Proof: Meaningful and as a Problem- Based Instructional Task First, inductive approach to find a pattern, make a conjecture, solve the problem Then prove.

Slides:

Advertisements

Similar presentations

Treasure Hunt Please complete the treasure hunt handout to become familiarized with the Common Core.

Advertisements

? Tulsa Community College- Engaged Student Programming.

? freely adapted from Tulsa Community College- Engaged Student Programming.

Shahzaib Mahmood Kureshi Action Plan. Long Term Goal To prepare today’s students for upcoming challenges of world by adopting 21 st Century skills, providing.

Examining Proofs ©Xtreem Geometry TEKS G.6E.

Sense Making and Perseverance Learning goal: Explore strategies teachers can use to encourage students to make sense of problems and persevere in solving.

Common Core State Standards K-5 Mathematics Kitty Rutherford and Amy Scrinzi.

1. Principles Learning Assessment Technology 3 Teaching Assessment Technology Principles The principles describe particular features of high-quality.

Common Core High School Mathematics: Transforming Instructional Practice for a New Era 7.1.

JRLeon Discovering Geometry Chapter 4.1 HGSH

Lesson 4-5 Proving Congruence – ASA, AAS. Ohio Content Standards:

Chapter 1 The Art of Problem Solving © 2007 Pearson Addison-Wesley. All rights reserved.

Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints and slopes of line segments.

1. An Overview of the Geometry Standards for School Mathematics? 2.

2.2 What’s the Relationship? Pg. 8 Complementary, Supplementary, and Vertical Angles.

Proofs of the Pythagorean TheoremProjector Resources Proofs of the Pythagorean Theorem Projector Resources.

A High School Geometry Unit by Mary Doherty

© 2013 UNIVERSITY OF PITTSBURGH Selecting and Sequencing Students’ Solution Paths to Maximize Student Learning Supporting Rigorous Mathematics Teaching.

Patterns and Inductive Reasoning

6.1 WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIP SUMMER INSTITUTE 2015 SESSION 6 29 JUNE 2015 SEQUENCING BASIC RIGID MOTIONS; THE KOU-KU THEOREM.

Susana Bravo. Why Projects? Project Based Learning is an approach to teaching that involves the use of projects and other hands on tools. It is an alternative.

Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007 by Akihiko Takahashi Building.

2.5 Postulates & Paragraph Proofs

Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc.,

2.4 Use Postulates & Diagrams

Estimating: Counting TreesProjector Resources Estimating: Counting Trees Projector Resources.

Making Math Easier for Kids By Besnik Keja Click on ABC for my research paper Click on my picture for video introduction.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 1.2, Slide 1 Problem Solving 1 Strategies and Principles.

Prove Theorems Advanced Geometry Deductive Reasoning Lesson 4.

Chapter 6 Quadrilaterals Pg. 318 Conceptual Objective (CO): YAY! New shapes!!! In this chapter we explore Quadrilaterals. What is a Quadrilateral? LATIN:

Postulates and Paragraph Proofs Section 2-5.  postulate or axiom – a statement that describes a fundamental relationship between the basic terms of geometry.

Paper Folding Challenge

Warm-up Write the following formulas 1.Distance 2.Midpoint What is the Pythagorean Theorem?

1 1-1 Patterns and Inductive Reasoning Objectives: Define: –Conjectures –Inductive reasoning –Counterexamples Make conjectures based on inductive reasoning.

 2012 Pearson Education, Inc. Slide Chapter 1 The Art of Problem Solving.

How to Structure a Proof. A Few Guidelines for Creating a Two-Column Proof Copy the drawing, the given, and what you want to prove. Make a chart containing.

E.O.I. TESTING April 17 th thru May 3 rd. Prepare by: Get appropriate amount of sleep Eat a nutritious breakfast Hydrate yourself Do Your Best On The.

CCSS 101: Standards for Mathematical Practice Class 3 March 14, 2011.

Using GSP in Discovering a New Theory Dr. Mofeed Abu-Mosa This paper 1. Connects Van Hiele theory and its levels of geometric thinking with.

Chapter Two: Reasoning and Proof Section 2-5: Proving Angles Congruent.

Lesson 21 Objective: Solve two step word problems involving all four operations and assess the reasonableness of answers.

