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On Beyond a Million: An Amazing Math Journey Author: David M. Schwartz Illustrator: Paul Meisel Publisher: Dragonfly Books Copyright: 1999 ISBN: 0385322178 Number of Pages: 32 Ohio Standards Alignment: Grades 6–10
This book provides a context for exploring extremely large numbers, including googol and beyond. Students involved in popping popcorn for an assembly have a popcorn machine that is out of control, and they are curious to find out the number of kernels popped. Since it is impossible to count fast enough, Professor X suggests “power counting” using powers of 10 to do the job. Many interesting facts involving large quantities emerge along the way.
Go to: How to Use This Book Highlights and Insights Related ORC Resources Ohio Standards


How to Use This Book

 Read the story to launch a middle grades lesson on exponents, large numbers, and infinity.
 This book could be assigned in the upper grades as an entertaining introduction to rules for exponents and scientific notation.


Highlights and Insights

 This book promotes number sense and allows students to learn about the use of exponents, powers of 10, and scientific notation in a way that appeals to them.
 The factoids provided as side information serve to show that large numbers are not isolated entities, but have applications in the real world.
 Vocabulary development is promoted when the names of large numbers are accurately given (e.g., quindecillion) instead of the generic references used in many books.
 The reference to months of the year can spark some crosscurricular discussion when students investigate why the ninth month is named September.


Related ORC Resources

A Mathematics Fantasy  The Million $ Mission Resource Type: Content Supports  Reference materials Discipline: Mathematics Grades: Grades 6–8 Professional Commentary: This site is a most engaging presentation of the classic problem in which a penny salary is doubled every day for a month. A stepbystep solution is presented, along with helpful visuals.... Exponents: Algebraic Powers Resource Type: Content Supports Discipline: Mathematics Grades: Grades 6–8 Professional Commentary: This site gives a concise review of all the rules for exponents in simplifying and evaluating algebraic expressions. Numerous worked examples illustrating all the trickiest points are included....


Ohio Standards

Number, Number Sense and Operations StandardBenchmarks (57) E. Use order of operations, including use of parenthesis and exponents to solve multistep problems, and verify and interpret the results. Benchmarks (810) A. Use scientific notation to express large numbers and numbers less than one. Grade Level Indicators (6) 1. Decompose and recompose whole numbers using factors and exponents (e.g., 32 = 2 x 2 x 2 x 2 x 2 = 2^{5}), and explain why "squared" means "second power" and "cubed" means "third power." 6. Use the order of operations, including the use of exponents, decimals and rational numbers, to simplify numerical expressions. Grade Level Indicators (7) 1. Demonstrate an understanding of place value using powers of 10 and write large numbers in scientific notation. Grade Level Indicators (8) 1. Use scientific notation to express large numbers and small numbers between 0 and 1. 

