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Descriptive Statement: Mathematical reasoning is the critical skill that enables a student to make use of all other mathematical skills. With the development of mathematical reasoning, students recognize that mathematics makes sense and can be understood. They learn how to evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize how those solutions can be applied. Mathematical reasoners are able to reflect on solutions to problems and determine whether or not they make sense. They appreciate the pervasive use and power of reasoning as a part of mathematics.
 

Topic/Unit Timeline	Cumulative Progress Indicators	Objectives	Suggested Activities	Materials	Evaluation
Mathematical Reasoning Timeline 1st Q All year	Building upon knowledge and skills gained in the preceding grades, and demonstrating continued progress in Indicators 2, 3, and 5, by the end of Grade 8, students will: Make conjectures based on observation and information, and test mathematical conjectures and arguments.	Construct solutions to word problems by using the guess and test strategy Hypothesize solutions based on statistical displays and verify their validity	See Lesson 3-7. See Putting It All Together activities in each chapter.	Investigations software "Mission: Mars" See teacher’s edition for a list of materials needed for each activity	"On Your Own" examples, teaching resources provided by the publisher Portfolio assessment
Timeline All year All year	Justify, in clear and organized form, answers and solution processes in a variety of problems.	Justify a solution to a problem by describing the processes used Identify the math concepts used in problem solving	In the Putting It All Together section of each chapter, the student must present his solution in a clear and organized form to a group. See samples in the text on pages 107, 110, 118, 122, 129,133, and many others.	See teacher’s edition for a list of materials needed for each activity Same as #1	Portfolio assessment Self assessment

 
 

Topic/Unit Timeline	Cumulative Progress Indicators	Objectives	Suggested Activities	Materials	Evaluation
Mathematical Reasoning Timeline All year All year	Follow and construct logical arguments, and judge their validity.	Judge the validity of the process used in problem-solving Explain the step-by-step procedure used in arriving at a solution	See Putting It All Together activities in each chapter. See Work Together activities in each chapter.	See teacher’s edition for a list of materials needed for each activity Same as #1	Portfolio assessment Group assessment
Timeline 1st Q All year	Recognize and use deductive and inductive reasoning in all areas of mathematics.	Draw logical conclusions about patterns using inductive reasoning Verify the steps of a solution using deductive reasoning	See Lesson 2-3. See samples in the text on pages 145, 146, 150, 154, 155, 159, and many others.	Calculator See teacher’s edition for a list of materials needed for each activity	Self assessment Same as #1
Timeline All year All year	Extend mathematical reasoning skills in other disciplines and in their lives.	Construct solutions to real-life problems using logical reasoning Demonstrate mathematical reasoning skills in science related activities and other disciplines	Look up "Critical Thinking" activities in the index for specific examples. Look up "Connections" in the index for specific examples.	See teacher’s edition for a list of materials needed for each activity Same as #1	Portfolio assessment Group assessment

 
 

Topic/Unit Timeline	Cumulative Progress Indicators	Objectives	Suggested Activities	Materials	Evaluation
Timeline All year All year All year	Use reasoning rather than relying on an answer-key to check the correctness of solutions to problems.	Rate group solutions to activity based problems using reasoning skills Select appropriate solutions to problems based on the students’ justification of their process  Assess the reasonableness of solutions using estimating skills	In cooperative learning groups, students will evaluate their solutions. For examples, see both vignettes for grades 7 and 8 found in the Math Curriculum Framework. Same as #1. The fourth step of the "Problem Solving Strategy Plan", which is found in every chapter, is Look Back. This step requires that students judge the validity of his work.	Whatever is appropriate to the problem under study Same as #1 See teacher’s edition for a list of materials needed for each activity	Group assessment Same as #1 Same as #1

 

Resources Mighty m&m Math Experiment  -Mighty m&m Math teaches fractions and percentages in a motivating and                                                                   mouth-watering way How to Solve Problems  -You have the opportunity to learn to solve problems easily and reliably. You only                                                    need to take the time to understand how problems are solved. This site shows you                                                    how to do this. Connections for the Future  -In a webquest, students utilize World Wide Web resources to obtain data which is then                                                             analyzed and used in various mathematical exercises.  Math webquests involve reasoning and                                                             critical thinking in a constructivist setting. Thinks.com  -fun and games for playful brains. Internet Math Challenge