Understanding Middle School Math Cool Problems to Get Students Thinking and Connecting

ISBN-10: 0325013861

ISBN-13: 9780325013862

Edition: 2009

List price: $36.25 Buy it from $12.00
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Description:

  A book of cool problems for middle school mathematics classrooms - does it get any better? Yes, it does. Art Hyde and his colleagues go far beyond providing a collection of problems. They address big ideas, make connections, nurture the use of varied representations, and provide vivid accounts of actual classroom implementation. - Judith Zawojewski Board of Directors, NCTM   Imagine handing students state-by-state data on the number of gallons of soft drinks sold per person in one year. Imagine using it to lead a vibrant problem-solving session in which students energetically pose and answer mathematical questions: Why does it say sold instead of consumed?   What IS a soft drink? Is it the same as soda? Who would collect this kind of data? Why would they collect it? How was gallons per person calculated? What was the total amount of soda sold in our state? How many 12 ounce cans is that? 20 ounce bottles? How many of each per person?   Understanding Middle School Math gathers 50 cool problems like this that lead to deep thinking. Problems such as the Renovation Problem, in which students uncover ideas about how perimeter, area, length, and cost affect a construction project. Or Chocolate Algebra, where they discover linear relationships among the pocket money available to buy two differently priced chocolate candies.   Arthur Hyde combines the latest research and decades of classroom experience to braid language, cognition, and math. His approach can help any student, including underprepared ones, with the rigors of math in middle school and beyond. He has created and adapted problems that strongly connect math to the real world, to students' lives, and to prior knowledge. Problems that scaffold content and processes, and give students multiple entry points into learning. Every problem has been extensively field tested and refined by classroom teachers. And for each cool problem practicing middle school teachers describe how they used it to differentiate over a wide range of students and extend learning.   For fantastic problems your students won't soon forget and teaching solutions that are exciting, substantial, and transformative, turn to Art Hyde. Read and use Understanding Middle School Math and pass your love of math on as you meet your classroom goals.
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Book details

List price: $36.25
Copyright year: 2009
Publisher: Heinemann
Publication date: 4/9/2009
Binding: Paperback
Pages: 280
Size: 7.50" wide x 9.25" long x 0.50" tall
Weight: 1.034
Language: English

Arthur Hyde is the author or coauthor of the Heinemann titles Understanding Middle School Mathematics; Comprehending Math; Best Practice, Fourth Edition; and Mathwise. A professor of mathematics education at National-Louis University , he received its Excellence in Teaching award. While teaching high school mathematics in Philadelphia , he developed a variety of creative methods for teaching math. He also obtained a doctorate in curriculum and instruction from the University of Pennsylvania , where he later was Associate Director of Teacher Preparation. He continues to work frequently in elementary and middle school classrooms and conducts extensive professional development programs on mathematics and problem solving in Chicago and its surrounding school districts.

Foreword
Introduction
What You Teach and How You Teach It
The Power of KWC: An Alternative to Key Words
Using KWC to Tap Prior Knowledge
Using KWC to Structure Group Learning
Using KWC to Deepen Connections
Extensions
Six Big Ideas
The Research on Mathematical Learning and Teaching
Engaging Prior Understanding
The Essential Role of Factual Knowledge and Conceptual Frameworks
The Importance of Self-Monitoring
Six Big Ideas: Building on Mathematical Research and Principles
Teachers Broaden Their View of Problem Solving
Making Connections Between the Problem and Their Lives
Creating Multiple Representations of Increasing Abstraction
Students Solving Problems: Same Concept, Multiple Contexts
Cognitively Based Planning for Language, Connections, Contexts, and Representations
Integrating Reading Comprehension Strategies and Math Processes via Cognitive Principles
Making Meaningful Connections Among Mathematical Concepts
The Connectedness of Strands
How Does This All Fit Together?
Numbers and Early Algebra
Algebra in the Classroom, Then and Now
Partial Products Like You've Never Seen Them
Starting Out with Base Ten Blocks and Graph Paper
Moving on to More Abstract Representations and Mental Math
Red Dots
Algebra Tiles
Partial Quotients
Andy's Inheritance
Square the Digits and Sum the Squares
Summing the Cubes
'The Irrational Tangram
Proportional Reasoning
What Proportional Reasoning Looks and Sounds Like in the Classroom
Shampoo Bottle
Cats and Rats
Making Seismometers
Developing Students' Proportional Reasoning Skills
Understanding Differences Between Additive and Multiplicative Transformations
Understanding Ratios
Understanding Rates
Interesting Applications of Rate
Algebraic Thinking and Modeling
Line of Best Fit and Linear Combinations
Positive Slope Situations
Inverse Linear Relations
Finite Differences: Quadratic, Cubic, and Beyond
Quadratic Equations
Cubic Equations
Conclusion
Geometry and Measurement
Multiple Representations for Solving a Geometry Problem
Ordering Shapes by Two-Dimensional Size
Measuring the Area
Make My Polygon
A Great Extension: Making Dodecagons
What's Your Angle?
Tessellations: A Different Way
Pythagoras 'R' Us
Pythagoras and Similarity
Primitive Pythagorean Triples (PPT)
Geometry and the Metric System
Silent Snow, Secret Snow
Conclusion
Data Analysis and Probability
Exploring Experimental Probability
Chevalier de Mere's Game of Chance
Inference and Prediction: Probability Bags
A Plethora of Pigs
Model Building with Montana Red Dog
Exploring Possible Outcomes in Theoretical Probability
Combination Pizzas and Permutation Locks
Product Versus Square
Montana Red Dog Follow-Up
De Mere's Bets Follow-Up
Concluding Thoughts
Appendix
References
Problem Index
Index
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