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Being an effective math educator is one part based on the quality of the tasks we give, one part how we diagnose what we see, and one part what we do with what we find. Yet with so many students and big concepts to cover, it can be hard to slow down enough to look for those moments when students’ responses tell us what we need to know about next best steps. In this remarkable book, John SanGiovanni and Jennifer Rose Novak help us value our students’ misconceptions and incomplete understandings as much as their correct ones—because it’s the gap in their understanding today that holds the secrets to planning tomorrow’s best teaching. The authors lay out 180 high-quality tasks aligned to the standards and big ideas of Grades 6–8 mathematics, including number systems, integers, ratio and proportion, equations and expressions, geometry, and statistics and probability. The tasks are all downloadable so you can use or modify them for instruction and assessment. Each big idea offers a starting task followed by: what makes it a high-quality task what you might anticipate before students work with the task four student examples of the completed task showcasing a distinct "gap" commentary on what precisely counts for mathematical understanding and the next instructional steps commentary on the misconception or incomplete understanding so you learn why the student veered off course three additional tasks aligned to the mathematics topic and ideas about what students might do with these additional tasks It’s time to break our habit of rushing into re-teaching for correctness and instead get curious about the space between right and wrong answers. Mine the Gap for Mathematical Understanding is a book you will return to again and again to get better at selecting tasks that will uncover students’ reasoning, better at discerning the quality and clarity of students’ understanding, and better at planning teaching based on the gaps you see.
Equal parts mail art, data visualization, and affectionate correspondence, Dear Data celebrates "the infinitesimal, incomplete, imperfect, yet exquisitely human details of life," in the words of Maria Popova (Brain Pickings), who introduces this charming and graphically powerful book. For one year, Giorgia Lupi, an Italian living in New York, and Stefanie Posavec, an American in London, mapped the particulars of their daily lives as a series of hand-drawn postcards they exchanged via mail weekly—small portraits as full of emotion as they are data, both mundane and magical. Dear Data reproduces in pinpoint detail the full year's set of cards, front and back, providing a remarkable portrait of two artists connected by their attention to the details of their lives—including complaints, distractions, phone addictions, physical contact, and desires. These details illuminate the lives of two remarkable young women and also inspire us to map our own lives, including specific suggestions on what data to draw and how. A captivating and unique book for designers, artists, correspondents, friends, and lovers everywhere.
With the help of Spectrum Data Analysis and Probability for grades 6 to 8, children develop problem-solving math skills they can build on. This standards-based workbook focuses on middle school concepts like operations, ratios, probability, graph interpretation, and more. Middle school is known for its challenges—let Spectrum ease some stress. Developed by education experts, the Spectrum Middle School Math series strengthens the important home-to-school connection and prepares children for math success. Filled with easy instructions and rigorous practice, Spectrum Data Analysis and Probability helps children soar in a standards-based classroom!
This teacher guide illustrates how to sustain successful implementation of the Common Core State Standards for mathematics, grades 6–8. Discover what students should learn and how they should learn it at each grade level. Comprehensive research-affirmed analysis tools and strategies will help you and your collaborative team develop and assess student demonstrations of deep conceptual understanding and procedural fluency.
Includes materials on adding, subtracting, multiplying, and dividing positive numbers; algebraic expressions; and solving and graphing equations.
This essential guide to building and using an inclusive STEM classroom library combines theory and lesson plans for educators of students in grades 6–8. Discover how to audit classroom collections to support exploration and discovery. Learn how to build STEM awareness and interest through reading, literacy activities, virtual resources, and more. Give your students the opportunity to dream about a career path where they can create, imagine, and build a better world.
Students love math games and puzzles, but how much are they really learning from the experience? Too often, math games are thought of as just a fun activity or enrichment opportunity. Well Played, Grades 6-8: Building Mathematical Thinking Through Number and Algebraic Games and Puzzles shows you how to make games and puzzles an integral learning component that provides teachers with unique access to student thinking. This third book in the series helps you engage students in grades 6-8 in discussions of mathematical ideas and deepen their conceptual understanding. It also helps you develop students' fluency with number systems; ratio and proportional relationships; expressions and equations, statistics and probability; and patterns, graphs, and functions. The twenty-five games and puzzles in Well Played, Grades 6-8 which have all been field-tested in diverse classrooms, contain: Explanations of the mathematical importance of each game or puzzle and how it supports student learning. Variations for each game or puzzle to address a range of learning levels and styles Classroom vignettes that model how best to introduce the featured game or puzzle. The book also includes a separate chapter with suggestions for how to effectively manage games and puzzles in diverse classrooms; game boards, game cards, and puzzles; assessment ideas; and suggestions for online games, puzzles, and apps. Well Played, Grades 6-8 will help you tap the power of games and puzzles to engage students in sustained and productive mathematical thinking.
A guide to quickly and reliably uncovering common math misconceptions in Grades 6-8 with convenient and easy-to-implement diagnostic tools.