This resource will enable students to determine flawed reasoning in a fraction comparison with unlike numerators and denominators.

This resource requires students to present the solution to a multi-step problem in the form of valid chains of reasoning, using symbols appropriately. Students must use the four operations with whole numbers to solve problems.

This site teaches Reasoning with Equations and Inequalities to High Schoolers through a series of 5909 questions and interactive activities aligned to 36 Common Core mathematics skills.

Try this fun problem! In any group of six people, what is the probability that everyone was born in different months?

Explores the theory and research related to information processing, focusing on attention, perception, memory storage and information retrieval. Also highlights work in artificial intelligence and cognitive neuroscience which serves to describe and explain cognitive processes.

This is a text-based STEM Inquiry, focusing on the mathematical standard of making inferences and justifying conclusions while evaluating reports based on data. The unit culminates in students presenting their findings comparing local to national data regarding the relationships between educational attainment and financial earnings.

A Guide to Good Reasoning has been described by reviewers as “far superior to any other critical reasoning text.” It shows with both wit and philosophical care how students can become good at everyday reasoning. It starts with attitude—with alertness to judgmental heuristics and with the cultivation of intellectual virtues. From there it develops a system for skillfully clarifying and evaluating arguments, according to four standards—whether the premises fit the world, whether the conclusion fits the premises, whether the argument fits the conversation, and whether it is possible to tell.

Microwave and RF Design: Modules focuses on the design of systems based on microwave modules. The use of modules has become increasingly important in RF and microwave engineering for rapidly realizing high performance microwave systems. When integration is ultimately to be used, building a system up using modules provides a rapid means of prototyping and testing system concepts. A wide variety of RF modules including amplifiers, local oscillators, switches, circulators, isolators, phase detectors, frequency multipliers and dividers, phase-locked loops, and direct digital synthesizers are considered. Detailed design strategies for synthesizing filters based on parallel coupled lines are presented. The reader will gain an appreciation of design by synthesis. This book is suitable as both an undergraduate and graduate textbook, as well as a career-long reference book.

Mathematical Reasoning: Writing and Proof is designed to be a text for the first course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are to help students:

· Develop logical thinking skills and to develop the ability to think more abstractly in a proof oriented setting.

· Develop the ability to construct and write mathematical proofs using standard methods of mathematical proof including direct proofs, proof by contradiction, mathematical induction, case analysis, and counterexamples.

· Develop the ability to read and understand written mathematical proofs.

· Develop talents for creative thinking and problem solving.

· Improve their quality of communication in mathematics. This includes improving writing techniques, reading comprehension, and oral communication in mathematics.

· Better understand the nature of mathematics and its language.

This text also provides students with material that will be needed for their further study of mathematics.

Mathematical Reasoning: Writing and Proof is a text for the first college mathematics course that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. Version 3 of this book is almost identical to Version 2.1. The main change is that the preview activities in Version 2.1 have been renamed to beginning activities in Version 3. This was done to emphasize that these activities are meant to be completed before starting the rest of the section and are not just a short preview of what is to come in the rest of the section.

Mathematical Reasoning and Investigation is designed to help you develop the ability to use mathematics to solve the kinds of problems that don't come with answers in the back of the book. We like to think of it as a mathematics book for people who think they're not good at mathematics. The work will be useful for anyone wanting to develop their own skills in reasoning and problem solving using mathematics, and for teachers and preservice teachers hoping to help their students to develop these same skills.

This resource allow teachers and parents to plan for and use Philosophical Inquiry in the classroom or in a small group setting. When we encourage students to think deeply and to express their thinking we see that it helps them to interact better as learning in general classroom discussions.

Intern Prescot Nelson at Succinct Psychology (Psychcinct), under the guidance of professor Daniel Reynolds, created the entire course series for the Psych2e Openstax textbook. We are allowing everyone to share and embed this resource.

A rubric in student language written for elementary students to self-assess the reasoning process.

A rubric in student language written for middle school students to self-assess thinking while reasoning.

Your basketball team is down by one point! Your teammate, who makes free throws about three-fourths of the time, is at the free-throw line. She gets a second shot if she makes the first one. Each free throw she makes is worth one point. If there is no time left, what are the chances you win the game without overtime?

Read about our new research on civic online reasoning in Sam Wineburg and Sarah McGrew's read more »