abstract Reasoning, and Problem Solving exercises challenge students to apply their acquired knowledge and reasoning skills to solve each problem.
• Thought Provoking exercises test the reasoning skills of students as they analyze and interpret perplexing scenarios.
Construct viable arguments and critique the reasoning of others.
• Students must justify their responses to each Essential Question in the Communicate Your Answer questions at the end of each Exploration set.
• Students are asked to construct arguments and critique the reasoning of others in specialized exercises, including Making an Argument, How Do You See It?, Drawing Conclusions, Reasoning, Error Analysis, Problem Solving, and Writing.
Model with mathematics.
• Real-life scenarios are utilized in Explorations, Examples, Exercises, and Assessments so students have opportunities to apply the mathematical concepts they have learned to realistic situations.
• Modeling with Mathematics exercises allow students to interpret a problem in the context of a real-life situation, often utilizing tables, graphs, visual representations, and formulas.
Use appropriate tools strategically.
• Students are provided opportunities for selecting and utilizing the appropriate mathematical tool in Using Tools exercises. Students work with graphing calculators, dynamic geometry software, models, and more.
• A variety of tool papers and manipulatives are available for students to use in problems as strategically appropriate.
Attend to precision.
• Vocabulary and Core Concept Check exercises require students to use clear, precise mathematical language in their solutions and explanations.
• The many opportunities for cooperative learning in this program, including working with partners for each Exploration, support precise, explicit mathematical communication.
Look for and make use of structure.
• Using Structure exercises provide students with the opportunity to explore patterns and structure in mathematics.
• Students analyze structure in problems through Justifying Steps and Analyzing Equations exercises.
Look for and express regularity in repeated reasoning.
• Students are continually encouraged to evaluate the reasonableness of their solutions and their steps in the problem-solving process.
• Stepped-out Examples encourage students to maintain oversight of their problem-solving process and pay attention to the relevant details in each step.