What is the question? 1) What is the question? Are there any words you do not understand, or want to clarify? What are you asked to find or show? Can you.

© 2013 UNIVERSITY OF PITTSBURGH Supporting Rigorous Mathematics Teaching and Learning Shaping Talk in the Classroom: Academically Productive Talk Features.

Connected Math Program Teaching and Learning Through Problem Solving.

Scaffolding for Geometric Growth Math Alliance November 2, 2010 Beth Schefelker & Melissa Hedges.

#1 Make sense of problems and persevere in solving them How would you describe the problem in your own words? How would you describe what you are trying.

13 strategies to use Powerpoint to support active learning in classroom.

In the last several lessons, you have described translations using coordinates. You have also developed strategies for determining where an object started.

02.1 WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIP SCHOOL YEAR SESSION 2 30 SEPTEMBER 2015 BUT WHAT IF MY YARD IS MORE OF A RECTANGLE?

GEOMETRY LESSON Make a list of the positive even numbers. 2. Make a list of the positive odd numbers. 3. Copy and extend this list to show the.

7.5 You Shouldn’t Make Assumptions

Geometry 5.2 Inside Out.

03.1 WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIP SCHOOL YEAR SESSION 3 14 OCTOBER 2015 EVERYTHING OLD IS NEW AGAIN.

Geometry 6.4 Geometric Mean.

Two Proofs, Same Theorem 1. Traditional approach 2. Teaching for Understanding approach via Problem-Based Instructional Task.

Making Math Meaningful Presented By: Jane Brouse Julie MacGregor.

Pedagogical Goals July 18, 2017.

Reasoning and Proof Unit 2.

Proving the Pythagorean Theorem

Proving the Pythagorean Theorem

Developing questioning

Lesson 4.7 Objective: To learn how to prove triangles are congruent and general statements using Coordinate Proofs.

Unit 5 Lesson 4.7 Triangles and Coordinate Proofs

Inductive & Deductive Reasoning Postulates & Diagrams

Geometry Unit 12 Distance and Circles.

Reflecting on Practice: Worthwhile Tasks

Patterns and Inductive Reasoning

Proving Congruence – SSS, SAS

Patterns and Inductive Reasoning

Presentation transcript:

Proof: Meaningful and as a Problem- Based Instructional Task First, inductive approach to find a pattern, make a conjecture, solve the problem Then prove deductively Then explain, discuss, compare, analyze, evaluate

Fido Problem and Proof Launch Fido guards a yard. Put Fido on a leash and secure the leash in the yard so that all of the yard is guarded and the shortest possible leash used. Can you find a solution if the yard is shaped like a circle? If so, what is the solution? How about if the yard is square-shaped? Other shapes? Now think about a triangular-shaped yard … (Adapted from PSSM, pp )

The Problem A yard is shaped like a right triangle. Fido will be on a leash and will guard the yard. Put Fido on a leash and secure the leash somewhere in the yard. Make sure Fido can reach every corner of the yard. Use the shortest leash possible. Where should you secure the leash?

What we did previously (or do it now) Work collaboratively on this problem. Use geometry software to help you. Propose a solution. Make a conjecture for a mathematical theorem. (Today we will prove, in several ways.)

What we did previously (or do it now) What is the solution to the problem? (See GSP sketch.) What is the geometry theorem? (See next slide.)

Fido Conjecture The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of a triangle.

Explore Examine the 4 diagrams (attached). Write a complete proof associated with each diagram. Put one proof on chart paper and be prepared to present and explain.

Summarize Present & explain proofs. Discuss the following: Describe the general strategy in each proof. What are some advantages and disadvantages of each general method of proof? How are the strategies and proofs similar and different? Are some proofs easier or more convincing to you than others? Why? What mathematical ideas are used in these proofs?

Fido Proof: lesson format Launch – Recall and discuss Fido problem (or do it now), state the conjecture Explore – Do and explain 4 proofs, in groups Summarize – Groups present, discuss summary questions Modify/Extend – locus problem, PSSM p. 358 Check for Understanding – Teacher task: How and what would you assess?

Proof: Meaningful and as a Problem- Based Instructional Task First, inductive approach to find a pattern, make a conjecture Then prove deductively Then explain, discuss, compare, analyze, evaluate