## 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.

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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

Algebra
- 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

Possible Activities:

Pre-Activity
- 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.

Post-Activity
- 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.

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Related Lessons Online:

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Resources to help students:

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Goldfish Resources

Fish image used with permission from: http://members.aol.com/sirchin/goldfish.htm

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