Fish Farm Part I  Teacher SupportFish Farm Part I Archived PoW  Student Version Fish Farm, Part I is no longer the current ESCOT Problem of the Week. The student version allows teachers to use the problem with their students without giving the students access to the archived answers. Teachers can use the link to the archived problem to get ideas of student thinking. The Fish Farm problem is designed to have students apply the concepts of ratio and equivalent ratio to distribute a set number of male and female fish into three ponds. Each pond has a target ratio of maletofemale fish. As the students move fish from the tank into the individual ponds, the numerical and graphical displays of the current numbers of male and female fish will change. The preactivity should help students begin to think about the concept of equivalent ratios, and how a ratio might be represented in a circle graph. The postactivity is an extension of the original problem, and should give students more opportunities to experience creating equivalent ratios in both numerical and graphical form. If you have something to share with us or suggestions for improving this page (something you tried and changed or a new idea), we would love to hear from you. Please email us. Alignment to the NCTM Standards  Grades 68
 understand patterns, relations, and functions  use mathematical models to represent and understand quantitative relationships Number & Operations  understand and use ratios and proportions to represent quantitative relationships;  develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios Representation  create and use representations to organize, record, and communicate mathematical ideas  select, apply, and translate among mathematical representations to solve problems  use representations to model and interpret physical, social, and mathematical phenomena Problem Solving  solve problems that arise in mathematics and in other contexts  monitor and reflect on the process of mathematical problem solving Communication  communicate mathematical thinking coherently and clearly to peers, teachers, and others  use the language of mathematics to express mathematical ideas precisely
 Review the concept of ratios in the form a:b.  Print out the matching tasks from the Web page All About Ratios by Cynthia Lanius. Have students work in small groups to discuss these tasks and make convincing arguments about their answers.  Have students discuss how to represent the ratio 2:3 in a circle graph. PostActivity  Have students find a DIFFERENT way to distribute all 26 fish among the three ponds.  Have students distribute the fish into the three ponds such that only 1 female fish is left in the large tank. Is there more than one way to distribute the fish and achieve the target ratios?  Have students distribute the fish into the three ponds such that only 1 male fish is left in the large tank. Is there more than one way to distribute the fish and achieve the target ratios?  Encourage students to develop a procedure and justification for determining whether two ratios are equivalent. [top] Related Lessons Online:
 All About Ratios by Cynthia Lanius  Ratio and Proportion Activities from MWCC/Devens Learning Center  Does More Wins Mean More Fans? from SCORE Mathematics  Population Ratios from SCORE Mathematics  Leonardo da Vinci Activity by Suzanne Alejandre Lessons for Ratios and Pie Graphs (in Adobe PDF format)  Forming Ratios and Pie Charts, from Destination Math from Riverdeep  An Assessment Worksheet from Destination Math from Riverdeep [top] Resources to help students:
Ratio and Proportion from the Math League Ask Dr. Math Archives  What is a ratio?  Ratios as fractions  Figuring ratios  What is the second number in a ratio?  The complete archive collection on Ratio and Proportion Previous MidPOWs related to ratios  Rites of Spring March 1620, 1998  Bill's Chili, April 27May 3, 1998  Pizza Pie  posted March 8, 1999 [top] Goldfish Resources
 How Many Fish Per Gallon?  Glimmering Goldfish Facts
