PPT-Operations and Algebraic Reasoning

Algebra Where have you seen students use or apply algebraic reasoning Where have you seen students struggle with algebraic ideas Refreshing our memory Glossary Table 1 take it out if you have it . An algebraic Riccati equation ARE is XA XRX 0 We associate a 2 matrix called the Hamiltonian matrix with the ARE A R The Hamiltonian matrix has some useful properties The eigenvalues of are symmetric about the imaginary axis To prove this assertion Unlock stories by generalising . number properties. ANDREW WILES. Why is this man so famous?. Fermat’s last theorem. No positive . integers satisfy the equation:. . n > 2.  . On doing mathematics…. - Charles Sanders Peirce. Using Models of Reasoning. A Return to Logos. Reasoning from Specific Instances. Progressing from a number of particular facts to a general conclusion. .. This is also known as inductive reasoning.. It’s Logical. What is Logic?. Logic. – The science of correct reasoning.. Reasoning. . – The drawing of inferences or conclusions from known or assumed facts. .. There are two main types of reasoning:. Unlock stories by generalising . number properties. ANDREW WILES. Why is this man so famous?. Fermat’s last theorem. No positive . integers satisfy the equation:. . n > 2.  . On doing mathematics…. SWBAT write an algebraic expression from a written expression.. Do Now. Lauren bought a DVD at Best Buy. The store was having a special with DVDs 10% off. If she got the DVD for $18, what was the original price of the DVD?. SWBAT WRITE ALGEBRAIC EXPRESSIONS USING GROUPING SYMBOLS AND . THE PHRASE LESS THAN. SWBAT WRITE WRITTEN EXPRESSIONS FROM ALGEBRAIC EXPRESSIONS.. Algebraic→Written. Algebraic Expression→ (x +2) · 5. Lecture Outline. Inductive Reasoning. Generalizations. Cause and Effect. Analogy. Deductive Reasoning. Syllogism. Enthymeme. Inductive Reasoning. Inductive Reasoning: Review. The process of citing a number of specific examples or . 02/16/17. How do we evaluate algebraic expressions?. How do we use the order of operations?. Today We’ll Discuss. Definition:. A collection of numbers and operation symbols is a . numerical expression. Translate each into an algebraic expression:. Two more than a number. . n. = number. 2+n. Translate each into an algebraic expression:. Two less than a number. n. = the number. n. -2. Translate each into an algebraic expression:. Representations . and . Proof. Learning Focus. Participants will:. deepen mathematical content knowledge of algebraic reasoning. develop awareness of key concepts associated with algebraic reasoning, . Assessment targets. Progress Map. Math. Learning Progression. 4 building blocks. Learning Progression. Item Design. Outcomes/Scoring. Assessment Quality. Bear Assessment System Stage 1. Focus on the process of learning and on individual student’s progress through that process . :. . It’s not just for geometry anymore. Denisse. R. Thompson. University of South Florida, USA. 2011 Annual Mathematics Teachers Conference. Singapore. June 2, 2011. “Reasoning mathematically is a habit of mind, and like all habits, it must be developed through consistent use in many contexts.” . Reasoning and Proof Geometry Chapter 2 This Slideshow was developed to accompany the textbook Larson Geometry By Larson , R., Boswell, L., Kanold , T. D., & Stiff, L. 2011 Holt McDougal Some examples and diagrams are taken from the textbook.