Advanced Common Core Math Explorations
Ratios, Proportions, and Similarity (Grades 5-8)
Stretch your students' mathematical imaginations to their limits as they solve challenging real-world and mathematical problems that extend concepts from the Common Core State Standards for Mathematics in Advanced Common Core Math Explorations: Ratios, Proportions, and Similarity. Model the solar system, count the fish in a lake, choose the best gear for a bike ride, solve a middle school's overcrowding problem, and explore the mysteries of Fibonacci numbers and the golden ratio. Each activity comes with extensive teacher support including student handouts, discussion guides, detailed solutions, and suggestions for extending the investigations.
Table of Contents
Preface A Note to Students A Note to Teachers Introduction Connections to the Common Core State Standards Teacher’s Guide Exploration 1: The Incredible Shrinking Universe Exploration 2: Ramps, Paints, and Hot Air Balloons Exploration 3: Gear Up! Exploration 4: Perplexing Percentages Exploration 5: Scaling a Tower Exploration 6: Keep It in Proportion Exploration 7: Grab Bag Exploration 8: Expanding and Contracting Exploration 9: Pythagorean Connections Exploration 10: Twist and Shrink References About the Author Common Core State Standards Alignment
Jerry Burkhart has been teaching and learning math with gifted students in Minnesota for nearly 20 years. He has degrees in physics, mathematics, and math education. He provides professional development for teachers and is a regular presenter at conferences around topics of meeting the needs of gifted students in mathematics...
The book provides step-by-step teacher guidance on how to support students for the deepest understanding. Each of the ten chapters is an exploration of a real-world problem that is subdivided into three stages with multiple problems per stage. Students will tackle real world problems, such as determining the size of bicycle gears, estimating the height of a transmission tower, and calculating distances among planets. The book comes with detailed teacher goals, recommendations on how to present the explorations, question prompts to guide students without telling them what to do, and multiple detailed approaches for each problem so students can improve their flexible problem-solving skills.Mindprint Learning, 3/18/16
[A] great resource for teachers of accelerated middle school students. . . Because of the adaptability of the problems, this book would be useful for a variety of grade levels, from fifth through eighth. It contains a treasure trove of rich tasks to engage top students. ,Kit Golan,Mathematics Teaching in Middle School, 12/1/16
Explorations are deep, rich, and open-ended. They are excellent DOK (Depth Of Knowledge) 3 experiences. The focus is conceptual understanding and discovery, not rules and rote practice. Students—and teachers—are encouraged to be prepared for what will be a productive struggle . . . I am learning to enjoy the “productive struggle” that comes when students work on real, conceptual understanding of topics in math. Advanced Common Core Math Explorations: Ratios, Proportions, & Similarity, Grades 5-8 provides such problems and gives teachers the support they need in using the problems in their classrooms.,Mickie Gibbs,MiddleWeb, 12/1/16