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 Algebra

 Enlarge One Grain Of Rice: A Mathematical FolktaleAuthor: DemiIllustrator: DemiPublisher: Scholastic PressCopyright: 1997ISBN: 0-590-93998-XNumber of Pages: 40Ohio Standards Alignment: Grades 5–10Rani, a clever girl, outsmarts her raja after he offers her a choice of reward for doing a good deed.  She requests that the raja give her one grain of rice on day 1, two grains on day 2, four grains on day 3, etc.  She requests that every day for 30 days he give her double the number of grains given on the previous day.  She teaches her greedy raja a lesson by using her accumulation of rice to feed her hungry village.Go to: How to Use This BookHighlights and InsightsRelated ORC ResourcesOhio Standards

 How to Use This Book This book can be used at a variety of grade levels. Younger students can be introduced to doubling patterns, while supplying them with a visual for the doubling process. Older students can be asked to write exponential equations to represent the doubling pattern. Tables and graphs of the equations can be made to enhance the understanding of exponential functions. Representations of the number of grains given each day and the total number of grains given after so many days can be explored. Graphs, tables and equations of different exponential situations can be compared. The doubling situation can be compared to other exponential relationships, such as tripling, quadrupling, etc. Students might compare, for example, doubling the amount of rice over thirty days and tripling the amount of rice over twenty days.
 Highlights and Insights Looking for patterns is an essential part of mathematics. This book helps students by introducing them to non-linear patterns that can be expressed in words, graphs, equations, and tables. This story helps younger students develop number sense and introduces older students to exponential functions in a most engaging way.
 Related ORC Resources One Grain of RiceORC# 10348Resource InformationResource Type: LessonsDiscipline: MathematicsGrades: Grades 6–8Professional Commentary: In this lesson, students take on the role of villagers in a developing country trying to feed the village. While listening to the book One Grain of Rice read aloud, students work collaboratively to come up with a bargaining plan to trick the raja into feeding the village....MORE...A Mathematics Fantasy - The Million \$ MissionORC# 571Resource InformationResource URL: http://math.rice.edu/~lanius/pro/rich.htmlResource Type: Content Supports -- Reference materialsDiscipline: MathematicsGrades: Grades 6–8Professional 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 step-by-step solution is presented, along with helpful visuals....MORE...E. coli Bacteria: Can't Live Without ThemORC# 10149Resource InformationResource Type: Content Supports -- Activities and rich problemsDiscipline: MathematicsGrades: Grades 9–12Professional Commentary: This problem uses a contextual situation of E. coli bacteria in the stomach....MORE...Exponential FunctionsORC# 5821Resource InformationResource Type: LessonsDiscipline: MathematicsGrades: Grades 9–11Professional Commentary: Students compare graphs of different members of the family of exponential functions. Students investigate, describe, and predict the effects of parameter changes on the graphs of exponential functions; describe limitations on the domains and range of these functions; and examine asymptotic behavior....MORE...NAEP Assessment Item, Grade 4: Recognize Pattern and ExplainORC# 1723Resource InformationResource Type: AssessmentsDiscipline: MathematicsGrades: Grades 3–6Professional Commentary: Given the values of increasing powers of 2, students are asked if 375 could be one of the products in this pattern. They must explain their answer....MORE...
 Ohio Standards Patterns, Functions and Algebra StandardBenchmarks (5-7)L. Analyze functional relationships, and explain how a change in one quantity results in a change in the other.Benchmarks (8-10)D. Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.Grade Level Indicators (5)6. Describe how the quantitative change in a variable affects the value of a related variable; e.g., describe how the rate of growth varies over time, based upon data in a table or graph.Grade Level Indicators (6)7. Identify and describe situations with constant or varying rates of change, and compare them.Grade Level Indicators (7)10. Analyze linear and simple nonlinear relationships to explain how a change in one variable results in the change of another.Grade Level Indicators (8)7. Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems.Grade Level Indicators (9)3. Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations.Grade Level Indicators (10)10. Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.