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Differentiate problem solving in your classroom using effective, research-based strategies. The problem-solving mini-lesson guides teachers in how to teach differentiated lessons. The student activity sheet features a problem tiered at three levels.
This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking.
In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.
Get your brain working with 200 grid-based logic puzzles from the Puzzle Baron! Filled with complex and fun brain teasers that range in difficulty, this book will put your mind into overdrive with hours of brain-challenging fun. Using the given backstory and list of clues, readers use pure logic to deduce the correct answer for each fiendishly tricky puzzle in Puzzle Baron's Logic Puzzles. Bring out your competitive side and check your stats against the average completion time, the record completion time, and the percentage of people who finish the puzzle. Check your work against the answer key and see how logical you really are! Perfect for adults or children, Puzzle Baron's Logic Puzzles is the ultimate challenge for those who love piecing clues and facts together. The brain is a wonderful thing to tease!
Thinking Skills, second edition, is the only endorsed book offering complete coverage of the Cambridge International AS and A Level syllabus.
Uncovers the surprising ways math shapes our lives—from whom we date to what we learn. How do dating sites match compatible partners? What do cell phones and sea coasts have in common? And why do computer scientists keep ant colonies? Jeff Suzuki answers these questions and more in Patently Mathematical, which explores the mathematics behind some of the key inventions that have changed our world. In recent years, patents based on mathematics have been issued by the thousands—from search engines and image recognition technology to educational software and LEGO designs. Suzuki delves into the details of cutting-edge devices, programs, and products to show how even the simplest mathematical principles can be turned into patentable ideas worth billions of dollars. Readers will discover • whether secure credit cards are really secure • how improved data compression made streaming video services like Netflix a hit • the mathematics behind self-correcting golf balls • why Google is such an effective and popular search engine • how eHarmony and Match.com find the perfect partner for those seeking a mate • and much more! A gifted writer who combines quirky historical anecdotes with relatable, everyday examples, Suzuki makes math interesting for everyone who likes to ponder the world of numerical relationships. Praise for Jeff Suzuki's Constitutional Calculus "Presents an entertaining and insightful approach to the mathematics that underlies the American system of government. The book is neatly organized, breaking down the United States Constitution by article, section, and amendment. Within each piece, Suzuki reviews the mathematical principles that went into the underlying framework."—Mathematical Reviews "A breath of fresh air. . . . A reaffirmation that mathematics should be used more often to make general public policy."—MAA Reviews
This book is designed to engage students' interest and promote their writing abilities while teaching them to think critically and creatively. Dowden takes an activist stance on critical thinking, asking students to create and revise arguments rather than simply recognizing and criticizing them. His book emphasizes inductive reasoning and the analysis of individual claims in the beginning, leaving deductive arguments for consideration later in the course.
A standards-based, comprehensive math intervention curriculum for the state of California. Designed for students identified with math deficiencies who have not responded to reteaching efforts or who have a sustained lack of adquate progress in mathematics. This program provides intensive focus on developing foundational understanding and skills. It provides explicit, scientifically based instruction emphasizing the five critical elements of mathematics proficiency: understanding, computing, applying reasoning/problem solving , and engagement.