PIKE PROBLEMS IN LAKE DAVIS    ALGEBRA I --- UNIT  5 ------- QUARTER PROJECT  

  Introduction   Standards   Objectives   Activities    Assessment    Materials

  Fishin' Blues Song                       

The objective for Lake Davis is to maintain a healthy and thriving trout population for this popular fishing spot in the Sierra Nevada Mountains. There are a variety of trout species (Brown, Rainbow, and Eagle Lake) found in Lake Davis. Because the trout population is supplemented each year through "planting", the percentage of each trout species can be modified and therefore is not a concern for biologists. Since the development of this water reservoir in the 1960s, many trophy fish have been caught, and the lure of this major fishing spot draws fishermen from all over the state and beyond. Catfish have also been seasonal favorites for anglers. The illegal introduction of the Northern Pike (and possible reintroduction since the poisoning of the lake) continues to be a concern for the State biologists as well as the local tourist industry. The fish population also provides a major habitat for our national symbol, the Bald Eagle. During the winter up to twenty eagles (which are endangered) can be spotted around the lake.

                                                                                       (Click on this Pike more on the Web about the problem in Lake Davis.)   

    (Mr. Gimbel's current catch?)

Your "company" (group) has tagged and released 100 trout into the lake. You must take samples from various locations and determine the populations of the fishes through proportional analysis. The ratio of the number of tagged trout to total trout in each sample is proportional to the total amount of tagged trout (100) to the total amount of trout in the lake. From these proportions, the number of catfish and pike can also be determined. Obviously, fish move around, so numerous samples must be taken and averaged to produce an accurate estimation of the fish populations. At least ten samples will be needed from various parts of the lake.

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Your company will be given a bag which represents Lake Davis. In the bag are various fish populations represented by beans and small elbow noodles. Pinto, pink, and small kidney beans represent the types of trout. Navy (white) beans represent the tagged trout. Catfish are represented by black beans, and pike by the elbow noodles. You will also be given a "net" (small cup) for taking samples from the "lake" and a "pond" (bowl) for counting the samples you take from "Lake Davis". Each time your company takes a "sample" from the "lake", tally each species in a chart.

Remember to make a column for "tagged" trout (white beans) AND also count them in the "untagged" trout column as they are part of the total trout population. Put the sample back in the lake and stir the "fish" with a ruler before taking another sample. This represents moving to another location on Lake Davis before sampling again. After taking 10 samples, average the number of fish in each column. The total number of trout, catfish, and pike in Lake Davis can be discovered by setting up proportions. Cross multiply the proportions to set up algebraic equations. Then solve each equation to determine the trout, catfish, and pike population levels. Total up the number of fish in the lake. Finally, calculate the percent of the total fish population each species represents.

The grade you receive for this project is equivalent to a full unit in the text book.  Your introduction and conclusions are worth 10% each.  Your circle graph and typing of the project are worth 15% each.   50% of your grade will be determined by your organization of data (Spread Sheet) and proper use of proportions and algebraic equations to solve for the population levels of each species of fish.  

Understand that this project is one example of your Expected Student Learning Results (ESLRs) for Writing Across the Curriculum and Technology.  Areas of Technology in which you will be demonstrating proficiency  are:  Word Processing, Developing a Spread Sheet and Graph, visiting web sites related to Lake Davis, and use of Scientific Calculator.  It is also an assessment of the following California State Algebra I Standards:

5.0 Students solve multistep problems, including word problems, involving linear equations in one variable and provide justification for each step.

13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems using these techniques.

15.0 Students apply algebraic techniques to solve percent mixture problems.

25.0 Students use the properties of the number system to judge the validity of results.

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Introduction   Standards   Objectives   Activities    Assessment