MATHbook and MATHia work in parallel to engage students with various learning experiences they need to truly understand middle and high school mathematics.
MATHbook is a record of student thinking, reasoning, and problem solving which includes a variety of problem types to actively engage and challenge students. Activities are sequenced to ensure investigation, classification, worked examples, peer analysis, and real-world and mathematical problem-solving.
MATHia is a guide for students as they learn and practice key mathematical concepts and skills. MATHia’s purpose is to coach students alongside you as they learn, practice, do, and look forward. The work students are doing in MATHia continually supports their work in MATHbook.
Carnegie Learning recognizes that students come to you with varying background knowledge. Both MATHbook and MATHia build on student strengths by providing a variety of question types within the student practice problems. Below are descriptions and examples of each problem type.
Students engage in explorations that promote engagement, curiosity, and experimentation.
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What INVESTIGATION looks like in MATHbook |
What INVESTIGATION looks like in MATHia |
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Students organize content into subcategories.
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What CLASSIFICATION looks like in MATHbook |
What CLASSIFICATION looks like in MATHia |
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Students examine example problems.
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What WORKED EXAMPLES look like in MATHbook |
What WORKED EXAMPLES look like in MATHia |
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Students are challenged to analyze strategies, make inferences, and correct errors in reasoning.
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What PEER ANALYSIS looks like in MATHbook |
What PEER ANALYSIS and ANIMATION look like in MATHia |
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Multiple opportunities are provided within each lesson for students to justify their reasoning. Thumbs Up, Thumbs Down and Who's Correct? problems specifically provide an opportunity for peer analysis.
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Just in Time Hints provide students with the opportunity to analyze their own errors in order to correct them.
Animations work as a peer for students, allowing them to analyze the mathematics as they watch. |
Real-World and Mathematical Problem-Solving helps students contextualize mathematics and improve their understanding.
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What REAL-WORLD AND MATHEMATICAL PROBLEM-SOLVING look like in MATHbook |
What REAL-WORLD AND MATHEMATICAL PROBLEM-SOLVING look like in MATHia |
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The problem types within each activity are listed in the instructional sequence section of the Lesson Structure and Pacing Guide pages of the Teacher’s Implementation Guide.
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