Advanced Common Core Math Explorations

Numbers and Operations (Grades 5-8)

Jerry Burkhart

• Publisher: Routledge
• Year: 2021
• Print ISBN: 9781618212634
• eBook ISBN: 9781000492996
• Edition: 1
• Topic: Education
• Subtopic: Teaching Mathematics

Students become mathematical adventurers in these challenging and engaging activities designed to deepen and extend their understanding of concepts from the Common Core State Standards in Mathematics. The investigations in this book stretch students' mathematical imaginations to their limits as they investigate the numeration systems of creatures from another planet, create and solve stories and problems with extreme numbers, use place value to design their own new divisibility strategies, and play with a strange kind of number line specially designed to multiply numbers without a calculator. Each activity comes with detailed support for classroom implementation including learning goals, discussion guides, detailed solutions, and suggestions for extending the investigation. There is also a free supplemental e-book offering strategies for motivation, assessment, parent communication, and suggestions for using the materials in different learning environments.Grades 5-8

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• A Note to Students
• Introduction
• Connections to the Common Core State Standards
• Exploration 1: Triangle Sums Students learn about the process of mathematical exploration by solving a problem of equalizing sums along the sides of a triangle
• Exploration 2: Torran Math Students investigate the mysterious numeration system used on the planet Torr, whose inhabitants have only two fingers on each hand!
• Exploration 3: Number Line Magnifiers Students take a close-up look at comparing, rounding, and operating on decimals when they turn a "microscope" on the number line
• Exploration 4: Million, Billion, Trillion One million, one billion, and one trillion are large numbers—but how large? Students learn about place value and scientific notation as they explore this question
• Exploration 5: Discovering Divisibility Tests By using place value to analyze divisibility tests, students learn what makes them work, and even how to create their own tests!
• Exploration 6: Visualizing Decimal Multiplication Most of us learn one way to multiply decimals, but when students visualize what is really happening, they can understand and even create many different methods
• Exploration 7: Think Like a Torran! Students return to the planet Torr and learn how the Torrans use their version of place value to perform calculations. They even explore the Torran version of decimals!
• Exploration 8: Extreme Calculations Students expand their understanding of scientific notation as they create stories and carry out calculations on "extreme" numbers
• Exploration 9: Multiplication Slide Rules Students play with strange number scales m which multiplication turns into addition. They discover unexpected connections to place value and powers of 10.
• Exploration 10: Factor Blocks and Radicals Students use prime number blocks to explore squares and square roots. They use their new knowledge to write mathematical expressions in creative new ways
• Appendix: The Building Blocks Model
• References
• About the Author
• Common Core State Standards Alignment