Fish Farm Part I -- Teacher Support
Fish 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 male-to-female 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 pre-activity should help students begin to think about the concept of equivalent ratios, and how a ratio might be represented in a circle graph. The post-activity is an extension of the original problem, and should give students more opportunities to experience creating equivalent ratios in both numerical and graphical form.
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Alignment to the NCTM Standards - Grades 6-8
- 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
- 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
- solve problems that arise in mathematics and in other contexts
- monitor and reflect on the process of mathematical problem solving
- 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.
- 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.
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
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 16-20, 1998
- Bill's Chili, April 27-May 3, 1998
- Pizza Pie - posted March 8, 1999
- How Many Fish Per Gallon?
- Glimmering Goldfish Facts